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Critical review of challenges for representing climate change in physical models

Deliverable 8.I

Full Report

Status: Final

Date: Wednesday, 07 December 2016

EC contract no 654110, HYDRALAB+

Deliverable 8.1 Representing climate change in physical models

Version 1 2 Wednesday, 07 December 2016

DOCUMENT INFORMATION

Title Critical review of challenges for representing climate change in physical models

Editors Stuart McLelland (UoH); Wietse van de Lageweg (UoH); Edwin Baynes (Université

de Rennes)

Contributors Jochen Aberle (NTNU) William Allsop (HR Wallingford) Jasper Dijkstra (Deltares) Karl-Ulrich Evers (HSVA) Xavi Gironella (UPC) Pierre-Yves Henry (NTNU) Bas Hofland (Deltares) Jordi de Leau (UPC) Andrea Marzeddu (UPC) Frederic Moulin (CNRS) Stephen Rice (Loughborough) Moritz Thom (FZK) Rüdiger U. Franz von Bock und Polach (Aalto University) Conceição Juana Fortes (LNEC) Teresa Reis (LNEC) Maria Graça Neves (LNEC) Rute Lemos (LNEC) Ana Mendonça (LNEC) Rui Capitão (LNEC) Filipa Oliveira (LNEC) Francisco Sancho (LNEC) Eunice Silva (HR Wallingford) Francisco Taveira Pinto (UPORTO) Paulo Rosa Santos (UPORTO)

ACKNOWLEDGEMENT

The work described in this publication was supported by the European Community’s Horizon 2020

Programme through the grant to the budget of the Integrated Infrastructure Initiative HYDRALAB+, Contract

no. 654110.

DISCLAIMER

This document reflects only the authors’ views and not those of the European Community. This work may

rely on data from sources external to the HYDRALAB project Consortium. Members of the Consortium do not

accept liability for loss or damage suffered by any third party as a result of errors or inaccuracies in such data.

The information in this document is provided “as is” and no guarantee or warranty is given that the

information is fit for any particular purpose. The user thereof uses the information at its sole risk and neither

the European Community nor any member of the HYDRALAB Consortium is liable for any use that may be

made of the information.



1. TABLE OF CONTENTS

Document Information ...................................................................................................................................... 2

Acknowledgement ............................................................................................................................................. 2

Disclaimer .......................................................................................................................................................... 2

2. Executive Summary ................................................................................................................................... 6

3. Introduction: Climate change and physical modelling .............................................................................. 8

Approaches to experimental physical modelling .............................................................................. 9

Representing climate change in physical models ............................................................................ 11

4. Scaling of morphodynamics in time ........................................................................................................ 17

Representing climate change in physical models of fluvial morphodynamics ................................ 17

4.1.1. Introduction ............................................................................................................................. 17

4.1.2. Background .............................................................................................................................. 18

4.1.3. Scaling ...................................................................................................................................... 19

4.1.4. Bed load model types .............................................................................................................. 30

4.1.5. Suspended load models ........................................................................................................... 33

4.1.6. Tidal models with movable bed............................................................................................... 34

Scaling Morphodynamic processes in coastal models .................................................................... 36

4.2.1. Results from previous experiments ......................................................................................... 36

4.2.2. Critical analysis of knowledge-gaps and future developments ............................................... 37

Representing flood events in physical models ................................................................................ 39

4.3.1. Available forcing data to take into account climate change ................................................... 39

4.3.2. Limits of the steady flow approaches ...................................................................................... 40

4.3.3. Flow unsteadiness coupled with sediment transport dynamics ............................................. 40

4.3.4. From the single flood event towards a sequence of floods .................................................... 45

4.3.5. Incorporating time-scales associated with plants or biofilms ................................................. 45

4.3.6. Incorporating animals .............................................................................................................. 46

4.3.7. Metrological issues .................................................................................................................. 46

5. Impact of Climate change on coastal storms and structure modelling ................................................... 50

Introduction to representing climate change in a coastal environment ......................................... 50

Storm event sequencing and rubble mound breakwaters .............................................................. 51

5.2.1. Design and procedures of coastal and harbour physical testing ............................................. 51

5.2.2. Damage description of rubble mound structures in a changing climate ................................ 52

5.2.3. Damage description to non-standard and existing structures ................................................ 53

5.2.4. Damage progression ................................................................................................................ 54



5.2.5. Wave run-up and overtopping ................................................................................................ 55

5.2.6. Oblique waves ......................................................................................................................... 56

5.2.7. Storm event sequence test methodologies ............................................................................ 59

5.2.8. Sea-level rise ............................................................................................................................ 65

Application of Multi-variable analysis for wave overtopping ......................................................... 69

5.3.1. Overview .................................................................................................................................. 69

5.3.2. Developing levels of sophistication in multi-variable analysis and testing ............................. 69

5.3.3. Metocean variables of potential interest ................................................................................ 72

5.3.4. Flood risk and structure variables of potential interest .......................................................... 73

5.3.5. Methods and aspects of multi-variable analysis of interest.................................................... 74

5.3.6. Example JPA curves ................................................................................................................. 75

5.3.7. Choosing test conditions ......................................................................................................... 77

5.3.8. Rigorous 'total' probability of overtopping ............................................................................. 77

5.3.9. Wave overtopping discharges ................................................................................................. 78

Measurement techniques and Innovation ...................................................................................... 79

5.4.1. Cross-sectional profiles ............................................................................................................ 82

5.4.2. Terrestrial laser scanners ......................................................................................................... 82

5.4.3. Stereo photogrammetry .......................................................................................................... 83

5.4.4. 3D printing ............................................................................................................................... 83

5.4.5. Knowledge-gaps and future developments ............................................................................ 84

Physical modelling applications and developments to represent a changing climate.................... 85

5.5.1. Use of high-density iron ore .................................................................................................... 85

5.5.2. Single layer armours ................................................................................................................ 86

5.5.3. Multifunctional artificial reefs ................................................................................................. 87

5.5.4. Future developments .............................................................................................................. 89

6. Impact of Climate Change on Sea Ice ...................................................................................................... 91

General Processes and Impacts ....................................................................................................... 91

6.1.1. Retreating Ice Cap and Decreasing Ice Thickness .................................................................... 92

6.1.2. Permafrost and Coastal Erosion .............................................................................................. 94

6.1.3. The Marginal Ice Zone (MIZ) .................................................................................................... 99

The Impact of Climate Change on Socio-economic Behaviour ..................................................... 100

Physical Modelling in Ice Tanks ..................................................................................................... 101

6.3.1. State of the Art ...................................................................................................................... 101

6.3.2. Modelling Challenges related to Climate change .................................................................. 102

Laboratory Experiments with Wave-Ice Interaction ..................................................................... 103



7. Impact of Climate Change on Eco-hydraulics ........................................................................................ 105

Overview ........................................................................................................................................ 105

Representing the impacts of climate change on biostabilization in physical experiments .......... 105

7.2.1. Impacts on biofilm growth and biostabilization .................................................................... 107

7.2.2. State of the art: physical experimental designs .................................................................... 111

7.2.3. Future recommendations - Can we use surrogates instead? ................................................ 115

Parametrisation of aquatic vegetation in hydraulic and coastal research .................................... 120

Measuring organism stress and behavioural integrity in flume facilities ..................................... 121

7.4.1. Introduction ........................................................................................................................... 121

7.4.2. Key challenges and research questions ................................................................................. 122

7.4.3. Information gaps ................................................................................................................... 124

8. Numerical modelling of biogeomorphological interactions in relation to climate change adaptation 125

Introduction ................................................................................................................................... 125

State of the art in numerical modelling of biogeomorphology ..................................................... 126

8.2.1. Scales and model types ......................................................................................................... 126

8.2.2. Processes ............................................................................................................................... 127

Key numerical modelling results in fluvial and coastal biogeomorphical settings ........................ 131

8.3.1. Numerical modelling of hydromorphological vegetation dynamics in rivers ....................... 131

8.3.2. Numerical modelling of salt marsh development ................................................................. 134

Knowledge gaps and future developments in numerical modelling of biogeomorphological

interactions ................................................................................................................................................ 138

8.4.1. Organism properties and the importance of diversity .......................................................... 138

8.4.2. Plant tolerance limits ............................................................................................................. 139

8.4.3. Combination of soil and (ground)water ................................................................................ 140

8.4.4. Upscaling from near field to landscape ................................................................................. 140

9. References ............................................................................................................................................. 141



2. EXECUTIVE SUMMARY

The critical review (Task 8.1) is an analysis of the methods and results from previous and on-going research

programmes that attempt to use (or have used) physical models to assess the potential impacts of climate

change. The review considers models that represent coastal, estuarine and fluvial environments plus

experiments that address climate adaptation with regard to sediment dynamics, morphodynamics,

ecosystems, ice and structures. This review of existing experimental methods will outline the current state-

of-the-art and will inform the experiments undertaken in Tasks 8.2-8.6 so that protocols and techniques are

developed to add value and significantly advance the capacity and outputs of physical modelling facilities.

Global climate change is a grand challenge facing the Earth over numerous spatial and temporal scales (IPCC,

2014). In addition to observing the natural environment and numerical modelling of future scenarios, physical

modelling in the laboratory can assist in developing an improved understanding of how Earth systems

operate and respond to environmental changes. Physical modelling provides an innovative approach to help

understand the impacts of climate change on coastal, estuarine and fluvial systems and to test the efficacy

of potential adaptation strategies. These are both essential to improve environmental management over

long time-scales. Non-linear feedbacks between processes over different temporal and spatial scales, tipping

points, increased variability and higher frequency and magnitude of extreme events such as storms, and

complex interactions between biology, morphodynamics and hydrodynamics are considered knowledge gaps

in our understanding of climate change impacts and are key focus areas for future research efforts.

Climate change involves long time scales and physical modelling for climate change adaptation faces the

challenge of incorporating and scaling non-linear responses across a range of temporal and spatial scales

resulting from long-term changes in event frequency and magnitude. Until today, most considerations on the

impact of climate change on the aquatic environment have been based on stationary boundary conditions

reflecting a possible future climate state. Focusing solely on the final stage of a future scenario neglects that

climate change is a progressive process which develops over time. In general, the ability to replicate the

prototype system in the laboratory decreases with increasing spatial and temporal scales (i.e. 1:1 models

versus analogue models). Adequate model replication of system change and adaptation for timescales of

10s-100s of years remains challenging but materials such as lightweight sediments may provide innovative

solutions.

For coastal environments, most climate-change scenarios predict an increase in sea level, increasing

storminess, more frequent extreme events and changes in the dominant wave direction. This may induce

responses such as beach and dune erosion, inundation of low-lying coastal areas, increases of wave

penetration into harbours, failure of the existing coastal and harbour protection structures, and failure of

structures to protect the coast from erosion. The studies on run-up, overtopping and damage evolution under

climate change scenarios depend upon physical model testing, currently mostly tests are two-dimensional

but improved results may be obtained from three-dimensional setups. Future research efforts will address

the role of oblique waves, innovative storm event methodologies, sea-level rise, artificial reefs and other

Building with Nature approaches for coastal impact and adaptation studies.

Sea ice is found in remote polar oceans and covers, on average, about 25 million km2 of the earth which

represents about 7% of the Earth’s surface and about 12% of the world’s oceans. The extent of the Arctic sea

ice has reduced significantly in recent years with a large expanse of open water now present adjacent to a

dynamically changing ice cover, called the Marginal Ice Zone (MIZ). Most engineering such as shipping and

offshore activities take place in the MIZ but currently there is insufficient understanding of the air-ice-ocean



system to operate safely and effectively in this region. Therefore, future physical modelling will focus on i)

ship-ice interactions, ii) wave-ice interactions, and iii) the behaviour of different ice types.

Understanding the complexity of the interactions between aquatic biological systems and their physical

environment is a critical condition for the sustainable management of aquatic environments and their

ecosystems into the future. Sea-level rise, temperature changes, increased storm intensity and frequency,

and related flooding and erosion events are processes expected to trigger shifts in the dynamic interactions

between ecology and hydraulics. Many aspects of these interactions are still to be investigated and many

answers will most probably be found at the different discipline interfaces, which are the least studied and

most poorly understood. A number of key focus areas for physical modelling of these biologically active

surfaces are identified and include i) plant-flow interactions and behavioural integrity, ii) biofilm behaviour

and biostabilization, and iii) replication of the behaviour and effects of plants and biofilms using physical and

chemical surrogates to decrease timescales and increase the level of control.

Physical and numerical modelling complement each other in studies exploring climate change impact,

adaptation and mitigation. Numerical models can be useful predictive tools because they can cover multiple

spatial and temporal scales and they can easily be forced with a multitude of climate change scenarios. For

management purposes of the future natural environment, they will need to represent both physics

(hydraulics and morphology) and ecology, and importantly, the interaction between these disciplines, which

may be informed by innovative physical modelling experiments.

This review is written to synthesise the state-of-the-art on environmental hydraulic modelling in recognition

of the upcoming challenges associated with adaptation for climate change. It is intended to be used by the

wider European scientific community, subject specialists, industry and a range of stakeholders. Future

physical modelling experiments within the Hydralab+ network will be informed by this review and provide

opportunities for the wider hydraulic community to engage with and collaborate on urgent issues associated

with climate change impacts on rivers and coasts.



3. INTRODUCTION: CLIMATE CHANGE AND PHYSICAL MODELLING

Global climate change is a grand challenge facing the Earth across numerous spatial and temporal scales

(IPCC, 2014). 41% of the world’s population, including 21 of the 33 world ‘megacities’, are located within 100

km of coastlines (Martinez et al., 2007). Understanding and adapting to the potentially irreversible and

detrimental impacts associated with rates and magnitudes of shifts in climate is therefore a fundamental

priority for these dynamic environments. Expected impacts in coastal, estuarine and fluvial systems include

altered hydrological regimes and sediment fluxes (Nijssen et al., 2001; Syvitski et al., 2005), variations in biota

distribution and growth patterns (Harley et al., 2006), and more frequent extreme events such as storm

surges (Lowe and Gregory, 2005), floods (Garssen et al, 2015) and droughts (Garssen et al., 2014). There is

also the potential for changes in the frequency of extreme wind events, higher waves, and changes of the

dominant wave direction (Mori et al, 2013, Karambas, 2015). The feedbacks and interactions between these

processes are currently poorly constrained (Table 1). However, these changes in key processes are likely to

induce morphodynamic responses such as beach and dune erosion, river channel change, inundation of low-

lying areas and increased flood risk with the potential for failure of the existing protection structures.

Much of our understanding of the impacts of future climate change is derived from numerical models (e.g.

IPCC, 2014), developed from simplified empirical relationships between complex driving processes and

calibrated/extrapolated from field evidence that is often limited by the temporal and spatial scale at which

it is collected (Refsgaard et al., 2006). Thus, to reduce the uncertainty of numerical models in forecasting

environmental change as a result of shifts in the climate system, a more accurate parameterisation of the

complex, and often non-linear, interactions, feedbacks and responses to forcing is required.

One such approach to developing this improved understanding of how Earth systems operate and react is

through experimental modelling of these systems in the laboratory (Paola, 2000; Thomas et al., 2014;

Tambroni et al., in press). For example, recent experimental work has been used to calibrate numerical

models of in-channel flow processes around vegetation (Dijkstra and Uittenbogaard, 2010; Marjoribanks et

al., 2015) and landscape-scale river delta development processes under a constant rising sea level (Liang et

al., in press). Complex systems can be easily simplified in the laboratory (e.g. Bouma et al., 2005), timescales

of change can be shortened (e.g. Paola, 2000), and the impacts of individual forcing mechanisms on system

behaviour isolated and quantified (e.g. Wong and Parker, 2006; Lamb and Dietrich, 2009). These

opportunities inform and develop quantitative theory and reduce the associated uncertainty in the

parameterisation of numerical models. Experimental physical modelling therefore provides an integral tool

for understanding and modelling environmental systems because the provide an opportunity for

understanding the dynamics of complex physical processes and the development, calibration and validation

of numerical models that can simulate how systems evolve in the future under a range of conditions (Figure

1).



Figure 1. Conceptual diagram showing the coupling between the natural environment and experimental physical and numerical modelling techniques.

APPROACHES TO EXPERIMENTAL PHYSICAL MODELLING With every physical experimental physical study for any application, there exists a need to ensure that the

modelled behaviour and processes are relevant for application to natural settings. For a true replication of

natural environments, a direct 1:1 scaling given processes with the model Froude number matching that of

the physical model and the natural prototype (e.g. Stratigaki et al. 2011), but this approach has severe

limitations especially when large spatial or temporal scales or complex behaviour are under study (Hasbergen

and Paola, 2000; Bonnet, 2009). In addition, direct replication does not enable prediction of progressive

changes in system forcing at any faster rate than reality, which limits this type of modelling to a given state

and has limited application for forecasting in advance of system change.

There are a number of different approaches to experimental modelling of flow and sediment dynamics that

divert from a direct 1:1 scaling. Froude scale modelling (FSM) adopts the approach of scaling given processes

with the model Froude number matching that of the prototype natural system but the simultaneous

similarity of the Reynolds number may be relaxed. Scaling flow characteristics using Froude-similarity and

taking into account specific scaling criteria for sediment transport allows for scaled versions of a specific

geomorphic feature to be analysed (see Chapter 4 on Scaling of morphodynamics in time4, Hughes, 1993,

Peakall et al., 1996 and Johnson et al., 2014a for further discussion of how to scale different parameters

within experiments appropriately, including different scaling behaviour for hydraulics and sediment

transport depending on the aim of the study). However, scale reduction of mobile bed problems using Froude

scale modelling combined with dynamic morphology is ultimately limited by sediment properties due to the

increasing dominance of cohesive forces as sediment sizes get smaller.

An alternative approach to physical modelling referred to as analogue modelling was first advocated by

Hooke (1968). In this approach, a formal scaling between the experimental conditions and a target natural



system is not sought or achieved (Peakall et al., 1996; Paola, 2000). Rather, the experimental setup is treated

as a system in its own right (‘an analogue’), with qualitatively similar behaviour to the natural setting, possibly

achieved through different processes, allowing the size and duration of experiments to be drastically reduced.

This provides the opportunity to explore and quantify a wide range of processes and behaviours within a

controlled system with a greater degree of flexibility (e.g. Hasbergen and Paola, 2000; Lague et al., 2003, Tal

and Paola, 2007, Malverti et al., 2008; Paola et al., 2009; Wickert et al. 2013; Kleinhans et al 2015). The results

from the studies that use this ‘similarity of process’ technique are not ideally suited to direct representation

of specific natural settings, but this trade-off enables a wider range of scales and forcing conditions to be

investigated experimentally, and can still be used to help inform the underlying quantitative theory of the

physical processes at work in natural settings. This approach has a number of potential advantages,

particularly in terms of increasing the spatial scale of experiments to incorporate more connectivity and

therefore better representation of autogenic feedback among components of a system, as well as enabling

simulation of longer timescales and therefore the improved representation of allogenic forcing (Figure 2).

Figure 2. The relative application of different approaches for experimental modelling, with different approaches being more appropriate for modelling processes over different spatial and temporal scales.



REPRESENTING CLIMATE CHANGE IN PHYSICAL MODELS Physical modelling provides an innovative approach to help understand the impacts of climate change on

coastal, estuarine and fluvial systems and to test potential adaptation strategies (Liang et al., in press).

However, at present, there are significant challenges in representing changes in climate forcing in

experimental physical models because of the complex interactions and non-linear feedbacks between

processes over different temporal and spatial scales. Physical modelling of large-scale landscape evolution

(e.g. mountain ranges or deltas) have been instrumental in identifying the complex internal dynamics of these

systems. Hasbergen and Paola (2000) showed that even under ‘steady state’ conditions, the landscape is

never static with oscillations in erosion rate and ridge migration occurring despite the experimental system

undergoing constant forcing. These behaviours can only be identified when models represent sufficient scale

to incorporate the feedbacks between connected processes in the system. Similarly, Tal and Paola (2007)

demonstrated the autogenic response of a small scale braided river system to increased bank cohesion

induced by alfalfa colonisation.

An important anticipated impact of climate change is to introduce an external (allogenic) forcing component

to these systems such as an acceleration in rising sea level (IPCC, 2014), larger storm surges (Lowe and

Gregory, 2005), or increased magnitude and frequency of flooding (Fowler and Hennessy, 1995). The forcing

will operate in addition to the dynamic response of the systems to constant internal (autogenic) forcing. Thus,

an important requirement for experimental models is to be able to simulate the target system (i.e. coasts,

estuaries or rivers) under constant forcing and also be able to introduce an additional external driver to the

experimental conditions. Associated with this, measurement and monitoring techniques are required to be

able to isolate and quantify the difference between the response to the autogenic and allogenic forcing

(Figure 3).

Future climate regimes are likely to be characterised by increased variability and higher frequency and

magnitude of extreme events such as storms (King et al., 2015) or storm surges (Lowe and Gregory, 2005).

More frequent higher magnitude storms could have a drastic impact on environmental systems in terms of

the proportion of ‘geomorphic work’ carried out by individual storm events over long timescales (Wolman

and Miller, 1960).

Variations in the frequency of individual storm events of a given size can also have significant impacts on the

dynamics of these systems. Most systems have a characteristic ‘recovery timescale’ whereby the conditions

gradually return to an equilibrium (Brunsden and Thornes, 1979; Allen, 2008). For example, the frequency of

flood events in fluvial systems can also directly impact the growth and characteristics of riparian vegetation

(Garssen et al., 2015). If the recurrence interval of flood events becomes smaller than the characteristic

recovery timescale (i.e., the time required for vegetation to re-colonise in a system), the riparian vegetation

will never recover and the environment will be permanently transformed (Garssen et al., 2015). Meanwhile,

vegetation in a system that does not experience frequent flooding can develop until the density exceeds the

uprooting capacity of the flow preserving only the signal of the impact of vegetation in controlling the river

morphology (Crouzy et al., 2013). In addition, higher magnitude storm events will increase the likelihood that

thresholds within a system will be (Schumm, 1979, Mori et al, 2013), potentially causing a significant or

catastrophic change within the system that can have a long lasting legacy on (for instance) landscape

morphology (Baynes et al., 2015), or manmade structures.



Figure 3. Conceptual diagram indicating different forcing regimes in coastal, estuarine and fluvial systems under climate change. (A). A progressive increase in a constant forcing over a long time scale (e.g. sea level rise). (B) A forcing regime characterised by extreme events (e.g., storms/floods). (C) A forcing regime characterised by higher magnitude extreme events, but of the same frequency, compared to (B). (D) A forcing regime characterised by extreme events of the same magnitude as (B), but occurring more frequently. (E) A forcing regime characterised by extreme events that are both more frequent and of a higher magnitude compared to (B).

Sea level rise is identified to be most likely consequence of climate change in the coastal zone (IPCC, 2007;

see Table 1). Overtopping or run-up events generally occur when extreme or near-extreme waves and high

water levels occur simultaneously. Estimation of overtopping discharge rates depends therefore on the joint

probability of two different extreme events, but these two variables are rarely statistically independent so

their joint probability of exceedance cannot be determined from the product of their individual probabilities.

The ability to accurately predict, or to accurately calculate the probability of wave overtopping or run-up and

the resulting damage to coastal protection structures is therefore of great importance. Physical modelling

needs to be adapted to cope with these challenges without simply extending the ranges and durations to be

tested.

Perhaps the most understudied component of environmental systems in experimental models are the

interactions between biology, morphodynamics and hydrodynamics. Incorporating biology adds to the

complexities of modelling longer time-scales with changes to flora and fauna occurring either independently

from climate change itself as in the case of invasive species like signal crayfish in rivers (Mathers et al., 2016a,

b) or as a result of climate change altering biome extents or growth rates (Harley et al., 2006).The biological

component of coastal, estuarine and fluvial systems, from small scale microbial activity to larger scale plants



and animals are located at the interface between water and sediment transport systems and are particularly

sensitive to climatic changes such as variations in temperature that shift species growth patterns in a non-

linear way (Harley et al., 2006; Garssen et al., 2015). Thus, for a holistic representation of these

environmental systems in experimental models, the biological component has to be actively represented and

the feedbacks and interactions between biota and sediment/water transport have to be monitored (Thomas

et al., 2014).

Figure 4. Schematic diagram of example fluvial, estuarine and coastal/marine environments, with the areas identified where climate change impacts will be experienced. See Table 1 for details of expected changes in the environments induced by climate change.



The inclusion of the biological component is complex however, partly due to the difficulties of transplanting

live plants (or animals) from nature into the laboratory while avoiding or minimising damage to their health

and ensuring that the transplanted organisms continue to behave in the same way under experimental

conditions as in nature (Johnson et al., 2014b). Additional problems to overcome are the disparities between

timescales of response to different forcing mechanisms for biota and sediment transport processes (Thomas

et al., 2014). As stated above, the magnitude and frequency of individual extreme events is important in

determining the amount of geomorphic work carried out in terms of sediment transport (Wolman and Miller,

1960) but the biological component may respond to more gradual shifts in temperature over longer

timescales (Harley et al. 2006). Including both event-scale response and long term responses of the biological

component within these systems is thus an important requirement for facilities conducting physical

experiments.



Table 1. Details of expected climate change induced impacts on fluvial, estuarine and coastal environments. Experimental modelling studies can be used to understand these processes and test possible adaptation strategies.

Climate induced

change in forcing

Predicted change Associated impact on coastal, estuarine and fluvial

environments

Source

Global mean

surface

temperature

By 2100: 0.3-1.7 oC temp rise (scenario RCP2.6)

2.6-4.8 oC temp rise (scenario RCP8.5)

Implications for vegetation growth in all

environments

IPCC (2014)

Sea level By 2100: 0.26-0.55 m (scenario RCP2.6)

0.45-0.82 m (scenario RCP8.5)

70% of coastlines worldwide experience

change within 20% of global mean

Drowning of coastal and estuarine environments.

Encroachment of saline water and associated impacts

on biota. Increased aggradation of river deltas,

accelerated channel and floodplain deposition and to

higher channel avulsion frequency

IPCC (2014),

Jerolmack

(2009)

Storm surges Largest increase in 50 year return period storm-surge height at

UK coastline = 1.2 m (Scenario A2)

Increased risk from hazards (e.g. coastal flooding,

coastal erosion) associated with storm surge events

Lowe and

Gregory (2005)

Precipitation Scenario RCP8.5: Increase in mean precipitation in high

latitudes and equatorial Pacific. Decrease in mean precipitation

in mid-latitudes

Increase in extreme precipitation over most of mid-latitude

landmasses and wet tropical regions become more intense and

more frequent

Rivers: increased frequency and magnitude of higher

peak flows, and possible prolonged drought periods

with associated impacts for riparian vegetation

distribution. Potential shifts in timing of seasonal

hydrological regimes.

IPCC (2014);

Garssen et al.

(2014; 2015)

Waves Latitude dependent: Coasts and estuaries Wang et al.

(2004)



0.6-1 m increase in 20 year return period wave height in NE

Atlantic between 1990 and 2080.

Wave with 20 year return period in 1990 will have 4-12 year

return period in 2080

Oceans Increased ocean warming and ocean acidification leading to

expansion of Oxygen minimum zones and anoxic ‘dead zones’

Coasts: potential for shifts in vegetation coverage and

growth areas

IPCC (2014)



4. SCALING OF MORPHODYNAMICS IN TIME

REPRESENTING CLIMATE CHANGE IN PHYSICAL MODELS OF FLUVIAL MORPHODYNAMICS This section examines the current ‘state-of-the-art’ for the representation of climate change in physical

models that represent morphodynamic change, with an emphasis on fluvial morphology and less detail

on coastal environments. Some specific references to coastal studies are included and there is

substantial overlap between the two domains although the dimensionless numbers need to be

redefined using different parameters (but their form remains essentially the same).

The modelling of suspended sediment transport is not covered in as much as detail as bed load – this

is due to the fact that bed load is more important for the morphodynamic evolution of river systems.

Instead, the emphasis is set on the effect of time scales since these are critical for modelling climate

change. Climate change defines the (varying) boundary conditions for designing and running the model,

but not the scaling laws themselves. However, the latter govern basically the overall design.

Not every referenced study is described in depth as there are many and most studies are based on the

same scaling laws. Last but not least, the focus is set on physical models and no numerical models are

described.

4.1.1. Introduction

Physical modelling is an important tool in hydraulic research and an established technique for the

design and testing of hydraulic structures. The high degree of experimental control in both physical

scale and process models allows for the simulation of varied or rare environmental conditions and

hence to obtain measurements for conditions which cannot be measured at the prototype or prior to

the construction of hydraulic structures (Hughes 1993). Moreover, physical modelling provides an

essential link between field observations and theoretical, stochastic and numerical models which are

required to predict the impact of environmental changes on aquatic ecosystems (Thomas et al. 2014).

Physical modelling can therefore play a key role for the development of a better understanding of

climate change related impacts by improving our ability to predict these impacts and, thus, to help

adapt to climate change related challenges (Frostick et al. 2011, 2014).

Climate change involves long time scales and physical modelling for climate change adaptation faces

the challenge of incorporating and scaling non-linear responses across a range of temporal and spatial

scales resulting from long term changes in event frequency and magnitude. Until today, most

considerations on the impact of climate change on the aquatic environment have been based on

stationary boundary conditions reflecting a possible future climate state. Focusing solely on the final

stage of a future scenario neglects that climate change is a progressive process which develops over

time. In particular, the morphology of riverine, estuarine and coastal environments will develop

progressively over time in response to long term changing boundary conditions. In order to address

challenges related to climate change it is therefore crucial to develop an understanding of how these

environments will adapt to this change over time and finally behave under a different climate regime.

Focusing on the modelling of morphodynamic processes in scale models, this section addresses the

crucial issue of how to compress or extend the relation between model time and real time. For this

purpose, we will review existing methods for the representation of morphodynamic processes over



longer time scales in scale models addressing scaling laws and highlighting scale effects and their

limitations.

4.1.2. Background

The morphology of alluvial river channels, estuarine, coastal and marine environments is governed by

the complex interaction between sediment transport and flow processes (e.g., Church 2002, 2006, van

Maanen et al. 2016) as well as further important factors such as hydrology, sediment yield, succession,

land use, and sea level rise (e.g., Blum and Törnqvist 2000, Lane et al. 2007, Pelletier et al. 2015,

Nicholls et al. 2016). The processes governing sediment transport and morphological development

depend on a wide range of spatial and temporal scales ranging from a few seconds at the grain scale

(e.g., incipient motion, grain motion) through hours and days (e.g., movement of bed forms such as

dunes, scouring at bridge piers), years and decades (e.g., evolution of floodplains) to geological time

scales (e.g. evolution of catchments) (Kern, 1994, Kleinhans et al. 2015).

Physical scale models are a useful tool to simulate and investigate the corresponding complex

processes and feedback mechanisms given that their design reflects the spatial and temporal scale of

the problem under investigation. They have been used for more than 100 years to investigate the

interaction between flow, sediment transport, and morphology. An example for an early investigation

in regard to erosion processes is the erosion of canal beds due to propeller jet erosion by Krey (1911).

Since then such models have been used to study and enhance the understanding of many different

sediment transport and morphological processes across different spatial and temporal scales (e.g.,

Kleinhans et al. 2015).

Figure 2 and Figure 5, redrawn from Peakall et al. (1996), present a schematic overview of different

model types and their ability to replicate the relevant spatial and temporal scales of the prototype.

Prototype models represent a 1:1 replica of the prototype in which flow and sediment dynamics can

be recreated with little or no difference from the prototype. Such models are mainly used to study

physical processes at the smallest spatial and temporal scales (e.g., incipient motion, bed form

generation). Froude scale models are a common engineering tool for the design of hydraulic structures

covering larger spatio-temporal scales while distorted models (models with different geometrical scale

ratios in the horizontal and vertical directions), and unscaled analogue models attempt to reproduce

some selected properties of the prototype (Peakall et al. 1996). In these models the time passes faster

than in the prototype which makes them attractive to study climate change effects. However, as will

be outlined below, their design can be challenging since the time scales for flow dynamics are generally

quite different from the fluvial process time scales (Tsujimoto 1990).



Figure 5. Schematic view of the balance between the ability of model-types to replicate the prototype and spatial/temporal scales (Figure modified from Peakall et al. 1996).

4.1.3. Scaling

The scaling laws used to design hydraulic models can be derived based on a dimensional analysis (e.g.,

Buckingham 1914, Barenblatt 2003). An important prerequisite for the design of a physical model is

the dynamic similarity ensuring a constant prototype-to-model ratio of masses and forces acting on

the system (e.g., Einstein & Chien 1956, Yalin & Kamphuis 1971, Kobus, 1984, Hughes 1993, Frostick et

al. 2011), i.e. that the derived dimensionless parameters are equal in model and prototype. A perfect

dynamic similarity is not achievable for model scales deviating from the prototype scale, i.e. it is not

possible to design a downscaled model so that the relative influence of each individual force acting on

a system remains in proportion between prototype and model, and corresponding scale effects for

coastal and fluvial scale models are discussed in e.g. Yalin (1971), Hudson et al. (1979), de Vries et al.

(1990), de Vries (1993), Hughes (1993), Ettema & Muste (2002), Sutherland & Whitehouse (1998),

Heller (2011). Scale models need therefore to be designed in a way that important force ratios are

maintained while providing justification for neglecting other force ratios. Neglecting force ratios can

result in scale effects if the model is operated at boundary conditions where the neglected force ratios

are important; in other words, there will be a divergence between up-scaled model measurements

and real-world prototype observations. Scale effects become more significant with increasing scale

ratio and their relative importance depends on the investigated phenomenon (Heller 2011), i.e. scale

effects will have to be accepted.

The most commonly used scaling criteria for fluid flow is the Froude-scaling requiring similarity in the

Froude number Fr = U/(gh)0.5 in model and prototype, where U denotes the flow velocity, g the

gravitational acceleration, and h the water depth. This scaling law, ensuring the constant ratio between

inertia and gravitational forces in model and prototype, is most significant for open channel flows so



that the water surface will be adequately replicated in the model (Kobus, 1978). There exist further

hydraulic scaling criteria (Kobus, 1978, Novak et al. 2010) which may be mentioned when highlighting

scale effects in different model types below.

In the following discussion it is assumed that the model studies are carried out with water as model

fluid so that the ratio of fluid properties in model and prototype such as fluid density r, fluid dynamic

and kinematic viscosity randr, respectively are equal to 1; the subscript r denotes the ratio between

model (m) and prototype (p). Moreover, scale effects due to fluid temperature will not be considered

although it worth mentioning that Young & Davies (1990) used heated water (30 °C) in their

experiments in order to improve the similarity in Reynolds numbers. Finally, although beyond the

scope of this review, it is worth mentioning that scaling considerations for morphological processes in

extra-terrestrial environments is also possible (e.g., aeolian dunes on Mars and Venus; Claudin &

Andreotti 2006).

Fixed bed models

Fixed bed models are characterized by a stable bathymetry (i.e. no sediment transport). Considering a

uniform open-channel flow with a fixed-bed in a wide channel, i.e. a width to depth ratio > 30 so that

the hydraulic radius can be replaced by the water depth h, a dimensional analysis results in

Fr fct. Re, ,

kS

h (4.1)

where Re = Uh/denotes the Reynolds number, k/h the relative roughness (with k = roughness length

scale which is often expressed in terms of the grain diameter d), and S is the slope. Within a Froude-

scaled model the flow Reynolds-number Re = Uh/ will differ between the model and prototype.

Therefore, to avoid scale effects, the flow regime in both the model and prototype needs to be fully

turbulent. Moreover, the relative roughness (or submergence h/k) and the slope need to be the same

in a Froude model. The roughness can be scaled considering similarity in the Darcy-Weisbach friction

factor, which in turn depends on h/k, or alternatively in the Chézy-coefficient or Manning number. In

distorted models which are characterised by different horizontal and vertical length scales Sr ≠ 1. Thus,

the distortion leads to scale effects in the flow field (see e.g. Lu et al. 2013, Zhao et al. 2013) and it can

be described that geometric similarity is replaced by geometric affinity (de Vries, 1993). Distortion is

not acceptable in a model where the vertical velocity components are important, but vertically

distorted models are acceptable for uniform, non-uniform and unsteady flow conditions with relatively

slow vertical motion (Novak et al., 2010). For example, considering scale models of rivers, the

horizontal dimensions involved are commonly much larger than the vertical dimensions and this will

lead to unrealistic scale models if the vertical scale (hr) is selected equal to the length scale (Lr) (de

Vries 1993). Additional care needs to be taken in regard to potential scale effects due to water surface

tension in the water depth in the model is low (e.g. Hughes 1993; Peakall & Warburton 1996, van Rijn

et al. 2011) or if the model is operated with varying background water levels (e.g., to simulate tidal

effects) since the effect of wetting and drying bank material will change its behaviour, especially when

using lightweight material (LWI 2010).

Based on the similarity in Fr it becomes possible to derive the hydraulic time scale tr (e.g. Kobus 1978):



rr

r

Lt

h (4.2)

In this equation, Lr denotes the scale ratio for the horizontal length scales between model and

prototype (Lp/Lm) and hr the corresponding vertical scale. For a non-distorted model tr = Lr0.5 showing

that time related to bulk flow processes in the model passes faster than in the prototype.

Movable bed models

Movable bed models represent a two-phase flow with a solid (particles) and fluid (particles) phase (e.g.,

Yalin 1959). While the flow is generally Froude-scaled, the similarity in sediment movement depends

on a set of additional dimensionless parameters which are the grain Reynolds-number Re* = vd

densimetric Froude number (Shields-number) Fr* = vsgd], relative sediment density s

relative submergence h/d (which is already found in the fixed bed model), and relative fall speed vs/u*

(see e.g., Yalin, 1971, Hughes 1993, Peakall et al. 1996 for details). In these definitions, s denotes the

sediment density, u* the shear velocity (u*2= ghS), and vs the fall velocity. In order to obtain perfect

similitude for sediment transport processes, all these quantities would have to be equal in the model

and prototype, therefore assuming that water is used in both model and prototype rr = 1):

*,r *rRe 1rd u (4.3)

2

**,rFr 1r

s rr

u

d

(4.4)

, 1s r (4.5)

1r

r

h

d

(4.6)

,

*,

1s r r

r r

v L

u t (4.7)

Equations (4.3) – (4.7) have been formulated for unidirectional flow conditions. In the case of wave

action, wave characteristics become important and need to be considered for scaling of

hydrodynamics (e.g. Yalin & Russell 1962, Le Mahaute 1970, Hudson et al. 1979, Hughes 1993, Van Rijn

et al. 2011). Note also that for unidirectional flows the shear velocity can be determined via u* = (ghS)0.5

so that for such conditions equation (4.4) can be written as:

2

*rFr 1r

s r rr

h

L d

(4.8)

A general problem encountered in the scaling of shear velocity u* (or bed shear stress) is that this

similitude assumes a flat bed which is not necessarily the case because the bed topography of most

coastal and alluvial environments is characterized by bedforms or other morphological features (e.g.,

Hughes 1993, LWI 2010). If this bed topography or ‘form roughness’ is not adequately scaled, scale

effects will automatically be induced.



The criterion defined by equation (4.7) essentially corresponds to the ratio of the Rouse-number in the

model and prototype and hence it is most important for suspended load transport when considering

unidirectional flow. Inserting the hydraulic time scale given by eq. (4.2) into this equation yields:

r rh L (4.9)

i.e. the dynamics of the suspended load transport can only be modelled exactly using an undistorted

model, but it may be reasonable to relax this criterion for models focusing on bed load transport. Low

(1989) found in experiments that used lightweight materials with different specific densities 1 s

< 2.5 and a grain diameter of d = 3.5 mm, that the specific volumetric bed load transport rate q is

related to u*r/vsr by a simple power relation and that qs u*6 and vs

-5. Zwamborn (1966) argued that

the Fr* criterion is essentially the same as the u*r/vsr-criterion and that a good similarity in river

morphology can be expected between model and prototype if the latter criterion is used together with

an appropriate friction criterion and near similarity in Re*. Grasso et al. (2009) found that equilibrium

beach profiles can be obtained in scale model tests with lightweight materials using the Froude,

densimetric Froude and Rouse numbers as scaling criteria (the Rouse number corresponds basically to

equation 4.7).

Gorrick & Rodriguez (2014) used a non-distorted model of a sand-bed stream to demonstrate the

importance for scaling of Fr* and Re* (the latter was expressed in terms of Re*Fr*-0.5) as well as the

sediment size distribution. They acknowledged scale effects due to incorrect scaling of relative

roughness in such models (i.e. violation of equation 4.6) but found that for sediment beds with bed

forms, or in other words situations where the bedform drag is larger than grain friction, the relative

submergence criterion may be violated as dune dimensions depend mainly on the densimetric Froude

number.

In general, well-designed movable bed models have been shown to be a valuable tool for studying

morphodynamic processes and features across a wide range of spatial scales for, different river

channel morphologies and coastal environments (e.g., Bruun 1966, Hudson et al. 1979, Hughes 1993,

Peakall et al. 1996, Paola et al. 2009, LWI 2010, Green 2012, Kleinhans et al. 2014, Bennet et al. 2015,

Yager et al. 2015, Kleinhans et al. 2015). There are many different studies looking at, for example, the

effect of training structures on water bodies; local and reach wide morphological development of sand

bed rivers through braided gravel bed rivers; step-pool systems to beaches and coastal areas. A

detailed overview of each individual study is beyond the scope of this review but this section highlights

some specific examples. Table 2 reviews some of the major studies dealing with experimental

applications of lightweight sediments and associated time scales/distortions.

In all these studies it is identified that, in practice, complete similarity in all dimensionless ratios for

the combination of scaling laws for fixed and movable bed models is not possible. In fact, scale effects

need to be accepted in movable bed models meaning that some of the criteria have to be relaxed to

be able to design practical experimental models. Depending on which similarity criteria is/are violated,

Hughes (1993) defined different bed load model types which are briefly introduced here and discussed

in more detail below: Best models maintain all geometric ratios between model and prototype as well

as the similarity in sediment density. Lightweight models are designed to maintain similarity in both

Re* and Fr* thereby violating intentionally the criteria given by equations (4.5) to (4.7), i.e. including

the sediment density criterion. Densimetric Froude models are similar to lightweight models with the

difference that the similitude in Re* is relaxed while sand models fulfil only the scaling criteria in regard



to the sediment density ratio. Thus, in regard to the classification according to Figure 5, best models

correspond to a Froude model, lightweight and densimetric Froude models can be classified as both a

Froude or distorted model, respectively, and sand models can generally be classified as analogue

models.

In addition to these bed-load model types, Hughes (1993) defined suspension-dominated models which

are more common in coastal modelling applications than in alluvial river studies. In such models, the

dominating physical process is the uplift of the particles due to turbulence induced by waves or

currents and their transport in the water column. In the case of waves, such models require the

consideration of different physical parameters for the definition of scaling criteria and laws according

to equations (4.3) - (4.7) than bed load models, such as the characteristic velocity (gHb)-0.5 instead of

the shear velocity u* in equations (4.3), (4.4) and (4.7), and the breaking wave height Hb instead of

water depth h in equation (4.6) (Hughes 1993). More details in regard to the scaling laws considering

or neglecting the fall-speed dependency for such models can be found in e.g., Hughes (1993) and van

Rijn et al. (2011). From this and the explanation above it becomes obvious that the scaling criteria for

suspended load models differ from those of bed load models; it is only possible for one transport mode

to be simulated following similarity criteria while the other mode will be affected by scale-effects.

Nonetheless, there exist model-tests where it was attempted to simulate both modes (e.g., Grasso et

al. 2009). Although not too common, suspended load models have also been considered for the

investigation of the behaviour of suspended sediments in e.g. for meandering channels (e.g., Lu et al.

2013) or in groyne fields (e.g., Yossef & de Vriend 2010).

Table 2. Lightweight sediments (experimental applications) and large time scaling/distortions. Abbreviations used for the publication type: Rp-Review paper; Ep-Experimental paper; Tp-Theoretical paper; R-Report; Ur-Unpublished report.

Name Publication type

System scaled/studied

Modelling approach Additional comments

Ettmer et al. (2015)

Ep Live-Bed Scour at Bridge Piers

No scaling. Test of empirical laws.

Lightweight Polystyrene Bed (rel. density 1.06)

Kleinhans et al. (2015)

Rp/Ep Biomorphodynamics of rivers and deltas

Characterization of scale effects in the ratio bar pattern and bar length to channel width.

Geometric scale effect absents but time scaling problematic as it integrates multiple processes (sediment transport, floodplain formation, bank failure/stratigraphy and riparian vegetation)

Viparelli et al. (2015)

Ep Sediment sorting and selective transport by weight

No scaling. Use of lightweight sediments for testing sorting/transport processes.

Downstream lightening and upward heavying. Particle mixtures with rel. densities from 1.5 (lightweight) to 4.

Gorrick & Rodriguez (2014)

Rp/Ep Sand-bed stream Undistorted Froude scaling and graded

1/16 model with various types of lightweight sediments (test of pros & cons).



lightweight sediments

Scale effects due to incorrect scaling of relative roughness

Vermeulen et al. (2014)

Ep River scale model of a training dam

Froude and Shields scaling with lightweight sediments. Nearly undistorted geometry.

Good reproduction of bed forms (dunes/channels) with lightweight sediments but overestimation sediment mobility: amplification scouring, absence deposition.

Petuzzelli et al. (2013)

Ep Beach profile morphodynamics

Irregular wave conditions and geometries based on Froude scaling. Use of lightweight materials.

Testing scalability of a benchmark test from 1/15 to 1/50 and 1/100 with different materials covering densities between 1150 kg/m3 and 2650 kg/m3 and median diameters from 0.07 mm to 1.5 mm. In addition to settling velocity, mobility rates and beach profile morphodynamics depends on particles intrinsic characteristics

Bing-quian et al. (2012)

Ep Bed forms and bar system in gently curved river channel

Distorted/undistorted (densimetric) Froude model

Derivation of the scaling laws from 1-dimensional equation of motion, continuity equation, bed deformation equation and the formula of bed load transport. Confirmation of the bester suitability of a distorted model to predict bed forms compared to a undistorted model

Ettmer & Orlik (2012)

Ur Dunes in unidirectional flows characterised by bed material with wide-grain size distributions simulated using

Scaling based on sedimentological diameter D* and ratio of mean velocity to fall velocity as well as ratio of Re*/Fru*

2

Investigation of mixtures of lightweight materials; dune shapes observed in corresponding sand experiments could be reproduced



lightweight materials

LWI (2010) Ur A stretch of the trained Oder river

Distorted lightweight model to simulate morphodynamic development based on different river training structures

Investigation related to morphodynamic time scales related to dune movement under different hydraulic conditions indicating dependence of morphodyanmic time scale from hydraulic conditions

Gill and Pugh (2009)

Tp/Ep Sediment transport processes

Modified-lightweight (Froude) model, adjusting sediment density and slope of the model to correct for constant dimensionless transport rate.

Scaling laws derived based on keeping the relationship between dimensionless bed shear and dimensionless unit sediment transport. The particle size and density is based on the fall velocity.

Grasso et al. (2009)

Ep Transients and equilibrium states of intermediate cross-shore beach morphology

Undistorted Froude scaling and nearly scaled Shields number, Rouse and Dean numbers (similar regimes).

Length scale about 1/10 and time scale about 1/3.

Paola et al. (2009)

Rp Stratigraphic and geomorphic experiments

Internal/external similarity. Scale independence.

Natural scale independence characteristic of morphodynamics. Quantitative understanding of the origins and limits of scale independence better suited than dynamic scaling.

Wilson et al (2007)

Ep Mississippi river delta

Froude law and particles scaled so that incipient motion and resuspension were similar in model and prototype.

Horizontal scale 1/500, vertical 1/12000, morphological time scale 1/17857 (1year=30min in model)



Kocyigit et al. (2005)

Ep Tidal-induced transport in a squared harbour

No proper scaling undertaken, but use of a lightweight sediment with a tide period of 355 seconds

Direct comparison numerical/experimental work, test of sediment transport formulae for lightweight sediment

Moreton et al. (2002)

Rp/Ep Braided alluvial architecture and subsurface permeability

Generic Froude scale model (relaxation on the scaling of the grain size magnitude)

In addition to comments for Moreton (2001); geologically similar sedimentary sequences of coarse-gravel braided alluvium.

Gaines and Smith (2002)

Rp Loose-beds Review and analysis of 16 large scale and 14 small-scale models to assess the primary factors required for morphologic similarity

Morphologic similarity based on Mean squared and cumulative frequency error between prototype and model. Similarity of sediment motion based on incipient particle mobility, the general state of sediment mobility, and the particle’s suspension characteristics.

Madej et al. (2009)

Ep Channel responses to varying sediment input

Froude and Shields stress similarity according to bankfull conditions of the study reach

Spatial scale 1/100. Distorted Froude-scale model of the reach and undistorted model of a generic gravel-bed channel that is steeper and coarser than prototype.

Moreton (2001)

Thesis, Chapt5

Effect of sediment supply grain size on down-basin braided alluvial architecture

Generic Froude scale model (relaxation on the scaling of the grain size magnitude)

Spatial scale:1/50. Sediment composition: 20% sand, 80% gravel. Scaled hydrographs and sediment input

Wallerstein et al. (2001)

Ep Large woody debris (LWD) flows

Distorted Froude-scaled, Shields scaled, scaled drag for submerged LWD

The time scaling ratio was 1:11.45, thus geomorphic adjustments were modelled in only 45 hours

Peakall et al. (1996)

Rp/Tp Fluvial Geomorphology

Review of the scaling of time in movable bed models via

Effect of the distortion of the timescale ratio for long-term processes



dimensional analysis of the physical processes and event magnitude-frequency (hydrograph scaling).

not known – to be investigated. Scale modelling hydrographs can enhance time-scale compression.

Pugh and Russel (1991)

Tp Mobile sediment beds

Froude scaling with use of the Shields function

Adaptation of the Taylor dimensionless unit sediment discharge curves to determine the appropriate sediment diameters specific gravity.

Petters (1990)

Ep Sediment transport in large alluvial rivers with very low slopes

Distorted Froude scaled lightweight sed. (Bakelite). Then adjustment velocity for scour ignition (lost Froude condition)

Froude condition lost leading to analogy modelling (comparison patterns)

Low (1989) Ep Bed load Transport No scaling law applied but description of the transport of lightweight sediments (test of Einstein-Brown and a modified Smart formulas).

Lightweight sediment transport rate proportional to the sixth power of the shear velocity and inversely proportional to the fifth power of the grain fall velocity.

Vollmers and Giese (1972)

Ep Estuarine tidal morphodynamics

Distorted Froude scaling. Choice of lightweight sediment based on Gehring (1967)’s method

Horizontal scale 1/800 and vertical 1/100. Distortion of tide period to match expected bed deformation. Final timescale 1/705 (1day = 2min in model).

Le Mehauté, B. (1970)

Tp/Rp Movable beds in Fluvial/Coastal systems

Review of (Froude) similitude relations for movable bed; “Lacey”-type relationships for geometrical distortion

Conditions of similitude for beaches are generally less stringent than for rivers (condition on bottom roughness). Discussions on time scale ratios and the use of lightweight materials.

Zwamborn (1966)

Ep Large river morphodynamics

Modified-lightweight (Froude) model

The Froude criterion was replaced by the scaling the ratio shear-to-settling velocities,



Time scales for movable bed models

Hydrodynamic processes usually occur at a much shorter time scale than morphodynamic processes

and, as will be shown below, time-scales related to different morphological processes do not

necessarily coincide in physical models (e.g. Yalin 1971). This can, in turn, result in undesired scale-

effects which become more significant with decreasing experimental model scale (i.e. of the

reproduction of the prototype).

The determination of sedimentological time scales in movable-bed models is difficult and often

subjective. In fact, the sedimentological time-scale cannot be freely chosen as it is results from the

chosen scales of the other model parameters (Gehrig 1978) and depends hence on which scaling

criteria is intentionally violated. Moreover, there is the need to distinguish between different time

scales for different morphological processes such as individual grain movement (tsg,r) and the evolution

of the bed surface in the vertical () and horizontal (tLr) directions, respectively. Corresponding time

scales are presented in general terms in Table 3.

According to Yalin (1971), the movement of an individual bed load grain is governed by the geometrical

scale of the particle diameter d and the kinematic scale u*, respectively resulting in the time scales tsg,r

defined by equations (4.13) and (4.14), where equation (4.14) results from the additional requirement

of similarity in Re*.

Considering the temporal development of a movable bed surface in an experiment, different scales in

the horizontal and vertical directions need to be taken into account. For fluvial environments, the most

keeping a near similarity in Re*.

Einstein and Chien (1956)

Tp/Ep Rivers with movable bed

Distorted Froude scaling, implying the use of lightweight material.

Detailed scaling procedure derived from the friction, Froude, sediment transport, zero sediment-load and laminar sublayer criteria. Discussion of the issue of loss of similarity and various scaled time scales.

Bagnold (1955)

Ep Transport processes No scaling. Exploratory work on transport of very lightweight material

Characterisation of the effects of particle low inertia on transport processes. Sediment relative densities from 1.06 down to 1.0025

USACE (1936)

R Bed load material Investigation of the suitability of lightweight materials to simulate bed load transport

Identified suitable materials were further investigated related to their critical tractive force; data charts provided



common approach to derive the time scale for the formation of a movable bed surface is based the

comparison of the model response time to known prototype response times (Einstein & Chien 1956,

Vollmers & Giese, 1972; Kamphuis 1975, in Hughes 1993). This is typically achieved by considerations

of the variation of the bed surface level in vertical direction with time and the volumetric sediment

transport rate q, i.e. the Exner equation (e.g., Paola & Voller 2005, Coleman & Nikora 2009). Thus, the

corresponding time scale can be defined according to (e.g., Tsujimoto 1990, Hughes 1993):

1r r rr

r

L ht

q

(4.10)

where denotes the porosity of the bed material. A similar formulation can be obtained considering

the movement of river dunes assuming their geometrical similarity in model and prototype (LWI 2010).

Introducing the dimensionless volumetric bed load transport rate q* = q / (du*), equation (4.10) can be

rewritten according to

* *

1r r rr

r r r

L ht

q d u

(4.11)

Assuming similarity in q* in model and prototype (i.e. q*r = 1), equation (4.11) represents the basis for

equations (4.15) to (4.18) in Table 3 for which it was assumed that u*r = (hrSr)0.5 = hrLr-0.5. Note that for

geometrically similar grains with a similar grain-size distribution (1 - r = 1 (Gehrig 1978). Also, for

practical purposes, the sediment transport rate is often determined from existing bed load formulae.

Using such relationships in (4.11) instead of a measured q* can result in different time scale calculations.

Equation (4.19) in Table 3 was derived by Yalin (1971) and describes the time scale related to the

evolution of the mobile bed surface in horizontal direction. This equation is based on single grain

movement considerations and the relation of the diameter scale with the longitudinal scale.

Comparing the different time scales given in Table 3 and eq. (4.11) it becomes apparent that

tr < tLr < tr < tsgr (4.12)

i.e. the vertical evolution of the bed surface is the quickest followed by the longitudinal displacement

of the grains and the hydrodynamic time scale. The slowest time scale is the individual motion of a

grain (Peakall et al. 1996). Further time scales than the ones discussed here may be derived based on

the consideration of the evolution of morphodynamic features such as meander bend migration rate,

floodplain evolution and biological development (Tal & Paola 2007, Kleinhans et al. 2015, and

references therein).

Time scales for models with suspended load were summarized by e.g. Hughes (1993) and van Rijn et

al. (2011), but in almost all cases a morphological time-scale of suspended models was derived

corresponding to tr = hr0.5 (where the vertical length scale characterizes wave characteristics).



Table 3. Time scales for bed load dominated models, ρr = μr = νr = 1, and assuming u* = (ghS)0.5.

Time scale Eq. Criteria and comments Source

0.5 1

,

sg r r r rt d L h

(4.13) - individual grain movement Yalin (1971)

2

,

sg r r rt L h

(4.14) - individual grain movement - similarity in Re*

Yalin (1971)

r r rt L h

(4.15) - similarity in dimensionless transport rate - similarity in Re* - porosity equal in model and prototype

Yalin (1971)

1.5 1 1r r r rt L d

(4.16) - similarity in dimensionless

transport rate Gehrig (1978)

2.5 2 1r r r sr rt L h

(4.17) - similarity in dimensionless

transport rate - similarity in Fr*

Gehrig (1978)

7

1.5 6 1r r r r rt L h d

(4.18) - similarity in dimensionless transport rate - similarity in Fr* - near similarity in Re*

Tsujimoto (1990)

1.5 1

Lr r rt L h

(4.19) - individual grain movement Yalin (1971)

4.1.4. Bed load model types

Best Models

Best models are defined by similarity in the geometric ratios between model and prototype, i.e. hr = Lr

= dr and sediment density, i.e. s,r = 1 or (sr =1. Due to the similarity of the material the porosity

ratio r can also be assumed to be 1. Best models are hence undistorted Froude models fulfilling by

definition the criteria given by eqns. (4.4) to (4.6). Besides the fall velocity criteria according to

equation (4.7), best models violate the grain-Reynolds number criterion which for this model type

corresponds to Re*r = Lr1.5. Therefore, best models should be operated in hydraulic rough conditions,

i.e. Re* > 70, to avoid scale effects arising through viscous forces as Re* in prototype conditions will be

larger than in the model. The limitation of best models in regard to the scale factor arises from the

requirement to scale the sediment with the same factor as the model length scale. If for example fine

sand is already present in the field, then this restriction could easily result in the requirement to use

potentially cohesive sediments representing a problem due to the different properties of cohesive

sediments compared to granular material. To minimize this issue, special materials may be used such

as Ballotini or the model types as described below.

The sedimentological time scales are identical in best models focusing on unidirectional flows (tsg,r = tr

= tLr = Lr0.5) and are equal to the hydraulic time scale tr. This model type is typically used in studying the



evolution of bed surfaces and transport mechanisms in laboratory investigations using downscaled

grain-size distributions of the prototype bed material with a hydraulically rough flow regime (e.g.,

Aberle & Nikora 2006). Best models offer the opportunity to study the effects of hydrographs on bed

evolution due to the identical time scales (see Section 4.3 for further discussion of experiments to

model flood hydrographs).

Lightweight models

As indicated by the name, a model sediment is used in lightweight models which has a lower density

than the prototype sediment. Lightweight models as defined by Hughes (1993) are designed to

maintain similarity in both Re* and Fr* and this requirement relates the sediment density scale directly

to the sediment grain diameter and length scales via (s - )r = dr-3 and (s - )r = hr

3Lr-1.5, respectively

(note that the latter relationship assumes that bed shear stress can be determined from the depth-

slope product; Vollmers & Giese, 1972). Moreover, lightweight models can only keep similarity in

relative submergence (hr/dr = 1) if Lr = hr4. Lightweight models are therefore prone to a range of scale

effects due to the incorrect scaling of sediment density and particle size as well as the differences in

bed porosity and bed characteristics, hence liquefaction of the bed, and suspended sediment transport

will not be correctly represented in the experimental model (Hughes 1993, Petruzelli et al. 2013). Thus,

lightweight models need to be distorted using a different ratio and as a consequence, a direct

quantification of the model results is difficult and such models require careful calibration. An example

for such a model is the Elbe tidal model described by Vollmers & Giese 1972) or the model study carried

out by Gorrick & Rodriguez (2012). Note that Yalin (1972) recommended to study dunes in modelling

studies using lightweight models in order to keep similarity in both Re* and Fr*. However, an aspect

that has not yet been treated is how model distortion and the different sediment properties affect bed

form shape and kinematics.

The time scales for lightweight models can be derived as tsg,r = (s - )r-2/3, tr = hr

3(1-)r (s - r-2/3, tLr =

hr2(s - )r

-1 thereby assuming qr* = 1 and that bed shear stress can be determined from the depth slope

product. The derived scaling ratios indicate that the similarity conditions for lightweight models can

result in rather impractical scaling ratios. Zwamborn (1966) therefore recommended to replace the Fr*

criterion by (u*/vs)r = 1 while keeping near similarity in Re*.

Densimetric Froude models

Densimetric Froude models are similar to lightweight models with the difference that the similitude in

Re* is relaxed. This relaxation gives more flexibility in specifying model parameters (Hughes 1993) as

only similarity in Fr* is required. This requirement in turn gives a general definition for dr according to

dr = u*r2(s - )r

-1 (see equation(4.4)) or, for unidirectional flows (equation (4.8)) dr = hr2(s - )r

-1Lr-1.

The time scales for densimetric Froude models are given by equations (4.17) and (4.18) where the latter

formulation by Tsujmoto (1990) was derived by considering the Manning-equation in the derivation of

the scaling law, i.e. additional similarity in bed roughness. Densimetric Froude models are typically

distorted and operated with lightweight materials. Their design is, however, challenging due to the

multitude of scaling laws that need to be considered (e.g. Bing-Qian et al. 2001, 2012) and hence they

are prone to scale effects as discussed in the above sections. In this context, Gill & Pugh (2009) outlined

a method based on the fall velocities of particles to address potential scale effects in Re* if Re*m < 100

while Re*p > 100 (see also Pugh & Russell 1991).



Many practical applications of such models indicate their suitability in studying morphodynamic

processes within river reaches as well as for coastal environments (e.g. Hughes 1993, Paolo et al. 2009,

LWI 2010). In fact, densimetric Froude models have often been used to study the development of

particular river reaches thereby assuming hydraulic rough conditions (e.g. Vermeulen et al. 2014 and

the models at the Federal Waterways Engineering and Research Institute, Germany, as summarized in

LWI 2010). For the latter studies the theoretical time scales according to Table 3 ranged between 1:173

to 1:2020 while the comparison with scales determined from field data indicated that the real time

scales ranged between 1:1192 and 1:4000. This indicates that in most models the time scales are only

roughly met and that there is a need for further investigations in regard to this topic. Note also that

most of the model studies mentioned in Section 4.1.1. can be classified as densimetric Froude models.

Sand models

Sand models fulfil only one of the scaling criteria defined by equations (4.3)-(4.7) which is the sediment

density ratio (eq. (4.5)). According to Dalrymple (1989; cited from Hughes 1993), sand is the preferable

model sediment for coastal transport models. However, such models do not comply with the Fr*

criteria which can result in significant errors. Kamphuis (1985; cited from Hughes 1993) stated that the

non-similarity of Re* and Fr* in such models will result in erroneous modelling of sediment transport

at low flow velocities and that the period of rest for sediment particles is exaggerated in such models

during wave cycles. In general, sand models may also correspond to analogue or small-scale models

which are discussed in the next section.

Analogue and small scale models

The evolution of the morphodynamics over larger spatial (and temporal) scales is often investigated in

so called small-scale model or micromodels (e.g., Davinroy et al. 2012). Such models aim to reproduce

the original existing conditions in the prototype and its future response to climatic or anthropogenic

forcing. Moreover, such models also offer the opportunity to investigate different physical phenomena

at reduced costs (e.g., Stagonas 2010).

Analogue models are designed to study analogies between the model and prototype and are not

designed to provide keep strict similarity in the above scaling criteria although they can theoretically

be classified according to the model-types defined above. In any case, micromodel design should

include an assessment of sediment mobility (e.g. Ettema & Muste 2002), which is often achieved using

the Shields regime diagram. However, the aforementioned model types are generally stricter in terms

of similarity criteria than analogue or small-scale models for which the validation depends on the

judgement of similitude in bed-sediment movement (Ettema & Muste, 2002) or on the operator due

to the lack of a specific methodology for describing the degree of morphodynamic similarity in model

studies (Gaines & Smith 2002). Moreover, Gaines & Smith (2002) stated that the implementation of

micromodel or similar small-scale loose-bed modelling requires the development of new measuring

techniques in order to accurately determine model parameters.

Analogue or small-scale models models have been used to study the effect of sediment supply or

sediment composition on the alluvial architecture of river systems (e.g., Moreton, 2001, Braudrick et

al. 2009, Kleinhans et al. 2014, 2015), to investigate the effects of vegetation on a braided morphology

under the simplest conditions (e.g., Tal & Paola 2010), or to study the development of alluvial fans,

river deltas and landscapes (e.g., Whipple et al. 1998, Paola et al. 2009, Ganti et al. 2011, Reitz &

Jerolmack 2012, Kleinhans et al. 2014, 2015)



For example, Willson et al. (2007) reported a scale model focusing on river and sediment diversions in

the lower Mississippi river delta with Lr = 1:12,000 and hr = 1:500 and a model sediment with a density

s = 1050 kg/m³ covering 77 river miles and an area of about 3526 square miles. In this model, the flow

was scaled via the Froude law and the sediment was scaled based on considerations for incipient

motion of the particles so that incipient motion and resuspension were similar in model and prototype.

The resultant sediment time scale was given by the authors with 1:17,857 (one year of prototype time

equals roughly 30 minutes of model time). This model was run for different scenarios, including sea

level rise, and used to enhance the general understanding of the impact of planned measures on

aspects of concerns to the public and State and Federal Agencies.

Further bed load models with lightweight materials

The use of a lightweight material in a physical modelling experiment does not necessarily mean that it

is a lightweight model as such materials can also be used in densimetric Froude models, analogue

models (see above), or to study physical processes within a dimensionless framework. In fact, there

exist a range of movable bed scale model studies in which such sediments have been used (for an

overview of the materials see e.g., Franco 1978, Bettes 1990).

Probably the best known example is the study of Shields (1936) related to incipient motion. However,

lightweight materials have also been used to study local erosion processes such as scour development

downstream of weir structures (e.g., Ettmer 2004 and references therein), bridge piers and abutments

(e.g., Fael et al. 2006, Meyering 2012, Ettmer et al. 2015) and the impact of jets (e.g., Rajaratnam &

Mazurek, 2002). The latter studies, in particular, made use of the fact that erosion processes are

accelerated when lightweight sediments are used instead of natural fluvial sediments, i.e. that the

equilibrium dimensions of the scour can be reached faster. However, studies related to the impact of

event sequencing on the development of scour are rare.

The design of the scale model scour studies with lightweight materials is also generally based on

similarity in the densimetric Froude number, although in these studies it is defined slightly differently

from equation (4.4) since the shear velocity is replaced by a representative and measurable flow

velocity due to the complex hydraulic flow patterns (e.g., Ettmer 2004). Similarly, incipient motion is

often characterized by considering the ratio of flow velocity to the critical flow velocity resulting in

incipient motion, although the latter is often subjectively biased (e.g., Ettmer 2004; Wang et al. 2013).

Ettmer & Orlik (2012) attempted to use lightweight material with a similar particle diameter but

different densities in order to simulate the grain size distribution of a sand-mixture. Their scaling

criteria were based on the dimensionless particle diameter D* (also known as Bonneville parameter),

the ratio of flow to settling velocity, and a dimensionless parameter defined by Ettmer (2004)

considering the resistance at the grain-scale. Their experiments revealed a range for these

dimensionless parameters in which the dunes formed in the lightweight material showed good

agreement in relation to bed both geometry and kinematics. However, the effect of sorting and

selective transport of particles by material density (see Viparelli et al. 2015) needs to be taken into

account in such models.

4.1.5. Suspended load models

The mechanism of suspended sediment transport is different from the mechanism of bed load

transport, therefore the modelling of suspended sediment transport requires the consideration of

different physical parameters and scaling criteria such as the ratio of settling velocity to shear velocity,



i.e. the Rouse number. Turbulence is an important parameter in suspended load models and the

transport is closely linked to the hydrodynamic time scale so ideally such models should be undistorted,

which is significantly different from the types of bed load model described above. If distorted, the

distortions should not be so large that the type of sediment transport changes (i.e. from bed load to

suspended load or vice versa). In general, many of the scale effects discussed above can also occur in

suspended load models (e.g., the grain size of the model sediment should not fall in the cohesive range

etc.) and they are not repeated here.

Focussing on the development of beach and profile erosion during coastal storm events with high

energetic waves, USACE (1989) and Kriebel et al. (1987) recommended the use of the criteria stated

by Dean (1985) for the design of such models. These should be designed as undistorted Froude scale

models and keep similarity of the fall speed parameter (ratio of wave height and the product of wave

period and fall speed). Moreover, these sources explicitly mentioned that scale effects due to viscosity,

surface tension, or cohesiveness of particles should be avoided so that the character of wave breaking

can be simulated properly.

4.1.6. Tidal models with movable bed

Tide effects are important in estuarine regions resulting in alternating flow patterns governed by the

tide wave and the freshwater supply (Schwarze and Vollmers, 1978), which in turn affect flow and

sediment transport processes. Reproducing tidal flow patterns (which can be seen as long waves,

Hughes, 1993) in scale models is possible using the aforementioned scaling criteria for fixed bed

models (mainly Froude-number scaling) taking into account tide characteristics (including neap-spring

tides).

Reproducing tidal flows in scale models requires a careful selection of the model boundaries and scales

taking into account the tidal regime and flow, respectively. In case the tidal regime will be altered, the

tidal wave may be partly reflected so that it will be dampened upstream of the reflexion point and

consequently amplified downstream of the reflexion point so that water levels and tidal discharges will

be changed up to the point of the tidal limit. If the tidal flow will be altered, one can expect that only

the distribution of the tide-waters and hence flow velocities in the flow cross-section will be altered

without affecting the amount of water that is exchanged during a tidal sequence. This means that, in

the latter case, tidal flow characteristics are only locally altered. Both issues need to be considered

when choosing the model boundaries and scale (Schwarze and Vollmers, 1978).

Planning tidal models with movable beds, a detailed time-related analysis of morphological changes is

required based on a literature review and analysis of available data. Such considerations enable

insights into causes and tendencies of sediment transport patterns and reproducing historical stages

of morphodynamic development of the tidal reaches enables the estimation of the time scale (Giese

and Vollmers, 1978). Moreover, it needs to be kept in mind that that the cohesive properties of

estuarine mud cannot be reproduced correctly in scale models and that density currents and Coriolis

acceleration are hardly to realize in distorted models with movable beds (Vollmers & Giese, 1972).

According to Price and Thorn (1993), the most successful tidal models have been small scale models

focusing on the reproduction of gross-sedimentary features and not fine details. Moreover, Giese and

Vollmers (1978) stated that the simulation of morphodynamic features by considering just a few tidal

cycles is not sufficient. In fact, in their study of the Elbe-estuary in Germany they found a

morphodynamic equilibrium only after modelling a time span of 15 years (corresponding to 186 h in



the model). This shows that such models require patience and that subsequently the number of

possible experiments is limited.

For the construction of large tidal models Giese and Vollmers (1978) recommended to determine the

first the horizontal and vertical scale ratios taking into consideration the available space and pump-

capacity of the laboratory. Estuarine models are typically distorted (e.g. Giese and Vollmers 1978) and

the horizontal scale can be rather small due to the large areas that need to be modelled (e.g., scales

of 1:500 – 1:1000 according to Price & Thorn 1993). Care needs to be taken in regard to the vertical

scale ratio so that water levels can still be determined with a sufficient accuracy (e.g., Higuchi et al.

1987 constructed a tidal scale model with hr = 1:500). The hydraulic time scale for distortion ratios

larger than 1:5 can be determined from the Froude-scaling law, while for distortion ratios smaller than

1:5 the hydraulic time scales need to be empirically determined due to scale effects associated with

the reproduction of the bed roughness and relative submergence (Giese and Vollmers 1978, Higuchi

et al. 1978). The characteristics of the movable bed material is generally given by the available material

which is typically lightweight material in such models.

Further detailed considerations on the planning of tidal models and examples for corresponding model

studies can be found in, e.g., Kobus (1978), Giese and Vollmers (1978), Higuchi et al. (1978), Pierce and

Thorn (1993), Wu et al. (2003) and Zhao et al. (2003) to name just a few specific studies.



SCALING MORPHODYNAMIC PROCESSES IN COASTAL MODELS Research on scaling laws related to coastal sediment transport modelling and morphological evolution

was intensively active in the seventies and eighties (e.g., Noda, 1972; Kamphuis, 1972; Vellinga, 1982;

Hughes, 1983), when physical modelling was the only practical method available to address

morphodynamic changes over longer time-scales. Despite those significant contributions, Dalrymple

(1989) summarised the state-of-the-art in physical modelling of coastal processes. The physical

modelling techniques that were developed included using artificial materials (mostly lightweight, non-

sand) in the laboratory to cope with problems derived from the sediment scaling laws (see also Section

4.1.4), as well as using distorted models (with different vertical and horizontal length scales, see also

Section 4.1.3). A summary report with several scaling examples from coastal to river sediment

dynamics, and using lightweight materials, is also given in Migniot (1994).

More recently, van Rijn et al. (2011) re-analysed the scaling laws for beach and dune erosion processes.

Since all the important dimensionless numbers that characterize sediment transport dynamics cannot

be satisfied simultaneously, they proposed that it is sufficient for accurate scale modelling that these

dimensionless numbers are constrained within a certain range, rather than imposing a fixed value. Van

Rijn et al. (2011) suggested that for coastal scale models, the most relevant requirement is to attain

similarity of the cross-shore equilibrium bed profiles between prototype and model, particularly in the

surf zone and the beach and dune zone. In practice this means that the most important criteria for

experimental design is the accurate representation of the beach and dune erosion volumes. Following

this principle, a general set of scaling laws were derived, valid for both beach and dune erosion volumes

under storm conditions with dimensionless parameters describing the equilibrium erosion volumes

that are the same in model and prototype.

Also recently, Grasso et al. (2009) used a lightweight bed material to reproduce successfully

underwater beach cross-shore profile changes in equilibrium and transient stages, through the choice

of appropriate scaling laws (Froude similarity, and densimetric Froud and Rouse numbers, see also

Section 4.1.2).

4.2.1. Results from previous experiments

Van Rijn et al. (2011) concluded that the morphological time scale (𝑛𝑇𝑀) depends on the depth scale

(𝑛ℎ), the length scale (𝑛𝑙), the sediment size scale (𝑛𝑑50) and the sediment density scale (𝑛𝑠−1) as given

by

𝑛𝑇𝑀 = (𝑛𝑙 𝑛ℎ⁄ )𝑝(𝑛𝑑50)𝑞(𝑛𝑠−1)𝑟(𝑛ℎ)𝑠

where the exponents p, q, r and s can be determined by laboratory model data. Assuming r=1, and

using results from experiments conducted in Hydralab III at three different scales, they found that:

𝑛𝑇𝑀 = (𝑛𝑙 𝑛ℎ⁄ )1.4(𝑛𝑠−1)(𝑛ℎ)0.4

which accurately represents beach erosion volumes. Alternatively, from model experiments where

𝑛𝑠−1=1, they also found the following expression to produces reasonable results for dune erosion

volumes:

𝑛𝑇𝑀 = (𝑛ℎ)0.56



which is similar to that of Vellinga (1982), 𝑛𝑇𝑀 = (𝑛ℎ)0.5 = 𝑛𝑇, where 𝑛𝑇 is the wave period scaling.

That is, according to Vellinga’s relation, the morphological time scale is equal to the wave period scale

(see also Equation 3.2).

It is further noted, from the CERC longshore sediment transport (LST) equation, where the LST rate is

proportional to the alongshore component of wave power, that assuming equal porosity between

model and prototype, one can obtain the following expression for the morphological time scale:

𝑛𝑇𝑀 = (𝑛𝑙 𝑛ℎ⁄ )2(𝑛𝑠−1)(𝑛ℎ)0.5

This equation, derived from LST similarity, is similar to the one from van Rijn et al. (2011) derived from

(cross-shore) beach erosion volume similarity, but with slight differences in the value of exponents

which suggest that the ratio between horizontal and vertical length scales is more significant for the

morphological time scale.

4.2.2. Critical analysis of knowledge-gaps and future developments

Although the expressions above give an indication of the morphological scaling, they do not relate

directly to the wave climate or the wave time series. For physical models of coastal morphodynamics,

it is common practice to simplify the wave field into a series of relevant wave conditions (e.g., Khan-

Mozahedy et al., 2016) and conduct the tests over a sufficiently long time period so that significant

morphological changes are observed or the model approaches a (near or quasi-) equilibrium state (e.g.,

Freire et al., 2008).

In numerical modelling of coastal morphodynamics, several approaches have been used to reduce the

computational time and increase the effective period of simulation (e.g., Walstra et al., 2013). The

most commonly used approach includes a morphological acceleration factor that speeds up the

morphodynamic time scale relative to the hydrodynamic timescale. In these cases the interaction

between the hydrodynamic fields and the bathymetry may be relaxed by only updating these fields at

certain intervals. Recently, Benedet et al. (2016) reviewed several different wave representation

methods with an “equivalent” morphological response; concluding that the energy flux method (and

the “Opti“ method, based on transport patterns from model simulations) showed the best results, in

terms of accurately representing the sediment transport produced by a very high resolution wave

climate with a reduced set of wave conditions. However, they also recognise that there are limitations

in the use of this methodology, and it is not the most adequate solution for some cases (e.g., in mild

wave climate coasts, where morphology changes are dominated by episodic major storms). Assuming

that a process-based morphodynamic numerical model is capable of reaching equilibrium conditions,

Roelvink and Reniers (2012) suggest that one approach to achieve realistic bathymetries on the long-

term scale is to allow the model to evolve the bathymetry under typical wave conditions. Thus, for this

type of physical model models, climate change forcing can be accounted by changing the typical wave

conditions.

Analytical morphological time-reducing methodologies based on synthetic hydrodynamic criteria,

tested through process-based numerical modelling, are expected thus to provide indications to cope

with long-term effects in physical modelling, where climate-change variables (such as the mean sea

level, the wave height and wave direction distributions, and the extreme waves’ frequency of

occurrence) play an important role. These morphological-enhancement methodologies or procedures



are thus the basis to be tested, applied and verified for laboratory experiments, particularly linked with

long-term time-series.



REPRESENTING FLOOD EVENTS IN PHYSICAL MODELS In fluvial systems, if we discard the unsteadiness at very short time-scales associated with the

turbulence, the next most relevant time-scale corresponds to the discharge history of the river system

which is ultimately driven by the atmospheric forcing. It is this hydrological time-scale which ultimately

interacts with other time-scales of the system (sediment transport, plants and biofilm growth cycles,

animals) to produce complex dynamics and is controlled by climate.

4.3.1. Available forcing data to take into account climate change

The impact of climate change on the future evolution of fluvial systems is currently predicted using

atmospheric forcing (e.g. temperature, precipitation) predicted by general circulation models (GCMs),

combined with basin scale hydrological models taking into account all the water reservoirs and transfer

processes. A good illustration of the kinds of hydrological models used for such predictions can be

found in Arsenault et al. (2015), who calibrated such models on even years of available datasets and

validated them on odd years for stream flows in North America, before comparing their relative

performances using different criteria. Calibrated hydrological models can then be driven by future

climate scenarios in order to predict changes to fluvial systems. Crude approaches incorporate

predicted changes (precipitation and temperature increases for instance) directly in time-series used

for model calibration and validation (e.g. Islam et al., 2012). Without spatial and/or temporal

refinement for the forcing of hydrological models by GCMs, only low frequency components of the

hydrology (month an annual mean values) can be explored with these approaches. As discussed in

Seidou et al. (2012), appropriate downscaling schemes must be applied to GCMs forcing to achieve

better validation between the hydrological models and the observations. Such downscaling can be

done dynamically, by using, for example, Regional Climate models (RCMs) at the interface between

the GCMs and the hydrological model, and/or, to infer local rain fall time series from derived

statistically from predictions by the GCMs, increasing the confidence in hydrological model predictions.

With such improvements, predictions for the stream flow and annual flood peaks can be evaluated

with greater confidence (e.g. Huziyh et al. (2013); Wang et al. (2015). Predictions can then be analysed

to estimate climate change impact on flood peaks and frequency, as shown in Figure 6.

Figure 6. Figure from Huziyh et al. (2013). Ensemble averaged normalized frequency of occurrence of 1-day high flow events for current 1970–1999 (left y-axis) and future 2041–2070 (right y-axis) period for 6 watersheds. The numbers correspond to watershed indices given in Table 1 of Huziyh et al. (2013). Inset shows changes to normalized frequency of occurrence from current to future climate.



Such predictions can also be analysed in order to estimate the impact of climate change on floods with

different return periods. However, while floods with 10 or 30 year return periods are easily inferred

from such simulations, far longer and therefore costlier simulations are required for floods with longer

return period.

4.3.2. Limits of the steady flow approaches

In many situations, knowledge of the peak flow for different return period floods is considered

sufficient to constrain the design of civil engineering structures. For instance, in the study of dam

failure by Chen et al. (2015), a 1/250 scaled physical model is used, where the inflow is maintained

constant during the tests, corresponding to “typical” flow discharges in the field (forced by rainfall or

earthquake, respectively). Such constant inflow conditions for the flume test (based upon Froude

similarity for the flow) are relevant in that case since the dam breaking event is rapid, with an expected

duration that is shorter than the typical duration of the flood event. It is worth pointing out that in

most of these studies, the non-dimensional time scale is the hydraulic one, i.e. inferred from Froude

similarity.

Yet, there are many other situations where different time-scales are interacting and where not only

the peak flow discharge is relevant, but also the duration and even the shape of the complete flood

hydrograph. Such situations in civil engineering are encountered when progressive damage of easily

erodible structures are of interest. For instance, Schillinger (2011) used a physical model to study the

effect of unsteadiness and event sequencing on scour patterns and amplitude near a pier, simulating

flood events with a duration too short to lead to equilibrium patterns for the scour. As a consequence,

the scour dynamics is strongly dependent on both the flow peak intensity and its dynamic pattern. In

this example, the ultimate scour depth is not the same as that that would have been obtained by

modelling a steady flow with a discharge based upon a flood peak.

4.3.3. Flow unsteadiness coupled with sediment transport dynamics

All physical modelling of unsteady flow with sediment transport are to some extent facing conflicting

time-scale issues associated with the different time-scales governing hydraulics and sediment

dynamics (e.g. see Table 3). One time-scale is associated with the hydraulics itself, which may be

downscaled to the physical model using classical Froude similarity. However, other different time-

scales are associated with the sediment transport dynamic, including the time-lag to achieve vertical

equilibrium for suspended sediment transport (also called the sedimentation time-scale), sorting and

armouring effects that have their own time-scale, and the time scale for the growth and migration of

bedforms. It is nontrivial to distinguish among all available time-scales to which extent the physical

model is representative of the full scale processes.

Tilting recirculating flumes play a major role in such studies, since they allow easily to achieve uniform

flow conditions respecting the Froude similarity hypothesis, representative of the flow conditions

found in the rivers at reach scale. Generally, flood events are represented by triangular hydrographs

with possibly an asymmetry between the rising and falling stages, see figure 2 for two examples. In

most flume experiments, the gradual increase and decrease of discharge are reproduced by stepped

hydrographs with a number of steps for each hydrograph strongly dependent on the complexity of the

flume control equipment (from as few as 3 or 4 step changes to a virtually continuous change in

discharge).



Figure 7. Typical simulated hydrographs in recirculating flume experiments. From Ahanger et al. (2008) on the left, and from Lee et al. (2004) on the right.

In most of flume experiments, as shown in Lee et al. (2004), the sedimentation time-scale is

significantly longer than the hydraulic time-scale, justifying the latter one (and therefore the Froude

similarity) to scale the hydrographs for the flume experiments.

For symmetrical hydrographs and uniform flow conditions, an unsteadiness parameter P can be

introduced, defined as P = (yp-y0)/(tdu*), based upon the water depth difference between the flood

peak yp and the base level y0 , and td the flood duration and u* the bed friction velocity. This parameter,

along with the total flow work Wk which integrates the flow volume associated with the flood, control

the sediment transport rate. Different equivalent unsteadiness parameters are given in other studies,

like U/(h/t) in Ahanger et al. (2008), with U the bulk flow velocity, and (h/t) the rate of change

for water depth, which can be interpreted roughly as 1/P. In studies by Ahanger et al. (2008) and Lee

et al. (2004) with well-sorted sediment beds, increasing P leads to increasing hysteresis between the

sediment transport rate during the rising stage and falling stage of the flood event (see Figure 7).

However, different hysteresis patterns are found in the two studies, a clockwise hysteresis for

suspended sediments in Agangere et al. (2008), and an anti-clockwise hysteresis for bed-load transport

in Lee et al. (2004).

Figure 8. Hysteresis in instantaneous sediment transport rate qs during a flood for suspended sediment on the left with clockwise behaviour (figure from Ahangere et al. (2008) where q is the instantaneous flow discharge) and bed-load transport on the right with anticlockwise behaviour (figure from Lee et al. (2004) where y is the instantaneous water depth, and the rising and falling stages are represented by solid lines and dashed lines, respectively).



In the bed load transport experiments of Lee et al. (2004), the hysteresis between the rising and falling

stages of the flood for sediment transport result essentially from a lag between bedform formation

and the imposed hydrographs This demonstrates that bedforms are never in equilibrium for high

values of the unsteadiness parameter, since higher sediment transport rates are triggered when

bedform develop late during the rising stage whilst lower sediment transport rates result from

bedforms developing and persisting during the falling stage.

This importance of bedform growth and decay throughout a hydrograph sequence has motivated

many studies on the bedform dynamics for non-stationary flows, focusing mainly on step changes in

discharge as the simplest model to address this question. Previously, comparisons have been done

between the growth time-scale of bedforms and the time-scale of unsteady flow to investigate the

resulting bed patterns. For instance, Tubino (1991) introduces an unsteady parameter U which

compares the flow unsteadiness time-scale to the bedform growth rate time scale to predict the final

height of alternate bars in a flume with equilibrium heights being found experimentally and

theoretically only for low values of U. Recently, Martin et al. (2013) combined bedform dynamics

(gradual merging or coarsening of small scale patterns towards larger ones) with flood-like unsteady

flow forcing to explain more quantitatively the hysteresis in sediment transport rates observed by

other authors like Lee et al. (2004). By introducing a relevant time-scale called “reconstitution time”

for bed form growth and decay and comparing it with the flood time-scales, they are able to explain

the appearance of an hysteresis for “fast” floods that corresponded approximately with the high values

of the unsteady parameter P. As shown in Figure 9, the processes associated with the growth of

bedforms during the rising stage and their decay in the falling stage are complex and very different. As

discussed by Martin et al. (2013), the former relies on gradual collision and merging of small structures

towards larger ones, while the latter relies on the formation of secondary small scale structures that

progressively cannibalize the larger structures formed during the rising stage.



Figure 9. Figure from Martin et al. (2012) showing the bed-form evolution during the rising (on the left) and falling (on the right) stages of a flood. In the upper panels successive longitudinal bed profiles are plotted through time. Lower panels show colour maps of bed elevation.

Independently from this analysis of bedform dynamics during flood-like unsteady events to explain the

discrepancy with equilibrium-state sediment transport prediction, other studies have also investigated

the role of sediment sorting and bed armouring during unsteady flow events and more specifically,

under successions of unsteady events. Mao (2012), detailed laser scan bed surveys following three

different hydrographs which show that even if the grain size of the bed remain invariant, significant

changes occurs in terms of vertical roughness and rearrangement of particles and sediment structures.

In their experiments with gravel bedload transport and no bedforms, a clockwise hysteresis is also

found for sediment transport rates, associated with the evolution of the bed sediment surface layer

during the hydrograph event. They observed that the bed roughness increased proportionally to the

magnitude of the hydrograph, and then reduced during the falling stage of hydrographs because

sediment surface becomes organized into structures. For long hydrograph events, the bed eventually

returns to its initial roughness. For the short/high-magnitude hydrograph, a rougher bed surface

remains at the end of the flood event.



Figure 10. Figure from Mao (2012) showing clockwise hysteresis in bed load sediment transport rate qs and in transported sediment Dt during a short /high magnitude flood on the left and during a long/ low amplitude flood on the right for a bimodal grain size dist distribution (d50 ratio around 5). Rising and falling stages of hydrographs are identified by solid lines and dashed lines respectively. Stars are the sediment transport rates under equivalent equilibrium conditions (from Mao et al., 2011).

In many recent studies, the apparently contradictory previous results concerning for instance the

clockwise or anticlockwise hysteresis for flood-like hydrographs have been put to some extent on

account of ill-designed experimental facility protocols. In particular, it appears that experiments with

well-sorted bed sediment but without recirculating sediment are strongly affected by the artificial zero

sediment input condition at the upstream boundary. However, even constant sediment input at the

upstream boundary may be subject to criticism since it will produce an imbalance between the input

and the output sediment discharge which may generate artificial bed elevation fluctuations at the

flume scale. This clearly gives an advantage to tilting, sediment recirculating flume facilities, but also

offers potential opportunities for annular flumes.

The use of annular flumes offers is an alternative to solve the issue of input and output boundary

conditions. However, the similarity with the field flow is then highly distorted in the sense that only

the flow velocity can be changed for a fixed water level. To simulate flow events in these facilities

requires to focus on similarity at the bed level, i.e. insure that the shear stress follows the same pattern

as found in the simulated flood event(s). This approach has been adopted by Cofalla et al. (2012) to

investigate the effect of resuspension on the toxicity of the river water during a flood by performing

physico-chemical measurements and exposing living rainbow trout. In their protocol, they applied a

hydrograph selected to reproduce at 1:1 scale the evolution of the bed shear stress for a reference

field condition. Due to the use of living trout, they could not downscale the real flood for the flume,

but their approach could be extended to downscaled physical models using friction velocity and near

bed conditions as a reference.



4.3.4. From the single flood event towards a sequence of floods

Beyond the problem of hysteresis in sediment transport rates associated with individual flood events,

there remains the issue of the role of inter-flood flow regimes and the time-scales associated with

flood sequences. In the study of Mao (2012) focusing on bed surface rearrangement, the author

stresses that the antecedent flow history (duration and sequences of disturbances) should be taken

into account to predict sediment entrainment and transport even for fluvial systems that are not

limited by sediment supply. In the study of Martin et al. (2013) focusing on bedform growth and decay

during a flood event, the same consideration is emphasised, particularly when sequences of short/

high amplitude flood events are concerned.

Whilst sediment transport dynamics at the scale of an individual flood event are poorly understood,

studies investigating the impact of sequences of floods are rarer. Wong and Parker (2006) clearly

illustrate the experimental difficulties associated with studying sequences of events. The authors

performed experiments by recirculating well-sorted sediment at a constant rate in a flume where

identical flood-like hydrographs were successively realized until a mobile bed equilibrium was achieved

away from the upstream weir. Between 30 and 50 hydrograph cycles were required to achieve this

equilibrium state. Near the entrance, the bed elevation follows a cycle synchronized with the flood

hydrograph, whereas away from it, the bed elevation remains constant, with a slope parallel to the

water surface which oscillates with the hydrograph cycle. As explained by the authors, the river bed

far away from the entrance accommodates the erosion and aggradation near the entrance by adapting

the bed load rate. In these experiments, explored flow regimes were chosen to prevent the formation

of bed-forms which would have add complexity to the study.

4.3.5. Incorporating time-scales associated with plants or biofilms

Plants and biofilms are important components of river ecosystems and have an impact on sediment

transport as well as geochemical fluxes in aquatic systems. Plant canopies, depending on their

geometry and mechanical properties, may be seen as a drag source for the flow, and can act as a

protective layer preventing sediment entrainment or reducing sediment transport rates. Biofilms also

strongly affect the critical threshold for sediment transport and there are many studies that have been

carried out to quantify their impact on flow structure.

However, of more interest here is the mirror role of the hydraulics as a driving force for their growth

and then, their geometrical and mechanical properties. As pointed out by the meta-analysis of Garssen

et al. (2015), the river hydrology modifications driven by climate change, especially in terms of flood

intensity and frequency, are very likely to also modify plant diversity and distribution.

Unfortunately, the time-scales associated with plant and biofilm growth in the field are very large when

compared to the time-scales of physical modelling experiments in the laboratory. For photosynthetic

biofilms in rivers, for example, growth cycles are associated with time-scales of around 30 days, which

correlates approximately to inter-flood periods in the field (see i.e. Boulêtreau et al., 2010).

Macrophytes or riparian vegetation generally develop and grow over much longer time-scales. For

biofilms, another issue is the extreme versatility of this biological agent whose growth and composition

adapts very quickly to flow conditions during growth; for example, Graba et al. (2013) demonstrated

that in steady flow growth experiments the biofilm optimized its mechanical properties to fit the

imposed steady forcing, and were very easily detached by a very slight increase of flow velocity.

Incorporating field representative flow unsteadiness (day or week typical discharge fluctuations)

becomes then important to grow a laboratory biofilm representative of its field counterpart.



Since plant and biofilm time-scales are inherently hard to downscale in flume experiments using

classical Froude similarity approaches or even distorted models, it is more convenient to use living or

artificial surrogates. For plants, many studies now rely on the use of alfalfa (see for instance Bertoldi

et al., 2014) whose size and growth time-scale fit with a downscaling approach to physical modelling

of sediment and flow dynamics. For biofilms, no such living surrogate is available for downscaling, but

two approaches can be adopted (investigated as part of task 8.5). Firstly, chemical surrogates can be

used to simulate the adhesion effect on sediments. Secondly, instead of the whole growth cycle of the

biofilm, only the early growth stage can be used, and controlled by nutrient input and flow conditions

to achieve the desired level of adhesion on sediments. The main drawback of the chemical surrogate

approach is that it cannot represent the dynamical behaviour of a real growing biofilm. The main

advantage is that the cohesion properties are more easily controlled than for a biofilm in its early

growth stage.

4.3.6. Incorporating animals

As well illustrated by the study of Cofalla et al. (2012, see Section 3.3.4 above), the use of the same

animals in the field and in the flume generally requires the reproduction of the same flow conditions

at the scale of the animals, leading to 1:1 scale experimental models. As for plants and biofilms, the

use of equivalent smaller species or young animals could allow downscaling for the physical modelling,

but raises many questions in terms of “equivalence” from the biological point of view. Moreover,

whereas the length-scales can be reduced by this approach, time-scales for living animals are not that

easily shortened. An easier approach consists in reproducing artificially the impact of living organisms,

like bioturbation and other sediment reorganization or grazing, which offers some possibility for both

spatial and time downscaling.

4.3.7. Metrological issues

For the experimental study of unsteady flow regimes in flumes incorporating movable bed and/or

living organisms, the time-dependence of the forcing raises issues only partially encountered in steady

flow experiments.

First of all, for the measurement of flow velocity, all the flow regimes of interest are fully turbulent

which requires some time-averaging to estimate correctly the relevant velocity component statistics

(in particular the vertical profiles of the mean streamwise velocity �̅� and the Reynolds tensor

component 𝑢′𝑤′̅̅ ̅̅ ̅̅ whose value near the bed leads to the friction velocity u*). As shown, for instance in

Florens et al. (2013), if the time convergence is too short (based upon the number of independent

measurements), large estimation errors will be found for such quantities. In most of the studies cited

above, vertically integrated quantities are normally considered (water depth and discharge) with

uniform flow conditions, in order to access directly to the friction velocity u* for instance. In steady

flow conditions without formation of large bed-forms, this requirement for time-convergence the flow

components is easily addressed since the choice of the number of independent measurements is free

(independent measurements means here uncorrelated). In experiments with unsteady forcing, or even

with steady forcing but the formation and migration of bedforms, this unsteadiness adds to the

inherent turbulence unsteadiness. This is particularly critical in downscaled physical modelling where

flood events are represented by a limited number of steps with short duration (like in Mao, 2012), and

for which the number of available independent measurements along 15 minutes can be very low.

Furthermore the presence of bedforms or large roughness patterns leads to heterogeneity in the bed

morphology which also requires spatial averaging in the horizontal plane, with similar convergence



issues (see Florens et al. (2013) for considerations over a simple rough pattern). Under the assumption

of local time and spatial ergodicities, it is clear that all velocity measurement techniques that will

provide the experimentalist with many independent (spatial and temporal) measurements will provide

significant advantage.

These issues are also relevant for other measurements, like bed elevation and sediment transport rates.

For instance, in the study of Lee et al. (2014), the authors are confronted with highly fluctuating

estimates of the sediment rate transport associated with the formation of bed-forms combined with

flow unsteadiness. In Mao (2012), some hydrographs were reproduced three times to obtained

ensemble mean estimates, and the bed surface structure was analysed by stopping the flow to have

enough time to record images of the bed. In Martin et al. (2013), bed topography during the

experiments was measured by successive sonar scans along the longitudinal direction. Each transverse

crossing takes 10s, fast enough to produce timely and spatially resolved bed topography maps even in

unsteady flow conditions. Whereas such tools are now available for bed topography measurements

including underwater laser scans, new acoustic or optical techniques are still lacking for velocity

measurements.

For velocity measurements, acoustic methods are widely used in the context of experiments in large

flume facilities since they can operate in turbid water conditions. Point measurement instruments such

as 3D vectrino are now widely used, and provide users with instantaneous velocity measurements in

sampling volumes which can be approximated as cylinders of 6mm diameter and 3-15 mm height

(depending on the measurement conditions), working at 50 Hz. As raised above, the main limitation is

that such measurements are extremely time consuming when applied to highly inhomogeneous

and/or unstationary flow conditions. In most of the experimental facilities, integral time scales Tint are

typically of the order of the second for typical turbulent boundary layers, and therefore, acquisition

durations Tacq at each point takes generally 3 to 5 minutes to get enough uncorrelated measurements

(around N=Tacq/Tint independent realisations of the turbulent fluctuations) to estimate correctly the

mean flow quantities, and, with some errors, the second order statistics (Reynolds tensor

components 𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ̅). Moreover, the sampling volume limits the measurements to flow regions far away

from the solid boundaries, in the vicinity of which the turbulence integral lengthscales become too

small.

Acoustic profilers solve one of the issue raised above, since they provide almost simultaneous

measurements along a profile. The sampling volume is also smaller, typically 6 mm diameter and 1 to

4 mm long, at least for profiles 3 cm long. One of the main limitation is the fact that the sampling

volume tends to grow as the distance from the instrument becomes larger, because of acoustic wave

diffraction and diffusion. In most measurement configurations, the instrument is located near the

surface, looking down towards the bottom, meaning that the sampling volume grows near the bottom,

where the turbulence integral lengthscales get smaller and smaller, limiting the accuracy of the

acoustic measurement there. Moreover, this technique is sensible to unexpected reflections on solid

boundaries, and gives unrealistic measurements for even the upper part of a plan canopy, for instance.

On the other hand, recent developments with acoustic profiles aim at using the backscattered acoustic

signal not only to measure velocities, but also particle concentrations (see Thorne and Hurther, 2014).

This approach would allow simultaneous measurements of the velocity and sediment concentration,

allowing to calculate the sediment turbulent fluxes in suspended and even bed-load transport regimes.



Optical methods derived from the now classical 2D-2C PIV technique, are a big improvement in terms

of spatial convergence, at least for clear water conditions. In 2D-2C (two dimensional two components)

PIV, velocity measurements are performed in a plane where a laser sheet illuminates seeding particles

advected by the flow. The number of points where the velocity velocity is measured is therefore far

larger than for point or profile acoustic methods. Recent camera sensors are typically 2000x2000

pixels2, yielding around 250x250 measurement nodes with 16x16 pixels2 interrogation boxes and an

overlap of 50%. Moreover, depending on the measurement field of view, spatial resolutions of around

the millimetre or even below are easily achieved, far better than those of acoustic methods. This

advantage of the 2D-2C PIV technique over acoustic methods is tempered by the requirement of very

clear water conditions to achieve such performance, and the limitation of the measurements to only

two velocity components.

Figure 11. on the left, raw particle images recorded by a CCD camera for different levels of turbidity (NTU ranging from 5 to 26) and different view angles from above, for a flow above a canopy of hemispheres (from Rouzès et al., 2014). On the right : calculated vertical profiles of the double-averaged longitudinal velocity above and inside the canopy of hemispheres for the most turbid conditions.

Studies like those of Camero et al. (2013) and Rouzès et al. (2014) have shown that the PIV technique

could accommodate slightly turbid flow conditions, and that the use of a stereoscopic version, also

called 2D-3C (two dimensional three components), could give access to the lacking velocity component

and to measurements inside canopy flows (see Figure 11). Such developments increase the advantage

of optical methods over acoustic methods. However, it should be pointed out that in the two studies

cited here, both cameras and laser sources are located above the water surface, using a glass window

to access to the water flow. In large flumes, this limitation could be discarded by using submersible

cameras and laser sources (see i.e. Tricito et al., 2007 for an example for small scale 2D-2C PIV

measurements).



Fully 3D-3C PIV techniques are of two types. Tomographic 3D-3C PIV technique relies on multiple

camera recording and volume illumination of seeding particles to reconstruct an intensity volume

representative of particle position. Scanning 3D-3C PIV technique relies on a linear and extremely fast

linear displacement of a laser sheet to obtain a similar result. The second technique gives a far better

spatial resolution, but is limited by the ability of the system to scan very quickly two successive volume

of particles. The tomographic 3C-3D PIV technique is now deployed in flume experiments but mainly

for simple geometries (like in Xingyu et al., 2014).

The scanning 3D-3C PIV technique has been used only for slow flows such as stratified turbulence of

shallow water dipoles (see i.e. Albagnac et al., 2013). In the context of strongly inhomogeneous and

unstationary flows in large flume facilities, the main issue is a lack of time and spatial convergence for

the measurements. Therefore, a 3D-2C (3 dimensional 2 velocity components) PIV technique would be

a first step towards more relevant measurements for these flows. A scaning system, even slow, could

correspond to these expectations, allowing 2D-2C classical PIV calculations between two successive

planes, as long as an overlap still exists between the two laser sheets.

When comparing tomographic vs scanning 3D-3C PIV techniques, it is also worth pointing out that

tomography cannot generally deal wit high concentrations of PIV particles, limiting therefore the

spatial resolution. Moreover, the scanning technique offers also an easier optical access, with only one

camera perpendicular to the laser sheet, where tomography requires generally 3 or 4 cameras with

inclined view axis.



5. IMPACT OF CLIMATE CHANGE ON COASTAL STORMS AND STRUCTURE

MODELLING

INTRODUCTION TO REPRESENTING CLIMATE CHANGE IN A COASTAL ENVIRONMENT Most climate change scenarios predict, in addition to mean sea-level rise, the increase of sea

storminess, more frequent extreme events and changes of the dominant wave direction. To ensure an

adequate performance for a wide range of coastal structures including seawalls, vertical and rubble

mound breakwaters in such scenarios, adaptive structures have to be designed, aiming at not

increasing significantly the structure dimensions and the associated costs. This means that it is

necessary to characterize and measure further the response of these structures to climate change,

particularly wave run-up, wave overtopping and hydraulic stability, as well as how altered overtopping

conditions impact on the stability of adjoining elements, particularly rear slope armour. The same

happens with the influence of the angle of wave attack on the structure response, which may represent

significant savings (compared to perpendicular wave attack), especially for very oblique waves, for

which the increase in stability and reductions in run-up / overtopping may be greatest.

Climate change scenarios may significantly modify responses such as beach and dune erosion,

inundation on low-lying areas leading to increased flooding risk of the coastal zone, increase of wave

penetration into harbours, failure of existing coastal and harbour protection structures, and failure of

structures to protect the coast from erosion. In practice, the threat of these increased responses may

be matched by adaptation of coastal and harbour defence strategies based, for example, on adapted

structures (both new and existing ones), and supported by adapted physical modelling, including multi-

variable analysis on test conditions, adapted methodology for conducting the tests and the use of up-

to-date / new measurement techniques for prototype and/or physical modelling.

The studies on run-up / overtopping and damage under climate change scenarios generally require

physical model testing at 2D and/or 3D setups. The 2D tests allow a simple, detailed analysis of the

basic phenomena, but do not account for 3D effects (such as angle of wave attack, spatial distribution

of run-up / overtopping / damage). It is always difficult to perform simultaneous measurement of

overtopping and damage at the rear slope in a narrow channel or in a constrained 3D space (the

measurements need to be offset).

In practice, analysis of climate change effects (given the uncertainties in making such predictions) may

require very many simulations to correctly reflect the response probabilities. Physical model tests

cannot therefore be used on their own to give the full set of results, but will instead be used to adjust

and/or calibrate appropriate semi-empirical methods that will then be embodied in multi-criteria

simulations.



STORM EVENT SEQUENCING AND RUBBLE MOUND BREAKWATERS

5.2.1. Design and procedures of coastal and harbour physical testing

In coastal and harbour structures design, analytical, empirical and numerical methods are used to

compute their hydraulic and structural performance. These methodologies involve a certain degree of

simplification of the real situation, in which the level of simplification increases with the complexity of

the structure, of the bathymetry, of the wave climate, and of the number and nature of the

phenomena to be studied. In practice, most design case studies are unique. The further the structure

or design conditions depart from previous experience or from idealised configurations on which the

empirical design methods are based, the larger the uncertainties using these methods are.

For complex hydraulic structures, physical models therefore become necessary to achieve a sufficiently

accurate and economical final design. Physical model tests are also required where the importance of

the assets being defended (and/or of the structure itself) is high, when the structure stability is not

assured by analytical models, semi-empirical formulae, or numerical models, when designs have to be

optimised, when wave overtopping is a major parameter of the study, when complex phenomena are

analysed, when the bathymetry or the structure geometry is complex, and when transitions between

structures / sections are to be studied (Hughes, 1993; IAHR, 2011, Wolters et al, 2007, 2009).

In physical models of coastal and harbour structures, fixed design water levels are usually considered,

coupled with design wave conditions. High tide levels are often used to test the upper part of the

structure whereas the toe stability is often tested against low tidal levels. Defining overtopping

performance may require running a number of tests at different water level. So, extreme water levels

are not always the most critical design condition in stability testing (e.g. Kortenhaus, 2005; Muller et

al., 2008).

Design wave conditions are usually provided for different return periods (typically between 1 and 100

years), and includes studying the significant wave height, the peak or mean wave period, the peak or

mean wave direction and the duration of the storms (or of a sequence of waves) along the measured

/ estimated wave data duration. Despite the possible existence of a joint probability distribution of

some of these representative variables, this is not a procedure usually considered in physical modelling.

Additionally, a correct description of storm evolution is not available and therefore not taken into

account for analysing damage evolution and overtopping. Nevertheless, recent literature (e.g. Muller

et al., 2008) shows arguments for a different approach to determining the exposure duration or

probability for coastal/harbour structures: the exposure duration or its probability is linked to the

combined probabilities of storm wave heights and water level variations rather than to the maximum

values of either.

Usual procedures for model testing depend on the objectives of the particular model study.

Incremental loading procedures are typically used in structure stability testing (Owen & Allsop, 1983;

Wolters et al, 2007; IAHR, 2011). A test series of individual tests with increasing intensity (Hm0/Tp) are

used (typically 3 – 7 tests) up to design wave conditions. Usually these tests are followed by an overload

test for testing reserve stability, typically 10% to 20% higher than the design wave height. The duration

of each individual test is typically about 500-3000 waves. The number of waves should usually be ≥

1000 to be statistically relevant, Reis et al. (2008), although Romano et al (2015) argue that 500 waves

may often be sufficient.



The incremental loading procedures in physical modelling describe rising storm conditions. However,

it is known that the wave period / steepness can vary significantly during a rising / falling storm and

that structural failure does not necessarily occur during the rising storm (e.g. Owen & Allsop, 1983;

Muller et al, 2007).

5.2.2. Damage description of rubble mound structures in a changing climate

To reflect life-time exposure, model test structure are generally not repaired between individual tests

so that an assessment can be made about the cumulative damage after several storm events. Usually

the armour layers and toe are reconstructed after a complete test series.

Some of the most commonly used damage indicators are the percentage of damage for all armour, Nd,

or the number of displaced blocks per width of one block, NOD (both based on counting the number of

individual units that have been dislodged) or the dimensionless erosion area, S (based on determining

the volumetric change in areas where armour units have been displaced) (CEM, 2016;

CIRIA/CUR/CETMEF, 2007; IAHR, 2011). Other less common damage indicators include the cover depth,

dc (Davies et al., 1994) and the eroded depth, de (Melby & Kobayashi, 1998). Rubble mound armour is

generally said to have failed once the filter layer is exposed or once a critical damage value is exceeded.

Critical values of damage percentage Nd, NOD and damage parameter S for varying materials (rock,

concrete armour units) and varying armour thicknesses are presented in the Rock Manual

(CIRIA/CUR/CETMEF, 2007) or in CEM (2006). In the case of single-layer armouring of concrete units,

usually no damage and only minor rocking is accepted under design conditions (CIRIA/CUR/CETMEF,

2007). These numbers and criteria are difficult to apply directly to, for example, breakwaters with a

berm, structures with several armour grading in one cross-section, and roundheads.

Damage is usually assessed using profilers, laser scanners and photographic techniques (Figure 12).

Digital overlay techniques are employed to assess rock and concrete unit movements. Photographs

(taken before and after the test) and videos are also used to assess structural/toe stability. For larger

model structures with extensive damage, profilers are often used to assess the damage area.

Mechanical profilers are usually the most robust technique to measure damage. However for certain

types of armour layers, they cannot be applied. Acoustic, laser and stereo photogrammetric techniques

are also applied successfully, although they are typically limited to the measuring area.

Figure 12. Damage assessment performed at LNEC using photographic techniques.



Recently, Hofland et al. (2011, 2014) have examined, in 2D and 3D physical model tests, a new damage

parameter for rock slopes based on the dimensionless damaged depth (E) in combination with a

measurement technique (digital stereo photography, DSP). This technique, developed by Deltares, was

also used at the Hydraulics, Water Resources and Environment Division of the Faculty of Engineering

of the University of Porto, Portugal, to map the 3D damage progression in the armour layer of a rubble

mound breakwater built on a geometric scale of 1/35 (including front slope, rear slope and roundhead),

for several wave conditions including climate change effects (i.e. sea-level rise and wave height

increase).

5.2.3. Damage description to non-standard and existing structures

For non-idealised structures, a subdivision of design S-values for different parts of the structure may

be needed. For instance, for damage to submerged rock structures, a subdivision of inner slope, outer

slope, and crest is frequently applied for the determination of S. As damage can occur on the

intersection of these subsections, this makes the evaluation of damage not straightforward. Burcharth

et al. (2006) chose, for instance, an S value of 0.5 to represent ‘initial damage’ to the various parts of

submerged structures. However, it is unclear how this should change when the geometry is changed,

and which values would describe other damage states.

When evaluating a curved section like a roundhead, the structure is often divided into sectors over

which the damage is determined. The width (and height) over which the damage has to be averaged

to obtain these values can vary, and this considerably influences the resulting value of the damage

number. For instance, a formula was given by Burcharth et al. (2006) for the representative width to

determine S from the number of displaced rocks on a submerged roundhead. With the definition that

was applied, negative S-values can appear for crests that are submerged more than 1Hs. The erosion

depth automatically has a (maximum) value for each part of the structure that is considered. Its design

value is not (as) dependent on the value of the slope or shape and size of the structure (part

considered). It is also related to the damage criterion of exposure or washing out of the filter layer,

which is often defined as being ‘failure’ of the structure.

A complicated three-dimensional part of many breakwaters is the roundhead. Damage to roundheads

has been studied by various authors (e.g. Matsumi et al., 2000; Vidal et al., 1991; Guiducci et al., 2005;

Comola et al., 2014). Most damage is often reported to occur at the rear side of the roundhead

(typically at an angle β of 90° to 135° from the wave direction).

The waves that travel over the side of the roundhead can form water jets that give large loads on the

armour units (Figure 13). However, the largest damage is sometimes also reported to occur at the front

section (e.g. Van Gent & Van der Werf, 2010). Comola et al. (2014) describe tests on a breakwater

roundhead with a 1:1.5 slope. They observe that shorter wave periods give more damage to the front,

and longer wave periods give more damage to the rear of the roundhead. Also damage progression

seemed to be faster at the rear side.

Hofland et al. (2014) performed detailed stereo-photogrammetry measurements of the average

damage pattern to 8 identical roundheads (Figure 13). The results show that the radial length of the

erosion hole, L, is smaller at the rear side of the roundhead than at the front section. Therefore, most

damage numbers, except the dimensionless damage depth, E, do not have a direct link to exposure of

the under layer. So it appears that the question whether there is “more damage” to the front or rear

size of the breakwater roundhead depends on the definition of damage. Also, the variation of damage



(one test compared to the other) was so large that the answer to this question varied between

apparently (identical) tests.

Figure 13: Wave attack on the structure (Hofland et. al, 2014).

5.2.4. Damage progression

Structures will usually be loaded by many storms in their lifetime. The progressive damage after several

storms is usually estimatted by using the fact that S is proportional to Nzb in a damage formula, where

Nz is the number of waves in a storm (test), and b a fixed value, e.g. 0.5 in the Van der Meer (1988)

formula for damage to rock layers. To obtain the incremental damage to an already damaged armour

layer, for each sea state with a certain duration the initial damage is increased as if the initial damage

was obtained by a certain duration of the new sea state, and the incremental damage is then

determined for the extra time. This seems a justified procedure (see e.g. Van der Meer 1999, Melby &

Kobayashi, 1998) when the water level remains at the same position. However, if the water level

changes (due to tide or sea level rise), the damage to the armour layer is inflicted at another location

and its development might well be different. If one imagines two erosion holes caused by wave

exposure at two different water levels, as indicated in Figure 14, it can be seen that the eroded area

(damage number S) is increasing very much due to the second scour hole, while the maximum local

erosion depth E, that represents the remaining cover of the under layers, can be unaltered, as the

minimum cover of the underlayers is unchanged. To be able to use the local damage parameter E in

the evaluation of structures, first more experience with its use has to be obtained.



Figure 14: Sketch indicating the principle of incremental damage to a rock slope with increasing water level.

5.2.5. Wave run-up and overtopping

Wave run-up is usually assessed using resistance type wave gauges or step-gauges (pressure sensors

embedded in the mound slope) and photographic techniques (Figure 15). Wave overtopping is usually

assessed by collecting the overtopping water in trays or tanks and measuring the overtopped water

volume or mass. The number of overtopping events can be assessed by a wave gauge at the crest of

the breakwater or by continuous water level measurements (volume or mass) within the overtopping

tray or tank.



Figure 15. Measurement of run-up and overtopping carried out at LNEC using: (top) a resistance type wave gauge located at the armour slope, a wave gauge at the crest of the structure, an overtopping tank and a load cell behind the structure for continuous overtopping measurement; (bottom) overtopping tank with five chambers to measure the spatial distribution.

The maximum permissible values for wave overtopping depend on the structure type and the

requirements of the stakeholders. They vary with the type of structure, the use of the structure and

exposure of the structure. Owen (1980), the EA Overtopping Manual by Besley (1999), and the EurOtop

manual (2007) have derived advice on allowable overtopping limits. British Standards Institution (BSI,

1991), the CEM (2006), and the Rock Manual (CIRIA/CUR/CETMEF, 2007), have all repeated some of

those guideline values.

Several former investigations on wave run-up and overtopping of (impermeable and permeable)

coastal/harbour structures aimed at quantifying the influence of oblique wave approach on mean

overtopping discharge, water layer thickness and velocities through the development of empirical

formulas were done for the determination of a reduction factor for wave obliquity, γβ (e.g. De Waal &

Van der Meer, 1992; Galland, 1994; Hebsgaard et al., 1998; Oumeraci et al., 2002; Napp et al, 2003a,

2003b, 2004; Kortenhaus et al., 2006; EurOtop, 2007; Lykke Andersen & Burcharth, 2009; Van der Meer,

2010; FlowDike, 2012; Nørgaard et al., 2013). However, most of the formulas did not consider very

oblique wave approach. Very recently, Bornschein et al. (2014) studied wave run-up and overtopping

on a slope considering wave attack angles from 7.5 to 112.5°.

The importance of wave grouping on breakwater stability is well known. Johnson et al., 1978, for

instance, showed that certain sequences of waves may produce more damage to rubble mound

structures than individual waves, of the same height, dispersed through the temporal sequence of

incident waves. As a result, new wave synthesizing techniques where developed to allow controlling

the reproduction of wave grouping in the laboratory to better reproduce what is expected to occur at

a particular location in the prototype. The filtered white noise technique determines implicitly the

statistical distribution of wave groups. So, provided that tests are sufficiently long, the availability of

information about wave groups on the real sea states it is not an essential requirement.

5.2.6. Oblique waves

To optimize new structure design and the safety assessment of existing structures, it is important to

analyse the impact of the angles of wave attack on the wave run-up / overtopping and damage. For

very oblique waves, for which the increase in stability and the reduction in run-up / overtopping is the

largest, there are limited data available in existing literature. Moreover, it is important to enhance the

application of non-intrusive measurement techniques, as video or digital stereo photography (DSP).

Limited data are available for very oblique waves, for which the increase in rubble mound stability

might be the largest. Several authors have proposed guidelines on how to take into account the effects

of oblique waves (e.g. Galland, 1994; Yu et al., 2002) but they did not cover very oblique wave

approaches, and the Rock Manual (CIRIA/CUR/CETMEF, 2007), does not support any reduction factor.

More recently, Wolters & Van Gent (2010) and Van Gent (2014) performed model tests to assess the

effects of oblique waves on the stability of rock slopes and of cube armoured rubble mound

breakwaters, focussing on wave directions between perpendicular (0°) and parallel (90°) to the

longitudinal structure axis, with long and short-crested waves.

Regarding wave run-up / overtopping, very recently, Bornschein et al. (2014) studied wave run-up and

overtopping on a slope considering wave attack angles from 7.5 to 112.5º. The tests were performed



under the CornerDikeproject and used 4 water levels, 5 different wave periods and corresponding wave

heights, for long and short-crested sea states. Wave run-up was measured with capacitive gauges and

video cameras (with a MATLAB-procedure for image data processing and a similar one to the video

analysis), while wave overtopping was measured with weighing cells. Only impermeable smooth slopes

of 1(V):4(H) were considered. The authors derived values for the reduction factor for wave obliquity,

γβ, for the angles of wave attack from 7.5 to 112.5° and recommended further investigations with

angles greater than 112.5°. They observed a significant lower influence of very oblique wave attack on

wave run-up and overtopping for short-crested waves than for long-crested waves. For both type of

waves, they observed values of the reduction factor regarding wave run-up slightly higher than those

for overtopping.

Concerning structure stability, Wolters & Van Gent (2010) and Van Gent (2014) performed a set of

physical model tests to assess the effects of oblique waves on the stability of rock slopes and of cube

armoured rubble mound breakwaters (single and double layers), mostly on a 1:1.5 slope. The physical

model tests focussed on wave directions between perpendicular (0°) and parallel (90°) to the

longitudinal structure axis, with long and short-crested waves. A series of test runs were performed

with an increasing wave height between 0.025 m to 0.274 m and constant wave steepness of sm = 0.03

or 0.04 (only for a few tests). The damage to the armour layers was recorded by taking digital overlay

photographs before and after each test, and counting the number of stones and cubes that were

displaced more than one unit diameter. For a number of tests with rock surveys of the armour layer

envelope were also performed with a mechanical profiler. The authors concluded that:

1. the few available formulae that include wave obliquity underestimate the effects of oblique

wave attack;

2. the influence of obliquity is largest for long-crested waves in the case of rock slopes, whereas

for cube armour slopes such a difference has not been observed;

3. the influence is larger for cubes in a single layer than for cubes in a double layer and for rock;

4. the influence of oblique waves is relatively small for small wave angles (e.g. β<15°), much

larger for larger wave angles (e.g. β>30°), and this influence does not increase much for the

largest wave angles (e.g. β>70°).

They provided a design guideline to account for effects of oblique waves on the stability of rock slopes,

armour layers with a double layer of cubes and armour layers with a single layer of cubes (Figure 16).

Van Gent (2014) recommends further study of the effect of wave obliquity on the stability of rubble

mound structures for: a) other slope angles, especially gentler rock slopes; b) other values of wave

steepness, to cover values of the surf similarity parameter outside the range of ξm = 2.2-3.5 for rock

and ξm = 3-3.5 for cubes; c) interlocking armour units. Van Gent (2014) studies did not include wave

run-up or overtopping analysis.



Figure 16. Comparison of prediction methods describing the influence of oblique waves on armour stability (Van Gent, 2014).

Recently, Hofland et al. (2011, 2014) have examined, in 2D and 3D physical model tests, a new damage

parameter for rock slopes, based on the dimensionless damaged depth (E), in combination with a

digital stereo photography (DSP) measurement technique. The dimensionless damaged depth (E), first

introduced by Melby & Kobayashi (1998), has the advantages of: being able to accurately quantify the

condition of a structure after testing, without being dependent on the armour type; being based on

local damage, so several structure parts can easily be assessed separately (Figure 17); being less

dependent (than other damage indicators) on the size of the section over which it is determined; being

applicable to more complex 3D structures (e.g. roundhead). The authors have shown that this

parameter is good to express spatial variability of armour damage but its adequacy to express temporal

variability still needs to be shown. DSP can measure damage relatively easily, with high accuracy and

fine resolution (Figure 17), but it requires the flume or basin to be emptied prior to the measurement,

which is time consuming, especially in basins. The authors recommended further analysis of the

proposed method and further study of 3D cases with locally decreased stability, like a roundhead.

Figure 17. Left: cross-section with profile before and after tests (top) and corresponding distribution of E (bottom); Centre: profile of structure toe, measured with mechanical profiler (top) and with DSP; Right: fully automated mechanical profiler (Hofland et al., 2011, 2014).



5.2.7. Storm event sequence test methodologies

Historically, the significant wave height is considered the main design value among other variables

such as the wave period and water level. Moreover, storm history could lead to progressive failures

related to armour stability and overtopping. It means that a correct description of storm evolution is

fundamental for analysing the damage and overtopping progression.

Li et al. (2014) developed a multivariate dependency statistical model to simulate and extrapolate

storm sequences from limited observations that includes four steps: (i) fit each observed storm

parameter with marginal distributions; (ii) construct the dependency structure; (iii) simulate the wave

climate from the obtained joint probability; and (iv) give the discrete storm events a time sequence by

using the simulated storm frequency. So, from univariate marginal distributions, in the past decades

research led to various methods to study bivariate descriptions of wave conditions (e.g., joint

probability of extreme significant wave heights and sea levels) and, more recently, to copula functions

applied to multivariate simulations, allowing to correlate two or more variables without changing their

marginal distributions. Li et al. (2014) used Archimedean and Gaussian copulas to build a multivariate

dependency structure for the significant wave height, storm duration, surge level and peak wave

period with the purpose of simulating wave climates. The wave direction was treated individually by

fitting to an empirical distribution. Based on the simulations, a large number of synthetic storm surge

events can be obtained by the incorporation of the storm frequency (Fs), defined as the storm number

per month.

Frequently, most attention is given to single extreme events (e.g., 1-in-100-years storm). For example,

when estimating beach erosion or analysing the stability of coastal structures. But it is nowadays

recognised that the cumulative impact of several smaller, closely spaced storms may result in equal,

or sometimes larger issues, as demonstrated by Splinter et al. (2014) for the Gold Coast, Queensland,

Australia. In this study, storm sequencing did not significantly affect the total eroded volumes, but the

individual storm volumes were influenced by the antecedent state of the beach. This gains enhanced

importance in a climate change environment.

The classical test methodology therefore starts with the selection of a return period (typically between

1 and 500 years) associated to the type and functionality of the designed structure. Associated to this

return period, a significant wave height could be calculated starting from wave buoy data and assuming

that the sea state time series of the extreme events follow a probability density distribution (often

Gumbel and Weibull distributions are considered, see Mathiesen et al. (1994)). More challenging is the

selection of the associated wave period. Typically, some adjustments from the historical data set are

made to correlate wave height to wave period. However, the correlation between these two variables

generally presents a big scatter.

Other test methodologies generally perform tests representing the rising storm with constant wave

steepness, considering that offshore wave steepness stays approximately constant during the build-

up of the storm (Owen & Allsop, 1983). Typical wave steepness associated to storm conditions range

from 0.035 to 0.06.

Another approach using copula functions (multivariate distribution functions whose arguments are the

marginal distributions of initial variables) for designing structures was proposed by Soldevilla et al

(2009). The characteristics of extreme multivariate events are analysed in terms of significant wave

height at the storm's peak (Hs,peak) and the concomitant mean period (Tm,peak) of each of the storms.



Different Archimedean copulas are used by Corbella & Stretch (2013) which propose the use of

different Archimedean copulas. Martín-Hidalgo et al. (2014) proposed the Frank and Gumbel copulas,

which offer good results, that assign a mean wave period (Tm) to the significant wave heights. The

proposed theoretical density function is:

𝑓(𝐻𝑠, 𝑇𝑚, 𝜃) = 𝐶(𝑢, 𝑣, 𝜃)

∗(−𝑙𝑛𝑢)𝜃−1(−𝑙𝑛𝑣)𝜃−1

[(−𝑙𝑛𝑢)𝜃 + (−𝑙𝑛𝑣)𝜃]2−(1𝜃

){𝜃 − 1 + [(−𝑙𝑛𝑢)𝜃 + (−𝑙𝑛𝑣)𝜃]

1𝜃} (𝑢𝑣)−1𝑓(𝑢)𝑓(𝑣)

If a reasonable amount of real data information is available, it may be possible to synthesise the storms.

For example, Owen & Allsop (1983) examined all the major storms available within the recorded time

(the largest of which was about 70% of the design wave height) and use them to derive a nominal

extreme storm profile (Figure 18).

Figure 18. Example of design storm profile by Owen & Allsop (1983).

Practically all studies dealing with the subject of storm event modelling adopt the Equivalent Triangle

Storm model (ETS) as a synthetic one (Boccotti, 2000). According to Martín-Hidalgo et al. (2014), the

ETS model is acceptable for reproducing the damage progression of maritime structures but

underestimates damage for more developed sea states.

In the ETS model, the height of the triangle, a, in the parametric model proposed by Boccotti (2000) is

assumed to be equal to the significant height of the storm peak, Hs,peak, and the base of the triangle, b,

is the Equivalent Triangular Storm Duration, such that the maximum expected wave height of the

triangle storm, ETS, is equal to the maximum expected wave height of the real storm, Hmax, (see Figure

19).



Figure 19. ETS model parameters and example of modelling.(Martín-Hidalgo et al., 2014).

Martín-Hidalgo et al. (2014) proposed two new storm models to overcome the issues with the ETS

model:

1. the Equivalent Triangle Magnitude Storm model (ETMS)

2. the Equivalent Triangle Number of Waves Storm model (ETNWS).

The ETMS triangular approach is based on the storm magnitude, M (De Michele et al., 2007). In this

model, the triangle height is obtained in terms of the equivalent height, Hequiv, and the base, the

theoretical storm duration Dequiv, is established such that its magnitude (area describing the storm

history above HT), equals the real storm.



Figure 20. ETMS model parameters and example of modelling (Martín-Hidalgo et al., 2014).

The ETNWS approach considers that the theoretical triangle storm is defined in terms of the equivalent

wave height, Hequiv, and the real storm number of waves, Nz, for defining the triangle base. The storm

peak in all the models is assumed to be the middle of the storm history.

Figure 21. ETNWS model parameters and example of modelling (Martín-Hidalgo et al., 2014).



Martín Soldevilla et al. (2015) proposed three more storm models:

3. the Equivalent Magnitude Storm model (EMS)

4. the Equivalent Number of Waves Storm model (ENWS)

5. the Equivalent Duration Storm (EDS) model.

The EMS model is a generalization of the ETMS model proposed by Martín-Hidalgo et al. (2014). The

shape height is obtained in terms of the equivalent height, Hequiv, and the base, the theoretical storm

duration, Dshape, is established such that its magnitude (area describing the storm history above HT,

which is a concept introduced by De Michele et al., 2007), equals the real storm.

Figure 22. EMS model parameters and example of modelling (Martín Soldevilla et al., 2015).

The ENWS model is a generalization of the ETNWS proposed by Martín-Hidalgo et al. (2014). The shape

height is adjusted as a function of its equivalent height, Hequiv, and its base, the duration, in terms of

the real storm number of waves, Nz.



Figure 23. ENWS model parameters and example of modelling (Martín Soldevilla et al., 2015).

The EDS model, a generalization of the ETSD proposed by S. Corbella & Stretch, (2012); Stefano

Corbella & Stretch, (2012), takes the equivalent height, Hequiv, as a shape height, and base, D, the

duration associated to the time the real storm remains above HT.

Figure 24. EDS model parameters and example of modelling (Martín Soldevilla et al., 2015).

The authors analysed the aforementioned approaches by comparing the main armour layer's

progressive loss of hydraulic stability caused by real storms with the use of the empirical maximum



energy flux model (Melby & Kobayashi, 2011) and the overtopping evolution formula proposed by

Meer & Stam (1992).

The ETDS, ETMS and ETNWS models adequately reproduce damage progression. However, the most

versatile one is the new ETMS giving the best results for both typical sea storms and more developed

sea states. According to Martín Soldevilla et al. (2015), the EMS model generally gives the best results

for all storms (predominant sea, swell or both). The performance of the different theoretical shapes

analysed is a function of the relative influence of sea and swell wave components in the project area.

The triangle is recommended for typical sea storms whereas the trapezoid shape is much more

appropriate for more developed storm conditions. The parabola and trapezium shapes overestimate

damage in all storms. The results of the two triangles considered (isosceles & scalene) are practically

the same but the isosceles is recommended due to its greater simplicity.

Using the appropriate storm pattern and joint distribution functions, it may be possible to define the

complete evolution of the storm for the required lifetime, or return period, of the structure. It can be

used as a simulated storm associated to the design return period instead of the significant wave height.

In this sense, consideration of other variables (e.g. wave period and water level) is feasible and

essential for a complete structure optimisation.

5.2.8. Sea-level rise

The state-of-the-art in physical modelling of breakwaters and coastal structures was summarized in

the breakwaters chapter of the Hydralab III manual (Wolters et al., 2010). About the test sequence and

test conditions it states the following:

“Most models are tested at fixed water levels, each with a single wave condition. High tide levels are

often used to test the upper part of the structure whereas the toe stability is often tested against low

tidal levels. It should be kept in mind that extreme water levels are not always the most critical

condition in stability testing. Design wave conditions are usually provided for different return periods

(typically between 1 and 500 years return periods) including the significant wave height, peak or mean

wave periods, peak or mean wave directions and the duration of storm (or number of waves).”

In this chapter of the manual, no reference is made to sea level rise. The current practise is to simply

add the sea level rise that is expected during the lifetime of a structure to the maximum tested water

level.

Increased storminess as a result of climate change could directly increase the wave statistics at deep

water locations. But this is usually not anticipated. If the wave conditions for a certain structure are

depth limited, they will automatically be adapted in the physical model when sea level rise is added.

Due to the larger water depth seaward of the structure, the wave breaking will decrease, and wave

attack at the toe of the structure will increase. Long-term morphological changes could also affect the

wave conditions, but this is usually not taken into account, unless severe morphological activity is

observed.

The consequences of climate change may be better clarified using a reference example (Figure 25).

This figure shows the increase in exceedance probability due to sea level rise (Sekimoto et al., 2013)

for a coastal structure analysed in terms of overtopping performance. The probability density function

(PDF) of extreme waves is modified due to climate change effects. In addition, due to the expected sea



level rise, the maximum offshore wave height for which the structure still satisfies its performance

requirements for overtopping decreases from 𝐻𝑝01 to 𝐻𝑝02 . As can be seen from Figure 25, the

exceedance probability is expected to increase, not only due to the modification of the PDF but also

due to the reduction of the maximum allowable wave height that produces overtopping.

Figure 25. Effects of climate change in exceedance probabilities (Sekimoto et al., 2013).

The previous example demonstrates that probabilistic design methods shall be employed with

accurately projected environmental data for the future climate. This is transferable to the planning

and execution of physical model studies. Nowadays coastal structures should be designed to comply

with prevailing environmental conditions, but also including due allowances to account for the

predicted changes on it.

Climate change effects may also have impacts in port operations, due to the expected sea level rise

that will reduce the freeboard of quays and may increase sedimentation in the manoeuvring areas and

access channels, inducing more dredging. Alfredini et al. (2008, 2015), using a distorted physical model

including Santos Bay, Santos Harbour, Estuary and nearby beaches, built at the Coastal and Harbour

Division of the Hydraulic Laboratory of University of São Paulo, Brazil, carried out sedimentological

tests in a fixed bed model, by means of the model tracer technique using a fine sand with 0.125 mm

diameter. The estuarine roughness of the model was adjusted by increasing gravel dimensions in the

bed to fit the observational tidal propagation times measured at some characteristic points during

spring tide. Once calibrated and validated the model, a test was run to investigate 1.50 m tidal level

rise influence (intermediate scenario for the year 2100). Due to changes in the tidal prisms, variations



in the estuarine dynamics are expected and can affect channels positively or negatively depending on

the area considered. The results obtained in sediment transport tests revel that sea-level rise will

accelerate erosion at critical zones. An increasing of salinity intrusion can be expected in the estuarine

branches, pushing upstream the salt wedge, increasing problems for water intakes and changing

biological environment for the estuarine biota. A wetland flooding may also be expected, which may

produce serious impact for the aquatic biota and the loss of its sediment filter effect due to the

complex roots retaining sediments. The consequences would be very serious for both environment

and navigation activities. Maintenance procedures have to be modified due to changing of the zones

of concrete deterioration as consequence of mean sea level rise.

To cope with climate change and sea level rise, Burcharth et al. (2014) envisage that coastal structures

can be adapted in a variety of ways (Figure 26). These adapted structures will have to be evaluated for

their main functions, which usually comprises damage and overtopping measurements. While

overtopping can sometimes be evaluated using semi-empirical and/or numerical modelling, the

damage to these structures is still mainly evaluated using physical models. Thus, physical modelling

will be required in order to evaluate the impact of climate change and sea level rise and to validate the

design of upgraded structures. Some of the adaptation measures mentioned in Burcharth et al. (2014)

were applied in the reconstruction and repair of Portuguese coastal defence structures in the late 90’s

(Veloso-Gomes and Taveira Pinto, 1999).

Figure 26: Concepts of adapting coastal structures to sea level rise in which an increase in crest level is not acceptable (Burcharth et al. 2014).

With sea level rise, the wave attack will shift to higher elevations and the question is whether the

summation of incremental damage in terms of eroded area (e.g. Van der Meer, 1998, Melby &

Kobayashi 2011) will still hold. The local damage depth per location theoretically seems to be a more

accurate description for this.



A possible way of remediating the effects of sea level rise and increased wave attack on coastal

structures is to add a berm of large rock to a straight slope, as studied by Burcharth et al. (2014). By

adding a berm, the wave attack on the original upper slope will decrease, while the attack on the berm

can also be less than on the original slope (Van Gent, 2013). There are however significant dangers in

options c) and e) in that, rather than promoting wave breaking in front of the sea defence, some levels

of sea level rise may actually cause the severe breaking to focuss directly onto the defence structure

itself, see Mocke et al (2004). However, for a cross section like this no accepted allowed damage

numbers exist, so a local damage parameter seems a better way to describe the stability of these

structures. For the local damage parameter, accepted design values must be obtained (calibrated to

the S) first for standard slopes. Then, these can be used for non-standard slopes like roundheads

(Hofland et al. 2014). Moreover, existing coastal structures will have to be upgraded for climate change

and sea level rise. So the condition of the structure needs to be known in order to assess the required

upgrade. A good way to parameterize this existing state of the structure must also be obtained.



APPLICATION OF MULTI-VARIABLE ANALYSIS FOR WAVE OVERTOPPING

5.3.1. Overview

This section begins with a general discussion on the derivation and use of Joint Probability Analysis

(JPA) methods for application in analysis / design conditions for coastal structures such as seawalls and

breakwaters. Sections 5.3.2 to 5.3.5 of this note review the derivation of and use in testing of JPA

conditions. Some suggestions on their use are presented in section 5.3.6. Then, recent use of JPA

methods in practice is discussed in sections 5.3.7 to 5.3.8. Issues related to the modelling of wave

overtopping are discussed in sections 5.3.8 and 5.3.9.

5.3.2. Developing levels of sophistication in multi-variable analysis and testing

Extremes analysis is undertaken as a way of inferring values with a low probability of occurrence not

well represented within the source data. A 1:10 year return period value, for example, is the value

expected to be equalled or exceeded once, on average, per 10 year period.

Wave height is normally considered the most important variable for design of coastal structures. In the

early years of seawall / breakwater design, typically 35-50 years ago, an extreme (maximum) wave

height would be determined as the basis of design, using the best methods available. (Note: USA design

methods in the Shore Protection Manual, originally based on Hmax, started to move towards Hs or H1/10

only around 1983.) If required, a sea level (say MHWS) and wave period (perhaps based on a typical

storm wave steepness) would have been assigned to the design wave height.

In the UK around 1980 (30-35 years ago), the effect of wave period on overtopping became more

apparent, so wave period began to be considered as a variable only partially dependent upon wave

height (Figure 27). For coastal responses that are highly depth-limited, sea level might be considered

as the primary variable, with just an associated depth-limited wave height.

Figure 27. Example wave heights with an overlaid partially dependent secondary variable (e.g. wave period) distribution.

Again in the UK and the Netherlands, multi-variable assessment and allowances for future climate

change were beginning to become routine 20-30 years ago in coastal flood studies (and to a lesser

4

5

6

7

8

9

1 10 100 1000

Wav

e h

eigh

t (H

s, m

)

Return period (years)

Wave height

Wave period



extent river flood studies). Where a precise response of interest could be defined by empirical

equations or a simple model, continuous simulation would be used to hindcast a long sample of the

response based on simultaneous long samples of each relevant metocean variable of interest. For

practical computational purposes, joint probability analysis would normally be limited to two primary

variables (e.g. wave height and sea level, or river flow and sea level), perhaps with one or two

secondary variables (e.g. wave period) and/or one or two conditional variables (e.g. direction or

duration).

From about 5-20 years ago, the most common format for the results of a joint probability analysis was

joint exceedance of two primary variables. Analogous with single-variable extremes, the return periods

of each joint exceedance contour (Figure 28) correspond to the probability of a certain value of the

first variable (e.g. wave height or river flow) being exceeded at the same time as a certain value of the

second variable (e.g. sea level).

This format for JPA results came to attention in the UK following its use by HR Wallingford (1990) in an

assessment of the “Towyn storm” of February 1990 for the Welsh Office. Substantial flooding had

occurred in the North Wales village of Towyn when ~500m of sea defence were breached / overtopped

causing flooding to 2800 homes, flood depths up to 1.8m. Partly because of the public nature of the

follow-up study, and as the source data were not subject to the usual copyright and licence issues of

the time, extracts of the Towyn storm report were widely distributed amongst consultants and were

also used for educational purposes.

Figure 28. Example joint exceedance curves increasing with return period.

Although it would have been possible to work with a greater number of primary variables, those more

complex calculations would have been unwieldy and the results difficult to apply. The slightly simplified

joint exceedance format was adopted partly to bring joint probability analysis to a wider range of users,

as opposed to not doing it at all. From about 15 years ago, most relevant UK organisations were

comfortable with application of the joint probability and joint exceedance concepts. Additional

(secondary) variables would normally be assigned later in a less analytical way.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

8 9 10 11 12

Sig

nif

ica

nt

wa

ve

he

igh

t (m

)

Sea level (mCD)

Wave height and sea level joint exceedence extremes

1 year

10 year

100 year

500 year



In specialist modelling from about 20 years ago until now, it has been possible to create large sample

simulations of two (or sometimes three) variables, which could be converted more directly into

response (e.g. overtopping or perhaps flood depth) variables.

Figure 29. Example joint probability density extrapolation.

During the last 5 years, it has become computationally practical to create large sample simulations of

larger numbers of primary variables, with realistic distributions and extremes for each variable and

realistic dependencies between each variable-pair. Joint exceedance extremes can be extracted from

these simulations, but more effective ways of using these data are being developed. For example,

climate change allowances for different variables can be applied separately to each variable. The

sensitivity of any response (for example annual economic loss due to flooding) to climate change can

then be assessed precisely through processing firstly the original data and then the climate-changed

data. In Figure 30, one could count records above the two example failure lines. In the lower pane of

Figure 30, the blue present-day failure lines have been moved left by an amount corresponding to half

a metre of sea level rise, and the much greater number of “failures” can be seen by the large number

of dots above the red “future” failure lines.



Figure 30. Example application of joint probability density extrapolation to climate change impact on probability of flooding.

It is proposed that all relevant source variables, all relevant response variables, and all commonly used

methods of joint probability analysis be considered initially. These can be discussed, prior to selection

of a limited sub-set for use in design of the RECIPE physical and numerical modelling programme.

Ideally, the selections will be based on the variables, responses and methods where there is greatest

potential to minimise uncertainties in future flood defence studies.

5.3.3. Metocean variables of potential interest

For the design of typical coastal structures, say seawalls or breakwaters, the primary metocean

variables of interest may be:

wave height (e.g. significant wave height);



wave period (e.g. mean wave period) or wave steepness (indicative of wave height divided by

wave length), and here wind-sea and swell could be considered separately;

sea level (meaning tidal plus surge), and here high-tide and low-tide conditions could be

considered separately.

These primary variables are often assessed in an analytical way as independent variables. Other

secondary metocean variables of potential interest are:

wind speed

surge

wave direction

wind direction

Typically, wind speed, if required, will be taken as fully correlated with wave height. Typically, surge is

not used directly in coastal engineering studies, although it would provide a truer indication of

meteorological dependence with other variables than does total sea level, that would then omit tidal

variations. Typically, wave and wind direction are simply stated as being in a “most likely” range, but

sometimes different wave and/or wind direction sectors will be analysed separately. Potential

secondary aspects of the main metocean variables of interest are:

duration (e.g. of flooding occurring over high tide or over a river hydrograph);

sequencing of multiple events (relevant where damage accumulates);

distribution and sequencing of individual wave heights within a stationary sea state;

time-variance during an event (e.g. of wave height, sea level, surge or river flow);

wave spectral shape (e.g. spectral width, bi-modal sea conditions).

These are rarely treated as part of the JPA. Typically, where required, they are adopted after the

analysis in order to provide boundary conditions to subsequent numerical or physical modelling of

responses. However, it would now be computationally possible, although not necessarily practical or

even useful, to include all these variables and aspects in a joint probability analysis.

5.3.4. Flood risk and structure variables of potential interest

The main response variables of interest at coastal and flood defence structures are:

wave overtopping rate (both mean rate and peak rate);

damage to hard structures, and here we might consider structure crest, body and toe

separately;

erosion of soft flood defences such as earth banks, sand dunes, or shingle or rock ridges.

Secondary response variables of potential interest are:

wave run-up (e.g. level exceeded by 2% of waves);

breaching (i.e. a significant reduction in defence crest level);



“failure” (e.g. exceedance of one or more unacceptable thresholds of damage or flood flow

rate).

Potential secondary aspects of the main metocean variables of interest are:

duration (e.g. of significant flood flow rate occurring over high tide or over a river

hydrograph);

sequencing of multiple events (relevant where cumulative damage is of concern);

distribution and sequencing of individual wave heights within a stationary sea state;

time-variance during an event (e.g. of flood flow rate).

5.3.5. Methods and aspects of multi-variable analysis of interest

A long-running discussion point in joint probability analysis relates to whether to work in terms of the

probabilities of the metocean variables or the probabilities of the response variables. The probabilities

of the metocean variables could be captured by the empirical distributions of the source metocean

variables, together with, for example, the derived single-variable and joint exceedance extremes. The

latter could be captured through direct incorporation of response variables at an early stage of the

analysis, for example through continuous simulation of wave overtopping rate.

Advantages of working with metocean variable probability are that methods are well established and

reliable, and that, once estimated, the extreme values can be applied to different structures and

different climate-changed and/or development scenarios. Disadvantages are that joint exceedance

extremes are multi-valued and the probability of a response derived from metocean variable(s) in this

way is not equal to the probability of the metocean variable(s), as the same response may be caused

by different metocean conditions.

The main advantage of working with response variable probability is that it provides a result of direct

interest without needing to resolve any mis-match of probability between metocean and response

probabilities. The main disadvantages are that results obtained in this way are response-specific and

climate-change-specific, and the response function often not being known (for example for derivation

of physical model test conditions). A less obvious limitation is that there may be few instances of a

significant response even in a long sample of data, and that the response (e.g. breaching) may be

discontinuous and therefore not amenable to statistical extrapolation.

Aspects of joint probability analysis that could potentially be better understood as a result of

appropriately designed RECIPE tests include:

to which metocean variables are different response variables sensitive and, related to that,

how does metocean variable uncertainty propagate through to response variable sensitivity;

to which metocean variable-pair dependencies are different response variables sensitive

and, related to that, how does metocean variable-pair dependence uncertainty propagate

through to response variable sensitivity;

the mis-match between metocean joint exceedance probability and response probability;



if working with (multi-valued) metocean joint exceedance extremes, how many of the

multiple values need to be tested, and are they best specified in deep, intermediate or

shallow water;

if working with large simulations of three or more metocean variables, can preliminary

numerical analysis be used to develop physical model test conditions with return periods

based on expected response probability;

given the high inherent uncertainty in response variable estimation, is there any metocean

variable or aspect of joint probability analysis where refinement would offer a significant

reduction in overall response variable uncertainty.

5.3.6. Example JPA curves

In the analysis and design of most seawalls and many breakwaters, the primary analysis / design

conditions will now be derived from a Joint Probability Analysis (JPA) of total water level and wave

height as these two variables have the most significant impact on wave overtopping and armour

movement responses. An example output from a simplified JPA is shown in Figure 31. In this UK

example from studies reported by Allsop et al (2011), potential climate change for the 1:200 year

condition has been applied through:

sea levels 0.5m higher than present by 2080s;

wave heights 10% (offshore wave height) higher than present.

Figure 31. Example JPA for a higher-tidal-range site (UK).

A fairly similar example for a smaller tidal range (Brighton, UK) is reported by Chapman et al (2008)

and a number of return period combinations (restricted range) are illustrated in Figure 32.



Figure 32. Example JPA for a lower-tidal-range UK site, waves from SW.

At many coastal sites, waves at a (say) seawall will often be reduced by depth-limiting. These effects

will depend on beach slope, and on the local beach level, as well as the local water levels and wave

conditions. Calculating depth-limiting will then modify the JPA 'curves', as in the example illustrated in

Figure 33 developed for a particular point on a seawall at Margate (Outer Thames Estuary), and

assuming a given beach level and slope. The oblique 'depth-limit' lines limit the range of conditions

that can reach the seawall so the maximum wave heights are reached where those limits intersect the

'offshore' JPA curves.

Figure 33. JPA conditions for Margate showing depth limiting using Goda's (2000) method.

A more sophisticated approach (and one that is rather more complicated to produce) is to transform

all the 'measured' water level and wave height combinations in to the nearshore position, applying

appropriate wave transformations (including depth-limiting) in the process.

It is noted that wave height vs wave period JPAs are sometimes used in offshore engineering, but their

use is very rare in coastal engineering where variations of water levels in combination with wave height

are generally of greater importance than of wave steepness. That is not to ignore wave steepness per



se, but sensitivity to steepness / wave period can generally be assessed by manual 'tuning' of a small

number of additional combinations.

5.3.7. Choosing test conditions

To derive appropriate conditions for design / analysis, historically designers have chosen conditions

for model tests and/or analysis from each JPA curve derived for the return period of interest. It is,

however, important to note two particular features of these JPA curves:

1. At any single return period, there are an infinite number of combinations of water level and

wave height. There is therefore no single 'design condition', but there will be particular

combinations that maximise particular responses.

2. The combinations of water level and wave height that maximise different responses will

often be substantially different, and they cannot easily be identified without careful analysis.

Considering these, the highest wave overtopping on a seawall for instance will probably occur with a

relatively high water level in combination with a moderate - high (but not the highest) wave height.

Conversely, damage to an armoured slope may be greatest for a high wave height (inshore) with a

moderate – high water level. Damage to toe armour will probably be greatest at the lowest water

level commensurate with large wave heights.

The safest approach to specifying JPA conditions for physical model testing has therefore required the

exploration of each key response using the best empirical methods for each response, starting with

depth-limited breaking, then the main structure responses of interest. This procedure is then used to

'screen' potential test conditions and to identify candidate combinations to be used in the main

physical (or numerical) model tests. Even so, the careful designer may be faced with testing many

different combinations to be certain of identifying the 'worst' combined conditions.

5.3.8. Rigorous 'total' probability of overtopping

The JPA approaches discussed above involve a number of simplifications. Only a limited number of

metocean variables can be analysed in a rigorous way. More importantly, and not always understood

by users, is that the probability of the response variable (e.g. overtopping rate) derived via joint

exceedance analysis is not equal to the joint exceedance return period. To assume that they are equal

would be assume that the probability space represented by joint exceedance is a good approximation

to the probability space occupied by response exceedance. This is often not the case, and usually the

return period of an overtopping rate inferred from a joint exceedance curve is significantly less than

that of the joint exceedance curve. For use in sea defence design, it would therefore be necessary to

make a compensating conservative assumption somewhere else in the calculations, although this

approach has often been used in the past

An alternative approach, where a response function is known, for example overtopping rate at a

particular sea wall for a particular climate change assumption, is to convert directly from extrapolated

joint probability density to response. In this approach, every source (or extrapolated source) record is

converted to the corresponding response, the results of which can then be analysed using single

variable methods. For example, if the data set contains sufficient “events”, and the response is a

continuous variable (e.g. overtopping rate under non-impulsive conditions, but not breaching), then

extremes or simple ranking analysis can be applied directly to the inferred overtopping rate event data.



5.3.9. Wave overtopping discharges

The overtopping performance of seawalls and breakwaters has commonly been specified and/or

measured by the mean overtopping discharge, conventionally averaged over a test duration equivalent

to 1000 waves. In some instances, measurements of the mean discharge may be supplemented by

measuring wave-by-wave volumes to give the distribution of volumes. These will give the maximum

volume measured in those tests, but may be used to describe (for instance) the largest 5-10

overtopping volumes. Where the percentage of waves overtopping exceeds (say) 5%, then there are

sufficient individual volumes to make these results statistically robust. But for conditions of low

overtopping, relatively few individual waves will contribute to the mean discharge, and the

uncertainties attaching to any particular set of measurements will be relatively greater.

This effect is compounded by an effect discussed in the 2nd edition of the EurOtop manual (EurOtop,

2016) and illustrated here in Figure 34. Here a single mean discharge of 5l/s.m (itself a relatively high

limit) is given by four different wave heights (each with the appropriate different crest levels. What we

see is that the smaller wave heights (naturally with a small crest freeboard) give many small volumes

to give the mean discharge of 5l/s.m. Conversely, for the largest wave condition (with naturally a much

higher crest), the mean discharge is given by a much smaller number of overtopping volumes, but each

much larger. This effect will be even more marked when the target mean discharge is further reduced.

The implication is that robust definition of hazardous overtopping volumes may require substantially

longer tests to give statistically significant responses, particularly when testing for particularly low

mean overtopping limits. Alternatively, we may need to find a way to down-scale short sequences of

larger waves to give predictions for 'smaller' conditions.

Figure 34. Distribution of overtopping wave volumes for a mean discharge of 5 l/s.m, various wave heights; wave steepness sop = 0.04 and sea state duration of 1 hour.

These effects are particularly important for breakwaters and reclamation seawalls that defend

industrial processes (e.g. oil / gas processing and on-/off-loading, or power stations), where very low

mean discharges may be specified for relatively 'frequent' wave conditions, perhaps 1:1 or 1:10 year

return.



MEASUREMENT TECHNIQUES AND INNOVATION In order to accelerate data acquisition and analysis of wave run-up/overtopping and damage in

physical modelling, new measurement techniques (non-intrusive ones) have been developed. For

example, video monitoring, stereo photogrammetry, image comparing algorithms and motion analysis

procedures have all been investigated in recent modelling studies. There are a number of examples

from recent studies where stereo photogrammetry has been used to analyse static model structures.

Ferreira (2006) developed a stereo photogrammetric code for mapping 3D bathymetries and

structures based upon the reconstruction of stereo pairs, in which, refraction due to the air-water

interface is corrected. This means that, with such pairs, it is not necessary to empty the flume or tank

in order to get a good coverage of the complete armour layer. Further tests to assess the application

and accuracy of this technique were carried out by Lemos (2010) and Lemos and Santos (2012) to

measure damage in scale model tests of rubble mound breakwaters. Pedro et al. (2015) also used this

technique for damage assessment in scale models in conjunction with image-difference-detection

algorithms. Raaijmakers et al. (2012) mapped 3D bathymetries and structures based on

stereophotography through an air-water interface with a dense stereo algorithm. Hofland et al. (2011,

2014) examined 2D and 3D bathymetries and structures using a digital stereo photography (DSP) in

combination with a new damage parameter for rock slopes based on the dimensionless damaged

depth. For moving structures Malheiros (2009, 2013) describe a motion capture system for rigid bodies

based on stereoscopic vision which has been applied to the movements of moored ships. Video

monitoring was also used by Courela et al. (2015), enabling the determination of the number of

displaced/moving armour units, by tracking the blocks movements using video frames comparison.

More recently, Van Gent (2014) and Hofland & Van Gent (2016) used an image processing technique

to quantify and represent the damage to concrete armour layers of coastal/harbour structures,

focusing on settlement of the entire armour layer (Figure 35). The advantage of this technique is to

quantify armour layer settlement, which is usually qualitatively evaluated. The authors are still

assessing the accuracy of the technique.

Image analysis techniques have also been used to capture data on run-up and overtopping. Bornschein

et al. (2014) used video cameras, together with capacitive gauges, to measure wave run-up with

automated processing in MATLAB. Yoo et al. (2013) presented a system to monitor breakwater run-up

and overtopping which was developed using optical imaging and analysis techniques, where optical

image data bursts 20-minute long were processed and analysed to extract quantities of breakwater

run-up by means of image analysis techniques: (1) image calibration, (2) generation of cross-shore

image timestack, (3) identification of run-up trajectory. The computed values of run-up were compared

to those of incident waves, thereby deriving a relative wave run-up formula, i.e., an empirical relation

between incident wave height and run-up height. Andriolo et al. (2015) presented video-derived run-

up data collected at a beach on the Portuguese west coast. High resolution video data were used to

produce timestack images. Recently, Andriolo (2016) has investigated the potential for measuring

wave run-up remotely, using frames acquired by an optical video system and comparing these images

to data acquired by a wave gauge placed over the breakwater structure profile in physical modelling.

Results confirm how video imagery technique can support physical model experiments, namely by

filling wave gauge information gaps and by contributing to overcome other equipment limitations.



Figure 35. Settlement analysis on breakwater roundheads (Hofland & Van Gent, 2016).

Key features from previous work and highlight important results/outcomes

The stereoscopic vision system presented by Malheiros (2009, 2013) aims to measure the motion of

rigid bodies in real-time along its six degrees of freedom (6DOF) and was used in the measurement of

the motions of an oil tanker moored at the oil terminal of the Port of Leixões, Portugal, in the scope of

an R&D project. The developed stereoscopic system was able to measure with high precision in four

(out of the six) degrees of freedom of the moored ship model (Figure 36) in comparison with a

commercial motion tracking system composed of digital infrared cameras.

Results obtained by Yoo et al. (2013) showed that the relative wave run-up height on a typical

armoured breakwater with tetrapods, derived from the measured video and wave data, was

comparable to the range predicted by the general formulae. Andriolo et al. (2015) demonstrated that

timestack images allowed the measurement of the maximum swash elevation from a chosen profile

with a good comparison between a dataset of 36 measurements of Rmax (maximum run-up in a storm)

and R2% (run-up exceeded by 2% of incident waves in a storm) to several predictive formulae published

in the literature. Andriolo (2016) demonstrated the usefulness of timestack images in coastal

morphodynamics studies deriving wave celerity over a nearshore profile using a novel technique,

showed excellent agreement with shallow water linear wave theory. Discrete wave run-up

measurements obtained by video footage were processed to derive wave run-up empirical

parameterizations. Two formulations were derived in order to optimally describe swash elevation on

the beach slope during the monitored time.



Figure 36. Physical model in the wave tank of the Hydraulics, Water Resources and Environment Division of the Faculty of Engineering of the University of Porto (Malheiros, 2009, 2013).

The image processing algorithm developed by Courela et al. (2015) can easily detect armour units

movements. But, the identification of armour layer displacements is not yet possible and the algorithm

is currently being improved. In contrast, the digital stereo photography presented in Hofland et al.

(2011, 2014) can measure damage relatively easily, with high accuracy and fine resolution, but it

requires the flume or basin to be emptied prior to the measurement, which is extremely time

consuming, especially in basins.

The application of the code developed by Ferreira (2006) to surveys of the same scenery with and

without water, revealed that the error introduced by refraction due to the air-water interface was

negligible. Nevertheless, it required a very strict light and water turbidity control (Lemos, 2010). By

applying the same technique (Lemos & Santos, 2012) performed tests with different colour and pattern

arrangements of the armour layer blocks and demonstrated that the more heterogeneous the pattern,

the better the stereo photogrammetric reconstruction. The error (difference between the actual

maximum rock-fill level and its surveyed level) of this survey technique was of 2 mm. Stereo-

photogrammetric post-processing algorithms have been also developed in order to automatize profile

and surfaces extraction and representation, as well as eroded area calculation (Figure 37). The

conclusions that resulted from the tests carried out by Pedro et al. (2015) using stereo

photogrammetry and image differences detection algorithms were: a) Overestimation of the modified

areas due to slight water turbidity can be minimized by previously calibrating the algorithm of image

comparison; b) Damage progression trend was convergent with the damage progression evaluation

using the method of displaced units counting.



Figure 37. Surface and profile representation obtained from a stereo photogrammetric survey (adapted from Lemos & Santos, 2012).

Raaijmakers et al. (2012) tests using stereo photogrammetry found an accuracy of 1 mm and the error

did not increase for greater water depths, varying from a fully dry to a fully submerged model.

Raaijmakers et al. (2012) and Lemos & Santos (2012), who used stereo photogrammetry tools agree

on the following points:

stereo photogrammetry is a cost-effective technique;

survey errors obtained are negligible;

the extension of stereo photogrammetry to cope with an air-water interface has been proven

to work without decrease of accuracy; and

stereo photogrammetry proved to be insensitive to the water level, once water transparency

and light conditions are fulfilled.

5.4.1. Cross-sectional profiles

Damage measurement for the designs of new breakwaters is usually still done as it has been done for

decades. With cross-sectional profiles made to determine the damage to rock amour layers and

counting of the number of displaced rocks for concrete armour unit armour layers. The damage

numbers that are listed in the design manuals (e.g. CIRIA et al., 2007) are still based on the standard

low resolution measurement techniques. The measurement of damage must preferably be obtained

quickly without draining and refilling the flume or basin, which can take a considerable amount of time.

Therefore the measurement should be able to be performed through the water surface. Hence, often

mechanical profilers are still the preferred measurement device.

Several new methods have become available to scan the surface of a rubble mound breakwater in

order to obtain damage (erosion) values. With these techniques the surface can be obtained with mm

resolution and sub-mm accuracy. The main techniques used are terrestrial laser scanners and stereo

photogrammetry.

5.4.2. Terrestrial laser scanners

Standard terrestrial laser scanners can perform a direct distance measurement by measuring the time

it takes for a light pulse to reflect from a solid surface (either directly or by phase modulation). The



laser beam is usually rotated around in a plane by a rotating mirror (up to 10-100 rotations per second)

and several measurements per degree of rotation. The second degree of freedom is obtained by slowly

rotating this primary axis, or by traversing it over the object of interest. This technique gives a direct

measurement (in polar or cylindrical coordinates) of the model structure. The use of this technique for

breakwater modelling has recently become popular (e.g. Rigden & Steward, 2012; Molines et al., 2013;

Puente et al., 2014).

Figure 38: Application of a laser scanner in physical model (Puente et al. 2014). Left: model and scanner. Right: point cloud of measured model breakwater.

It is in theory possible to apply the measurement technique through a (still) water surface when the

water is clear. In airborne Lidar, examples are known where the bed of a river or coastal area is

modelled. However, no known physical modelling studies are known where the technique is applied

in such a manner. The laser should be mounted rather straight above the water surface in order to

prevent reflection of the laser beam on the water surface. This might hamper the use of the technique

in basins. For fully underwater work, experiments in HR Wallingford's Fast Flow Facility have used a

laser-scanner to measure scour formations around structures.

5.4.3. Stereo photogrammetry

Stereo photogrammetry works like the human eye. The setup of the technique consists of two digital

cameras with a known distance between each other that record a (digital) image at the same time. By

correlating the same points in both digital images, the distance of all the points relative to the cameras

can be obtained. By placing markers at known locations in the field of view, the measured elevations

can be transformed to an earth fixed coordinate system. By making a scan before and after a test

(series) the change in structural shape during the test can be quantified. The stereo photography

technique has been adapted for use with a (still) water surface in physical models (Raaijmakers et al.

2012 and Ferreira, 2006). However, though performed (Raaijmakers et al. 2012), the use of it in a basin

is still rather cumbersome. As the technique involves a processing step to come from raw images to a

point cloud, it requires in general more tuning and post-processing than the use of a terrestrial laser

scanner. Tests presented by Lemos and Santos, 2014 used Ferreira (2006) technique. However, to

overcome the time-consuming post-processing steps, two diferent algorthms were created in order to

authomatize surface and profile analysis for several profiles of obtained in different surveys.

5.4.4. 3D printing

3D printers may introduce an important innovation in physical model testing, by allowing the

production of complex-shaped armour layer blocks very accurately and, and the same time, perhaps



to simulate the internal strength of those units at model scale, according to the materials used in their

production, and avoiding a well-known model effect.

5.4.5. Knowledge-gaps and future developments

Potential areas for future research and development of the image analysis techniques to improve

experiments that address climate change are:

To use of the stereo photogrammetry in three-dimensional scale model tests, namely to study

the erosion of round-heads of breakwaters. The correction of the refraction, following the

work of Ferreira (2006), of the interface air-water is of utmost importance as it can speed-up

tests where the sea level rise is represented;

To apply stereo photogrammetry to the study beach erosion in scale model tests, trying to

refine photo acquisition in large scale models. A detailed study should be done, concerning the

accuracy of the technique, using different distances between the photographic equipment and

the model;

To develop versatile image processing software/procedures in order to mitigate/minimize

errors due to light and water abnormal interferences;

To develop a good practice manual on digital image acquisition and processing, including a

recommended workflow, applied to the experimental facilities;

To develop techniques of natural and artificial lighting positioning as to obtain the most accurate video

and picture stills in the experimental setup.



PHYSICAL MODELLING APPLICATIONS AND DEVELOPMENTS TO REPRESENT A CHANGING

CLIMATE Climate change is likely to have a significant impact on the structural and functional behaviour of

coastal and harbour structures. Significant savings may arise from adapted physical modelling to

characterize and measure the response of these structures to climate change. The output from the

adapted physical modelling will also contribute to support authorities with informed decisions on the

need (or not) for new structures and/or for maintenance or repair works, and also to support the

definition of the type of intervention needed.

Novel high-resolution measurement techniques have been introduced in physical modelling during the

last decade. However, the criteria that we use to classify the damage are still based on old fashioned

parameters. The current challenge is to use this increased amount of data and turn it into more

detailed knowledge that we can use to evaluate more precisely how to prepare coastal structures for

climate change. Another challenge is to enable the efficient use of the new techniques; to streamline

the robust execution of the measurements and the processing steps, such that they can be used in

more standard projects.

However, as well as dealing with the challenges for representing climate change in physical models, it

may be necessary to analyse how existing or new structures (optimized through physical modelling)

may be adapted to sustain extreme conditions associated with climate change. The aim is an optimal

design (or safety assessment) which does not increase significantly the structures’ dimensions and

associated costs.

Adapted structures may include:

the addition of iron ore waste and tailings (IOWT) to the composition of usual concrete

artificial armour units;

the use of single layer armour;

an incremental use of artificial reefs for coastal protection.

5.5.1. Use of high-density iron ore

The addition of high-density aggregates to concrete armour units will improve the armour unit stability,

reduce their dimensions and volume, with subsequent potential cost savings on construction and

maintenance of the structures. At the same time it might help solve problems associated with disposal

of such valuable residues, contributing to a safer and cleaner environment.

In Portugal, there are only three examples of locations where high density concrete units were used in

harbour areas: the Douro’s mouth rubble-mound breakwater (which was tested at LNEC; Silva, 2003),

the Aveiro north breakwater (tested at LNEC in 2008-2009; Silva, 2009) and the west and east

breakwaters of Sines harbour (also tested at LNEC; Silva, 1997), Figure 39. At Sines, the block units of

the structure’s head reach 105 tons while at Douro’s structure the elements are 8 tons. Although Sines

breakwater’ units show a good behaviour, the same does not happen to Douro’s units, where blocks

appear to have a higher damage than expected. The reasons for that are not yet clarified and this is a

field where further investigation is needed. Only the Swedish mining company LKAB has developed a



materials production project for coastal and river protection, "MagnaDense", through the use of iron

ore in the formation of dense concrete.

Figure 39. Maritime structures constructed with high density blocks: a) Douro’s mouth rubble-mound breakwater; b) North breakwater of the entrance of Aveiro Ria; c) East and west breakwaters of Sines port.

5.5.2. Single layer armours

The application of single layer armour, such as with cubes, is an innovative and cost-effective solution

for armour layers of rubble mound breakwaters under investigation since 1998 (e.g. Van Gent & Spaan,

1998; d’Angremond et al., 1999; Van Gent et al., 1999, 2001; Van Gent, 2003; CIRIA/CUR/CETMEF,

2007; Van Buchem, 2009; Van Gent & Luis, 2013; Almeida, 2013; Van Gent, 2014). The advantages of

the solution of single layer armour or armour units may be briefly summarized as follows:

The existing studies show that using cubes in a single layer armour is feasible and potentially

economically competitive as opposed to the other types of units for single layer armours (e.g.

interlocking units such as AccropodeTM, Core-locTM and Xblocs®) and undoubtedly

economically competitive with double layer blocks (Antifer and Tetrapod).

Besides the good performance in terms of stability of Cubes in a single layer, another

advantage of Cubes in comparison with complex interlocking units, is that placement of Cubes

below water is easier especially for regions where the visibility below water is too low that

demands use of professional divers to assist in the placement of interlocking units (Verhagen

et al., 2002). Also, by placing Cubes in a regular pattern an additional improvement in the

stability can be achieved (Frens et al., 2008).

Physical model tests with Cubes consisting of normal-density concrete or high-density

concrete indicate that it is feasible to construct layers with Cubes in a single layer; i.e., damage

occurred for significantly higher values of the stability number Hs /ΔD if units in a single layer

a) Douro

b) Aveiro

c) Sines



are applied. If for Cubes in a single layer approximately 10 times less damage (number of

displaced units) is accepted than for a double layer of Cubes, the performance of these armour

layers was found to be similar with respect to the stability under equal loading conditions (Van

Gent et al., 1999).

One of the reasons for the competitiveness of single layer Cubes compared to interlocking

armour units, is the simplicity of fabrication and placement. Single layer Cubes mean also a

lower amount of concrete needed as compared with the double armour layers.

Most studies have been based on physical modelling. However, the single layer armours with Cubes

resist mainly by gravity and lateral friction. Whilst gravity is well represented by physical models scaled

according to the Froude’s law, this is not the case with lateral friction between blocks. To increase the

reliability of the physical model results for this kind of structures, scale and model effects should be

carefully analysed and selected and associated reduction measures should be proposed based on

physical model studies, as well as on comparisons with prototype structures.

Single layers of Cubes have been applied permanently in Boa Vista Island (Cape Verde), in which the

main part of the trunk and the roundhead of the breakwater consist of single layer Cubes, based on

economic evaluation of the construction costs. This project involved Consulmar (Consultants;

Designers); LNEC (physical model testing for first solution); Deltares (physical model testing for final

solution), Somague (construction). At Punta Langosteira (Spain) most of the temporary roundheads

used during construction also consisted of single layer Cubes.

With improved physical model results, it is possible to further analyse the advantages of this innovative

solution, which may be considered as an adapted structure to face more serious environmental

conditions associated to climate change.

5.5.3. Multifunctional artificial reefs

Multifunctional artificial reefs (MFAR) are a relatively new approach for protecting the coast. It is a

submerged breakwater that has several purposes. In addition to protect the local coastline and

improve the surfing possibilities, a MFAR can enhance the environmental value of the area where it is

built. The advantages of a MFAR are that the visual impact is low and that with a proper design the

down drift erosion can be minimal. Regarding the functionality of a MFAR, much research has been

carried out on surfability, i.e. the possibility to surf a wave (for example Mead and Black, 2001 and

Henriquez, 2004, Rigden et al, 2013). Although there are several classifications of the breaker type, it

is generally accepted that the waves break by spilling, plunging, collapsing, and surging (Galvin, 1968,

1972).

According to Battjes (1974) these types of wave breaking are categorized according to the offshore or

inshore Iribarren number. The value of the (offshore / inshore) Iribarren number is determined by the

bottom slope, the wave height (offshore / inshore) and the offshore wave length. However, Henriquez

(2004) notes that the submergence of a submerged reef also has an influence on the breaker type. The

length of the slope of the reef could also have an influence on the breaker type. In fact, when the reef

has a fixed height and when identical wave conditions are used, deeper submergence automatically

means a breaking point nearer the crest of the reef, which implies a greater length of the slope

experienced by the wave.



Smith and Kraus (1991) performed a laboratory study for waves breaking over bars and artificial reefs.

They constructed the bar of marine plywood and tested six different design seaward angles and four

design shoreward angles with different breaking type conditions. However, their results were obtained

for narrow crested artificial reefs. Also, the influences of the structure submergence, of the length of

the slope and of the depth at the start of the structure on the breaker type and on the Iribarren number

were not studied.

Regarding the breaking behaviour on artificial reefs with a smooth slope, only one study has been

conducted in a wave flume by Corbett and Tomlinson (2002). However, even though several

submergences were tested, no analysis of the relation between the breaker type and the

corresponding Iribarren number was done. Furthermore, the influence of the length of the slope on

the breaker type and the corresponding values of the Iribarren number were also not investigated.

The transition values for submerged broad-crested artificial reefs were determined by Voorde et al.

(2009) taking into account the structure submergence and the length of the seaward slope, Figure 40.

Figure 40. Breaker type on a MAFAR in a 2D flume at LNEC (ten Voorde et al., 2009).

Recommendations for future work include the investigation of the wave shape over porous bottoms,

like geotextile sand containers, since the turbulence and the energy dissipation will be different than

over a rigid bottom, which is expected to have an influence on the wave shape. Also, for a proper

design of a reef to protect a local coastline, a morphological study has to be performed in which

longshore currents, accurate bathymetry, tide and wave angles have to be taken into account.

Concerning design methodologies and formulations of the different parts of single layers breakwaters

(toe armour layer and crest berm), recommendations are yet scarce and further investigation is

recommended (Luis and Van Gent, 2013).

Das Neves et al., 2015, analysed the hydrodynamic and morphodynamic changes produced in the

vicinity of nearshore submerged structures made of sand-filled geosystems. This interesting solution



for coastal protection has an advantage over more traditional materials such as concrete units or rock,

which is the limited and non-permanent impact on natural coastal processes. The analysis was focused

on sediment transport, wave reflection and wave-induced pressures. The sand-filled geosystems

proved to be efficient in retarding the offshore movement of sediments and in maintaining the

shoreline, even if instabilities due to elements' displacement and local scour have been observed

(Figure 41). The major weakness of this technique is their susceptibility to vandalism and propeller

damage which may rapidly destroy one or more bags.

Figure 41 - wave downrush over the submerged structure (das Neves et al., 2015).

5.5.4. Future developments

In the future, it would be preferable to test many more conditions to determine the entire probability

of failure, or at least determine the sensitivity of the response to certain parameters. With sea level

rise these analyses will involve even more tests. An objective for enabling these kinds of analyses is to

make testing more efficient. When the structure has to be rebuilt often for new tests, long

measurement durations are needed, or when a basin has to be drained after each of multiple tests to

obtain measurements, this will require a longer testing programme, which may make that full risk

assessments of such structures out of reach unless innovative approaches using physical models can

validate / calibrate semi-empirical methods, themselves to be used in multi-parameter simulations.

Concerns about climate change effects also highlight the need of environmentally friendly and novel

approaches to protect the coast and reduce the risk of flooding and erosion by applying, for instance,

non-permanent solutions with limited impact on the sand-filled geosystems (e.g., das Neves et al.,

2015), but also ecosystem engineering solutions (e.g., Ondiviela et al., 2014). This led to the

development of new experimental techniques to reproduce those new solutions in physical models to

reduce scale and laboratory effects. In addition, to slow-down climate change effects, interest in

renewable energies, namely in the marine renewable energies, has grown significantly in the last

decades to reduce green-house emissions and due to the high and untapped energetic potential of the

oceans (Taveira-Pinto et al., 2015).

Ondiviela et al. (2014) makes reference to several knowledge gaps in ecosystem engineering solutions,

namely, there is a need to better characterize how seagrass species characteristics (e.g. biomass, shoot

density, stiffness or morphology) influence the dynamics involved in wave and current attenuation and

sediment transport, to understand the performance of coastal defence systems that combine



seagrasses with artificial elements (e.g. breakwater or seawalls), as well as to develop tools to predict

the effect of climate change on seagrasses structure and functioning.

Since there is a significant uncertainty in predicting the effects of climate change in the variables driving

the design of coastal structures (i.e. there is uncertainty in projecting the sea level rise and predicting

the extreme events), the consideration of different future scenarios, projecting possible future realities

in the medium to long term, is usual either in numerical and physical model studies or in commercial

projects and planning (e.g., Townend and Burgess, 2004, Coelho et al., 2009, Lee et al., 2013). In

addition, it is worth mentioning that traditional deterministic design methods and tools are not able

to directly include uncertainties associated to those design variables and, consequently, to properly

account for expected or predicted future climate change.



6. IMPACT OF CLIMATE CHANGE ON SEA ICE

GENERAL PROCESSES AND IMPACTS Sea ice is found in remote polar oceans and covers, on average, about 25 million km2 of the earth which

represents about 7% of the Earth’s surface and about 12% of the world’s oceans (NOAA, Weeks 2010,

Shokr & Sinha 2015). Most of the world's sea ice is enclosed within the polar ice packs in the Polar

Regions (Arctic and Antarctic) which undergo a significant yearly cycling in their surface extent and

thickness. In reaction to the global warming the declared goal of the United Nations Conference in

Paris 2015 is to keep the average rise in temperatures below 2oC (United Nations, 2015). However, the

increase of mean temperature can be 2 to 3 times higher in the Arctic (Stephenson et al., 2011)

compared to the global average. This results in a reduction of seasonal and multiyear ice with varying

impact. One is sea level rise, to which the melting of mountain glaciers and polar ice sheets contribute

significantly as well as thermal expansion of the sea water (Chang et al. 2015). Furthermore, the

melting sea ice affects the surface temperature of the water which in turn has an impact on the North-

Atlantic storm track (Harvey et al. 2015). In addition to atmospheric warming, sea-ice decline over the

Barents Sea sector is partly caused by warm advection introduced by planetary waves and triggered

by the Gulf Stream (Sato et al. 2014)

Sea ice helps to keep polar climates cool, if there is sufficient expanse of ice to maintain a cold

environment. There is a positive feedback relationship between sea ice formation and global warming,

i.e. as the global temperature increases, the ice melts, and is less effective in keeping the climate cold.

The bright surface of the ice plays a role in maintaining cooler polar temperatures by reflecting much

of the sunlight (albedo effect). As the sea ice melts its surface area shrinks reducing the size of the

reflective surface and increasing the absorption of solar energy by the earth. Even though the size of

the ice floes is affected by the seasons, a small change in global temperature can strongly affect the

volume of sea ice due to the reduction in the reflective ice surface which keeps the ocean cool. This

initiates a cycle of ice shrinking and temperatures warming. As a result, the Polar Regions are the most

susceptible places to climate change on the planet (ref.: NSIDC).

Sea ice also affects the movement of ocean waters. During the ice growth process, much of the salt is

squeezed out of the frozen crystal formations, but some brine still remains frozen in the ice. The

drained brine becomes trapped beneath the sea ice, creating a higher concentration of salt in the water

beneath ice floes. This concentration of salt contributes to the density of saline water. In the Northern

Atlantic, the cold water of higher density sinks to the bottom of the ocean. This cold water moves along

the ocean floor towards the equator, while warmer water on the ocean surface moves in the direction

of the poles. This is referred to as “conveyor belt motion”, and is a continuously occurring process

(NSIDC). Ice also contributes to the attenuation and dissipation of waves (Montiel et al.,2016; Squire,

2007; Toffoli et al., 2015) which, for example, manifests itself in the Gulf of St. Lawrence. At this

location, seasonal sea ice has previously reduced the significant wave height by 12%, however wave

attenuation is expected to become negligible by 2100 (Ruest et al., 2015) due to trends of global

warming and related ice decay. Due to the action of wind, currents and temperature fluctuations, sea

ice is very dynamic, leading to a wide variety of ice types and features (e.g. level ice, pressure ridges,

ice floes, pack ice fields, etc.). These ice features may present a significant risk for offshore structures

in ice-covered waters and can be an obstacle to normal shipping routes through the Northern Sea

route and Northwest Passage.



6.1.1. Retreating Ice Cap and Decreasing Ice Thickness

The monitoring of sea ice extent began in 1970s with remote sensing techniques and observations

from ships. Its minimum extent has declined linearly at an average rate of 13.4% per decade. In

September 2012, sea ice retreat set a new record—reducing by an area about the size of Texas from

the previous record set in 2007. The new record extent lost 2.83 million km2 below the 1981 to 2010

average minimum. Figure 42 shows the monthly Arctic sea ice extent in September for the period 1979

– 2015, a decline of 13.4% per decade relative to the 1981 to 2010 average. Barber et al. (2009) reports

that in the northern hemisphere the ice thickness decreased in certain regions by up to 40 % and also

a significant decay of ice. The rotten ice has partly a negative freeboard, i.e. it floats below the water

surface, which allows wind driven swell to propagate far into the floe field and storms may even

contribute to flexural fracturing.

Forecasts of further increase in global temperature of 1-2oC may continue to accelerate the Arctic ice

reduction in the future (Wang and Overland, 2009). At the same time, storm frequency and intensity

have both increased in this region (Young et al. 2011).

Figure 42. (left) Monthly September ice extent for 1979 to 2015 shows a decline of 13.4% per decade relative to the 1981 to 2010 average. Credit: NSIDC; (right) Forecast of mean probabilistic Arctic sea ice extent for September 2015 (issued August 9, 2015). The forecast value, or expected September mean Arctic sea ice extent, is 4.55+/-0.35 million square kilometres. Credit: Andrew Slater, NSIDC.

Results of investigations regarding ice conditions performed by the Arctic and Antarctic Research

Institute (AARI) in St. Petersburg, Russia, show that long-term changes of the annual average surface

air temperature in the Arctic, the sea ice extent and other hydro-meteorological parameters are

characterized by cyclical fluctuations (Frolov et al., 2007; Frolov et al., 2009). These fluctuations were

observed simultaneously with the linear warming trend that is possibly a part of the 200-year cycle

(ACCESS, D.213).

The most significant fluctuation is found in a 60-year cycle. This cycle reflects all climate phenomena

in the Arctic that happened during the 20th century: air temperature decreasing in the beginning of

the century; Arctic warming in 1920-1940; cooling in the end of 1950th – middle of 1980th, following

warming from the middle of 1980th with the maximum in the beginning of 21th century (Sherstyukov

et al., 2010, Hansen J. et al., 2010, Humlum O., 2011). Changes of the sea ice extent in the Arctic Seas

https://nsidc.org/sites/nsidc.org/files/monthlyhighlights/files/2015/10/monthly_ice_09_NH.png

https://nsidc.org/sites/nsidc.org/files/monthlyhighlights/files/2015/10/Andrew-Slater.png



are characterized by negative linear trend. The changes with 60, 20 and 10 years fluctuations

demonstrate spatial peculiarities. The most intensive negative trend of ice extent (15% ice

concentration) was observed in the western Arctic seas (Barents Sea and Kara Sea). Linear trends in

the eastern seas (Laptev Sea, East-Siberian Sea, Chukchi Sea) are weaker, ice extent fluctuations are

characterized by a stronger inter-annual variability and 60-year cycle is weaker as well.

Fast ice thickness in the Arctic Seas

The thickness of the fast ice during the cold climate periods (1965-1975) is more than the mean annual

fast ice thickness. In Table 4 the fast ice thickness for various sites along the coastline of Arctic Seas is

summarised. It is shown that the most significant change was observed in the Kara Sea (up to 14%).

The fast ice thickness near the polar stations in the Kara Sea during the last period decreased by 18 cm

in comparison with the cold period. The maximum decrease was observed near the polar station

Dikson (24 cm). In the eastern seas the difference between average fast ice thicknesses in two periods

is insignificant and does not exceed 2% from the mean annual value. In the Kara Sea such changes are

in the range of 10% from the mean value (ACCESS, D.213).

Table 4. Fast ice thickness in Arctic seas during cold period (1965-1975) and warm period (2001-2011); data source: AARI.

Period Kara Sea Laptev Sea East-Siberian Sea Chukchi Sea

Amderma Dikson Tiksi Kigilyakh Ayon Valkarkai Vrangel Vankarem

1965-1975 129 cm 176 cm 228 cm 215 cm 191 cm 191 cm 180 cm 181 cm

2001-2011 116 cm 152 cm 224 cm 214 cm 178 cm 190 cm 172 cm 185 cm

Difference

13 cm 24 cm 4 cm 1 cm 13 cm 1 cm 8 cm -4 cm

10 % 14 % 2 % 0 % 7 % 1 % 4 % -2 %

At present, scientists expect that Arctic summer sea ice could eventually disappear. Conservative

estimates suggest that it is likely to disappear by the end of the century, while others suggest the Arctic

Ocean may be free of summer sea ice within two or three decades (NSIDC).

Sea ice thickness in the Baltic Sea

Areas covered with ice during winter, with particular relevance to Europe, are the Barents Sea, Kara

Sea and Baltic Sea. In Finland all harbours are ice covered in winter as well as many Swedish harbours.

The ice extent in the Baltic Sea is subjected to significant seasonal variations, but a clear trend is not

evident as shown in Figure 43. However, the ice thickness appears to be subject to a continuous

decrease (see Figure 44). The trends are defined by linear data fits and indicate a reduction in thickness

especially the Bay of Bothnia in the Northern Baltic Sea, where the thickest ice is found.



Figure 43: Ice extent in the Baltic Sea from Winter 1970/1971 to 2014/2015 (data from Vainio and Eriksson, 2016)

Figure 44: Maximum ice thickness at three areas in the Baltic Sea from winter 1980 / 1981 to 2014 / 2015 (data from Vainio and Eriksson, 2016)

6.1.2. Permafrost and Coastal Erosion

The coastal zone is the interface where land-ocean exchanges in the Arctic take place. The Arctic

coastlines are highly variable and their dynamics are a function of environmental forcing (wind, waves,

sea-level changes, sea-ice), geology, permafrost and its ground-ice content and morphodynamic

behavior of the coast (Rachold and Cherkashov, 2004). Coastal processes are initiated by

environmental forcing (e.g. sediment transport by waves, currents, sea-ice initiates and the

degradation of coastal permafrost). As a result the coastal response is erosion or accretion and results

in land and habitat loss or gain. Coastal processes in the Arctic are governed by Arctic specific

phenomena like sea-ice cover and the presence of onshore and offshore permafrost. During the winter

month November to May a relative thick landfast ice sheet protects the shoreline from hydrodynamic



forcing (waves). However after ice break-up in spring coastal sediments are transported by sea-ice

floes. Figure 45 schematically illustrates the major processes involved in Arctic coastal dynamics.

Figure 45 Arctic coastal processes and responses to environmental forcing (Rachold & Cherkashov, 2004).

The presence of onshore permafrost and ground ice affects the strength of soils. Many physical

geological factors, such as soil structure, grain size, ground composition, ice content, water content,

grain shape and mineralogy, influence the frost susceptibility of a soil. The presence of permafrost also

influences the hydrology and the hydraulic path in the frozen, partially frozen and thawed ground,

affecting the stability of a cliff. Permafrost can act as a hydraulic barrier, which will tend to create high

pore pressure in the active layer. Sub-sea permafrost has been found beneath the seabed of some

continental shelves (Walker, 2005).

In general, the sub-sea permafrost is a relic in that it formed when sea level was lower than its present

position and the present day continental shelves were subaerial (Walker, 2005). The presence and the

potential thawing of the sub-sea ground ice can create seabed thaw subsidence, increasing the water

depth in the nearshore area and influencing the coastal profile equilibrium (Are, 1988; Harper, 1978;

Hiller and Roelse, 1995). However, aggradation of newly formed permafrost is possible in tidal flats

where level ice freezes to the sea bottom, and hence provides direct heat exchange of atmosphere

with sea bottom.

Arctic specific hydrodynamic and metocean parameters like water temperature, storm frequency, and

presence and duration of sea ice cover are important parameters. Sea ice limits wind action and

restricts the wave energy reaching the coast during the winter months (Barnes et al., 1988; Kobayashi

and Reimnitz, 1988; Sellmann et al., 1972). Ice can furthermore protect the shore by cementing the

beach. Contrawise ice can contribute to sediment transport with the formation of frazil or anchor ice

in shallow water (Barnes et al., 1988; Osterkamp and Gosink, 1984).

Ice will also act as a geomorphological agent when it piles up on the coast; during thaw season when

ice rides up the shore, it can transport newly-formed ridges away from the coast, smoothing the shore



(Barnes et al., 1988; Hiller and Roelse, 1995). Blocks of sea ice may interact with nearshore sea bed

creating ice wallows (Reimnitz and Kempema, 1982). Shearing may occur offshore between the fast

ice and the floating ice to produce large pressure ridges with keels that can reach several meters in

height. If moved, these keels can rework surficial seabed sediments and create ice gouges, also called

ice scouring (Barnes et al., 1988).

Arctic storms occurring in the fall are known to have dramatic short-term erosive impacts on coastal

profiles (Hequette and Barnes, 1990; St-Hilaire et al., 2010). Hume and Schalk (1967) studied the

sediment movement along a segment of the Alaska coast west of Point Barrow between 1948 and

1962, and he reported that a single storm event, occurring October 1963, moved an amount of

sediment equivalent to 20 years of normal transport.

The Arctic coastal region is the transition zone between onshore and offshore permafrost and the

degradation of permafrost, which can be connected with the release of permafrost-bond greenhouse

gases (GHG), is concentrated in the coastal zone (Rachold and Cherkashov, 2004). During the short ice-

free period, the unconsolidated ice-rich, permafrost-dominated coastlines are rapidly eroded at rates

of several meters per year. It is assumed that the resulting coastal sediment, organic carbon, and

nutrient fluxes play an important role in the material budget of the Arctic Ocean.

Global and regional climate changes will significantly affect physical processes, biodiversity and socio-

economic development in the Arctic coastal areas (Rachold and Cherkashov, 2004). Horizontal coastal

retreat rates have been documented on Herschel Island for two different periods. MacDonald and

Lewis (1973) investigated coastal evolution On the Yukon Coastal Plain for the period 1954-1970 and

reported an average horizontal coastal retreat rate of 0.68 m/year. For the 1970-2000 period, Lantuit

and Pollard (2003) documented coastal retreat rates reaching 1.03 m/year. This 50% general increase

is moderated by the high local variability of erosional hot spots. Global warming is believed to be

responsible for the enhancement of erosional processes. McGillivray et al. (1993) showed that a longer

open water season, warmer sea temperatures and a reduced sea-ice extent would lead to greater

storm frequency, and hence, greater erosion (Lantuit and Pollard,2003).When the coastline of the

whole Arctic Ocean is considered, these major environmental changes take place under a large variety

of climate and ecological conditions (e.g. from continuous to discontinuous permafrost regions, from

arctic desert to forest tundra), under different geological and sedimentary conditions and under a

variety of marine conditions defined by wave environment, tidal regime and sea and shore ice extent

and duration (Allard and Hubberten, 2004).

During the 21st Century, with respect to climate warming, the chain of processes that lead to retreat

or progradation of Arctic coastlines is very likely to be affected by a decrease in sea-ice duration and

an increase in storminess, precipitation and air temperature. Figure 46 shows the wave action on the

ice covered shoreline Bylot Island, Nunavut.

Rising temperatures are altering the arctic coastline and much larger changes are projected to occur

during this century due to reduced sea-ice, thawing permafrost, and sea-level rise. Thinner, less

extensive sea-ice creates more open water, which allows more intensive wave generation by winds

resulting in increasing wave-induced erosion along arctic shores. Sea-level rise and thawing of coastal

permafrost intensify this situation. In some areas an eroding shoreline may combine coarse sediments

with frozen seawater forming huge ice blocks that transport sediment for distances over hundreds of

kilometer. These sediment-laden ice blocks pose danger for ships and further erode the shoreline as



they are driven by wind (CliC/AMAP/IASC, 2016). Figure 47 illustrates clean and sediment-laden sea

ice formed in the Beaufort Sea and exported to the Chukchi Sea, about 100 km north of Barrow, Alaska,

30 July 2006.

Figure 46 Wave action on the ice covered shoreline Bylot Island, Nunavut. (Source: R.B. Taylor, Geological Survey of Canada)

Figure 47 Clean and sediment-laden sea ice formed in the Beaufort Sea and exported to the Chukchi Sea, about 100 km north of Barrow, Alaska, 30 July 2006. Width of view is about 250 ± 50 m (Source: Hajo Eicken, University of Alaska, Fairbanks).

surging wave



In the estuary of the Yenisei River (Kara Sea) intensive ice-wedge melting in the near shore zone

occurred during the past 30 years. This had resulted to the formation of block relief and thermal

erosion also destroys massive grounds sheets up to 6-8 m thickness (Grebenets and Kraev, 2004 ).

Figure 48 shows an example of a typical eroded shoreline with a rocklike ice-bonded layer in the

Yenisei-Delta (Kara Sea, Russia).

Figure 48 Typical eroded shoreline with a rocklike ice-bonded layer in the Laptev Sea (Russia), (Photos: Courtesy Gerhard Kattner, AWI Bremerhaven)

During the past decade a large-scale change in the arctic atmospheric circulation took place causing a

shift in various oceanographic boundary conditions, e.g., decrease in sea-ice coverage, an increase in

riverine input and in air temperatures, and increased inflow of Atlantic water masses into the Arctic

Ocean and the Laptev Sea. These changing boundary conditions probably also influence the marine

environment (including the submarine permafrost) and the coastal zones of the Siberian Arctic shelf

seas (Hölemann et al., 2004).The evolution of Arctic coasts over the coming decades will be strongly

influenced by changes in the natural environment caused by the effects of climate warming. Over the

past decade increasing surface air temperatures have reached record levels. In 2010 record warm air

temperatures have been measured in the Canadian Arctic and Greenland.

In the past decade successive new record minima in Arctic sea-ice extent was observed and in 2010

the third smallest summer minimum sea-ice extent of the past 30 years occurred. At the same time,

the mean ice thickness has been decreasing, driven primarily by export of multi-year sea-ice. Less

extensive sea ice creates more open water, allowing stronger wave generation by winds. This,

combined with warmer sea-surface and ground temperatures, has the potential to increase erosion

along Arctic coasts. As an example the record warm sea-surface temperatures in 2007 contributed to

rapid coastal erosion in Alaska. Arctic ice shelves will continue more frequently to collapse due to

climate warming and the process of decreasing multi-year sea ice will continue.

Decadal-scale mean rates of coastal retreat are typically in the 1-2 m/year range, but can vary up to

10-30 m/year in some locations. The highest mean erosion rates are in the Beaufort Sea, the East

Siberian Sea, and the Laptev Sea. Recent results on erosion of ice-rich cliffs show the importance of

interaction between high sea-surface temperatures and the timing of ice break-up and freeze-up

combined with storm dynamics (Forbes, 2011).



6.1.3. The Marginal Ice Zone (MIZ)

The extent of the Arctic sea ice has reduced significantly in recent years (see Table 4), surpassing all

existing model predictions (Overland and Wang, 2013). Instead of an ocean mostly covered by a

continuous ice cover, the Arctic now has a large expanse of open water adjacent to a dynamically

changing ice cover called the Marginal Ice Zone (MIZ). It is in this zone that most of the future

engineering activities will take place (Gautier et al., 2009a, Stephenson et al., 2011). The opening up

of the Arctic increases the possibility of shipping and offshore engineering, however, there is the

insufficient understanding of the air-ice-ocean system to operate effectively in this region. In particular,

more open water in the Arctic has increased the wave intensity. As a consequence, wave propagation

through the dynamically changing ice covers in the MIZ has become an important topic for all maritime

operations in the Arctic (Evers and Reimer, 2015).Theoretical considerations related to ice breaking

and wave attenuation in the MIZ are described by Williams et al. (2013). In the MIZ close coupling

between waves, sea ice, ocean and atmosphere occurs (Williams et al., 2013), with small floes being

broken by surface waves. Waves may spread over long distances and their swell might propagate and

cause flexural failure of multiyear pack ice. The width of the MIZ is controlled by the exponential

attenuation of the waves imposed by the presence of ice-cover and the rate of wave attenuation

depends on wave period and the properties of the ice cover.

Waves and ice cover mutually affect each other. At the formation stage, waves create grease/pancake

ice from open water (Figure 49a). As the ice edge extends, waves damp out allowing the pancake ice

field (Figure 49b) to consolidate into solid ice cover. Subsequently, waves may break an existing ice

cover and, depending on their intensity, these waves may either leave the ice cover as a scattered

puzzle of ice floes (Figure 49c), continue to pulverize the ice floes into a brash ice field, or shape them

into anything in-between (Wadhams et al., 1986). On the other hand, ice cover also attenuates waves

and changes their velocity. The change in both attenuation and speed depend on the mechanical

properties of the ice cover. However, the mechanical properties of different ice covers, particularly as

a collection of frozen/broken/refrozen conglomerate as often present in the MIZ, are unknown (Evers

and Reimer, 2015). There are several theories based on different assumptions of how an ice cover

should be modelled as either a continuum, or as a collection of discrete deformable plates. However

the results of models based on these theories are very different.

Figure 49: Formation of pancake ice in a wave field in the Kara Sea (a), pancake ice (b) and newly fragmented ice sheet (c); (Evers & Reimer, 2015); Photo (b) source: National Institute of Water and Atmospheric Research (NIWA), The University of Waikato, Hamilton, New Zealand.

Very limited data are available to help build the necessary knowledge base for wave propagation in

the MIZ. A few field studies during Marginal Ice Zone Experiments, MIZEX, and some isolated field

campaigns in the Antarctic region have only shown that wave attenuation is strongly dependent on

frequency (Wadhams et al. 1986, 1988). The same ice cover can damp out high frequency waves over

(a) (b) (c)



a matter of metres, while leaving the swell untouched for hundreds of kilometres. Remotely sensed

data shows that oblique waves may change their direction upon entering an ice covered sea (Figure

50), which indicates that the wave speed changes between open water and ice covered region (Liu et

al., 1991). Laboratory studies of wave propagation over ice covers are scarce. One conducted in a small

wave tank at the University of Washington showed wave speed changes and attenuation both

occurred in a grease ice field (Newyear and Martin, 1997, 1999). Another in a larger wave tank in Japan

showed wave speed slowed down in pure elastic synthetic ice covers when the floe size was reduced

(Sakai and Hanai, 2002). At the Hamburg Ship Model Basin (HSVA) a study was done in a pancake ice

field to show that both wave attenuation and speed change took place (Wang and Shen, 2010).The

above field, remote sensing, and laboratory studies have only scratched the surface of the complex

wave-ice interaction problem. For a complete understanding necessary to guide Arctic engineering in

the MIZ, a systematic study is urgently needed.

Figure 50. SAR image from LIMEX (Liu et al. 1991). Wave refraction was measured.

Need for laboratory tests

While field data, in-situ or remotely sensed, are required to parameterize and validate models for the

new Arctic ocean, laboratory experiments provide a much more controlled and less expensive

alternative. Field environments may not be appropriate for studying multiple interacting mechanisms

as a large number of parameters may be unknown. Therefore, the controlled test environment in

model-scale offers a good alternative. There are several engineering projects/activities that have been

discussed for the new Arctic region: wind farms, oil/gas rigs, shipping routes, and oil spill mitigation.

Most of these will be located in the MIZ, where dynamically changing ice conditions prevail. While

different challenges may exist for various operation scenarios, all of them need to have an accurate

prediction of the wave climate (wave conditions).

THE IMPACT OF CLIMATE CHANGE ON SOCIO-ECONOMIC BEHAVIOUR Climate change and its impact on the environment offer new opportunities but also operational risks

in cold and polar regions. Those operations may range from tourism, fishing and shipping to mining

and hydrocarbon exploration and extraction. The Arctic region probably contains around 30% of the

world’s undiscovered gas and 13% of the world’s undiscovered oil with the resources expected to be

found in depths of less than 500 m (Gautier et al., 2009b). The decline is sea-ice thickness and

concentration eases or even first allows access to possible exploration sites of natural resources.



An Arctic Transport Accessibility Model (ATAM) presented by (Stephenson et al., 2011) predicts that

both the Northern Sea Route and the North Pole Route may become fully accessible by 2060 for vessels

with non-Polar ice classes. In addition to this it is predicted that another 1.8 million km2 of the Arctic

Ocean might become accessible. A consequence of melting Arctic sea ice is the commercial viability of

the Northern Sea Route, connecting North-East Asia with North-Western Europe. This will represent a

reduction in shipping distances and a decrease in the average transportation days by around one-third

compared to the currently used Southern Sea Route [via Suez canal]. This may result in a significant

shift of bilateral trade flows between Asia and Europe, diversion of trade within Europe, heavy shipping

traffic in the Arctic, and a substantial drop in traffic through Suez (Bekker et al. 2015).

Studies by the Canadian Ice Service indicate that sea ice conditions in the Canadian Arctic during the

30 years have been characterized by high year-to-year variability. This variability has existed despite

the fact that since 1968-1969 the entire region has experienced an overall decrease in sea-ice extent

during September. In the eastern Canadian Arctic, some years – 1972, 1978, 1993, and 1996 – have

had twice the area of sea ice compared with the first or second year that follows

(http://www.greenfacts.org). This year-to-year variability in sea ice conditions makes planning for

marine transportation along the Northwest Passage very difficult.

The opening of NSR is also supported by enhanced cargo tonnage, application of flexible tariff policy

and significant improvement of sea ice conditions along the navigational routes in summer. If the

present trend towards decreasing sea ice cover is sustained over the next 10-15 years, the navigation

period without icebreaker assistance will probably increase and the duration of transit will be

significantly shorter. However, the stochastic nature of environmental parameters still challenges long-

term climate forecasts. Regardless of the influence of global warming a necessity persists for

navigation along the NSR, with the need for a fleet of escorting icebreakers to guarantee reliable and

safe operations along the NSR in the future. The retreating ice extent and thinner ice affects the design-

requirements of structures and ships and may increase the demand for light ice-classed ships. The

future need of lighter ice classes may also apply on operations in the Baltic Sea.

PHYSICAL MODELLING IN ICE TANKS

6.3.1. State of the Art

Ice Tanks are refrigerated environments in which ice is produced to tests or scaled tests. The main

focus of ice tank operations has previously been the testing of ships in ice and offshore structures

operating in ice to assess their resistance in ice, which is the response force of the ice on the ship model.

The failure of ice is caused by downward bending leading to flexural failure (Enkvist, Varsta, & Riska,

1979; Atkins & Caddell, 1974; Ettema, Sharifi, Georgakakos, & Stern, 1991; Kämäräinen, 2007; Valanto,

2001). Consequently, the flexural strength is very important when considering the scaling of ice

properties. Other scaled ice parameters are the thickness and the elastic modulus and the applied

scaling similitudes are Froude and Cauchy (Atkins & Caddell, 1974; von Bock und Polach & Ehlers, 2015).

Froude scaling refers to maintaining the ratio between inertial and gravitational forces and Cauchy to

maintain the ratio between inertial and elastic forces. Despite fulfilling Cauchy similitude, model ice

might undergo plastic deformation, which leads overall to insufficient response stiffness under

bending conditions(von Bock und Polach, 2015).



6.3.2. Modelling Challenges related to Climate change

The response to climate change in physical modelling is driven by the societal needs that are affected

by the climate change. The interaction of ice with offshore structures can be categorized into two

scenarios: slow and fast impacts. A slow drifting ice sheet compressing against a structure causes loads

affected by strain rate effects within the ice (Sinha, 1982; Jones, 1991; Timco & Weeks, 2010).

Increasing access to Arctic waters requires assessments of model-scale ice to reproduce and scale the

compressive structure-ice interactions. Furthermore, as in such interactions inertial forces may be less

relevant other scaling methods might be considered and tested (Palmer & Dempsey, 2009). At higher

compressive ice-structure interaction speeds the formation of high-pressure zones is observed, which

may introduce significantly high pressures on small areas (Jordaan, 2001; Taylor & Jordaan, 2015;

Taylor et al., 2010; ISO 19906, 2010). The capacity of model-scale ice to reproduce compressive loads

and adequately reproduce interactions of high complexity is unknown and requires dedicated testing

and possibly a revision of modelling and scaling methods.

Furthermore, increasing winds and storms, decreasing ice and the interaction of waves and ice in the

Marginal Ice Zone (MIZ) are of increasing significance. As demonstrated in von Bock und Polach &

Ehlers (2013), model ice might undergo plastic deformations, which can lead in bending to larger

deflections than intended (von Bock und Polach, 2015). In ship-ice interaction where the failure force

is of high significance a larger deflection of the ice might be tolerable. However, for waves in ice its

break up is strongly dependant on the deflection introduced by the waves. Consequently, there is a

significant challenge to assess the plasticity under impact and possible modifications of model ice to

represent ice-wave interactions adequately.

Waves in ice

Current wave models such as the global ocean WAve prediction Model (WAM) does not include ice

cover effects. WAVEWATCH III (WW3) does incorporate ice effects, however only in a rudimentary

manner with ice cover being treated as a stepwise filter such that the fraction of wave energy flux at

any location varies linearly between 0 and 1. Two threshold values control the stepwise variation and

both relate to the local ice concentration (Tolman, 2003). Existing models for wave-ice interaction,

supported by field data, have shown a significantly more complex process (Squire, 2007).

In order to have a systematic investigation of wave attenuation and speed change in a laboratory

setting, below is a list of the most important parameters that require further investigation:

Ice types – grease, pancake, floes, consolidated, with a range of floe sizes and thicknesses.

Wave spectra – a broad range of frequencies and both low and high amplitude. The latter

is required to simulate nonlinear waves which are often present in storms.

Wave directions – a range of wave directions relative to the ice edge. Due to wave

refraction, energy propagation may be very different from the incoming wave direction.

This condition is constantly changing when the ice cover is altered by the wave condition.

Behind a fragmented ice field, structures may be safe from wave action, due to the high

scattering and collisional damping motion between floes. This condition can quickly

change after the ice cover freezes over, particularly so when compounded with ice edge

changes.



To properly study wave propagation under ice cover, a laboratory should be equipped with a large

wave basin so that long and fully-developed waves may be tested with minimal reflection from the

boundaries and also the capability to generate waves from different directions. There needs to be

instrumentation to measure wave characteristics, including directional spectra. It should have ice

production capabilities to create the various ice types mentioned above and the facilities to determine

the mechanical strength of the floes and the consolidated ice sheet.

The decreasing ice thicknesses on the Arctic shipping routes (Stephenson et al., 2011) and in the

northern Baltic Sea (Gulf of Bothnia) will affect the design of suitable ships, i.e. the design ice

thicknesses will be reduced. In model-scale testing the ice thickness is scaled geometrically with the

same scaling factor as the ship length, which will lead to thinner model ice sheets for tests. Currently,

many ice tanks set a minimum model-ice thickness of 15 mm, below which the scalability of

experimental results is uncertain. Therefore, modelling methods need to be investigated to produce

thinner ice sheets while maintaining accurate scaled properties. In this context also ice property

measurement techniques may need to be revised to account for the significantly weaker constitution

of the thin ice.

LABORATORY EXPERIMENTS WITH WAVE-ICE INTERACTION During the INTERICE-project Eicken et al. (1998) performed experiments in a wave field which primarily

addressed the effects of wind, current and wave conditions on the formation of pancake ice, the

evolution of ice cover morphology and ice microstructure and salinity of frazil ice. Wave damping and

its effect on the wavelength spectrum for different ice types was also investigated. It was found that

the frazil and pancake formation process depended on the presence of wind. Stable, uniform pancake

ice covers were formed in the absence of no wind, while under the presence of wind and under same

wave conditions a frazil layer continued to thicken without clear formation of pancakes. Given time,

pancakes coagulated with neighbours to form composite pancakes. The appearance of composites

coincided with a significant increase in wave damping. More details of the pancake ice evolution in the

experiments can be found in Leonard et al. (1998).

In 2001, an experiment to study pancake ice growth in a wave field has been conducted in the Arctic

Environmental Test Basin (AETB). For the tests a twin wave tank facility was built. Two wave generator

in the twin tanks with identical geometry produced different waves ranging from 0.5-0.9 Hz in the

same cold room. Data obtained from the experiment are used to identify the ice production rate that

may be attributed to wave actions and to determine the relation between the ice cover morphology

and wave characteristics (Shen et al., 2004).

In the framework of the REduced ice Cover in the ARctic Ocean (RECARO) project a number of different

experiments involving waves of different frequencies and amplitudes were conducted in HSVA’s Arctic

Environmental Test Basin (AETB). The simultaneous measurements of the same oceanic and

cryospheric parameters during the ice formation process should provide new insight into a large

variety of questions relating to the different regimes of ice formation: ice growth, brine drainage,

pancake ice formation, mechanical strength/crystal properties, optical properties and wave

attenuation (Wilkinson et al., 2009).



RECARO wave experiments were carried out by Wang and Shen (2010) to isolate the mechanical

actions of the waves from thermodynamic effects. A study was done in a pancake ice field to show that

both wave attenuation and speed change took place.

The experiences and results obtained in the various experiments carried out in the AETB regarding

waves and ice interactions have revealed that a larger basin than the AETB is required to perform

complex investigations on the behaviour of waves in the ice. Since 2015, the HSVA operates its Large

Ice Model Basin (LIMB) with mobile wave generators to execute extensive experiments with waves in

ice (Evers and Reimer, 2015).



7. IMPACT OF CLIMATE CHANGE ON ECO-HYDRAULICS

OVERVIEW In shallow-water fluvial and coastal flows, plants and other organisms affect flow resistance and

turbulence with implications for conveyance, bed and bank stability, sediment transport, nutrient

cycling and the dispersal of pollutants (e.g. Paul et al., 2014). In the context of climate change

adaptation, full understanding of the interactions between living organisms (particularly biofilms and

vegetation) and flow is important for at least two reasons.

First, under climate change, there is an expectation that alterations in spatial and temporal patterns

of rainfall, temperature and wind will alter sea levels and affect the amount and timing of river

discharge. These hydrological impacts will affect the hydraulic characteristics of the habitats that

plants and other organisms occupy. Changes in the distribution and seasonality of water depth,

velocity and other flow characteristics will be accompanied by a number of other physical changes that

have the potential to affect the health and composition of aquatic ecosystems, including changes in

water temperature, salinity, suspended sediment concentrations, CO2 concentrations, general

illumination and UV levels (e.g. Bornette and Puijalon, 2011). The anticipated ecological response is

one of shifts in the spatial and temporal composition of aquatic flora and fauna (Meyer et al., 1999;

Parmesan, 2006; Harley et al., 2006; Demars et al., 2014) including the potential for new and

accelerated invasions (e.g. Koncki and Aronson, 2015). These climate-driven changes in the distribution,

growth rates and seasonality of vegetation and biofilms will impact future hydraulic conditions and

local morphodynamics in rivers, estuaries and along coasts. Altered flows and patterns of sediment

erosion and deposition may then alter the risk profile of shallow-water hazards, including fluvial and

coastal flooding, river bank and coastal erosion and siltation of transport corridors. Such changes will

demand adaptation of river and coastal management operations and strategies. Furthermore, because

ecosystems interact with their physical environment, morphodynamic alterations may feedback to

biodiversity and ecosystem health, with implications for management of the total environment.

Second, living organisms may provide effective and sustainable tools that can be used alongside or

instead of traditional, ‘hard’ engineering practices to manage climate-induced changes in flows of

water and sediment and mitigate impacts on the performance of existing infrastructure.

Understanding how vegetation and biofilms affect drag, turbulence characteristics, velocity profiles,

particle erosion and deposition, bed reinforcement and other fundamental processes, has never been

more important than it is now.

Within this context, this chapter considers how microbial biostabilization, the integrity of organism

performance and behaviour, and vegetation parameterisation might be represented and managed

within flume facilities.

REPRESENTING THE IMPACTS OF CLIMATE CHANGE ON BIOSTABILIZATION IN PHYSICAL

EXPERIMENTS The term microbial biostabilization describes the potential of benthic biofilms to increase sediment

stability primarily by enhancing the binding (adhesion) between sediments and manipulating the

surface roughness. The biofilms, which consist of bacteria, microalgae, prokaryotes and fungi, secrete

a hydrated extracellular polymeric substance (EPS). EPS fulfils a number of ecological functions (e.g.,



retention of water, nutrient source and protective barrier; for a review see Flemming & Wingender,

2010) and can be regarded as a natural glue providing the mechanical strength of the biofilm-sediment

matrix by EPS strands interconnecting sediment grains (Figure 51). Biofilms typically grow at the

interface between water and sediments where they can form films or mats (Figure 51) with thicknesses

ranging from micrometres to millimetres (Okkerse et al., 2000; Bouletreau et al., 2011; Black, 2002;

Noffke et al., 2001).

Similar to plants, biofilms adapt to their surroundings for optimal growth, both mechanically as well as

structurally. In this context, their biostabilization potential is also affected by the biotic and abiotic

environmental conditions, which are likely to change in the next decades. Even though a number of

studies have demonstrated that a biofilm potentially enhances the stability of sediments by up to a

factor of ten compared to the sediment without biofilm (Tolhurst et al., 1999, Thom et al., 2015,

Droppo et al., 2007), studies on the impact of climate change on biofilm biostabilization potential are

rare.

Figure 51. Binding- and stabilization mechanisms of biofilms. Left: different types of biofilm-sediment interaction (for more details: Noffke et al., 2001). Middle and right: Low-temperature scanning electron microscopy (LTSEM) image of glassbeads stabilized by bacteria and diatoms at different scales (for more details see Lubarsky et al., 2010).

While most of the previous work concerning biofilms has focused on field studies (e.g. Amos et al.,

2003) where the impact of individual environmental conditions is overshadowed by the complexity of

the natural system, physical modelling with controlled boundary conditions is a more reasonable

approach to understand biostabilization cause-effect relationships (Black et al. 2002). To design a

physical experiment that can examine climate change effects requires a basic knowledge on the

importance of individual biotic and abiotic boundary conditions.

A major challenge is the representation of climate change induced variations across longer time scales.

So far, research has only focused on the present state and the short term development of

biostabilization in a system (e.g. Thom et al. (2015), Graba et al. (2010) or on seasonal differences by

field campaigns at the specific seasons (e.g. Widdows et al. 2000; Righetti & Lucarelli, 2010). To the

author’s knowledge, no physical experiments exist on induced morphological changes due to the

variability of biostabilization throughout the year, considering also the different phases of biofilm

growth (attachment, colonization, growth). This includes the much longer time scales (i.e. decades to

centuries) that are relevant when considering climate change effects. For such longer timescales

difficulties arise because “natural” biofilm growth cannot be accelerated without significantly



influencing the microbial community and thereby introducing unknown effects. For example,

Butterwick et al. (2005) demonstrated that by varying the growth temperature different organisms

dominate which do not resemble the original biofilm community.

The aims of this section are:

1) to review briefly the most important boundary conditions during the cultivation of a biofilm and

their expected impact. Those conditions will need to be taken into consideration when designing a

physical experiment on biostabilization to investigate potential future climate change effects (Part A);

2) to review the current state of the art of biostabilization physical experimental designs (Part B);

3) to inform the reader about the use of a surrogate materials, which could potentially allow long term

investigations to be conducted by artificially mimicking the stabilizing properties of biofilms at different

stages in their life cycle (Part C).

A successful use of these surrogate materials would also allow a broader community to investigate

biostabilization. Focusing on the erodibility, particularly the erosion threshold of biofilm-sediment

matrices, biological aspects are not reviewed in this section. Instead the reader is advised to consult

some other reviews (e.g. Gerbersdorf & Wieprecht, 2015, Battin et al., 2016, Grabowski et al., 2011,

Vasudevan, 2014).

7.2.1. Impacts on biofilm growth and biostabilization

Vegetation will be strongly affected by climate change as abiotic as well as biotic boundary conditions

change. Besides the most prominent example, global warming, there are other factors which will have

a direct impact on vegetation growth. For example, a reduction of light intensity due to sea level rise,

acidification, hydrodynamics providing nutrients and erosive forces are all likely to be affected by

climate change. The most important factors are reviewed here and need to be taken into account in

designing physical experiments. Examples of some typical ranges of these factors from selected studies

are presented in Table 5.

Biofilm growth

On freshly deposited sediments (e.g. after a storm event), the formation of a biofilm in a natural system

can be subdivided in three main phases, namely “attachment” (adhesion of cells to surface),

“colonization” (formation of a monolayer and a micro-colony) and “growth” (Figure 52).

It is intuitive to assume that the biostabilization potential will differ in these three main developmental

stages. However, the time needed for the biofilm to develop a stabilization potential depends on the

environmental boundary conditions. For example, Droppo et al. (2007) reported significant

stabilization effects (factor three) after just five days of growth, while the first minor effects of

biostabilization reported by Thom et al. (2015) were only visible after two weeks of growth.



Figure 52. The various stages of biofilm formation and development (from Vasudevan, 2014).

A general trend of biofilm growth is that it increases the erosion threshold over time to potentially

maintain a relatively stable state as reported by Fang et al. (2014). Thom et al. (2015) showed that

environmental conditions and seasonality have a large impact on the evolution of the erosion

threshold. However, experimental studies like these are scarce and the results should therefore be

treated with caution.

Hydrodynamics

The role of hydrodynamics is particularly important for the formation of a biofilm for a number of

reasons. First, it controls the efficiency of initial attachment of suspended microbes to the sediment.

Second, it is closely linked to the availability of nutrients to the biofilm during colonization and growth.

And third, the flow exerts a force to potentially detach the biofilm-sediment matrix.

Especially in the early phases of biofilm formation, the initial contact between advected microbes and

the substratum surface depends on the turbulent conditions of the flow. In the pioneering work of

Stoodley et al. (1999) it was reported that under laminar flow conditions, cell attachment to a surface

occurred sooner than under turbulent flow conditions. On the other hand, the coverage of the surface

was lower under laminar conditions than under turbulent conditions. The authors reasoned that even

though laminar flow conditions transported less cells to the surface (because of lower mixing rates),

cell attachment efficiency was higher because at the same time, there was lower detachment, related

to substantially lower fluid shear in laminar flow.

Higher flow velocities during growth enhance the availability of nutrients due to higher mixing rates.

More precisely, at higher flow velocities the thickness of the DBL (diffusive boundary layer), where

mass transfer is significantly lower than in turbulent diffusion, is decreased (Larned et al., 2004). In fact,

biofilms may suffer from nutrient deficiency in stagnant waters or at low flow velocities, even in



eutrophic systems. However, higher flow velocities also induce higher drag forces on the biofilm and

may result in detachment.

This trade-off between enhanced mass transfer and detachment is widely accepted (e.g. Stewart,

2012) and it has been demonstrated that biofilms adapt to their specific situation. For example, at low

flow velocities the biofilm produces filaments protruding into the water column to increase nutrient

availability. In contrast, biofilms tend to be more compact and also potentially more stable at higher

flow velocities (Pereira et al., 2002, Graba et al., 2013).

Light regime

Light quantity (i.e. intensity) as well as quality (i.e. intensity of different wavelengths) will be affected

by climate change. Light is the main source of energy for algae and even some bacteria (e.g.

cyanobacteria) to fix carbon and build up organic substances (Gerbersdorf and Wieprecht, 2015). The

photosynthetic active radiation (PAR, typically: 400–700 nm) is the range of radiation that can be used

by photosynthetically active organisms whereas the light intensity in µmol/m²s is a measure for its

strength. Increased light intensities can result in enhanced growth, but potentially also in an enhanced

production of oxygen bubbles that are produced below or on top of the surface of the biofilm and

create a destabilizing lift force (e.g. Sutherland et al., 1998, Mendoza-Lera et al., 2015). The intensity

of light can also be too strong, which might have a negative effect on biostabilization (Gerbersdorf &

Wieprecht, 2015).

It is important to note that even under no-light conditions (e.g. in a deep river channel, or as ‘‘deep

biota’’ Black et al. 2002) a biofilm will develop, which consists of non-phototropic bacteria.

Measurements made by Lubarsky et al. (2010) showed that bacteria produced a sticky EPS (as

measured by the MagPI: Larson et al., 2009), which indicates the high potential for bacterial biofilms

to stabilize sediments. On the other hand, no bacterial biofilm stabilization effect was reported in

Thom et al. (2015) in the course of their experiments. They suggested that bacterial biofilms need more

time to develop than their micro-algal counterparts.

Typical light intensities that have been reported in the literature range from 0 to approximately 240

µmol/m²s (see Table 5, also showing applied day/night cycles). To induce a nearly constant light

intensity in the PAR, a range of specialised fluorescent tubes are available.

Sediment

The selection of substrate for biofilm cultivation is essential when the erosion threshold of the biofilm-

sediment matrix is studied. Natural substrate (e.g. from a river or estuary) typically has a high content

of organic matter, nutrients and associated microbes, which are favourable for biofilm growth.

However, the downside is that these constituents need to be analysed to determine their impact on

biofilm growth. To relate these additional parameters to biostabilization effects is especially difficult if

experimental conditions need to be reproduced in a later experiment (e.g. to study the influence of

seasonality). A useful approach to circumvent this is to use artificial, inert sediment (e.g. glassbeads:

Thom et al., 2015).

The size of the sediment is crucial for erosional studies. With either too large or too small sediment

sizes, the biostabilization effect might not be relevant. Lick et al. (2004) analysed the initiation of

movement of different size quartz particles with added bentonite (to mimic cohesion/adhesion

effects) and reported that the major increase of critical bed shear stress for particles is between 100



and 400 µm. In further investigations, Fang et al. (2014) found that for particle diameters between

0.01 mm and 0.2 mm adhesive and cohesive forces dominated over weight and electrostatic forces.

Additionally, it needs to be considered, that with finer sediments the surface area offered for microbial

settlement and colonization is increased (as reviewed in Gerbersdorf and Wieprecht, 2015) and pore

spaces between sediments are smaller as well, which is in turn beneficial for the EPS to completely

smother the grains and thereby potentially enhance stability (Black et al., 2002) (Figure 51).

Water temperature

The IPCC (2007) predicts a sea surface temperature (SST) increase of 1.5-2.6C by the end of the 21st

century (compared to 1980-1999, after Meehl et al. 2007) This will ultimately affect growth rates of

biofilms as it is well documented that metabolic rates increase exponentially with temperature (Brown

et al. 2004). For example, Villanueva 2011 investigated biofilm formation by variation of nutrient

availability and temperature and reported that the biofilm formation at higher temperatures was

faster. Regulating water temperature in physical experiments is challenging as most flumes are not

equipped with heat exchangers. However, the long durations of many experiments, are associated

with water temperature increases due to the heat produced by pumping the water.

Seasonal succession

During the course of the year, physical, biological and chemical conditions change in systems where

biofilms are present and this also impacts their community composition. Some organisms are

outcompeted by others due to changes in factors such as water temperature, nutrient availability and

light intensity. This seasonal succession process (Figure 53) also influences the biostabilization

potential as was demonstrated by a number of researchers in different environments (e.g. Dickhudt et

al. 2009, Amos et al., 2003, Thom et al., 2015). In most of these studies, the stabilities are higher during

the warm seasons as compared to the colder seasons.

Figure 53. A typical seasonal succession of phytoplankton populations (From waterontheweb.org).



Salinity

Most knowledge on biostabilization comes from the marine environment, where biostabilization

effects are believed to be more important than in freshwater environments. The abundance of cations

in saltwater may be responsible for the seemingly higher potential for biostabilization of sediments

(see Gerbersdorf & Wieprecht, (2015) and references herein for more information on this topic).

However, recent physical experiments on biofilms cultivated in riverine freshwater systems indicate

an equivalently high biostabilization effect (Thom et al., 2015; Gerbersdorf et al. 2009).

7.2.2. State of the art: physical experimental designs

Only a limited number of studies are available in which aspects of biostabilization were investigated in

physical experiments. Most research so far was conducted in field experiments, for example in the

Venice Lagoon using benthic annular flumes (Amos et al., 2004) or on a tidal flat during different

seasons (Widdows et al., 2000). For fundamental studies on biofilm formation, flow cells are often

used (e.g. Stoodley et al., 1998). Flow cells are perfectly suited for fundamental research on biofilm

formation (e.g. mono species biofilms), but due to their rather small dimensions (Stoodley et al. 1998:

lxwxh = 200x3x3 mm) they are not very useful in cultivating and investigating natural biofilms for

erosion studies. Here, different experimental designs that have been used to investigate

biostabilization in hydraulic laboratories are reviewed, with consideration of the key parameters

considered in Part A. Table 5 summarizes the applied boundary conditions and aims of the studies

discussed.

Straight flumes are amongst the most widely used flumes for biofilm cultivation. Some flumes have

been purposely constructed for investigations on biostabilization (e.g. Singer et al., 2006, Thom et al.,

2015, Vignaga, 2012: “Ervine flume”), other studies have modified existing flumes for that purpose (e.g.

Graba et al., 2013, Vignaga, 2012: “Yalin flume”). Physical experiments on biostabilization in wave

dominated environments are rare; one of them was conducted in a wave flume (Droppo et al., 2007).

Other researchers used samples from nature and transported them to the laboratory. Larned et al.

2004 immersed acrylic plates in a river, which were later placed in large aerated tanks before the

measurements begin. Examples of different designs are illustrated in Figure 54.

Figure 54 Experimental setup. Left: (a) outflow tank, (b) pump, (c) inlet flow section with baffles, (d) biofilm growth section, (e) outlet flow section, (f) weir, (g) fluorescent tubes, (h) sediment cartridges, (i) bypass, (j) current abatement, (k) fine tuning valve. Right: view into one of the two containers with three identical straight flumes. The complete setup consists of six identical flumes. Flume dimensions are: lxwxh = 3.00x0.15x0.15 m. From Thom et al. 2015.

Water temperature

Keeping water temperature constant is vital for biofilm cultivation. Heating up of the water circulated

in flumes is likely, due to the higher performance demands of the pumps over several weeks. Heat



exchangers supplied with cold water can be used to control the water temperature (see e.g. Thom et

al. 2015). Another possibility to control the temperature is by placing the flumes in an air conditioned

room (Singer et al., 2006) or by partly replacing the water directly from a nearby river (Graba et al.

2010, 2013).

Light regime

Flumes can be equipped with fluorescent tubes (e.g. OSRAM Biolux®: Thom et al. 2015), hot wire spot

lights and LEDs (Vignaga, 2012) or neon tubes (Graba et al., 2010). To modify light intensities in an easy

way, the illumination source should be adjustable in height. Measuring light intensities can be done

using a radiometer. It should be ensured that the light intensities on the biofilm surface are

homogeneous; heterogeneities could result in spots of extreme or absent growth (Vignaga, 2012).

Common light intensities are given in Table 5.

Figure 55. Example of biofilm physical experiment setup from Graba et al. 2013. Top: Longitudinal view of the experimental flume; Bottom: Sketch of the principal laboratory flume, with locations of the PIV measurement access windows and the dimensions of the artificial cobbles.

Inoculation & Nutrients

Often natural river water is used as an inoculum (e.g. Thom et al., 2015, Graba et al., 2013). Normally

this water contains enough cells for the initial formation of biofilms and may even contain enough

nutrients (depending on the circulated amount of water and the duration of the experiments). To

obtain nearly constant nutrient conditions, Graba et al. (2013) replaced their water directly from the

Garonne River every four hours (Figure 56). A similar approach was used by Singer et al. (2006).

However, this procedure may require filtering to avoid contamination with larger organisms (e.g. insect



larvae) and suspended matter (Singer et al., 2006, Mendoza-Lera et al., 2015). To ensure sufficient

nutrient supply, some studies have added nutrient solutions to the recirculated water (e.g. Vignaga

(2012) mixed in BG11 solution, which is commercially available). Sediment samples from a natural

stream can serve as an inoculum (Mendoza-Lera et al., 2015) as they contain enough cells for a biofilm

to start growing.

Figure 56. Setup and components of the microcosm flumes in Singer et al. (2006). Lateral (a) and front (b) views, inlet (c), baffles (d), outlet and filter (e). Flume dimensions are: lxwxh = 1.30x0.02x0.02 m.

Reproducibility

Biofilm growth is heterogeneous and this also applies to its influence on biostabilization. Thom et al.

(2015) reported a high variability in erosion thresholds even from samples taken from the same flume.

To account for this heterogeneity, replicate measurements are strongly recommended. Mendoza-Lera

et al. (2015) used 12 flumes located in a greenhouse for that purpose. Thom et al. (2015) constructed

six identical flumes with individual water cycles, each holding 16 removable cartridges (containing the

sediment on which the biofilm grows) providing enough samples to monitor biostabilization over time

(Figure 54). Singer et al. (2006) built six sets of duplicate flumes (i.e. 12 flumes) and each flume was

paved with 104 ceramic coupons for cultivation (Figure 56). Vignaga (2012) used boxes that were

inserted into the “Yalin flume” for that purpose. Apart from hydrodynamic similarity, reproducibility

of biofilms involves investigations on biological parameters. Singer et al. (2006) and Schmidt et al.

(2015) both reported on the biological similarity of biofilms cultivated in purposely built flumes by

comparing EPS, chlorophyll-a (chl-a), biomass and community, and concluded that these constitute

valuable tools for biofilm characterisation.



Table 5. Selected studies, their aims and their applied boundary conditions during cultivation of biofilms.

Aim of Study Light Intensity

[µmol/m²s]

day/night cycle

[h/h]

Mean Flow velocity

[m/s]

(τbed [N/m²])

Water temperature

[°C]

Reference(s)

(1) specific hydrodynamic requirements of algal species;

(2) test their detachment resistance.

- 12/12 0.10/0.25/0.40 17-23 Graba et al. (2013)

(1) the biostabilization potential at different seasons and under different environmental conditions;

(2) overview on the mechanical processes in erosion.

0/50/100 8/16 0.07/ 0.13/ 0.17

(0.02/ 0.04/ 0.08)

15±0.15 Thom et al. (2015)

Describe and evaluate the reproducibility of flume microcosms by means of bacterial abundance, chlorophyll -a, biofilm surface area coverage and biofilm community composition.

23.2 12/12 0.071/0.18/0.43 20 ± 1°C (air conditioned room)

Singer et al. (2006)

(1) biostabilization for a range of grain sizes;

(2) flow modification;

(3) tensile strength analysis.

26 12/12 (0.42/0.64) 28 ± 0.5 ºC Vignaga (2012)

(Yalin flume)

Determine the potential of buoyant algal mats to lift sediments for a range of different grain sizes

240 - 0.029 ±0.017 18.7 ±0.3 Mendoza-Lera et al. (2015)



7.2.3. Future recommendations - Can we use surrogates instead?

Real interdisciplinary research involving ecological aspects in flume facilities is often hampered by the

unavailability of flumes, which provide suitable conditions for cultivation and testing (Rice et al., 2010;

Jonsson, 2006). As discussed in parts A and B, a multitude of environmental conditions need to be

controlled to simulate natural conditions and study their impact on sediment stability. In this context,

temperature control and salinity might be the most limiting parameters as few flumes are equipped

with cooling systems and experiments with saltwater are often not permitted due to accelerated

corrosion.

Another serious challenge, which is not strictly related to the representation of climate change effects

on biostabilization, is that long-term processes such as the response of natural biofilms to slow

warming over decades, cannot be easily accelerated. Moreover, studies on the effect of

biostabilization on morphology over longer periods need to consider the influence of short (e.g. after

a storm event: attachment, colonization, growth see Figure 52) and intermediate (seasonality:

different specialized organisms producing different quantities and qualities of EPS) variabilities. To

simulate all these effects in a laboratory setting in reasonable time using natural biofilms is

impracticable. Moreover, speeding up these processes by modifying environmental conditions will

affect the composition of the biofilm and consequently transferability of results to natural

environments. For example, Butterwick et al. (2005) demonstrated that by increasing temperature

from 25°C to 30°C, diatoms failed to grow and as such the biofilm characteristics were significantly

altered. This is further underlined by Rice et al. (2010) who noted that increasing temperature for

scaling reasons in ecohydraulic experiments generally “is likely to have a profound effect on organism

behaviour and survivorship”, thus should be treated with great caution.

In the Hydralab+ project, we will therefore investigate the feasibility of mimicking the natural

biostabilization potential by the use of chemical/biological surrogates. Potential candidates for these

surrogates are commercially available thickening agents, where some of them are even true microbial

polysaccharides (e.g. Xanthan gum), which are probably similar to natural EPS in their mechanical

properties and structure. However, to use these in biostabilization studies a number of research

questions need to be addressed:

1. Practical considerations for the use of surrogates in flume facilities

o How to mix the surrogates effectively such that their properties are reproducible?

Are the surrogate’s material properties stable over time (for long term experiments)

and at different temperatures?

o Biofilms are typically thin layers - how to produce these layers?

o How to visualize the surrogates - to get a detailed view on the erosion process?

o After the experiments - How can we remove the surrogate?

2. Exploring the mechanical similarities between surrogates and natural EPS

o What are the key properties to influence stability – how can we mimic those by using

surrogates?

o Does a higher quantity (i.e. mg/g sediment) increase the biostabilization potential?

Hypothetically, adding EPS to the sediment reduces the bulk density, which might

also lead to a destabilization.



o Is the mode of entrainment similar for natural EPS and surrogates?

3. Modification of properties

o Can we de-activate the surrogate (pH / temperature / ….) and maybe re-activate

later again for in-experiment cycling between bio and non-bio states?

Apart from Xanthan gum a number of other surrogates exist (e.g. guar, gum Arabica, algenic acid, agar

agar.) which potentially differ from each other in their properties. Furthermore, several studies have

demonstrated how to extract EPS from different organisms (De Brouwer et al., 2002; Dade et al. 1990),

so that EPS could potentially be used in these studies. Xanthan gum is probably the most well-known

surrogate and its properties are well documented. Therefore, the focus here is on Xanthan gum. The

following a review considers Xanthan gum properties and practical aspects, aimed at answering some

basic questions about its potential use in flume facilities.

Xanthan gum: Background information

Xanthan Gum is one of the most widely used and investigated thickening agent materials. It is a

microbial polysaccharide produced by the bacterium Xanthomonas campestris and used as a food

additive (E-415) and rheology modifier. It is commercially available as a fine powder which is added to

water to form a pseudo-plastic gum. Xanthan gum is thixotropic, which means that the viscosity

changes over time when shear is applied.

Practical aspects for the use of Xanthan gum in flume facilities

Mixing Xanthan gum for use in flumes can be straightforward. For example, Nugent et al. (2011) added

the powder to deionized water and then stirred the solution and mixed it with an immersion blender

for homogenization. They also used a salt solution to increase background cations, which resulted in

an increased stability compared to the results using deionized water. However, the conditions during

mixing can also significantly alter the mechanical properties of the solution. Rheological properties,

especially the viscosity of Xanthan gum, are affected by the production process and thus the

commercial products may have different properties as well. The rheological properties also depend

on temperature, both during dissolution (i.e. mixing) and during the measurements. Furthermore, the

biopolymer concentration, concentration of salts, and pH in the solution all result in different

stabilities (for a review on material properties, see Garcıa-Ochoa et al. (2000)).



Figure 57. Yield stress of different Xanthan gum concentrations mixed at dissolution temperatures of 25, 40, 60 and 80°C from Garcia-Ochoa (1994). Left Variation of yield stress with dissolution temperature at different Xanthan gum concentrations, TM =25°C; Right: Variation of yield stress with measurement temperature at different Xanthan gum concentrations, TD= 25°C.

It is unlikely that large-scale physical experiments will be conducted in the range of temperatures given

in Figure 57, but the possibilities of modifying the properties prior or even during the experiments is

a noteworthy aspect. Furthermore, the dependency of Xanthan gum properties on the

aforementioned factors indicates that great care should be taken in developing protocols that enable

reproducible production of Xanthan gum mixtures.

The mechanical similarities between natural EPS and surrogates

A natural biofilm is a complex three-dimensional structure consisting of different micro-organisms and

an EPS matrix, which is composed of voids, channels and dense areas (Flemming & Wingender, 2010).

Moreover, biofilms are highly heterogeneous, both spatially (on very small scales) and temporally (e.g.

Tolhurst et al. 2005). It seems impossible to account for all of these aspects by using a simple surrogate

like Xanthan gum. In fact, Perkins et al. 2004 noted that creating engineered sediments by addition of

surrogate EPS might not even resemble the biological/chemical compounds correctly, suggesting that

studies using surrogates potentially fail in investigating the role of polymers in biostabilization

processes. However, even though surrogates might not be good analogues of natural biofilm-

sediment substrates, the use of Xanthan gum is still useful for investigating biostabilization and

sediment erosion, wherein mechanical similarity, rather than chemical or biological similarity, is most

important.

Tolhurst et al. (2002) investigated the stability (i.e. the erosion threshold and the erosion rate) of

Xanthan gum at different concentrations by application of the “Cohesive strength meter” (CSM). They

found that the stability increased with Xanthan gum concentration. This trend has also been reported

by Black et al. (2001). Additionally, Tolhurst et al. (2002) compared their results to in-situ

measurements on biofilms that contained an equivalent quantity of EPS and found that the artificial

Xanthan gum - sediment mixture was approximately half as stable as their natural counterparts. They



hypothesized that the reasons for this difference were a) the quality (proteins and lipids) of the

Xanthan gum could have been different, and b) the characteristics of natural EPS as secreted by

organisms.

Figure 58. Low-temperature scanning electron microscope images (from Black et al. 2001) of (a) partially freeze-dried EPS “dissolved” in seawater (note the natural fibrillary network structure (scale bar 100µm)); (b) EPS and sand treated with 1.25gkg -1 EPS; low magnification image showing strands and threads of EPS (note the continuous swath of EPS down the right-hand margin (scale bar 1000 µm)); (c) high magnification view detailing polymer bridging between grains as well as interstitial EPS (scale bar 100 µm); (d) low magnification image at EPS concentration of 5 g kg -1 showing generally greater occlusion of pores by polymer (scale bar 1000 µm).

To support their findings, LTSEM images were taken and qualitatively compared. They reported that

at low concentrations the Xanthan gum is hardly visible and is probably adsorbed to the sediment

surfaces. At higher Xanthan gum concentrations, strands begin to form physical connections between

the grains. Structural aspects were also considered in Black et al. (2001) who reported that by

increasing the concentration, more and more voids were occluded by strands (Figure 58). Their results

indicate a moderate linear increase in stability with concentrations between 0 and 2.5 g/kg and an

unexpected high stability at 5 g/kg, which supports their structural observations.

Erosion flumes as well as other erosion devices measure the erosion threshold on a large area, thereby

integrating and averaging erosion induced by the complex flow characteristics. The sediment content

(or the sediment to EPS ratio) and the characteristics of the sediment (cohesive or non-cohesive) play

an important role in this context. Rheological parameters of the surrogate, such as viscosity or liquid



limit are material properties and can be determined independently from the sediment. Such

parameters may be useful to compare “natural” biofilm characteristics to the properties of surrogates.

It is intuitive to assume that biofilms and surrogates will behave mechanically similar if the key

mechanical properties are identical.

Another important material property is the adhesiveness (i.e. the glue-like effect) of the surrogate

which can be measured with the MagPI-IP system (Thom et al., 2015b). For example, it was found that

the pull-off force (a proxy for adhesion) increased with higher concentrations of the Xanthan gum

dissolved in water (Figure 59), which is in line with the trend of erosion thresholds reported by Black

et al. (2001) and Tolhurst et al. (2002). These findings suggest which parameters of a surrogate,

especially those of Xanthum gum, influence sediment stability. Such information is important given

the aim of successfully mimicking “natural” biostabilization effects.

Figure 59. Sediment stability trends as a function of increasing Xanthan gum (XG) concentration. Left: The pull-off force as a proxy for adhesion at different concentrations of XG dissolved in water (unpublished data); Middle: Stability as determined with the CSM at different concentrations of Xanthan Gum per dry weight sediment (Black et al., 2001); Right: Averaged stability as determined with the CSM at different concentrations of XG per dry weight sediment (after Tolhurst et al. 2002).



PARAMETRISATION OF AQUATIC VEGETATION IN HYDRAULIC AND COASTAL RESEARCH Although the interaction between flow and vegetation has been increasingly in the focus of

experimental works within the scientific community in the past decades, a large body of research has

focused on mimicking vegetation made of stiff elements such as cylinders, and thus omitted the

feedbacks of mechanical interactions (e.g., Johnson et al., 2014a; Aberle and Järvelä, 2015). Compared

to stiff elements, aquatic plants are mostly flexible and adopt a streamlined shape reducing their

projected frontal area to reduce their exposure to the flow attack (de Langre et al., 2012; Albayrak et

al., 2013). In addition, aquatic vegetation generally develops a phenotypic plasticity in response to a

change of an environmental factor (Gratani, 2014). Such change in the plant behaviour can be

triggered by any mechanical stress such as the transplantation into a flume or the sudden change of a

hydraulic regime (Read and Stokes, 2006; Puijalon et al., 2008), which can lead in some cases to a very

low life expectation in a flume (Johnson et al. 2014b). This is the reason why the development of inert

plant surrogates offers a sustainable solution to remove any bias introduced in a test by a potential

change of the plant’s behaviour in a field or flume environment. In addition, the development of inert

surrogates allows for a more controlled experimental validation of the analytical parametrisation of

plant-flow mechanical interactions, which currently lacks of a standard formulation (see Henry et al.

(2015) for a comprehensive review).

The design of plant surrogates can be adapted to target specific characteristics of the vegetation to be

studied, such as various biomechanical properties. This approach is necessary to quantify the way key

parameters such as flexibility and buoyancy determines a plant’s mechanical behaviour (e.g. Luhar

and Nepf, 2011), which in return affects the hydraulics of the system studied. Methods used to

produce plant surrogates can be either based on assembling various materials to reach the desired

structural complexity representing the targeted specie (Paul and Henry, 2014), or develop casting

techniques in order to have a better control of the plant morphology and allow for surrogate mass

production (Johnson et al. 2014a).

The development of surrogates relies on the good understanding of the plant biomechanical

properties and requires therefore extensive field data collection prior to the main experiments (Nikora,

2010). Although recent works are relying more and more on plant surrogates (see Johnson et al 2014a

for a non-exhaustive list), only few studies investigated the surrogate design process for complex

shaped aquatic plants, such as the work carried on by Paul and Henry (2014), and this process is yet

to be developed for freshwater aquatic vegetation.

In the context of changing fluvial systems, the use of plant surrogate offers the opportunity to better

control the interactions between aquatic vegetation and a changing hydraulic environment, without

the issue of phenotypic plasticity typical from biotic systems (Read and Stokes, 2006; Nikotra et al.

2010). However, if progressive changes of the vegetation properties are to be considered, surrogates

would need to be replaced on a regular basis during the experiment.

Plant surrogates offer new possibilities to test hypothesis and new patterns linked to changing fluvial

systems. Johnson et al. (2014a) detailed the various benefits and the limitations of using inert physical

surrogates, and these points will therefore not be detailed here. However, surrogate development is

still in its infancy and depends on a detailed knowledge of the morphology and biomechanics of the



specie of interest, and we present here some of the major issues yet to be tackled, in the context of

changing fluvial systems:

Seasonality: Aquatic plants do present morphological and potentially mechanical variations

based on seasonal patterns. In experiments, the potential interaction between the different

time scales such as the seasonal growth and the time between active and inactive hydrological

regimes needs to be taken care of. In the case of experiments involving time compression

(systems always active/in flood, see e.g. Paola, 2000) effects due to seasonal changes of plant

characteristics may be lost.

Mechanical tests: Implementation of well identified techniques within their domain of validity

to collect biomechanical data and if necessary, adaptation to the constraint of a field data

collection (Henry 2014, Henry et al. 2016). A good understanding of the plant biomechanical

properties requires the use of a solid dataset from real-life conditions (Nikora, 2010).

Systematic design procedures: In a laboratory representation of a hydraulic system, the

question of the required level of complexity of a plant surrogate is still open. As highlighted

by Denny (1988), it is critical not to fall into a purely engineering approach and redesign the

plant structure. The understanding of the existing structural organisation of a plant is a key to

the identification of the environmental factor that defined it, and should highlight the features

to be reproduced in an experiment, depending on the processes and scales to be investigated.

Systematic performance tests: Most important part in a design process, performance tests

should be conducted systematically to ensure that the dynamic behaviour of the surrogate

correspond to the original criteria, i.e. the reproduction of the process observed in nature

(flexibility, plant to plant interaction, effect on sediment transport).

Scaling plant properties: In theory, it is possible to scale down plant properties, which may

lead to a distortion in time and/or space of the hydraulic model Johnson etal (2014a), a

distortion of time (compression) being of high interest in the representation of fluvial system

evolution over larger time scales. In practice, no such work has been published to the best of

our knowledge, and investigations related to scaled plant properties are just about to start.

The potential interaction of this new distorted ‘plant time scale’ with the other time scales

applying to sediment transport and larger morphological evolutions is yet to be characterised.

It may be noted that the development of the use of plant inert surrogates may also help and be done

in parallel to numerical modelling studies replicating fluid flow around vegetation (Marjoribanks et al.

2014, 2015), whose effects can be included into larger numerical simulation addressing fluvial

adaptation at a larger space and time scale.

MEASURING ORGANISM STRESS AND BEHAVIOURAL INTEGRITY IN FLUME FACILITIES

7.4.1. Introduction

Laboratory experiments are widely used to investigate how biota affect drag, turbulence, velocity

profiles, sediment transport and other fundamental processes under controlled conditions, using

either live organisms or surrogates. While surrogate plants and biofilms have a number of advantages

including reproducibility and simplification, there are also benefits to using live organisms, including



better representation of physical structures and dynamic properties (Johnson et al., 2014a). In cases

where the research question is best addressed using live organisms, experimenters are then faced

with the significant challenge of keeping their plants or biofilms healthy within the experimental

facility.

Johnson et al. (2014b) emphasise two reasons why the health and well-being of live organisms used

in flume facilities is important: scientists have an ethical responsibility to avoid causing stress or pain;

researchers need to ensure that organism behaviour is relatively stress-free and therefore analogous

to wild equivalents. Without the latter, the integrity of experimental results is compromised because

stress may change the physiological and behavioural responses of vegetation or biofilms such that the

interaction with flow or with sediment transport is unrealistic. Of course, these organisms are often

stressed in their natural environment by competition for resources and by other ecological and

biological interactions. Their interactions with their environment are variable and complex, such that

there is no ideal stress-free state that must be mimicked. Nevertheless, a basic goal of most

experimental work will be to reproduce in the flume, behaviours that are typical in nature and, in that

case, low levels of stress are desirable.

Focusing on the use of vegetation, within hydraulics facilities, plants may be stressed by one or more

environmental factor including inappropriate water chemistry (salinity, pH, dissolved oxygen,

inorganic carbon), water temperature, substrate (physical and chemical properties), lighting (amount,

timing), and flow characteristics (depth, velocity, drag). Their health and behaviour may also be

affected by biological considerations, including insufficient nourishment (type, quantity, and timing),

competition for resources amongst individuals and, potentially, the introduction of pathogens.

Johnson et al., (2014b) provide a useful review of these main stressors and their management in flume

facilities. Most plants are able to tolerate a range of environmental conditions, with fatality beyond

limiting thresholds. As conditions become less optimal, but sub-lethal, the plant will adapt, potentially

altering the way in which it interacts with the flow. We know very little about these adaptations and

what they mean for hydraulic performance, but existing work suggests that the relations are likely to

be complex, especially where multiple stressors are present (e.g. Puijalon et al., 2007).

So, demonstrating that vegetation is not physiologically or behaviourally stressed during experiments

should be a standard element of any experiment involving live plants. Without that assurance it is

difficult to be confident that measured hydraulic and morphodynamic responses can be properly

assigned to treatment effects, not abnormal behaviour caused by the experimental environment.

While it may be relatively easy to detect serious ill-health or the death of a plant that is part of a flume

experiment, earlier stages of decline that affect the plants interaction with the flow, may go

undetected, potentially undermining the results obtained.

7.4.2. Key challenges and research questions

This leads to the identification of two key challenges for investigating plant-flow-sediment interactions,

not least, in the context of climate change adaptation: developing protocols that can be used to

monitor plant health or stress levels during flume experiments; and developing a fuller understanding

of how health and stress levels affect key plant structures, physiological responses and behaviours

that are relevant to flow and sediment interactions.



Meeting these challenges would provide experimenters with a basis for making objective decisions

about how stressed a plant is and whether the level of stress is sufficient to affect behaviour and

therefore the integrity of an experiment. Key questions are:

1. How does stress affect those physical characteristics of the plant that control flow

interactions?

2. What is a useful way to routinely measure stress in plants, in flume facilities?

3. At what stress levels do flow interactions cease to be realistic?

How does stress affect the physical character of aquatic plants?

Numerous structural and physiological plant characteristics are relevant to vegetation hydraulics

(Green, 2005; Neumeier, 2007; Tempest et al. 2015) including: stem and leaf buoyancy (Luhar and

Nepf, 2011); the strength, flexibility and elasticity of stems and leaves (Armanini et al., 2005; Paul et

al., 2012); the shape and size of stems, leaves and whole plants (James and Barko, 2000; Wilson et al.,

2003) and the density and arrangement of plant communities (Graham and Manning, 2007; Widdows

et al., 2008; Chen et al., 2011). Meike et al., (2014) provide a useful review of how these factors matter

via their impacts on drag, transfers of momentum and turbulence generation. Because stress affects

key structural and physiological properties, it is clear that stress will have implications for vegetation

hydraulics, but to our knowledge the nature of these relations has not been examined or quantified.

How might stress be measured in aquatic plants used in flumes?

Many of the techniques that have been developed for assessing stress in plants are associated with

environmental toxicological studies that seek to understand how environmental factors, including

anthropogenic pollutants, affect plant health. With objective measures of stress, insitu plants can be

used as indicators of environmental quality or act as sentinels of environmental degradation. Work on

aquatic plants, rather than terrestrial plants, is relatively and aquatic plants are perhaps underutilised

in biomonitoiing (Lovett Doust et al., 1994; Brain and Cedergreen, 2009). Nevertheless, studies have

linked changes in plant health and abundance to eutrophication, urban pollution and trace metal

contamination (Ferrat et al., 2003).

A key methodology involves the use of biomarkers – measurable symptoms evident in tissues, cells

and biological fluids – that reveal changes in the plant caused by an external stress. Stress biomarkers

can provide real-time indications of general or particular stressors. Crucially, biomarkers extend what

is possible using visible or morphological parameters thereby facilitating detection of stress prior to

obvious visible symptoms including chlorosis or necrosis (Ernst and Peterson, 1994; Brain and

Cedergreen, 2009). Some biomarkers focus on specific stresses: so, for example, the activity levels of

enzymes involved in the assimilation of nitrates and phosphates can indicate nutrient deficiencies and

specific phenolic compounds have been associated with grazing pressure, infection and heavy metal

pollution (Ferrat et al., 2003).

Other biomarkers provide a more general indication that a plant is stressed, but not necessarily what

the stressor is. Chlorophyll fluorescence is a widely used and robust means of measuring a plant’s

reaction to one or more environmental stressors, specifically by assessing damage to the plant’s

photosynthetic apparatus (Maxwell and Johnson, 2000). This technique has been used in different



seagrass species to identify stress associated with infection, heat, desiccation, inappropriate light

levels and metal and herbicide pollution (Ferret et al., 2003). Measurements are simple to make, not

least because portable chlorophyll fluorometers are relatively cheap and reliable, but aspects of the

underlying theory remain controversial so data interpretation requires care (Maxwell and Johnson,

2000). While it is likely that chlorophyll fluorescence could provide a cheap, relatively straightforward,

reliable and rapid means of measuring total levels of stress in flume vegetation, there is a need to

establish appropriate protocols and demonstrate the value of the technique for those stresses most

likely to affect plants in flume facilities.

How does stress affect the realism of plant-flow interactions?

Measuring levels of vegetation stress using an appropriate technique will provide a means to examine

the relations between levels of stress and the hydraulic performance of a plant. Hydraulic

performance refers to the degree to which a plant’s interaction with the flow is affected by structural

or physiological changes caused by environmental stress. Given the tolerance of many plants to broad

ranges of environmental conditions and the natural propensity for organisms in nature to be stressed,

it may be difficult to define a simple reference condition that represents ‘natural’ behaviour in the

absence of any stress. However it may be possible to identify levels of stress beyond which changes in

key structural or physiological characteristics have a clear impact on flow characteristics.

7.4.3. Information gaps

Maintaining behavioural integrity in flume experiments is not, therefore, simply a case of measuring

stress, but also requires understanding of the relations between measured stress, plant characteristics

and hydraulic performance. Developing this understanding requires work to develop a suitable

protocol for measuring plant stress in flume facilities and also work to relate stress levels to plant and

hydraulic responses. What are ideal aquatic plant species to work with in developing suitable protocols

for measuring and understanding the impact of stress? It is appropriate to focus on key or model

species because it is impracticable to develop this understanding for all aquatic plants. Key species

include those that are of widespread interest to the hydraulic engineering community, perhaps

because their potential value in green interventions has been recognised or because they are

widespread and known to strongly affect shallow-flow hydraulics. Model species are those which can

be used to represent the members of a wider plant group because they share common structural and

physiological characteristics.



8. NUMERICAL MODELLING OF BIOGEOMORPHOLOGICAL INTERACTIONS

IN RELATION TO CLIMATE CHANGE ADAPTATION

INTRODUCTION As a result of economic and population growth the pressure on coasts, rivers and estuaries is likely to

increase. Socioeconomic developments typically lead to stricter demands for safety or risk reduction,

while leaving less room for the natural dynamics that characterize these areas. At the same time,

anticipated sea level rise, higher temperatures and increased storminess resulting from climate

change are expected to intensify natural forcing and consequent dynamics [Nicholls et al., 2007]. More

and more, it seems likely that traditional, large-scale, hard engineering solutions are too costly -

financially or in terms of their impact on the ecosystem - and that nature-based solutions, which can

adapt to climate change, are a more viable option [Barbier et al., 2008, Narayan et al., 2016,

Temmerman et al., 2013, Spalding et al., 2013].

Sustainable management of such aquatic environments requires quantification of both the

geomorphological behaviour at any given moment (i.e. during a storm event) as well as the trajectory

of the development in time [Folke et al., 2005]. Such quantification must come from predictive tools

that also give insight in the uncertainty of their predictions, in relation to the non-linear behaviour of

the natural system. Physical experimental models and field experiments can provide quantitative

information but are limited in scale and time. Numerical models can be useful predictive tools because

they can cover multiple spatial and temporal scales and they can easily be forced with a multitude of

climate change scenarios. In order to be of use for the assessment of management issues in relation

to natural environments however, they need to represent both physics (hydraulics and morphology)

and ecology and the interaction between these disciplines rather than a single discipline [Camporeale

et al., 2013].

The aim of this section is to describe how the use of physical and numerical models for

biogeomorphology can complement each other in studies regarding climate change impact,

adaptation or mitigation. Biogeomorphology is a very broad field of interdisciplinary science.

Therefore, the overview of the present state of science is inevitably partial, but will give the reader

insight in some key aspects and references. The focus of this review is on vegetation but most

principles apply in similar fashion to other organisms that act as ecosystem engineers, such as corals,

shellfish reefs and biofilms as well as many invertebrates and fish. The term numerical models here is

used as a contrast to physical models, and actually implies process based computational fluid

dynamics models that solve some (simplified) form of the Navier-Stokes equations or similar

elementary partial differential equations for other media (i.e. soil, vegetation); not empirical models

that are solved numerically.



STATE OF THE ART IN NUMERICAL MODELLING OF BIOGEOMORPHOLOGY

8.2.1. Scales and model types

Interactions between organisms and hydro- and morphodynamic processes span a large range of

environments and spatial and temporal scales [Camporeale et al., 2013]. Likewise, numerical models

are available in many sizes and styles. The smallest describe the interaction of individual organisms,

sometimes of individual cells, with their environment, for example to simulate photosynthesis and

nutrient uptake [Koch, 1994] or reconfiguration [Dijkstra & Uittenbogaard, 2010] over a period of

seconds. The largest models cover the entire globe and are used for meteorological and oceanography

studies, such as the computation of storm surge levels in relation to coastal vulnerability [Muis et al.,

2016].

Most numerical models of relevance for climate change adaptation studies operate at a scale in

between these extremes, for example the scale of a river reach or estuary. On this scale, finite

difference or finite element, grid-based models such as Delft3D, Telemac and MIKE21 are applicable.

These models are based on considerable simplifications -e.g. only hydrostatic flow- that allow for fast

computations but limit the range of problems they can solve. For studies related to impact on banks

or coastal defences, scales of several tens to hundreds of metres are characteristic. Model types such

as SPH (Smooth Particle Hydraulics), VOF (Volume of Fluid) or LES (Large Eddy Simulation) can be

applied on this near-field scale of several tens of meters. These models, like COMFlow or OpenFOAM,

stay closer to the original differential equations and allow for the assessment of a wider range of

problems, at substantial computational cost.

Generally, hydromorphodynamic models involve a computational control shell that successively calls

hydrodynamic, sediment transport and bed level update modules, linked through a feedback loop

[Lesser et al., 2004, Figure 60]. The hydrodynamics are solved using the unsteady shallow water

equations for currents and the spectral wave action balance equations for waves [Booij et al., 1999].

Sediment transport rates are calculated using one of the many available sediment transport equations

[e.g., Engelund and Hansen, 1967 or Van Rijn, 2007a, b]. Bed level update is facilitated via the sediment

continuity or Exner equation. Biogeomorphic models add a fourth – biology-module to this scheme

and some also take seed or nutrient transport into account in the second step. Various types of biology

modules exist, which model vegetation, recruitment, growth, succession and mortality of vegetation:

rule-based cellular automata, physics-based habitat models and individual-based models.



Figure 60. General setup of hydromorphological models and the working of the Morfac concept. [From: Ranasinghe et al., 2001].

A major advantage of process-based numerical models is that they are –if used carefully- valid across

a range of scales and one can increase the spatial resolution in areas of specific interest for more

efficient computations. Another advantage is that some widely available engineering models use a

morphological acceleration factor (Morfac) that allows for simulations of morphological changes over

decades and even centuries, at least for uniform forcing conditions [Ranasinghe et al., 2011, Van der

Wegen et al., 2008]. Where Morfac applies boundary conditions sequentially, the Mormerge

technique [Roelvink, 2009] applies them in parallel, which renders the end result less sensitive to the

exact sequence. For bidirectional flows, the set of representative wave boundary conditions can be

determined with tools from the OPTI-routine [Mol, 2007]; such tools are also applicable to physical

experiments.

8.2.2. Processes

Flow is the key process in all simulations: water motion determines whether sediment is picked up,

how constituents are mixed, where they are transported and deposited and exerts stress on organisms.

At the same time, the flow is affected by the presence of the bed and organisms. This section discusses

how the presence of vegetation can be taken into account and how organism development can be

modelled.

Steady flow

In numerical modelling, representing vegetation started with the use of increased hydraulic roughness

factors that had been estimated using Q-h curves over vegetated river transects. Such empirical bulk

roughness values can be sufficient to simulate water levels and discharges, but lack predictive value



and are only weakly linked to vegetation properties. Kouwen and Unny (1973) were the first to

systematically derive roughness factors across a range of plant properties. Since then, interest

widened to understanding turbulence and transport in relation to the spatial structure and

submergence of plants [e.g. Nepf & Vivoni, 1995, Luhar & Nepf, 2013, and many others]. This

experimental work provided information to develop numerical models that simulate the effect of

plants on flow and turbulence based on the presence of rigid elements in (part of) the water column

[e.g., Baptist, 2007; Stoesser et al., 2009].

Because organism characteristics can have a considerable effect on landscape development [Bouma

et al., 2013], a physically correct representation of complex plant form and behaviour is important but

challenging [Marjoribanks et al., 2014]. Acquiring data on plant morphology is labour-intensive and

difficult due to the large variations between specimens and because not all plant parts contribute

equally to the drag [Wilson et al., 2008]. Laser scanning and multispectral photography techniques

[e.g. Västilä et al., 2013, Jalonen et al., 2015, Straatsma et al., 2007] can provide useful clues, but still

require further development. Numerical models like those of Marjoribanks et al. [2014] and Dijkstra

& Uittenbogaard [2010] relate hydraulic drag to vegetation buoyancy and elasticity (i.e. biomechanical

reconfiguration), but are too computationally expensive to be used at a landscape scale. Luhar & Nepf

[2011] offer a lighter, analytical approach based on the Cauchy-number (i.e. the ratio between

bending and restoring forces) that has not found its way to numerical models yet.

Waves

Being more complex than steady flow, the effect of organisms on waves is less well known.

Consequently, fewer numerical models are available to simulate this process and their results are

regarded as uncertain. Dalrymple [1984] developed a description for energy loss of regular waves by

representing the vegetation as vertical, ridged cylinders, using the relative vegetation height, diameter

and density and a drag coefficient CD. Vegetation motion is neglected and the drag coefficient is based

on empirical relations to the Reynolds or Keulegan-Carpenter number. This bulk drag coefficient is a

‘rubbish bin’ for many uncertainties: flexibility, buoyancy, response to different frequencies and plant

shape. Unlike steady flow, where CD is O(1), literature values for CD in waves vary from 0.08 to 50; a

warning for the lack of a sound physical understanding and a large uncertainty for the use of

vegetation as part of a coastal flood defence [Henry et al., 2015].

Mendez & Losada [2004] extended Dalrymple’s description to irregular waves. Suzuki et al. [2012]

incorporated that formulation in the open source spectral wave model SWAN, also adding limited

vertical and spatial variation of vegetation structure (Figure 61), thus creating the first easily applicable

numerical model for wave attenuation by vegetation on the landscape scale. Vuik et al. [2015]

successfully compared SWAN results to field observations of wave attenuation over a salt marsh under

mild storm conditions. Recently, a similar approach was incorporated in the near shore wave and

sediment transport model XBeach [van Rooijen et al., 2016], which opens up interesting opportunities

to study e.g. salt marsh erosion and reduction of water level setup during storms. XBeach has also

been applied to study the influence of coral reefs and climate change on wave-driven flooding of atols

[Quataert et al., 2015].



Maza et al. [2013] developed a VOF model to couple water and plant motion, which reduces part of

the uncertainty that would otherwise arise from using a bulk drag coefficient. Such models can be

useful to study the more extreme conditions that are relevant for the design of nature-based flood

protection measures that are limited by the size and husbandry possibilities of physical facilities

[Moeller et al., 2014].

Figure 61. Schematisation of vegetation as cylinders in SWAN.

Sediment transport

Many studies have addressed critical bed shear stresses and critical velocities for sediment motion

and resuspension on bare beds under currents and/or waves (e.g. Van Rijn, 2007a,b and references

therein). Literature on sediment pickup and deposition specifically within patches of benthic canopies

is very limited, however [e.g. Jordanova and James, 2003 (bed load); Le Bouteiller & Venditti, 2015],

especially given the range of patch densities and submergence ratios that can occur.

Some of these ‘bare bed’ transport formulas [like Van Rijn, 2007a,b; Engelund & Hansen, 1967]

perform quite well in numerical simulations of fluvial environments if the hydrodynamics (i.e.

reduction of bed shear stress) are simulated well [Vargas-Luna et al., 2015]. For suspended sediments,

also the alteration of the turbulent eddy diffusivity profile by vegetation is important [Lopez & Garcia,

1998] but not specifically addressed because the number of experiments on sediment transport in

and over vegetation is limited.

Specific effects of vegetation observed in physical experiments, like local scour around stems, the

presence of stems and leaves that act as a filter in the water column or the stabilizing root mat [e.g.

Bouma et al., 2007, Hendriks et al., 2008, Pollen-Bankhead & Simon 2010] are not yet incorporated in

sediment transport formulations in numerical models. The process of (re)suspension and transport of

sediment in the presence of vegetation in wave-dominated environments is largely unknown and

contrary to the common perception of vegetation preventing erosion, the opposite can occur too:

Tinoco & Coco [2016] observed that despite significant flow reduction inside dense arrays, the

resuspension of sediment increases with an increase in array density increases due to cylinder-scale

turbulence. Using an empirical coefficient to account for cylinder-scale turbulence, they propose an



alternative approach for the Shields parameter (Figure 62) to predict suspended sediment

concentration.

Figure 62. Modified Shields parameter to account for array turbulence at various array densities. From: Tinoco & Coco, 2016.

Organism development

Many simulation models for the development of ecosystems and organisms therein exist, with the

Lotka-Volterra model as the most well-known example of a simple predator-prey model, consisting of

a single pair of ordinary differential equations. For the complex real world, such a model is too

simplistic and more powerful systems are used, such as Ecopath for marine systems. In the field of

biogeomorphology, there is no single standard model, but often ecological models based on the

following principles are linked to morphodyanamic models:

physics-based habitat distribution models;

rule-based cellular automata;

individual-based models.

The habitat models predict the possible occurrence of habitats for organisms based on a set of physical

conditions like water depth, inundation time or salinity that occur over a representative period in time

via response curves, much like a GIS tool. In principle these models are static, but by generating new

maps of representative physical conditions over time, e.g. based on different flood frequencies, one

gets an impression of possible developments.

The rule-bases cellular automata resemble the habitat models, but add temporal dynamics such as

growth and clonal expansion, and enable feedbacks between species and between nearby cells.

Individual-based models are the most computationally intensive because they take (patches of)

individuals as the starting point, rather than model grid cells. This offers the possibility to get more

natural variation of organism properties in the model and consequently a more natural (dynamic

equilibrium; Folke et al., 2002) behaviour, but also requires substantial simplifications because

morphological models cannot deal with millions of individuals.



Good knowledge on tolerance limits (e.g. what is the critical wave load under which mangroves

collapse, or what is the minimum amount of light seagrasses need to stay healthy?) is essential for all

three model types. For the model types that simulate temporal dynamics, also growth and mortality

rates are crucial. Combined biogeomorphological models are very sensitive to settings for these rates,

but do enable studies of regime shifts that go beyond a simple set of differential equations, e.g. Carr

et al. [2010].

KEY NUMERICAL MODELLING RESULTS IN FLUVIAL AND COASTAL BIOGEOMORPHICAL

SETTINGS To illustrate the state of the art in numerical modelling of biogeomorphology, the approach and results

of two recent numerical model studies are discussed: for a fluvial environment [Van Oorschot et al.,

2015] and for a coastal environment [Schwarz et al., 2014].

8.3.1. Numerical modelling of hydromorphological vegetation dynamics in rivers

The dynamic interaction between river channel patterns and populations of riparian species is

important for river management because vegetation affects bend migration by increasing bank

stability and water levels by increasing flow resistance. Moreover, the presence of different types of

vegetation is related to ecosystem services such as recreation, nature and logging. Many studies have

described such interactions in rivers [e.g. Bertoldi et al., 2009; Gurnell 2014], but most are mainly

empirical and lack the quantitative understanding required for predictive river management models.

Van Oorschot et al. [2015] quantify effects of vegetation-type dependent settling, growth and

mortality with life-stage dependent hydraulic resistance on the morphodynamics of a meandering

river.

Figure 63. Flow diagram of processes and dynamic interactions in the combined hydromorphological-vegetation dynamics model of Van Oorschot et al. [2015].

Their model coupled a vegetation model in Matlab, which accounted for multiple vegetation types

depending on seed dispersal, colonization, growth and mortality to a two dimensional model for flow

and sediment transport in Delft3D (Figure 63). With this model, they compared river planform and



vegetation patterns for a scenario with dynamic vegetation properties to reference scenarios with

static vegetation and without vegetation.

Because of the simulation time of 300 years, the morphodynamics were simulated with a two-

dimensional depth averaged model, using the relation of Baptist et al. [2007] for hydraulic resistance

caused by vegetation, the Engelund-Hansen transport formula and a morphological scaling factor

(Morfac; section 8.2.1) of 30. Due to the specific implementation of the Baptist-relation in Delft3D,

the presence of vegetation affects the hydraulic resistance correctly, without an artificial and incorrect

increase in bed shear stress that would mess up sediment transport, as would be the result of an

increase of a standard bed roughness factor. For each ecological time step -the ecological updating

occurred 24 times per year-, the vegetation model retrieved bed levels, flow velocities and water

levels from the morphological model. Riparian trees of the Salicaceae family were selected as the

main vegetation types because these are the dominant ecosystem engineering species that grow on

river floodplains in Europe.

Two distinct typical Salicacaea were parameterised to resemble trees of the Salix and Populus genera,

each with general characteristics (maximum age, initial sizes, growth factors and dispersal timing) and

life stage-specific parameters (spatial density, drag coefficient and mortality rules). Salix disperses in

June, has a maximum age of 60 years and is more tolerant to flooding, whereas Populus disperses in

May, has a maximum age of 150 years and is more tolerant to desiccation. Settling of seedlings

occurred on moist substrate between minimum and maximum water levels during the dispersion

window. Vegetation growth was implemented as a logarithmic growth function depending on

vegetation age. Mortality was calculated at the end of each calendar year, depending on the days of

subsequent flooding and/or desiccation, maximum flow velocity, burial or scour and the maximum

vegetation age. Using a similar principle as habitat models, dose-effect relations (Figure 64)

determined the percentage of plants not surviving a physical stressor. The initial river planform and

boundary conditions were loosely based on the largely natural Allier River in France, using a flood

discharge of 400 m3/s in winter and 50 m3/s in summer.

Figure 64. Example of a dose-effect relations between morphodynamic pressure (e.g. inundation time) and mortality. From: Van Oorschot et al. [2015].



All three basic scenarios (bare, static vegetation and dynamic vegetation) displays typical behaviour

of rivers like the Allier River: lateral expansion and longitudinal migration of meander bends, with

periodical chute cut-offs. The rate of change and eventual river planform at the end of the simulation

differ considerably, however: The default scenario with dynamic vegetation shows an active

meandering behaviour, while the scenario without vegetation develops into low sinuous river.

Compared to the static vegetation that results in a static vegetation dominated state, the vegetation

patterns in the dynamic scenario reduce lateral migration, increase meander migration rate and create

a smoother floodplain. The simulated percentage vegetation cover in the dynamic scenario is of the

same order (10-20%, vs. 80% for the static scenario) as the real cover observed by Geerling et al. [2006],

but especially the 2-10 year vegetation class is underestimated considerably (2% vs. 10% in reality).

This indicates that the model provides more quantitatively realistic answers than many earlier

modelling efforts, but also that the error margin is still substantial.

Figure 65. Bed level and vegetation cover after 150 years of several scenarios used for a sensitivity analysis in Van Oorschot et al. [2015].



A sensitivity analysis for differences in dispersal timing, seedling survival, maximum spatial densities,

drag coefficient and growth strategy revealed considerable differences in bed level and vegetation

cover (Figure 65). This implies that changes in species distribution, e.g. native species being replaced

by invasive species as a result of climate change, can have strong effects on river morphology. The

model was not used to assess how these different river planforms affect discharge capacity or flood

levels. This would be an interesting application that would give insight in how important the exact

vegetation cover is to accurately predict flood levels, i.e. how small the error margin needs to be to

make the model suitable for answering management questions.

8.3.2. Numerical modelling of salt marsh development

Like river plains, salt marshes are ecosystems that support a variety of ecosystem services such as

providing a habitat for birds and fish, carbon sequestration and possibly flood risk reduction. Also like

river plains, salt marshes are complex environments and their development is the result of interactions

between ecological and physical drivers. Fagherazzi et al. [2012] provide an overview of numerical

models that simulate salt marsh evolution, focusing on survival under sea level rise scenarios. They

distinguish three spatial scales:

1. zero-dimensional (point) models at the smallest scales that simulate local elevation change

and net primary production. Example: Morris et al. [2002];

2. one- (transect) or two- (marsh platform) dimensional models that are often based on

biogeomorphic processes and require considerable computational effort. Example:

Temmerman et al. [2007];

3. landscape scale models that simulate general trends at large spatial scales. Example: Park et

al. [1986].

All these models follow roughly the same computational framework for salt marsh evolution (Figure

66). The deposition of suspended sediments onto the marsh platform is the dominant process that

determines spatial patterns; surface erosion is usually considered negligible due to the low energy

hydrodynamics. Most process-based numerical models also ignore the erosion of the marsh margin

as a result of wave impact, except for Tonelli et al. [2010] who used a numerical model solving the

coupled Boussinesq-nonlinear shallow water equations. Other issues are that even the more advanced

numerical models are hydrostatic, thus not fully capture full three-dimensional hydrodynamics,

consider the vegetation as rigid elements and assume fully turbulent flow whereas the low flow

velocities typical for a marsh might actually be in the viscous regime [Fagherazzi et al., 2012]. The

simulation of aboveground and belowground production of biomass, inorganic sedimentation and soil

consolidation is a feature of numerical models that physical models usually do not have due to the

long timescales, although the necessary parameterisations need to come from dedicated laboratory

or field experiments.



Figure 66. Simplified scheme of the interactions between ecology and morphology in salt marshes. From: Fagherazzi et al. [2012].

The study of Schwarz et al. [2014] is an example of a numerical modelling study of two different salt

marshes that compares the simulated landscape development to remote sensing observations, aiming

to establish a threshold for dominance of either vegetation-induced channel erosion or vegetation-

stabilized channel inheritance.

The model setup was largely similar to that of Temmerman et al. [2007], except for the use of an

ecological module in Delft3D-WAQ instead of Matlab. This vegetation module simulates

spatiotemporal changes in the stem density and -height of Spartina alterniflora. The morphodynamics

were modelled using Delft3D in a 2D depth-averaged mode, using a k-ε model that explicitly accounts

for the influence of rigid cylinders on drag and turbulence. Initial plant establishment is modelled

stochastically and lateral expansion of plants to neighbouring cells is modelled through a diffusion

equation. Like in the model of Van Oorschot et al. [2015], stem density and stem height are

characterized by logistic growth up to a maximum, whereas stem diameter is related to stem height.

Plant mortality is a result of inundation stress and bed shear stress exerted by flow; waves are not

included. The model is forced with a sinusoidal mesotidal tide (1.2 m), with the highest point of the

initial platform 0.2 m below the tidal amplitude, resembling conditions in the Yangtze estuary, China.

The sediment is also representative of the conditions there: D50=80μm; the equilibrium concentration

at the boundary and the sediment transport are determined according to Van Rijn [1993].

Morphological developments are sped up by using a Morfac of 24. Because vegetation is only present

during 8 months per year, a simulation time of one month represents 3 years of real time. The Pearson

correlation coefficient of the bathymetry reached unity within these 3 years, indicating the

establishment of a dynamic equilibrium. A Pearson coefficient of 1 means that the actual bathymetry

can still be changing, but that the changes have become uniform over channels and platform. Thus, it

can also be used as an indicator of self-organisation. The ecological and morphodynamic model



interact every 12 hours. The temporal representation of stress factors (e.g., mean, maximum or 90th

percentile) is not described.

Four scenarios of initial bathymetries were studied (Figure 67) all with the same vegetation

development settings: plain (uniform), shallow dense channels, shallow sparse channels with the same

volume and deep dense channels with a higher volume. When patches start to develop, some bare

areas develop into channels whereas at other bare areas the critical bed shear stress is not exceeded

and patches merge. This pattern is largely the same for all scenarios but differs in magnitude: The

dense shallow channels display some erosion in the channels and on the platform, whereas for the

sparse channels the erosion is more concentrated in the channels. For the deep channel scenario, the

effects are smaller but even more restricted to the channels.

Figure 67. Plan view of the modeling results for the four initial bathymetries used in this study (flat bathymetry (plain), shoal imposed channels with high density (shoal dense channels; Shoal ChD), shoal imposed channels with low density (shoal sparse channels, Shoal ChS), and deep imposed channels with high density (deep dense channels; Deep Ch)). (a) The configuration of the initial plant cover and (b) the plant cover after 3 years is shown as a percentage of the maximum stem density. (c) The morphologic evolution from initial bed level to (d) the bed level after 3 years is shown through the platform elevation in meters. (e) A comparison between the initial and final bed configuration is shown across a long-shore transect, indicated by the black line in b. (f) The sediment movement throughout our simulation is shown through the cumulative change in sedimentation/erosion after 3 years in meters. From Schwarz et al.

The results suggest that channel inheritance is the dominant mechanism if deeply incised channels

already exist before vegetation starts to colonize. This finding is in line with the ‘excess momentum’

concept discussed in Temmerman et al. [2007]. Without inheritance, differences in hydraulic drag

between plant species would become more important but multiple species were not studied. Likewise,

the authors remark that erosive processes will also be affected by the soil cohesiveness and soil

stabilization by plant roots, which were not studied either. Because erosion is limited to wet cells,

bank erosion is underrepresented. The coarseness of the grid (cell size 6m) means that feedbacks are



only resolved down to this scale and effectively leads to larger channels. The absence of waves has an

effect on sediment transport and likely allows the tide to create more intricate patterns that would

otherwise be flattened by waves, whereas a lack of temporal variations in forcing would result in a

steadier spatial pattern.

Due to the above, the model cannot completely reproduce the developments in the field but does

capture the main aspects of channel initiation and inheritance that are important for landscape

evolution. Nevertheless, models like these and the concept of ‘excess momentum’ are of practical use

in wetland rehabilitation or restoration efforts where they can be applied to optimize initial

topography in relation to hydrodynamics, sediment and plant properties to promote the often desired

spatial heterogeneity.



KNOWLEDGE GAPS AND FUTURE DEVELOPMENTS IN NUMERICAL MODELLING OF

BIOGEOMORPHOLOGICAL INTERACTIONS

8.4.1. Organism properties and the importance of diversity

A realistic representation of relevant organism properties such as dimensions, flexibility and buoyancy

is necessary to simulate the effect of organisms on hydrodynamics. For unidirectional flow, many

accepted techniques are available for this, ranging from a simple roughness coefficient, via k-ε

turbulence representations in engineering models, to fully coupled flow-plant bending models. Which

technique is most appropriate for the problem at hand depends on the time- and spatial scale of

interest [Nepf, 2012, Luhar & Nepf, 2013].

For waves, the state of the science is less advanced. Just a few wave models account for the presence

of vegetation and the range of drag coefficients in relation to wave conditions and plant properties

found in the literature is distressingly high. This is not solely a deficit of numerical models: there is no

literature that describes a physical experiment that could be used to fully understand wave-plant

interaction at the patch scale. Such experiments are typically hampered by the large facilities required,

as scaling this interaction is virtually impossible due to the different scaling laws involved [Thomas et

al., 2014].

On the topic of sediment transport in vegetated flows, numerical models are not up to the state of

the art of physical modelling, especially not for coastal environments where waves are involved. There

are numerous accepted formulas for sediment transport on bare beds that can be incorporated in

numerical models, and some [like Van Rijn, 2007a,b, Engelund & Hansen, 1967] perform quite well in

fluvial environments if the hydrodynamics (i.e. reduction of bed shear stress) are simulated well

[Vargas-Luna et al., 2015]. Some effects of vegetation observed in physical experiments, like local

scour around stems, its presence as a filter in the water column or the stabilizing root mat [e.g. Pollen-

Bankhead & Simon 2010] are not yet incorporated in sediment transport formulations in numerical

models. The process of (re)suspension and transport of sediment in the presence of vegetation in

wave-dominated environments is largely unknown and contrary to the common perception of

vegetation preventing erosion, the opposite can occur too [Tinoco & Coco, 2016].

To model landscape development, it is not sufficient to simulate only hydro- and morphodynamic

processes. Organism related processes such as colonization, growth, succession, competition and

mortality also require quantification to simulate vegetation dynamics because landscape

development is very sensitive to the rate of vegetation development [Perucca et al., 2007, Bärenbold

et al., 2016]. Here, numerical models have an advantage over physical models because they can cover

much longer timescales and multiple species, whereas physical modellers are constrained by the

availability of facilities and husbandry demands [Thomas et al., 2014]. We know that these processes

are steered by the physical and chemical environment in which the organisms live. See Figure 68 for

an example of how plants respond to different environmental conditions, and imagine the effects of

different plant morphology on flow and soil properties.



Figure 68. Types of grass meadows under four different management scenarios. From top to bottom: grazing, fertilizing and pesticides; hay and fertilizer, grazing and light fertilizer, hay without fertilizer. From: Wageningen University.

Ecological modellers have done a great deal to quantify these relations, albeit not on a time and spatial

scale that corresponds to that of numerical models for biogeomorphic development. Colonization or

lateral expansion of vegetation patches, for example, typically occur on the scale of decimetres or

meters per year, whereas the spatial resolution of numerical models for landscape development is

usually deca- to hectometres due to computational limits. Sub-grid techniques that allow for high-

resolution bathymetry and roughness on a coarse computational grid [e.g. Volp et al., 2013] may aid

to bridge this gap in the future.

8.4.2. Plant tolerance limits

The tolerance of organisms to environmental conditions is an organism property that deserves special

attention because this property determines whether organisms occur or not. Occurrence has a much

larger effect on hydro- and morphodynamics than properties like size and flexibility [Nepf, 2012],

although the importance of organism properties should not be ignored [Bouma et al., 2013]. Tolerance

limits are difficult to establish however, as they are not only species specific [e.g. Erftemeijer & Lewis,



2006] but they also depend on the combination of several stress factors such as light deprivation and

heat [Yaakub et al., 2013, de Los Santos et al., 2010] and they can change over time due to phenotypic

plasticity [e.g., Maxwell et al., 2014, Peralta et al. 2005]. Establishing coherent sets of tolerance limits

for key species in fluvial and coastal environments is therefore crucial. To model steady state

conditions, existing habitat suitability studies [e.g. Koch 2001, van der Heide et al., 2009] can provide

useful information. Tolerance under extreme conditions during events has been studied less, and is

often not just an organism property but also related to soil properties [Bywater-Reyes et al., 2015,

Bendoni et al., 2016]. The study of Bankhead et al. [2016] is a nice example of a combined numerical

and physical study to establish when conditions for vegetation removal occur.

8.4.3. Combination of soil and (ground)water

The great majority of numerical models have been made to simulate surface hydrodynamics or

groundwater dynamics or soil dynamics; either fluid or solid phase. For complex processes that

determine long-term landscape formation as well as critical changes (failure) during events such as

riverbank and salt marsh cliff erosion, the coupling of the two phases is relevant. Numerical methods

such as the Material Point Method [MPM; e.g. Abe et al., 2014, Tan, 2016] can provide crucial insights

in the behaviour of fluid-solid interfaces.

Groundwater can also be important for riparian vegetation dynamics [Gurnell, 2014], especially if the

groundwater table and soil moisture vary substantially as a result of the hydrologic regime or changing

land use (e.g., dam construction or removal). Examples of both surface- and groundwater models are

rare [e.g. Hooke et al., 2005] but are a logical extension for studies into landscape change.

8.4.4. Upscaling from near field to landscape

Landscape-scale models require simplification of processes to be applicable within reasonable

computation times. At the same time, small-scale processes at the individual plant scale or the patch

scale can be relevant for the development of the landscape. Integration of near field models that solve

the dynamics inside a meadow with larger scale models offers a pathway to better representation of

important processes. Such an approach can be offline, where the detailed model is used as a numerical

flume to derive parameterisations to be used by the large-scale model, or online where a small-scale

model is activated by an event in the large-scale model and feeds back the consequences after the

event. An example of such an application is dune development under sea level rise: the response to

gradually changing conditions is calculated by the large-scale model, whereas dune erosion during

storms –a very different process- is calculated by a dedicated small-scale model. Tools like BMI (Basic

Model Interface; Peckham et al., 2013) offer promising possibilities for robust model integration.



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