i

MORPHOLOGICAL CHANGES IN CHANNELS DUE TO CYCLONE

GENERATED HYDRODYNAMIC SHOCK

BY

MD. WASIF-E-ELAHI

MASTER OF SCIENCE IN WATER RESOURCES DEVELOPMENT

INSTITUTE OF WATER AND FLOOD MANAGEMENT

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

JUNE 2016

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Morphological Changes in Channels due to Cyclone

Generated Hydrodynamic Shock

A thesis by

MD. WASIF-E-ELAHI

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE IN WATER RESOURCES DEVELOPMENT

Institute of Water and Flood Management

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

June 2016

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CANDIDATE’S DECLARATION

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Dedicated to My parents

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ACKNOWLEDGEMENT

In the first place, I would like to thank the Almighty Allah for giving me the ability to complete

this research work. I would like to express my sincere and heartfelt gratitude to my supervisor

Dr. Mohammad Anisul Haque, Professor, IWFM, BUET, Dhaka for his constant guidance,

valuable advice, generous help and constructive discussion to carry out this research. I feel

proud and lucky to work with him. His keen interest in the topic and enthusiastic support for

my effort was a source of inspiration to carry out the study. I also express gratefulness to the

present Director Dr. Mashfiqus Salehin and former Director Dr. Md. Munsur Rahman, IWFM,

BUET, Dhaka, Dr. Rezaur Rahman, Professor, IWFM, BUET, and Malik Fida Abdullah Khan,

M.Sc., Deputy Executive Director (Operation), CEGIS, Dhaka for their comments on thesis

work that helped me a lot to improve the quality of the thesis.

I want to express my sincere gratitude to Dr. Md. Munsur Rahman, Team leader,

DEltas, Vulnerability and Climate Change: Migration and Adaptation (DECCMA) Project and

the modelling team of the project who have helped by providing valuable information in

different stages of my research work.

I would like to extend my thanks to Sumaiya, Tamanna Kabir, Mohiuddin Sakib, Fatin

Nihal and Tariq Omarr, M.Sc. students and PhD candidate at IWFM, BUET, who have helped

in different stages of my research work.

I would like to give thanks to all staff members of IWFM and all my friends for helping

and inspiring me in different ways.

I am very much indebtedness to my heavenly father whose encouragement and support

was a continuous source of inspiration for my higher study.

Finally, I wish to extend my gratitude to my family members for their moral support during my

research work.

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Abstract

River stability and response to changing environmental conditions are highly dependent on local watershed features and exposed environmental condition. During hydrodynamic shock like severe cyclones, stream power increases above normal levels, resulting in dramatic changes in the riverine landscape. In the natural landscape, cyclone generated storm surges can play a major geomorphic role, especially for sediment transport in channels and deposition on floodplains. The geographical location and climatic condition make Bangladesh one of the most cyclone prone countries in the world. For Bangladesh coast, not much information is available on changes in river morphology due to this phenomenon. To fill this research gap - present study aims to develop a semi-analytical model to assess the morphological changes in channels due to hydrodynamic shocks and apply the model for a cyclonic event in Bangladesh coast.

Changes in channel morphology depend on the channel characteristics. In this study channels are classified based on channel conveyance. During cyclone, the morphological changes in channel are mainly controlled by bed shear stress. To develop the semi-analytical model, width depth ratio is used as an indicator of channel morphology. From the Manning’s equation, the relation between channel geometrical shape factor (which is the ratio of channel conveyance and roughness) and channel width depth ratio is developed. Afterward width depth ratio is expressed as a function of channel geometrical shape factor. It is found that conveyance of a channel is directly proportional to the bed shear force. By introducing proportionality constant and assuming that change of channel conveyance due to bed shear force varies linearly, the non-dimensional relation between channel conveyance and bed shear force is established. Later the channel conveyance is replaced by channel geometrical shape factor in the non-dimensional relation. By substituting the width depth ratio with the function of geometrical shape factor in the non-dimensional relation and re-arranging, the semi-analytical model is developed.

Magnitudes of variables in the semi-analytical model are determined using the Delft 3D model simulations for different cyclone scenarios which are termed as hydrodynamic shocks. To determine the coefficients of the semi-analytical model, these variables are used. Delft Dashboard is applied to incorporate the cyclonic condition in the Delft 3D model simulations. Performance of the semi-analytical model is evaluated by comparing the model results with the Delft 3D model simulation. Performance of the model is found to be within ±0.5% to ±5% of error margin.

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Table of Content

Page No.

Certificate of Approval iii

Declaration iv

Acknowledgment vi

Abstract vii

Table of Contents viii

List of Figures xi

List of Tables xiv

Abbreviations xv

List of Symbols xvi

Chapter 1. Introduction

1.1 Brief Background of the Study

1.2 Rationale of the Study

1.3 Objective of the Study

1.4 Outline of the thesis

1

3

4

4

Chapter 2. Literature Review 6

2.1 River Classification and Morphology

2.2 Factors Governing the Morphological Changes of Channel

2.2.1 Response of channel

2.2.2 Change of channel in large scale

2.2.3 Thresholds for morphological change

2.2.4 Change of morphological characteristics during

cyclonic condition

2.3 Cyclone in Bangladesh

2.3.1 General

2.3.2 Reasons of severity of storm surges

2.3.3 Impacts of major cyclone on river morphology along

Bangladesh coast

2.4 Modelling of river morphology and application

2.4.1 Coupling of storm surge and morphology models

2.4.2 Model selection for the study: Delft 3D and Delft

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Dashboard

Chapter 3. Development of Semi-analytical Model 31

3.1 Channel Conveyance

3.2 Bed Shear Force and Change in Channel Morphology

3.3 Development of Semi-Analytical Model

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33

37

Chapter 4. Computation of Coefficients for the Semi-Analytical Model 39

4.1 Application of Numerical Model

4.1.1 Model parameters

4.1.2 Model grids

4.1.3 Model bathymetry

4.1.4 Model boundary conditions

4.1.5 Model validation

4.1.6 Numerical model result of cyclone SIDR

4.2 Channel Classification

4.3 Generating the Scenarios

4.4 Incorporating the Cyclone in Delft 3D

4.5 Computing the Variables for the Semi-Analytical Model

4.5.1 Calculating the cross sectional area and wetted perimeter

4.5.2 Calculation of bed shear force

4.5.3 Generating relation between geometric shape factor and

bed shear force

4.5.4 Computation of coefficients

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Chapter 5. Application of Semi-Analytical Model 57

5.1 Application of Semi-Analytical Model for Different Scenarios

5.2 Application of Semi-Analytical Model for cyclone SIDR

5.3 Sensitivity of Model Results

5.4 Application of the Semi-Analytical Model without the Application

of Delft 3D Model

5.5 Comparison of the Model Results with Measured Cross Section

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Chapter 6. Conclusions and Recommendation 76

6.1 Conclusions

6.2 Limitations of the Model

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6.3 Recommendations for Future Study 77

References 78

Appendix 85

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List of Figures

Figure No. Page No.

Figure 2.1 Channel pattern as a function of channel slope and bankfull

discharge

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Figure 2.2 Independent and dependent variables impact on channel

morphology

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Figure 2.3 Spatial and temporal scales of channel response variables in

alluvial rivers

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Figure 2.4 Work and scale of channel change accomplished for flood

events of different magnitude and duration

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Figure 2.5 Channel change depends on the overlap between frequency

distributions of driving and resisting forces for different

scales of morphologic response

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Figure 2.6 Cyclone tracks along Bangladesh 18

Figure 2.7 Locations of embankment breaching in Polder-32 area 20

Figure 2.8 Comparison of satellite images of Nalian River between year

2008 and 2014

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Figure 2.9 Picture of new narrow channel formation at weak point 23

Figure 2.10 Picture of new narrow channel formation at embankment

cutting point

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Figure 2.11 Breaching of Embankment at Kamarkhola canal 24

Figure 2.12 Newly constructed sluice gate at Kamarkhola canal 25

Figure 4.1 Domain of the large model (a) and locations of the model

validation (b)

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Figure 4.2 Magnitude of bed shear stress at the time of landfall for

cyclone SIDR

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Figure 4.3 Magnitude of flow velocity at the time of landfall for

cyclone SIDR

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Figure 4.4 Resultant erosion/sedimentation at the time of landfall for

cyclone SIDR

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Figure 4.5 Relation between geometric shape factor G and WDR for

different dimensions of channels

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Figure 4.6 Hypothetical tracks of different strengths of cyclones 49

Figure 4.7 A typical channel cross-section 50

Figure 4.8 Variation of bed shear force for cyclones with variable

strengths

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Figure 4.9 Relation between geometrical shape factor and bed shear

force for channel with low conveyance

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Figure 4.10 Relation between geometrical shape factor and bed shear

force for channel with medium conveyance

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Figure 4.11 Relation between geometrical shape factor and bed shear

force for channel with high conveyance

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Figure 4.12 Relation between geometrical shape factor and bed shear

force for channel with very high conveyance

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Figure 4.13 Schematic representation of ranges of coefficient i 55

Figure 4.14 Schematic representation of ranges of coefficient j 55

Figure 4.15 Schematic representation of ranges of coefficient a 56

Figure 4.16 Schematic representation of ranges of coefficient b 56

Figure 5.1 Variation of WDR with time for low conveyance channel

when cyclone condition is HSC

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Figure 5.2 Variation of WDR with time for medium conveyance

channel when cyclone condition is VHSC

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Figure 5.3 Variation of WDR with time for high conveyance channel

when cyclone condition is VHSC

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Figure 5.4 Variation of WDR variations with time for very high

conveyance channel when cyclone condition is VHSC

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Figure 5.5 Temporal variation of measured bed shear force for the

channel where the semi-analytical model is applied

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Figure 5.6 Variation of bed shear stress and flow velocity as a function

of non-dimensional bed shear force

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Figure 5.7 Comparison of model WDR with measurements for VHSC 62

Figure 5.8 Variation of WDR with different values of i for very high

conveyance channel during VHSC

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Figure 5.9 Variation of WDR with different values of j for very high

conveyance channel during VHSC

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Figure 5.10 Variation of WDR with different values of a for very high 64

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conveyance channel during VHSC

Figure 5.11 Variation of WDR with different values of b for very high

conveyance channel during VHSC

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Figure 5.12 Variation of WDR with time after applying modified

coefficients

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Figure 5.13 Time series of measured non-dimensional bed shear force at

the mouth of Baleswar estuary during cyclone SIDR

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Figure 5.14 Variation of WDR with non-dimensional bed shear force at

the mouth of Baleswar estuary.

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Figure 5.15 Comparison of time series of WDR between the model and

the measurements at the Baleswar mouth

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Figure 5.16 Model application when water depth and depth average

velocity are known

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Figure 5.17 Variation of bed shear stress as a function of depth average

velocity

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Figure 5.18 Model application when only velocity of flow is known 70

Figure 5.19 Steps of the model application when no data is available 72

Figure 5.20 Temporal variation of WDR during cyclone SIDR at

Bishkhali mouth

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Figure 5.21 Variation of WDR with bed shear force during cyclone SIDR

at Bishkhali mouth.

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Figure 5.22 Change of planform in Bishkhali estuary due to cyclone

SIDR

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Figure 5.23 Comparison of the semi-analytical model result with the

observed planform

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List of Tables

Table No. Page No.

Table 4.1 Delft 3D morphology model parameters 39

Table 4.2 Reliability of Delft 3D morphology model 42

Table 4.3 Channel classification based on conveyance 46

Table 4.4 Channel properties that are used to generate the scenario of

model runs

47

Table 4.5 Classification of different intensities of cyclone 48

Table 4.6 Computed coefficients values for different channel types 55

Table 4.7 Ranges of coefficients variations for different channel types 55

Table 5.1 Coefficient values of the semi-analytical model 57

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ABBREVIATIONS

IWFM Institute of Water and Flood Management

BWDB Bangladesh Water Development Board

MoE Ministry of Environment

CEGIS Center for Environment and Geographic Information Service

IWM Institute of Water Modelling

WB World Bank

BUET Bangladesh University of Engineering and Technology

BMD Bangladesh Meteorological Department

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LIST OF SYMBOLS

V = Mean velocity of flow (m/s)

R = Hydraulic Radius (m)

S = Slope of channel

Q = Flow discharge (m3/s)

A = Cross-sectional area of channel (m2)

n = Manning's roughness coefficient

K = Conveyance of channel (m3/s)

G = Geometrical shape factor of conveyance

B = Width of the channel (m)

D = Depth of the channel (m)

휏 = Bed shear stress (N/m2)

훾 = Specific weight of water (1000 kg/m3)

P = Wetted perimeter (m)

F = Bed shear force (N)

WDR = Width depth ratio

a,b,i,j = Coefficients

휌 = Density of water (kg/m3)

푓 = Friction factor

H = Water depth (m)

LSC = Low strength cyclone

MSC = Medium strength cyclone

HSC = High strength cyclone

VHSC = Very high strength cyclone

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CHAPTER ONE

INTRODUCTION

1.1 Brief Background of the Study

River morphology deals with the interaction between flowing water in rivers

and their environment. River stability and response to changing environmental

conditions are highly dependent on local watershed features and exposed environmental

condition (Buffington, 2012). At larger spatial and temporal scales, altered

environmental conditions may cause changes in channel properties (Montgomery and

Buffington, 1997) and planform morphology. Possible change in channel type can be

presented in terms of slope, confinement, discharge and sediment supply. In some

cases, this change can be related to the specific process like coastal hydrodynamic

process (Montgomery, 1999). By Leopold and Wolman (1957), the shape and pattern of

a natural channel is governed by the combined effects of climate, rocks and

physiography of the region where the channel is located. Channel width is largely

determined by effective discharge (Biedenharn et al., 2000) which is bankfull discharge.

Changes of channel are controlled by the discharge and sediment load provided by the

drainage basin (Leopold and Wolman, 1957). This change of channel is directly linked

to bed mobility and can be evaluated by comparing the bankfull shield stress to the

critical value for incipient motion of the median grain size (Buffington, 2012).

Tropical storm surge, large floods, landslides and earthquake can produce

significant geomorphic features. In contrast, smaller floods in the Valley and Ridge can

produce such erosional and depositional features that probably require thousands of

years to overcome the effects (Jacobson et al., 1989). During hydrodynamic shock like

severe cyclones, stream power increases above normal levels, resulting in dramatic

changes in the riverine landscape (Gupta, 2000; Terry et al., 2008). In the natural

landscape, cyclone-induced storm surges also play a major geomorphic role, especially

for sediment transport in channels and deposition on floodplains (Gupta, 1988; Terry et

al., 2002; Kostaschuk et al., 2003). Tropical cyclones are one of the most devastating

natural disasters (Mohanty et al., 2014; Pattanayak et al., 2014) globally. Tropical

cyclones (also known as hurricanes or typhoons) can generate extreme floods in parts of

the tropics and subtropics between about 10° and 30° of latitude. Accounts of the

resulting high shear stress and unit stream power, enhanced stream conveyance,

2

sediment transport and storage, and channel forms are now available in nature for a

limited number of streams in Australia, South Asia, and the Caribbean. These extreme

floods generated from tropical cyclones tend to occur in a regular interval of decades

rather than return periods of 50 years or 100 years flood. Such tropical cyclones

generated extreme floods, which occur on the decadal scale, can determine the size and

coarse sediment of many river channels in the hurricane-affected areas. Other high

flows, which are relatively smaller and occur between the storm surge induced large

floods, build spatial morphological features in such channels. The final form of affected

channel, therefore, is a function of three different parameters- sizes and frequencies of

floods, and sediments (Gupta, 2000). Modified channels of this type have been reported

from many areas: northeastern Australia (Wohl, 1992 as cited in Gupta, 2000), India

(Gupta, 1995 as cited in Gupta 2000), and the Greater Antilles group of islands in the

Caribbean (Ahmad et al, 1993 as cited in Gupta, 2000). Channel formation and

preservation depend on the magnitude of flood in arid region like arid central Australia

(Bourke and Pickup, 1999).

The geographical setting of Bangladesh makes the country vulnerable to natural

disasters (MoEF, 2005). This vulnerability is increased more due to its dense population

(Choudhury, 2007). Geographic setting and river morphology contribute to regular

disasters in Bangladesh. Almost three-fourths of Bangladesh border is surrounded by

mountains and hills, along with the funnel-shaped Bay of Bengal in the south. Such

geographic settings have caused of life-giving monsoon rains, but also, make it more

vulnerable to natural disasters. The major disasters those are concerned in Bangladesh

are the occurrences of flood, cyclone and storm surge, flash flood, drought, tornado,

riverbank erosion, and landslide (Hossain, 2008). Among these disasters, the cyclone is

considered as the major and most devastating to the human habitation of this country.

Of the 508 cyclones that have originated in the Bay of Bengal in the last 100 years, 17

percent have hit Bangladesh, amounting to a severe cyclone almost once every three

years. Of these, nearly 53 percent have taken more than five thousand lives

(Khalequzzaman, 1976 as cited in Sharbari, 2012). In the early 1960s for optimizing the

crop production, 37 polders, and 282 sluice gates were constructed by Bangladesh

Water Development Board (BWDB) under the Coastal Embankment Project. Poldered

areas in southwest Bangladesh have lost 1.0–1.5m of elevation, whereas the

neighboring Sundarban mangrove forest has remained comparatively stable (Auerbach

et al., 2015). One major consequence of this elevation loss occurred in 2009 when

3

several polders (e.g. polder 5, 32) were overtopped due to storm surge and breached out

during cyclone AILA. It caused inundation of large areas of land for up to two years

until embankments were repaired. During this period, tide-induced sedimentation rate

was higher than normal rate in newly connected channels. According to Auerbach et al

(2015), newly shaped landscape received tens of centimeters of tidally deposited

sediment, equivalent to decades’ worth of normal sedimentation. Cyclone AILA caused

damage to an already weakened embankment system (due to lack of proper

maintenance and time being) and washed away 1,742km of embankments, creating

regular flooding during high tide for over a year after the cyclone. Due to these reasons

evaluation of morphological change of channel in Bangladesh coast for cyclone induced

hydrodynamic shock is a vital task.

1.2 Rationale of the Study

Development of river morphology in an estuarine environment is a complex

phenomenon. Mechanism of sediment transport is more complex during the

hydrodynamic shock event like cyclone generated storm surge. The Ganges-

Brahmaputra-Meghna (GBM) delta is one of the most dynamic tide-dominated deltas in

the world. The coastal regions of Bangladesh are subject to severe cyclones almost

every year. During cyclone AILA in 2009, a significant change was observed in river

planform in the area of polder 32. Currently many modeling suites like Mike21, Delft-

3D, SOBEK, SMS etc. are available for the simulation of river morphodynamics and

hydrodynamics. These are all numerical models that need expert knowledge and special

setup of computing base to simulate natural phenomena related to river morphology.

As a result, it is not possible to quick assessment of morphological change with limited

information due to hydrodynamic shock generated from cyclone generated storm surge.

A quick assessment of morphological changes due to storm surge generated

hydrodynamic shock is necessary to identify morphologically vulnerable river location

after or before a storm surge. This information will add value to emergency planning

during disaster management. This study is expected to contribute to fill the gap in

scientific knowledge in this particular area.

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1.3 Objectives of the Study

The main objectives of this research are:

1. To identify the driving parameters of physical processes causing changes in

channel morphology.

2. To develop a semi-analytical model to assess morphological changes in

channels due to cyclone generated hydrodynamic shock.

3. To apply the model for a cyclonic event in Bangladesh coast.

Outcome of the study is the semi-analytical model that can be used to compute

morphological changes of rivers/ estuaries due to any cyclonic event (for example storm

surge) with minimum information and relatively simple calculations

1.4 Outline of the thesis

The first chapter of the study gives a brief presentation on the channel

morphodynamics and different hydrodynamic shock events. It emphasizes the exposure

of cyclone generated storm surge as hydrodynamic shock on Bangladesh coast and need

of proper understanding the channel response before and after the hydrodynamic shock.

It also includes the objectives of the current study.

The second chapter consists of the available information and studies that has

been used for this research to achieve the objectives. Literature reviews have been

summarized in this chapter on: (i) River classification and Morphology; (ii) Factors

governing the morphological changes of channel; (iii) Cyclone in Bangladesh and (iv)

Modeling of river morphology and application.

The third chapter describes the semi-analytical model development to assess

morphological changes in channels due to cyclone generated hydrodynamic shock (e.g.

storm surge).

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Chapter four presents the methodology to compute the coefficients of the semi-

analytical model. This chapter also describes the application of the numerical which is

required to generate the required data to compute the model coefficients.

Chapter five describes the application of the semi-analytical model for a wide

range of scenarios. Finally chapter six describes the conclusions of the study. This

chapter also describes the limitation of the semi-analytical model which is developed in

this study. Recommendations are suggested for further refinement of the model.

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CHAPTER TWO

LITERATURE REVIEW

2.0 Introduction

River sedimentation and morphological process are a complex phenomenon in

nature. Morphological changes of the river due to hydrological regime and manmade

intervention is a regular process. The changing of morphological characteristics

depends on the type of the river. Different types of rivers act differently to the changing

boundary conditions and driving parameters like discharge, sediment load etc.

2.1 River Classification and Morphology

Channels can be classified based on several characteristics like cross-sectional

dimension, slope, degree of entrenchment, width to depth ratio, sinuosity and trend and

types of morphological change. Channels are classified in different ways by different

researchers to achieve specific goals. Most developed river classifications based on

channel pattern (i.e., planform geometry) are broadly divided into two approaches: (a)

quantitative relationships (which may be either empirical or theoretical) and (b)

conceptual frameworks (Buffington and Montgomery, 2013). Based on observed data

and experiment result, Leopold and Wolman (1957) classified channels into straight,

meander and braided channel by applying quantitative approach. Leopold and Wolman

(1957) developed a threshold between meandering and braided rivers (specified in

Figure 2.1). The changes in channel pattern were presented as a function of discharge

and channel slope. Several studies (Lane, 1957 as cited in Buffington and Montgomery,

2013; Leopold and Wolman, 1957) also specified that grain size, sediment load,

riparian vegetation, channel roughness, width and depth affect the channel morphology.

Different patterns of rivers are specified by applying conceptual framework in Schumm

(1985). Based on the nature of the materials through which a river flows, stream

channels are classified into bedrock, semi-controlled and alluvial. Behaviors of different

types of channels vary due to exposed environmental condition. Alluvial channels have

the most varying patterns and shifting nature due to alluvium characteristics. Alluvium

is eroded, transported and deposited with the change of sediment load and water

discharge.

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Figure 2.1: Channel pattern (meandering, straight, braided) as a function of channel

slope and bankfull discharge (Buffington and Montgomery, 2013).

Brice et al. (1978 as cited in Schumm, 1985) recognized three basic types of alluvial

channels that are characterized by degrees of sinuosity, braiding and anabranching.

There were 11 sub-classes in quantitative classifications and 16 sub-classes in

qualitative classifications. Anatomising channels are unique from the anabranched

channels as the individual branches of the channel can be meandering, straight or

braided. From the laboratory study, Schumm and Khan (1972) represented straight,

meandering and braided in terms of sinuosity versus valley slope. Schumm (1977)

proposed a more useful approach to classify channel type from straight, through

meandering to braided channels with no abrupt breaks in between. While classifying the

channel type, there is a range of planform patterns together with the use of an

examination of the geomorphological features displayed by the channel. A generalized

relationship between sediment load, channel stability and channel form was presented

in Schumm (1977) .

According to Leopold and Wolman (1957), channel cross-section and pattern

are controlled by the discharge and sediment load provided by the drainage basin. They

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showed the interaction of the several variables in channel shape from the observed

characteristics of the channel. From their observation, channel width is a function of

bankfull discharge, in combination with the characteristic resistance of bed and bank to

scour. Bed shear varies with the change of channel width. Larger width of channel

increases the shear on the bed at the expense of that on the bank which is reverse for

narrow width. During the high flow of discharge, width adjustment can take place

rapidly and with the erosion or deposition of relatively small volumes of debris, a

relative stable width at high flow is a primary adjustment. The inter-adjustments

between channel depth, flow velocity, slope and roughness tend to accommodate the

further stability of channel. Channel roughness is determined by the particle size which

is an independent factor related to drainage basin. Roughness is also a function of

characteristics of bed configuration in channels carrying fine materials. By Leopold and

Wolman (1957), a particular slope is associated with the roughness where roughness is

independently determined as well as discharge and sediment load. At the width

determined by the discharge, flow velocity and channel depth must be adjusted to

satisfy a quasi-equilibrium state in accord with the particular slope (Langbein and

Leopold, 1964). When roughness also is variable, depending on the changing bed

configuration, then a number of combinations of velocity, depth and slope will satisfy

equilibrium. These adjustments of several variables tending toward the establishment of

quasi-equilibrium in river channels drive to the different channel patterns observed in

nature. Leopold and Wolman (1957) separated meandering and braided rivers

depending on bankfull discharge and slope of the channel (Figure 2.1). It can be seen

that for a certain bankfull discharge river planform changes from meandering to braided

with increase in longitudinal slope of the channel. Against the complex range of driving

variables and boundary conditions for controlling the channel form, only two

parameters (slope and bankfull discharge) were considered to quantify the geomorphic

threshold between meandering and braided. But there is not an individual threshold that

actually exists.

From the above discussion, it is evident that discharge affects morphological

features heavily. For the current study, by applying quantitative approach, channels are

classified based on the conveyance capacity of the channel derived from the Manning's

equation (George and Schneider, 1989). Detail steps applied for channel classifications

are described in Chapter Four.

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2.2 Factors Governing the Morphological Changes of Channel

There are many hydrological and morphological factors which can initiate the

morphological change of a channel. Channel accommodates these changes by

adjustment of its own properties like grain-size, width-depth, gradient etc ( Langbein

and Leopold, 1964). These adjustments may take short time (for example few minutes )

or long time (for example a century) depending on the initiating event (Buffington,

2012). Hydrological characteristics are important factor to control the river

morphological changes. During hydrodynamic shock like a cyclone, the change of river

planform depends on several hydrological factors like drainage network, sediment load,

upstream discharge etc.

2.2.1 Response of channel

Rivers are opened to changing environmental conditions over multiple spatial

and temporal scales. Response of the river is regulated to varying degrees by the

imposed environmental conditions and human activity. River morphology is controlled

by topography (valley slope and channel confinement), discharge (magnitude,

frequency and duration of runoff events), sediment supply (volume, capacity and

frequency of sediment delivery) , vegetation (bank strength, roughness) and in-channel

wood debris. According to Hogan and Luzi (2010), factors controlling channel

morphology are divided into independent variables (that are imposed on the watershed)

and dependent variables ( that adjust to the imposed conditions). Dependent variables

like sediment supply, discharge and vegetation are depending on the independent

variables like the geologic, climatic and human activities (Montgomery and Buffington,

1993; Buffington et al., 2003, as cited in Hogan and Luzi, 2010). The relation between

independent and dependent variables is specified in Figure 2.2. Channel morphology is

the result of the combined influence of dependent and independent landscape variables.

The channel responds to changes in these variables by adjustments in one or many of

the dependent channel variables (Figure 2.2).

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Figure 2.2: Independent and dependent variables impact on channel

morphology. (Hogan and Luzi, 2010)

River stability and response to changing environmental conditions are highly

dependent on local context (e.g. channel type, the nature of imposed sediment,

hydrologic and vegetation regimes. imposed anthropogenic constraints, and the legacy

of past natural and anthropogenic disturbances). Rivers can show a broad range of

responses to changing inputs of water, sediment, and vegetation over human time

scales. Channel response may range from small- scale adjustment of channel

characteristics (grain size, width, depth) to large-scale alteration of reach morphology

and planform pattern.

Geology Climate Human

Frequency, volume and caliber of

sediment

Frequency, volume and duration of

streamflow

Riparian vegetation: bank stability and local

flow hydraulics, in channel large woody

debris (orientation and position)

Sediment supply Stream discharge Vegetation

Width, depth, bed slope, grain size, bedforms, sinuosity, scour depth

Independent Landscape Variables

Dependent Landscape Variables

Dependent Channel

Variables

11

Figure 2.3: Spatial and temporal scales of channel response variables in alluvial rivers

(Partly after Knighton, 1998, as cited in Buffington, 2012).

From Figure 2.3, it is evident that the width and depth is the common part of

grain size, bedforms and stream gradient. Changes in any part of channel response

variables have impact on the width and depth of the channel. According to Buffington

(2012), successive, overlapping, spatial and temporal scales of morphological response

in alluvial channels include:

(1) Grain-scale adjustment, comprising:

a) Local changes in grain size, packing, protrusion, and friction angle;

b) Development of micro-grain forms (e.g., particle clusters, stone cells)

c) Formation of textural patches (i.e., grain-size facies).

(2) Bedforms adjustment: Changes in the type, size, and frequency of bed topography,

ranging from micro-bed forms (e.g., ripples, bedload sheets) to macro-bed forms or

channel units (individual bar, pool, step, and riffle topography).

(3) Reformed channel geometry (e.g., changes in local cross-sectional width, depth, and

downstream variation of those features).

(4) Reformed stream gradient due to reach-scale aggradation/incision and changes in

channel sinuosity. Here, stream gradient is distinguished from valley gradient, which is

not adjustable in the short term.

12

Figure 2.4: Work and scale of channel change accomplished for flood events of

different magnitude and duration (Costa and O’Connor, 1995 as cited in Buffington,

2012). Total work (shaded area) is identical to the events, but the scale of channel

change is greater for the high-magnitude event.

2.2.2 Change of channel in large scale

Larger scales of channel response reflect the cumulative action of smaller-scale

processes, particularly sediment transport of bed and bank materials. Hence, a

progression of successive scales of response can be projected, with the grain-size

adjustment being the first order response (Figure 2.3). Furthermore, because alluvial

rivers show mutually adjusting channel characteristics, changes in any one parameter

can influence all of the others.

The magnitude of channel change that occurs for a disturbance depends on the

amount of work accomplished by the event [flood magnitude times duration (Wolman

and Miller, 1960)] and the time needed for a given scale of response to occur. Wolman

and Miller’s (1960) classic magnitude–frequency argument emphasizes the

effectiveness of frequent, moderate-sized events in accomplishing geomorphic work

over the long term, but large-scale changes in morphology require large events (Figure

2.4). Similarly, different temporal scales of disturbances (seasonal to centennial) will

exhibit characteristic scales of response. Seasonal changes are frequent, typically small-

magnitude events that will lead to similarly small degrees of channel change [e.g., bed

loosening and changes in grain-size structure and texture as seasonal floods begin;

(Milhous, 1973, as cited in Buffington, 2012)], while annual peak floods are typically

moderate-sized events that lead to moderate scales of channel change (e.g., altered

cross-sectional widths and depths). Over decadal scales, rare infrequent events (e.g.,

13

50–100-year floods or debris flows) may cause significant channel change followed by

a period of relaxation from the disturbance (recovery or attainment of some new

equilibrium state; Bull, 1991, Simon and Rinaldi, 2006 as cited in Buffington, 2012).

From the above, it appears that the scale of channel change depends on the event

size and frequency. Total change of channel is dependent on the capacity of work

accomplishment by the event. In this study, time lengths of the cyclonic events are

considered from the historical cyclone events of Bangladesh coast.

2.2.3 Thresholds for morphological change

Geomorphic systems are generally nonlinear and depending largely on their

threshold dominated nature (Phillips, 2006). Geomorphic thresholds can be defined as

the condition at which there is a significant landform change. These thresholds are

classified into intrinsic (Changes will take place without changing the external variable)

and extrinsic (Response of a system to external influences occurs at) thresholds

(Schumm, 1979). Rivers are subjected to thresholds that define significant changes in

processes and morphology and distinguish typical riverine landscapes and habitats.

These thresholds are set by the conditions that govern river channel process and form,

amongst which the most important factors are the flow regime, the quantity and caliber

of sediment delivered to the channel, and the topographic setting (which determines the

gradient of the channel) (Church, 2002). These factors control the sediment transport

regime and the character of alluvial deposits along the channel.

Changes of channel occur systematically along the drainage system as flow,

gradient and sediment character change. So a characteristic sequence of morphological

and habitat types are found in channel. The sequence is closely related to stream

capability to move sediment and with bank stability. The riverine landscape is affected

seasonally by flow thresholds and human actions frequently dictate the character of the

riverine landscape. Human activity can accelerate thresholds crossing which changes

these features significantly. Streamflow determines the regime of a river channel and

since runoff is highly correlated with drainage basin area, river channel regime varies

systematically throughout a drainage basin (Leopold, 1994 as cited in Church, 2002).

Stream flow varies continuously in time according to recent weather and seasonal flow

history, whereas channel morphology remains relatively fixed in the short-term.

Varying flows moving through fixed channel geometry create additional thresholds of

temporal significance.

14

Figure 2.5: Channel change depends on the overlap between frequency

distributions of driving and resisting forces for different scales of morphologic response

(Buffington, 2012).

Morphological changes depend not only on exposed conditions but also on previous

historical events. Most geomorphic processes display thresholds for occurrence;

channel response will depend on the probability of a given disturbance exceeding the

response threshold, the magnitude of which also varies with channel type. Hence, the

likelihood of a given channel change will depend on the degree to which the probability

distributions of driving environmental conditions (changes in discharge, sediment

supply, vegetation) overlap with the probability distributions of process thresholds that

lead to changes in channel characteristics (i.e., overlap of driving versus resisting forces

as shown in Figure 2.5).

From the above discussion, it is evident that every morphological parameter of

alluvial river plays an important role in morphological change. However, it always

depends on the flow regime, magnitude, frequency of the event, threshold values and

bed mobility especially bed shear stress of the particular channel.

2.2.4 Change of morphological characteristics during cyclonic condition

Tropical cyclones generate extreme floods and storm surges in parts of the

tropics and subtropics between about 10° and 30° of latitude. Accounts of the resulting

high shear stress and unit stream power, enhanced stream conveyance, sediment

transport and storage and channel forms are available for a limited number of streams in

15

Australia, South Asia and the Caribbean (Gupta, 2000). These events tend to occur at an

interval of decades, rather than as 50 year or 100 year floods. An important feature of

hydrological behavior during tropical cyclones – when rivers begin to rise soon after

heavy rainfall starts, the water becomes more turbid at the same time. This is because

during rising stage of a storm hydrograph, the sediment concentration carried by a river

generally increases. In addition, powerful cyclone-induced floods are among the few

occasions when coarse bedload sediments are set in motion and transported

downstream. Exceptional amounts of suspended sediment and bedload sediment

transport reflect the ability of cyclone floods to erode and reshape various features in

the fluvial landscape (Terry, 2007). Measurement of sediment transport during a

tropical cyclone is limited due to logistical difficulties in collecting sample overbank

flows and within-channel sediment movement during extreme flood conditions.

The concentration of suspended particles varies considerably within a river’s

cross-section, depending on the erodibility of the riverbed and floodplain, the shear

stress of the flow and the height above the channel bed. At any individual study site, the

ratio of the supply of fine sediment to the total suspended load of the river will fluctuate

over the duration of a flood event, depending on bank failure, erosion patterns in the

watershed and many other factors. This can give relationships between suspended

sediments and river discharge that are hysteretic in form. It means that the peak in

suspended sediments may either precede or lag the peak in water discharge. An

investigation in the Rewa River in Fiji have been able to provide some information on

suspended sediment transport during TC Joni and TC Kina as part of an environmental

assessment of the Rewa basin by a private consulting company (NSR Environmental

Consultants, 1994 as cited in Kostaschuk et al. 2003). A total of 12 rising-stage water

samples were collected from TC Joni and 13 from TC Kina. Laboratory analysis of the

particle grain sizes showed that the samples comprised both fine materials, sometimes

called the wash load and suspended riverbed sands. The sand fractions within the

samples reflect the large shear stresses generated in the river flow during the floods

(Kostaschuk et al. 2003).The highest sediment concentration of 950 g/L was observed

early in the flood event on 1 January 1993. Later on during the main period of flood, the

samples had much lower sediment concentration. This probably reflects exhaustion of

sediment supply from channel and catchment sources. The suspended sediment

concentrations measured in the Rewa River during these tropical cyclones are some of

the highest ever recorded during river floods, in both tropical and temperate regimes

16

(Kostaschuk et al. 2003). During TC Kina, the highest clear-water boundary shear stress

of 61 N/m2 was observed for 8809 m3/s instantaneous discharge. Several studies (e.g.

Xu, 1999 as cited in Kostaschuk et al. 2003) have shown that hyper-concentrated flows

can cause extensive erosion of river beds because of enhanced boundary shear stress in

the sediment-water mixture. Sediment transport only starts when the sufficient force

(lift and drag) is provided by bed shear stress to exceed the weight force (gravity) and

any cohesive effects acting to stabilize the bed sediment ( Allen, 1985; Nielsen, 1992,

as cited in Hughes et al., 2010). This is usually expressed in terms of exceeding the

critical bed shear stress required for sediment entrainment (e.g. Sleath, Soulsby, as

cited in Hughes et al., 2010). The basic work on sediment entrainment and critical bed

shear stress can be found in Shields (1936 as cited in Buffington, 2012).

From above, it can be concluded that, during cyclonic condition, a large amount

of sediment is transported by flow in different phases of flood and storm surge event

which caused morphological changes of the channel. Bed shear stress and flow velocity

increase due to exposed cyclonic conditions which play a vital role in sediment

transport. In this study, bed shear stress is counted as the driving parameter for the

morphological changes of the channel.

2.3 Cyclone in Bangladesh

As the cyclone (Ghurnijhor-local name) is a common name in Bangladesh for its

destructive evidence in past. In this study, only cyclone generated hydrodynamic

shocks are considered to compute the changes in channel morphology. From the

historical properties of the past cyclones, duration of the hydrodynamic shock events

and their strengths are assumed in several classes which is described in detail in

chapter four.

2.3.1 General

Bangladesh is recognized as a global hotspot for tropical cyclones by UNDP

(UNDP 2004, as cited in Adams et al., 2011). Nearly every year, cyclones hit the

country's coastal regions in the early summer (April-May) or late rainy season

(October- November). Between 1877 and 1995, Bangladesh was hit by 154 cyclones,

including 43 severe cyclonic storms, 43 cyclonic storms, and 68 tropical depressions

(IMD 2010, as cited in Adams et al., 2011). On average, a severe cyclone strikes the

country every three years (GOB 2009, as cited in Adams et al., 2011). A tropical

cyclone forming in the Bay of Bengal has a lifetime of one week or longer. The height

17

of the surges is limited as high as 10 meters in the coast. When propagating into the

shallower inland coastal areas, the heights of these waves are further increased due to

shallow water effect. The frequency of a wave (surge plus tide) with a height of about

10 m is approximately once per 20 years. A storm surge of approximately once in 5

years has a height of about 7 m [surge plus tide (Khan, 1995)].

Historical cyclone tracks across Bangladesh are specified in Figure 2.6.

Since 1970, Bangladesh has experienced 36 cyclonic storms resulting in over 450,000

deaths and immeasurable economic losses. Although the polderization of the whole area

has been done since 1960’s but the frequency and high intensity cyclonic storm surge is

making this embankment vulnerable day by day. Detail description of economic loss

and devastation history can be found in World Bank report (Adams et al., 2011).

Figure 2.6: Cyclone tracks along Bangladesh

(Source:

http://www.islandnet.com/~see/weather/events/sigcyclonebangladesh.htm)

18

2.3.2 Reasons of severity of storm surges

The main reason of devastation due to cyclone is the cyclone generated storm

surge. The severity of storm surge is very high in Bangladesh coast due to several

factors.

Bangladesh is facing about 40% of the world’s total impact from storm surges

(Murty and El-Sabh 1992). The reasons for this significant impact include the

recurvature of tropical cyclones in the Bay of Bengal; the wide, shallow continental

shelf, especially in the eastern part of the country; the high tidal range; the triangular

shape at the head of the Bay of Bengal, which helps to funnel sea water pushed by the

wind toward the coast, causing further surge amplification; the nearly sea-level

geography of the coastal land; and the high-density population and coastal protection

system. Detail of these factors can be found in Ali (1999) and Dasgupta et al. (2014).

According to Ali (1999), the Meghna estuary region experiences the most surge

amplifications.

In this study, these local modification factors like tidal amplification, the impact

of continental shape, island effect, track properties etc. are not considered. For the

simplified calculation, all the hypothetical cyclone tracks are assumed to make their

landfall in 90 degree angle to the hypothetical channels. However, all these factors are

included in the real case simulation of cyclone SIDR.

2.3.3 Impacts of major cyclones on river morphology along Bangladesh coast

Major cyclones made their impacts in many ways in Bangladesh. Economic loss

and death toll are the important effects due to the cyclone which are noticed at past (Ali,

1999). These events had also impacts on planform of the coast, rivers and estuaries

which are either not noticed or neglected compared to other losses. In this section,

evidences of morphological changes in the affected area due to major cyclone are

described.

The southwest coastal region of Bangladesh has unique brackish water

ecosystem consists of tide dominated rivers, estuaries, streams and water-filled

depressions. In addition, there are 123 polders in the coastal area of Bangladesh

constructed in early 60’s to protect the land from tidal flooding and salinity intrusion.

From several studies (For e.g. Allison, 1998, Goodbred and Kuehl, 1998, Rogers et al.,

2013; as cited in Auerbach et al., 2015), it can be stated that protected (enclosed by

polders) area in southwest Bangladesh, have lost 1.0–1.5m of elevation, whereas the

19

neighboring Sundarban mangrove forest (not poldered) has remained comparatively

stable. By Auerbach et al. (2015), this elevation loss occurred due to interruption of

sedimentation inside the poldered area, combined with accelerated compaction, removal

of forest biomass, and a regionally increased tidal range. One example of this elevation

loss was observed in 2009 when the embankments of several large poldered areas

breached during cyclone AILA, leaving large areas of land tidally inundated for upto

two years until embankments were repaired. Despite sustained human suffering during

this time (United Nations, 2010, Humanity Watch, 2010; as cited in Auerbach et al.,

2015), the newly reconnected landscape received tens of centimeters of tidally

deposited sediment, equivalent to decades’ worth of normal sedimentation.

According to Auerbach et al. (2015), the most affected area due to cyclone

AILA is polder 32 in Dacope, where cyclone AILA caused five major breaches in the

embankments. The polder 32 is situated in Dacope Upazila of Khulna District near

Sundarban. The polder is surrounded by Sibsha and Dhaki River to the west and North,

Chunkuri, Bhadra and Sutarkhali River to the east and south. Topographically, this area

is flat and developed by sedimentation process of the three mighty rivers (Ganages,

Brahmaputra and Meghna River) of the country. The polder area is crisscrossed by a

large number of creeks. The total area is basically flat with the central part a bit higher

than the surrounding land. Locations of embankment breaching (denoted as EB in

Figure 2.7) in Polder 32 are shown in Figure 2.7.

20

Figure 2.7: Locations of embankment breaching in Polder-32 area

Nalian River

Shibsa River

Shuterkhali River

Sundarban

Polder-32

Dhaki River

Direction of Storm

surge

21

Figure 2.8: Comparison of satellite images of Nalian River between year 2008 and 2014

(Kabir, 2014)

Comparison between the channel shape before (2008) and after cyclone AILA

(2014) is shown in Figure 2.8. It is found that there are some locations where

embankment is breached due to the high velocity of water. In some breached locations,

22

channel widths are widened due to conccurent flooding due to tide (Figure 2.12). At

some specific points, new channels are formed due to embankment breaching which is

later prevented by constructing closure in the embankment.

There are several reasons for the embankment breaching. Due to increased

demand for shrimp farming in the region, people cut the embankments at several places

and made some narrow channels to conveysalt water for shrimp farms. Shrimp farming

was the dominating practices at the polder 32. In many places of the embankment,

people inserted pipes to avail salt water into the area and constructed some narrow

channel to carry the salt water into the shrimp farms. These activities created some

weak points at the embankment. When storm surge with high intensity hit these weak

points of the embankment, these points started to breach and man-made canals re-

formed into a new shape. It is widened and looks like anatural canal. The channel was

5ft to 6ft wide before breaching. As the polder was opened for a long period of time,

this canal became wide under regular tidal action. As the area of polder 32 was

dominated by shrimp farming, there were many places where polder was cut for salt

water intrusion. The interventions over interventions make the natural disaster more

disastrous. There are lots of places over the polder 32 where embankment breached in

such a way where six new sluice gates are constructing by BWDB.

23

Figure 2.9: Picture of new narrow channel formation at weak point (Kabir,

2014)

Polder-

24

Figure 2.10: Picture of new narrow channel formation at embankment cutting point

(Kabir, 2014)

Figure 2.11: Breaching of Embankment at Kamarkhola canal (Kabir, 2014)

25

Figure 2.12: Newly constructed sluice gate at Kamarkhola canal (Kabir, 2014)

When storm surge of cyclone AILA propagated through the Dhaki river, the

Gulbonia canal was eroded at the embankment breaching point and at the connection

point of Nalian river. Location of the breaching (EB-2) is shown in Figure 2.7. This

canal widened at whole length of the canal but the canal bed became higher due to

sedimentation in the canal and deposition of mud from the canal bank and

breached embankment. Later the closure of embankment was made at approximately 1

km inside. The Gulbonia canal, a small channel created from Dhaki river after

travelling 2 km is connected with the Nalian river. At this connection point, the

erosion of canal bank occurred. Later BWDB constructed a new embankment at both

side of the Nalian River. Thus, the connection of Gulbonia canal with the Nalian river

was lost. More detail of the morphological process and embankment breaching of

polder 32 can be found in Auerbach et al. (2015). Several new channels are formed and

widened in the polder 32 area. Cyclone AILA caused damage to an already weaken

embankment system and washed away 1,742km of embankments creating recurring

flooding during high tide for over a year after the cyclone.

From the above discussion, it is evident that cyclones have the ability to change

planform. Due to the impact of storm surge cause by cyclone AILA, several channels

were widened and new channels were formed.

26

2.4 Modeling of River Morphology and Application

River sedimentation and morphological processes are among the most complex

and least understood phenomena in nature. There are many modeling suite like Delft3D,

CMS-M2D, Q3DCAM, SMS are available which can simulate coastal flows and

morphological changes due to storm surge, wave or tsunami. Modeling the effects of

these extreme events is important for the design of coastal structures, sediment

management, shoreline protection, maintenance of navigation channel, etc. The

numerical models can be used in a cost-effective way comparing to physical model

study in order to refine and optimize designs of coastal structures. These kinds of

modeling approaches are being used in large-scaleprotection project like the Lousiana

coastal protection and restoration and the Mississippi Gulf coast defense (Kuiry et al.,

2014). In reach scale study, these numerical models are also frequently used by

researchers and planners to compute shoreline change, cross-shore sediment transport,

long time change of morphodynamic processes etc (e.g. Ding et al., 2015). In the

context of Bangladesh, numerical modeling approaches are regularly practiced at

various levels (e.g. Alam and Matin, 2013, Haque et al., 2015, Elahi et al., 2015).

2.4.1 Coupling of storm surge and morphology models

Several studies were done on the modeling of storm surge impact on channel

morphology in the past (e.g. Stockdon et al., 2007; Kuiry et al., 2014; Ding et al., 2015,

Sánchez-Arcilla et al., 2014). Different modeling approaches were applied to evaluate

the impact depending on the purpose.

In Stockdon et al (2007), a sequential modeling approach was applied to

quantitatively assess the predictive capabilities of the storm-impact scale model to

calculate the coastal response to the hurricane. The storm-impact scaling model

(Sallenger, 2000 as cited in Stockdon et al, 2007) was used to compute the

morphological changes like shoreline and beach volume change. For this computation,

the required data like water table were taken from the result of different models. Storm

surge levels and astronomical tides were calculated using the FLOW module of Delft-

3D. The near shore wave fields for hurricanes were modeled using Simulating Waves

Nearshore (SWAN) (Booji et al., 1999 as cited in Stockdon et al., 2007). Beach

morphology and coastal changes were extracted from digital elevation models (DEMs).

By applying all the model results in the storm-impact scaling model, the morphological

27

changes were presented in swash, collision, overwash and inundation zone. Finally, the

calculated morphological changes were compared with the observed that showed the

accuracy of 55.4%. In the study, cumulative shoreline change, beach volume, and slope

change were presented as the morphological response to storm surge.

In Ding et al. (2015), modeling of morphological changes due to three typhoons

of 2008 in the Danshui river estuary was carried out by applying an integrated coastal

process model named CCHE2D-Coast (Ding et al., 2013a as cited in Ding et al., 2015).

This model is capable of simulating multi-scale hydrodynamic and morphodynamic

processes of free-surface water flows such as river flows, tidal currents and waves,

storm surges induced by tropical cyclones, sediment transport, and morphological

changes. It systematically integrates four major sub-models for simulating deformations

and transformations of irregular/multi-directional waves, tropical cyclonic barometric

pressure and wind fields along storm tracks, tidal and wave induced currents and

morphological changes. From the model result, simulated water surface elevation,

significant wave height and flow velocity vector were compared with the measured data

during typhoons from gauge station for validation. Snapshots containing velocity

vector, water level and significant wave height for three typhoons were presented. To

represent the morphological changes, simulated bed level were shown on a map as

contour line and compared to the measured bathymetric survey of the study area. In the

study, sediment boundary conditions were not specified like sediment concentration or

flux variation during the typhoons.

A numerical simulation methodology was developed and implemented to

evaluate and assess engineering design solutions for storm surge damage reduction

along the south shore of Long Island, New York, USA by Cañizares and Irish (2008).

This simulation methodology was applied to understand the interaction between barrier

island morphodynamics and nearshore and bay storm hydrodynamics induced by wind

surge and waves at a regional scale. The Delft-3D was used to simulate nearshore and

bay stormwater levels and barrier island morphodynamics, where the storm profile

model SBEACH(Larson and Kraus, 1989 as cited in Cañizares and Irish, 2008)was

employed to predict the barrier island topography used in Delft-3D (Cañizares et al.,

2005 as cited in Cañizares and Irish, 2008). The Delft3D model configuration used in

this study was not able to capture the morphodynamic response of the barrier island

during the wave runup and overtopping conditions which occur as storm waters rise

prior to inundating the barrier island. Therefore, the SBEACH model was applied to

28

compute pre-inundation dune lowering along the study area. The nearshore and bay

hydrodynamic model are dynamically coupled with the wave and morphological

models developed using the general Delft-3Dmodeling system. Meteorological input

forcing for the offshore and nearshore hydrodynamic and wave models included high-

resolution wind and barometric pressure fields were developed by using a Planetary

Boundary Layer model (Thompson and Cardone, 1996 as cited in Cañizares and Irish,

2008). Offshore tidal boundary conditions were taken from the ADCIRC database

(Mukai et al., 2002 as cited in Cañizares and Irish, 2008). At the end, simulated

topography and water level during the storm were compared with the observed data.

Bottom friction and sediment parameters were appropriately adjusted and empirical

calibrations were performed for the pre-conditioning the dune lowering calculation.

Therefore, developed modeling strategy in the study was robust enough to apply in any

sandy coastal region with a high confidence.

A 2D/3D hydrodynamic and sediment transport model for the Yangtze Estuary

of China was developed by Hu et al. (2009). The main goal of the study was to develop

a basic tool for estuary management and assessing the impact of human interventions

on the estuary. Different modules of Delft-3D like Flow, Wave, Wind and Sediment

were used to set up of the model. After a series of model verifications with observed

data like water level, sediment concentration, vertical salinity distribution and flow

direction, the model was applied for evaluating the storm surge effect and

morphological change of estuary. Simulated wind field, wind speed, and direction,

significant wave height and direction were compared with the respective observed

values. By applying the model setup, morphological change of Jiuduansha Shoal was

assessed for the different scenarios of sediment load which showed a hypothetically

correct result.

Comparison of different numerical coastal models can be found in Ding and

Wang (2008). It specified a brief review of recent developments of integrated

coastal/estuarine models for simulations of coastal and estuarine morphological

processes and applications to coastal flood management and erosion protection. It

showed the advancement of the integrated coastal models to simulate coupled coastal

hydrodynamic and morphodynamic processes by taking into account the combined

effects of astronomical tides, waves, winds, river flows, and their complicated

interactions with beach erosion, sediment transport and morphological changes in

coastal and estuarine waters.

29

From the above discussion, it can be concluded that sediment boundary

conditions are not clearly specified in most of the studies due to lack of measured data

during the cyclones. Sediment load can come from various sources like land erosion,

floodplain etc which is very difficult to include in the simulation due to lack of

quantitative data. Though, such kind of sediment load has a significant impact on the

evolution of channel bed. As a result, it always adds more errors and uncertainty in the

morphodynamic simulation results. Though modeling of morphodynamics has

limitations, it is capable to capture realistic features and successfully used in many

research works.

2.4.2 Model selection for the study: Delft 3D and Delft Dashboard

The Delft-3D is open source (http://oss.deltares.nl/web/opendelft3d) which is

well verified and widely applied in different parts of the world. It has several modules

like flow, salinity, temperature, sediments, pollutants and tracers. All these modules can

be applied in coupled way in Delft-3D and physical processes like wind, wave, and

secondary flow can be included in the computation. It can also incorporate the man-

made impact (like Dredging and dumping) in the simulation.

The FLOW module solves the depth-averaged or 3D shallow water equations on

a rectilinear or curvilinear grid. In the WAVE module, the wave transformation is

computed by the third-generation wave model SWAN (Booij et al., as cited in Trouw et

al., 2012). It includes wave propagation, generation by the wind, non-linear wave-wave

interaction, and dissipation. The WAVE and FLOW modules can be coupled online at

regular interval to account for the effects of waves on the flow and to provide flow

boundary conditions for the wave transformation. Sediment transport in combined

waves and currents is computed with an advection-diffusion equation and morphology

can be boosted up with a morphological acceleration factor (MORFAC). More details

about the Delft3D model can be found in Lesser (2009).

30

As a morphology model, Delft-3D is used successfully in several studies (e.g.

Elias et al., 2006; Cañizares and Irish, 2008;Alam and Matin, 2013, Hu et al., 2009,

Elahi et al., 2015). Delft Dashboard is frequently used by researchers and planners due

to its easy operational interface and fast simulation time. Applications of Delft

Dashboard can be found in Condon et al., (2013), Laknath et al.,(2014), and Rahman et

al, (2015). In this study Delft-3D and DDB is used to evaluate the morphological

change due to cyclone-induced storm surge.

31

CHAPTER THREE

DEVELOPMENT OF SEMI-ANALYTICAL MODEL

3.0 Introduction

This chapter describes the semi-analytical model which is developed to compute

changes in channel morphology due to change in bed shear force. The bed shear force is

considered as a measure of different hydrodynamic scenarios, for example,

hydrodynamic shock due to cyclone generated storm surge. In subsequent sections of

this chapter, theoretical development of the semi-analytical model is described.

3.1 Channel Conveyance

Morphological changes of channel may take place in various ways like the

changes in channel slope, channel width-depth ratio, planform etc. All the changes of

the channel morphology cumulatively affect the conveyance capacity of the channel.

The channel conveyance represents the carrying capacity of a channel based on its

geometry and roughness characteristics and independent of the channel slope. During

cyclonic event, channel morphology gets affected due to cyclone generated storm surge.

During the passage of flood water in a channel due to storm surge, a very high bed

shear stress is generated at the channel bottom which is manifold larger than the usual

bed shear during normal flow condition. As a result, conveyance capacity of the

channel changes rapidly and the channel attains a new morphological equilibrium.

From Manning’s equation (George and Schneider, 1989),

푉 = 푅 푆 ……….

(3.1)

Where, V is mean velocity of flow, R is hydraulic radius, S is slope of the channel and

n is manning’s roughness coefficient. Now the discharge is

푄 = 퐴푉 ……….

(3.2)

32

Where, Q is flow discharge and A is cross sectional area. By replacing Equation 3.1 in

Equation 3.2, we get,

푄 = 퐴푅 푆 ……….

(3.3)

By rearranging Equation 3.3,

= 퐴푅 ……….

(3.4)

The right hand term of Equation 3.4 is simply based on channel geometry. Other than

the S term, all other terms of Equation 3.4 are related to channel cross section and its

features. These terms together are referred to as the conveyance (K) of the channel

(George and Schneider, 1989).

퐾 = 퐴푅 ……….

(3.5)

In Equation 3.5, all the terms are related to channel cross section except n. These terms

together termed as the geometrical shape factor (G) of conveyance (K). So,

퐾 = 퐺 ……….

(3.6)

Where,

퐺 = 퐴푅

퐺 = 퐴 ……….

(3.7)

33

Here, P is the wetted perimeter of channel. For the rectangular channel cross section

and bankfull condition, water depth is equal to channel depth, then Equation 3.7 can be

written as,

퐺 = 퐵퐷( ) which can be further re-arranged as:

퐺 = ( )

( ) ……….

(3.8)

Where, B is channel width and D is channel depth. Equation 3.8 will be applied to

compute the geometrical shape factor of conveyance. The geometrical shape factor of

conveyance is dependent on width and depth of the channel.

3.2 Bed Shear Force and Change in Channel Morphology

From the Equation 3.6, it is evident that channel conveyance is proportional to

geometric shape factor (G) which represents the channel morphology. During cyclone,

channel morphology changes due to the high bed shear stress (Kostaschuk et. al., 2003).

The bed shear stress can be computed by the depth-slope product and for small values

of slope (Hickin, 1995) it is calculated as

휏 = 훾푅푆 = 훾 푆 .......... (3.9)

Where, 훾 is the specific weight of water, R is the hydraulic radius, A is cross sectional

area of channel, P is the wetted perimeter and S is the channel slope. From the Equation

3.9, it is evident that the bed shear stress depends on the channel cross section.

Assuming bed shear force works on the total wetted area per unit length of channel, we

have:

퐹 = 휏 ∗ 푇표푡푎푙푤푒푡푡푒푑푎푟푒푎푝푒푟푢푛푖푡푙푒푛푔푡ℎ표푓푐ℎ푎푛푛푒푙

= 휏 ∗ (푃 ∗ 1)

= 훾퐴푃 푆 ∗ 푃

34

So the bed shear force for total wetted area per unit length of the channel is expressed

as:

퐹 = 훾퐴푆 ……….

(3.10)

Equation 3.10 will be used to compute the bed shear force during the bankfull condition

for a known channel cross section. Hereafter, for the bankfull condition of the channel,

the bed shear force will be termed as reference bed shear force and channel conveyance

will be termed as reference channel conveyance.

Equations 3.5 and 3.10 show that both conveyance and bed shear forces are

directly proportional to cross sectional area. So,

퐾 ∝ 퐴

퐹 ∝ 퐴

Hence, it can be said that conveyance of a channel is directly proportional to the bed

shear force.

퐾 ∝ 퐹

∝ .......... (3.11)

Where, Ko is the reference channel conveyance, Fo is the reference bed shear force.

To change the ‘proportional sign’ into ‘equal to’ sign in Equation 3.11, it is assumed

that change of channel conveyance due to bed shear force varies linearly. With this

assumption and using Equation 3.11, non-dimensional relation between channel

conveyance and bed shear force is expressed as:

= 푖 + 푗 .......... (3.12)

Where, i and j are coefficients. Using Equation 3.6, Equation 3.12 can be written as:

35

= 푖 + 푗 ……….

(3.13)

Where, Go is the reference geometrical shape factor. Equation 3.13 can be used to

compute change in channel conveyance due to change in bed shear stress. Using

principle of least squares, the coefficients i and j are expressed in terms of variables

G/Go and F/Fo,as (see Appendix-A for detail derivation):

푖 =∑ /

∑ − ∑ / ∗∑ ( / ∗ / ) (∑ / ) ∗∑ /(∑ / ) (∑ / )

.......... (3.14)

푗 = ∑ / ∑ ( / ∗ / ) (∑ / ) ∑ /(∑ / ) (∑ / )

.......... (3.15)

Here m is the total number of variable which are used to determine the coefficients i &

j.

From Equation 3.8, geometric shape factor is 퐺 = ( )

( )

By expanding the terms of (퐵 + 2퐷) , we have

(퐵 + 2퐷) = 퐵 + − + − + − + ⋯ .......... (3.16)

In Equation (3.16) the higher order terms of D having n ≥ 2, where n represents

exponent of D, have coefficients that are less than unity and decreases with the increase

of n (see Appendix-A for details). So, ignoring the terms containing n ≥ 2 will not

significantly affect the value of (퐵 + 2퐷) (see Appendix-B for details). With this

simplification, Equation (3.16) becomes:

(퐵 + 2퐷) = 퐵 + .......... (3.17)

The term (퐵퐷) in Equation (3.8) is expressed as:

36

(퐵퐷) = (퐵퐷) ∗ (퐵퐷) .......... (3.18)

Using Equations (3.17) and (3.18), Equation (3.8) is written as:

퐺 =(퐵퐷) ∗ (퐵퐷)

퐵 + 4퐷

3퐵

퐺 =3퐵 (퐵퐷) ∗(퐵퐷)

3퐵 + 4퐷

퐺 = ∗ ..........(3.19)

Dividing Equation (3.19) by 퐷 and rearranging, we have

퐺 = 3퐵 퐷3퐵 + 4퐷

퐷

퐺 =퐵퐷 ∗

3퐵퐷3퐵 + 4퐷

퐺 =퐵퐷 ∗

13퐵 + 4퐷

3퐵퐷

퐺 =퐵퐷 ∗

12 + 1

23퐵 + 4퐷

3퐵퐷

퐺 =퐵퐷 ∗

12

3퐵 + 4퐷3퐵퐷

+퐵퐷 ∗

12

3퐵 + 4퐷3퐵퐷

퐺 = ∗ + ..........(3.20)

The ratio in Equation (3.20) is generally termed as width depth ratio. In this study, the

ratio is abbreviated as WDR and is used as a measure of morphological change of the

channel. Replacing by WDR and assuming that the effects of the terms and

on WDR are represented by two coefficients a and b, Equation (3.20) is written

as:

37

퐺 = 푎(푊퐷푅) + 푏 ……….

(3.21)

Where (detail of the derivation is given in Appendix-C),

푎 =∑

∑ 퐺 − ∑ ∗∑ ( )( ) ∑ ( ) (∑ )(∑ ) ∑ ( )

.......... (3.22)

푏 = ∑ ∑ ( )( ) ∑ ( ) (∑ )(∑ ) ∑ ( )

.......... (3.23)

Here, mm are the total number of variables used to determine the coefficients a & b.

3.3 Development of Semi-Analytical Model

The semi-analytical model is developed by relating WDR with bed shear stress.

With the change of bed shear stress, morphological change of the channel is computed

by computing WDR of the channel. Dividing Equation (3.21) by 퐺 , we have

= ( ) .......... (3.24)

Using Equation (3.13) and re-arranging, we have

푎(푊퐷푅) + 푏퐺 = 푖

퐹퐹 + 푗

푊퐷푅 = 퐺 푖 + 푗 − 푏 .......... (3.25)

Where i is given by Equation (3.14)

j is given by Equation (3.15)

a is given by Equation (3.22)

b is given by Equation (3.23)

Equation (3.25) is the required semi-analytical model. This model can be used to

compute change of WDR for changing bed shear force for a wide range of

hydrodynamic scenarios. Cyclonic event generates a hydrodynamic scenario that can be

termed as ‘hydrodynamic shock’.

38

In present study, magnitudes of variables are determined from Delft 3D model

simulations for different cyclone scenarios which are termed as hydrodynamic shocks.

The model is termed as ‘semi-analytical’ because of the semi-empiricism involved in

computing the coefficients i, j, a and b. In this study, these coefficients are prescribed

by using Delft 3D model simulations. A large number of hydrodynamic scenarios are

generated that results morphological changes of channels of different geometrical

dimensions. These scenarios are used to compute wide range of coefficient values i, j, a

and b. This is described in Chapter Four.

39

CHAPTER FOUR

COMPUTATION OF COEFFICIENTS FOR THE SEMI-ANALYTICAL

MODEL

4.0 Introduction

This chapter describes the methodology which is used to prescribe wide ranges

of coefficient values. These coefficient values have to be used with the semi-analytical

model described in Equation (3.25). Following sections describe the methodology and

recommended set of values of the coefficients.

4.1 Application of Numerical Model

The parameters required to compute the coefficients are generated by applying a

numerical model. In this study, Delft 3D morphology model coupled with the Delft

Dashboard are applied to compute the required parameters. The Delft Dashboard is

applied to capture the required cyclone scenarios as hydrodynamic shock. A calibrated

and validated Delft-3D morphology model for Bangladesh coast is applied for this

purpose. Detail of the model can be found in Elahi et. al., 2015 and Nihal et. al., 2015.

4.1.1 Model parameters

Various physical parameters, conditions and constants of the model parameters

are specified in the Table 4.1.

Table 4.1: Delft 3D morphology model parameters

Properties Value Remarks

Grid Spherical co-ordinate

system

Layer-1

Time step 10 min

Process Sediments Non-cohesive

Initial conditions Uniform values Water level= 0

Sediment

concentration = 0

Boundaries Total discharge at Time series

40

upstream boundary

and water level at

downstream boundary

Hydrodynamic

constants

Gravity 9.81 m/s2

Water density 1000 kg/m3

Roughness Manning formula 0.00025-0.02 Spatially variable

Horizontal

viscosity/diffusivity

1-10000 Spatially variable

Sediment

Reference density for

hindered settling

1600 kg/m3

Specific density 2650 kg/m3

Dry bed density 1600 kg/m3

Median sediment

diameter (D50)

100 um

Initial sediment layer

thickness

0.5 m

Morphology Morphological scale

factor

1

Spin-up interval

before morphological

change

720 min

Minimum depth for

sediment calculation

0.2 m

4.1.2 Model grids

In this study, two different grids are used for two different models. A large grid

covering the Bangladesh coast is constructed to simulate the morphological changes

due to cyclone SIDR. On the other hand, a small grid is constructed to simulate

morphological changes in various small channels that are mainly used to compute the

coefficient values for the semi-analytical model. For the large grid, grid sizes vary from

263m x 186m to 1164m x 1704m. For the small grid, a uniform grid size of 100m x

100m is used.

4.1.3 Model bathymetry

41

For simulations in Bangladesh coast with the large grid, the bathymetries of the

rivers/ estuaries are specified by using measured cross sections collected within the

ESPA-delta project of BUET (http://www.espadelta.net/). The inland ground elevation

data are collected from the Center for Environmental and Geographic Information

Services (CEGIS), Bangladesh which is generated from FINNMAP Land Survey 1991,

National DEM from FAP19.The ocean bathymetry is specified by using the open access

data from General Bathymetric Chart of the Oceans (GEBCO) and can be found at

http://www.gebco.net/.

For simulation with the small grid, the bathymetries are generated with various

combination of widths and depths (is explained in section 4.3.1) but with a realistic

mild slope of 0.00005 (Hassan, et. al., 1999).

4.1.4 Model boundary conditions

Model requires two boundary conditions – upstream discharge and downstream

water level. For the large grid model which is used to simulate cyclone SIDR along

Bangladesh coast, upstream discharge boundary is specified using the measured data

from Bangladesh Water Development Board (BWDB) for the year 2007. For

downstream boundary, sea surface elevation computed from an ocean model GCOMS

(S. Kay et al. 2015) for the year 2007 is used. For the small grid model, both discharge

and water level boundaries are computed to maintain a bankfull condition of the

channel. For example, boundary conditions of a channel with 1000m width and 5m

depth, discharge at upstream boundary is computed as 4107 m3/s which is can be

‘conveyed’ in the channel for a bed slope of 0.00005. The corresponding water level at

downstream of the channel is computed as 5m. Due to lack of sediment data during

cyclonic events in Bangladesh, no sediment load is specified in model boundaries.

4.1.5 Model validation

Morphology model is validated by computing the reliability indicator described

by Haqueet.al. (in preparation) as:

푅푒푙푖푎푏푖푙푖푡푦 = 100−∑

∑∗ 100 ……….

(4.1)

42

Here, Reliability is a new model reliability measure indicator introduced by Haque et al

(unpublished) and is shown to quantify performance of a dynamic model realistically.

Reliability = 100 % means the model is 100% reliable with respect to measured values.

Here W and W are the measured and the model values at any instant of

time t, W is the average of the measured values, t is any time instant, T is total

duration for both the measured and model values and n is the total number of values.

The model reliability values are presented in Table 4.2

Table 4.2: Reliability of Delft-3D morphology model

Domain of the large model and locations of model validation are presented in Figure

4.1.This large model is applied to compute the required parameters for the semi-

analytical model.

River name

BWDB Station name

Measured erosion/deposition rate (cm/month)

(For a long Period of data

which is more than 10 years)

Model

erosion/deposition rate (cm/month)

(10 years)

Reliability %

Bishkhali (CES)

BIS16 -0.0122 0.1912 49.26 BIS15 -0.1426 -0.1504 BIS14 -0.4637 -0.4430 BIS12 0.3157 0 BIS11 0.0083 -0.0837

Lower Meghna (EES)

ML2 -0.7832 0 41.80 ML5 0.2265 -0.0023 ML7 -0.2471 -0.0010

Rupsa (WES)

RP10 -0.9200 -0.2532 50.86 RP13 -0.6169 -0.3153 RP14 (n/a) -0.3492 Overall Model reliability over the estuarine systems 47.30

(b) (a)

43

Figure 4.1: Domain of the large model (a) and locations of the model validation (b).

4.1.6 Numerical model result of cyclone SIDR

As measured morphological data during cyclone is not available in Bangladesh,

Delft-3D model is used to simulate the condition of cyclone SIDR in Bangladesh

coast. Details of the model results can be found in Elahi et. al. (2015). This model

result is used to compare computed morphological changes during the application of the

semi-analytical model. Model generated bed shear stress, flow velocity and resultant

erosion/sedimentation at the time of landfall during cyclone SIDR in Bangladesh coast

are shown in Figure 4.2, 4.3 and 4.4 respectively.

Figure 4.2: Magnitude of bed shear stress at the time of landfall for cyclone SIDR.

Landfall location

44

Model result shows visible morphological changes at the mouth of Baleswar estuary

and Bishkhali estuary. In these locations, bed shear stresses are also found high. The

Baleswar and the Bishkhali estuaries are selected as the study site to apply the semi-

analytical model. Special phenomenon like embankment breaching is not considered

during this application.

Figure 4.3: Magnitude of flow velocity at the time of landfall for cyclone SIDR

Landfall location

45

Figure 4.4: Resultant erosion/sedimentation at the time of landfall for cyclone SIDR

4.2 Channel Classification

The relation between geometric shape factor (G) and width-depth ratio (WDR)

is described by Equation 3.20. This equation is used to generate a wide range of values

of G and WDR. The results are shown in Figure 4.5.

Affected estuarie

46

Figure 4.5: Relation between geometric shape factor G and WDR for different

dimensions of channels

A close observation of Figure 4.5 shows that values of G are clustered into four distinct

ranges. As G and channel conveyance K is related (Equation 3.6), the clusters of G can

be used to classify the channels based on channel conveyance. Accordingly, following

channel classification is proposed based on different ranges of values of G.

Table 4.3: Channel classification based on conveyance

Channel Conveyance Values of G Low 0 – 25000 Medium 25001-50000 High 50000-100000 Very High >100000

4.3 Generating the Scenarios

A number of scenarios are generated using the Delft 3D model which are used

to compute the values of the coefficients i, j, a and b. A specific scenario is constructed

by combining a specific channel property and cyclone intensity. Channels with

different conveyance capacities are used for this purpose. Channel properties with

different conveyances are shown in Table 4.4. Using these channel properties, a total of

140 scenarios are generated.

0

25000

50000

75000

100000

125000

150000

175000

200000

225000

250000

275000

0 500 1000 1500 2000 2500 3000

G

WDR

Low

Medium

Very High

High

47

Table 4.4: Channel properties that are used to generate the scenarios of model runs

Width (m)

Depth (m) Remarks 1 3 5 10 15

Conveyance of Channel Channel slope is 0.00005.

500 Low Low Low Low Low 1000 Low Low Low Medium High 3000 Low Low Medium Very High Very High 5000 Low Medium High Very High Very High

10000 Low High Very High Very High Very High 15000 Low High Very High Very High Very High 30000 Medium Very High Very High Very High Very High

From the last 40 historical cyclones, those made landfalls in Bangladesh coast

and near the coast, observed maximum wind velocity, pressure drop and cyclonic days

are specified in Table 4.5. The longest cyclonic duration was 11 days in 1993 cyclone

and the shortest duration was 2 days during the cyclones of 1995, 1996, 2007 and 2011.

Maximum wind speed of 260 km/hour and pressure drop of 9800 Pa was observed

during the cyclone of 1999. In this study, a storm surge generated by cyclonic event is

considered as a hydrodynamic shock. From the combination of observed maximum

wind speed, pressure drop and cyclone-day, hydrodynamic shocks of cyclones are

classified as Very High Strength Cyclone (VHSC), High Strength Cyclone (HSC),

Medium Strength Cyclone (MSC) and Low Strength Cyclone (LSC). These four classes

of cyclones are incorporated in Delft-3D Dashboard-Flow-Morphology model for all

the channel sections which are mentioned in the Table 4.4.

Table 4.5: Classification of different intensities of cyclones

Duration of cyclone (Days)

11 6 (SIDR) 5 2

Max wind velocity (Km/hr.)

260 213 170 83

Max Pressure drop (Pa) 400 Low 5100 Medium 6600 High 9800 Very High

4.4 Incorporating the Cyclone in Delft 3D

48

Tropical Cyclone Tool available in Delft Dashboard (DDB) developed by

Deltares (Delft Dashboard Team 2013, as cited in Laknath et al., 2014) is used for the

generation of atmospheric conditions during the cyclonic event. It generates the

surface wind and pressure fields on a moving circular spider web grid for the given

track information data, based on the Wind Enhancement Scheme (WES) following

Holland (Holland, 1980, as cited in Laknath et al., 2014). This generated spider web

grid file is used in Delft-3D Flow-Mor coupled model to assess the impact of cyclone

generated storm surge. On the basis of historical intensities of cyclones, different

strengths of cyclones are produced as mentioned in the Table 4.5. The cyclone tracks

generated by using DDB are specified in the Figure 4.6.These cyclone tracks are

assumed to make landfall in 90 degree angle to the channel cross section, as the

longitudinal landfall of cyclone produces the maximum inundation in floodplains

(Sakib et al., in preparation).

LSC MSC

HSC VHSC

49

Figure 4.6: Hypothetical tracks of different strengths of cyclones

4.5 Computing the Variables for the Semi-Analytical Model

The required variables of the semi-analytical model to compute the model

coefficients are computed from numerical model results. The variables computed

include - the bed level elevations, magnitude of bed shear stress, depth average velocity

and cross sectional area. The cross-sectional area is calculated from the bed level

elevations and the bed shear force is calculated from the bed shear stress. From the

computed time series of cross-sectional area, change of WDR is calculated.

4.5.1 Calculating the cross sectional area and the wetted perimeter

The cross-sectional area of the channel is calculated from bed level elevations of

the channel by applying the trapezoidal formula

퐴 = ℎ 푏 + (ℎ +ℎ )푏 + ⋯+ ℎ 푏 ……….

(4.2)

Where, h is the bed level elevation and b is the distance between each point. The

schematic figure of a typical cross-section is shown in Figure 4.7. The shaded area of

Figure 4.7 is the cross-sectional area of channel. The wetted perimeter of the channel

for the bankfull condition is computed by the Equation(4.3). Detail process of the cross-

sectional area and wetted perimeter calculation can be found in Rosca et al.(2015).

푃 = 푏 + ℎ + 푏 + (ℎ − ℎ ) + ⋯+ 푏 + ℎ ……….

(4.3)

50

Figure 4.7: A typical channel cross-section.

4.5.2 Calculation of bed shear force

In present study, the Van Rijn’ 84 equation for bed load transport is utilized.

This equation is also used in Delft 3D morphological computation (Delft 3D-Mor). The

formula is commonly used for situations without waves and calculates the bed load

transport rate according to the non-dimensional particle size. According to the Van

Rijn’ 84 formulations (Deltares 2011), bed shear stress is calculated as:

휏 = 휌 푓 푢 ……….

(4.4)

Where, 휌 = density of water, u = depth average velocity,푓 = friction factor which is

expressed as (Deltares 2009):

푓 = . ……….

(4.5)

51

Where, H is water depth and D90=1.5D50. From Equation 4.4 and 4.5, bed shear stress is

related with depth average velocity and water depth. The magnitude of bed shear stress

is extracted from the model results. Multiplying the bed shear stress of the channel with

the total wetted area per unit length, the bed shear force is obtained. The wetted

perimeter is calculated by using the Equation 4.3.

Figure 4.8: Variation of bed shear force for cyclones with variable strengths

From the Delft-3D morphology model, variation of bed shear force for cyclones with

variables strengths are shown in Figure 4.8. The figure shows that increased strength of

cyclones usually generates high bed shear force.

4.5.3 Generating relation between geometric shape factor and bed shear force

To calculate the required variables for the semi-analytical model, relation

between geometrical shape factor and bed shear force is established based on model

simulation results of 140 scenarios. Following the channel classification as described in

section 4.2, these relations are clustered into four different classes and are shown in

Figures 4.9 to 4.12.

8

10

12

14

0 50 100 150 200 250 300

F/Fo

Time (Hour)

Bed Shear Force

Low strength

Medium strength

High strength

Very high strength

52

Figure 4.9: Relation between geometrical shape factor and bed shear force for channel

with low conveyance

Figure 4.10: Relation between geometrical shape factor and bed shear force for channel

with medium conveyance

0.99500

1.00500

1.01500

1.02500

1.03500

1.04500

0.00 5.00 10.00 15.00 20.00 25.00

G/G

o

F/Fo

Channel type: Low conveyance channel

0.99500

1.00500

1.01500

1.02500

1.03500

1.04500

0 5 10 15 20 25

G/G

o

F/Fo

Channel type: Medium Conveyance Channel

53

Figure 4.11: Relation between geometrical shape factor and bed shear force for channel

with high conveyance

Figure 4.12: Relation between geometrical shape factor and bed shear force for channel

with very high conveyance

0.99500

1.00500

1.01500

1.02500

1.03500

1.04500

0 5 10 15 20 25

G/G

o

F/Fo

Channel type: High Conveyance Channel

0.99500

1.00500

1.01500

1.02500

1.03500

1.04500

7 8 9 10 11 12 13 14 15 16 17

G/G

o

F/Fo

Channel type: Very High Conveyance Channel

54

4.5.4 Computation of coefficients

Using the numerical model simulation results for 140 scenarios as described

above, coefficients of the semi-analytical model is computed by using Equations (3.14),

(3.15), (3.22) and (3.23). The required variables to compute the coefficients are

geometrical shape factor, shear force and WDR. As the main objective of study is to

assess the morphological changes of channel due to cyclone, the values of i and j are

determined for the cyclonic conditions. The values of i and j are computed by applying

Eq. (3.14) and Eq. (3.15) respectively for cyclonic events. The values of a and b are

computed by applying Eq. (3.22) and Eq. (3.23) respectively for a wide range of WDR

and geometrical shape factor as specified in Figure 4.5. To determine the values of

coefficients i and j, a database comprising channel conveyance and bed shear force is

generated by applying numerical model (Delft-3D) for different intensities of cyclones

on different channels. Computed values of coefficients are specified in Table 4.6. Based

on these values, coefficients are re-arranged in different ranges depending on channel

conveyance. Different ranges of coefficients are shown in Table 4.7. Schematic

representation of these ranges are shown in Figures 4.13 to 4.16.

55

Table 4.6. Computed coefficients values for different channel types

Channel conveyance type i j a b Low -1.6 x 10-5 0.999916 8.0883 5910 Medium -4.5 x 10-5 1.000132 7.3698 28127 High 246.8 x 10-5 0.980801 11.001 65290 Very high -3.5 x 10-5 0.999814 43.018 112917

Table 4.7. Ranges of coefficients for different channel conveyance types

Type i j a b Low -3.5 x 10-5< i < 246.8 x 10-5 0.999814 < j < 1.000132 7.3698 < a < 11.001 0 < b < 25000

Medium i < -3.5 x 10-5 0.999916 < j a < 8.0883 25000 < b < 50000 High 0 < i and starts from 246.8 x

10-5 j < 0.999814 8.0883 < a < 43.018 50000 < b < 100000

Very high

-4.5 x 10-5< i < -1.6 x 10-5 0.980801 < j < 0.999916 11.001 < a and starts from 43.018

b >100000

Figure 4.13: Schematic representation of ranges of coefficient i

Figure 4.14: Schematic representation of ranges of coefficient j

Figure 4.15: Schematic representation of ranges of coefficient a

56

Figure 4.16: Schematic representation of ranges of coefficient b

To get the best model result, optimum combination of coefficients values need to be

identified.

57

CHAPTER FIVE

APPLICATION OF SEMI-ANALYTICAL MODEL

5.0 Introduction

This chapter describes application of the semi-analytical model that has been

developed in chapters 3 and 4. In subsequent sections of this chapter, model

applications in a wide range of scenarios are presented.

5.1 Application of Semi-Analytical Model for Different Scenarios

The semi-analytical model is applied for different hydrodynamic scenarios.

These scenarios are generated by Delft 3D model along with Delft Dashboard. For

application of the semi-analytical model, required variable like bed shear force for the

respective hydrodynamic scenario is calculated by applying Equations (4.2), (4.3),

(4.4) and (4.5). Reference bed shear force and reference geometrical shape factor are

computed by applying Equations (3.10) and Eq. (3.21). Using the reference bed shear

force (F0) and reference geometrical shape factor (G0), and knowing the resulting bed

shear force during a cyclone (F), the change in channel morphology represented by

WDR is computed by using Eq. 3.25. Required coefficients values are used for the

respective channel class. From the prescribed ranges of coefficient values as shown in

Table 4.7, the coefficient values that are computed for different channel classes for

different scenarios are given in Table 5.1. The model result is compared with the Delft

3D model result. The simulation result of Delft 3D model is termed as ‘measured

values’ when comparing the results of the semi-analytical model with the Delft 3D

model results. Results of the semi-analytical model for each of the channel classes are

presented in Figures 5.1 to 5.4.

Table 5.1. Coefficient values of the semi-analytical model.

Channel conveyance type i j a b Low -1.6 x 10-5 0.999916 8.0883 5910 Medium -4.5 x 10-5 1.000132 7.3698 28127 High 246.8 x 10-5 0.980801 11.001 65290 Very high -3.5 x 10-5 0.999814 43.018 112917

58

Figure 5.1: Variation of WDR with time for low conveyance channel when cyclone

condition is HSC (see Section 4.3). The model shows 0.5% error.

Figure 5.2: Variation of WDR with time for medium conveyance channel when cyclone

condition is VHSC (see Section 4.3). The model shows 1% error.

69.7069.8069.9070.0070.1070.2070.3070.4070.5070.6070.70

0 20 40 60 80 100 120 140

WDR

Time (Hour)

Low Conveyance Channel: 500m x 7m

Measured_WDR

Model_WDR

138.00138.50139.00139.50140.00140.50141.00141.50142.00142.50143.00143.50

0 50 100 150 200 250 300

WDR

Time (Hour)

Medium Conveyance Channel: 1000m x 7m

WDR_measured

Model_WDR

59

Figure 5.3: Variation of WDR with time for high conveyance channel when cyclone

condition is VHSC (see Section 4.3). The model shows 1.9% error.

Figure 5.4: Variation of WDR variations with time for very high conveyance channel

when cyclone condition is VHSC (see Section 4.3). The model shows 5% error.

5.2 Application of Semi-Analytical Model for Cyclone SIDR

Applying the large grid model (Bangladesh coast model), morphological

changes are computed in Bishkhali and Baleswar Estuaries during cyclone SIDR

390

400

410

420

430

440

0 50 100 150 200 250 300

WDR

Time (Hour)

High Conveyance Channel: 3000m x 7m

WDR_Measured

WDR_model

1850

1900

1950

2000

2050

21002150

2200

2250

2300

0 50 100 150 200 250 300

WDR

Time (Hour)

Very High Conveyance Channel: 15km x 7m

WDR_Measured

WDR_model

60

(Section 4.1.6). The semi-analytical model is applied in these cases and compared with

the Delft 3D model results (termed as measured values).

The estuaries mentioned above fall into Very High Conveyance Channel

considering the values of geometric shape factors. For this specific application,

coefficient values are fine-tuned based on the ranges of values presented in Table 4.7.

The channel with VHSC for which the model is applied has a dimension of 15km x 7m.

As mentioned before, the Delft 3D model result is termed as ‘measured value’. From

these measured values, we get the bed shear force for VHSC and the results are shown

in Figure 5.5. In the same channel, measured variation of bed shear stress and flow

velocity are shown as a function of non-dimensional bed shear force (Figure 5.6).

Figure 5.5: Temporal variation of measured bed shear force for the channel where the

semi-analytical model is applied.

8.008.208.408.608.809.009.209.409.609.80

0 20 40 60 80 100 120 140

F/Fo

Time (Hour)

Bed shear force variation: VHCC

61

Figure 5.6: Variation of bed shear stress and flow velocity as a function of non-

dimensional bed shear force

From Figures 5.5 and 5.6, time series of non-dimensional shear force is computed.

Using this time series along with reference geometrical shape factor, temporal variation

of WDR is computed by using Eq. (3.25) and the results are shown in Figure 5.7.

Specified coefficients values in Table 5.1 for very high conveyance channel are used.

This gives morphological changes of the channel when the cyclone crosses over it.

0

1

2

3

4

5

0

1

2

3

4

5

8.00 8.50 9.00 9.50 10.00

Flow

vel

ocity

(m/s

)

Bed

shea

r str

ess (

N/m

2)

F/Fo

Bed shear stress (avg)

Flow velocity (avg)

1800

1900

2000

2100

2200

2300

0 20 40 60 80 100 120 140 160

WDR

Time (hour)

Measured_WDR

Model_WDR

62

Figure 5.7: Comparison of model WDR with measurements for VHSC.

5.3 Sensitivity of Model Results

As mentioned earlier, it is always possible to refine the values of the coefficients

within the range as described in Table 4.7. In order to test sensitivity of the model

results with the change of coefficient values, different values of coefficients from the

described ranges are applied for a very high conveyance channel (15km x 7m) with

VHSC. During application of the model with each of the coefficients, other coefficients

remain the same as specified in Table 5.1. Results are presented in Figures 5.8 to 5.11.

It is evident that, coefficient j is the most sensitive coefficient and it is convenient to

adjust and re-adjust coefficients i and a for refinement of the model.

Figure 5.8: Variation of WDR with different values of i for very high conveyance

channel during VHSC (see Section 4.3)

1200

1400

1600

1800

2000

2200

0 50 100 150 200 250 300

WDR

Time (hour)

WDR variations with different values of i

i = -3.5 x 10^-5

i = -1.5 x 10^-5

i=100 x 10^-5

i=150 x 10^-5

i = 245 x 10^-5

63

Figure 5.9: Variation of WDR with different values of j for very high conveyance

channel during VHSC (see Section 4.3)

Figure 5.10: Variation of WDR with different values of a for very high conveyance

channel during VHSC (see Section 4.3)

-2800-2300-1800-1300

-800-300200700

120017002200

0 50 100 150 200 250 300

WDR

Time (hour)

WDR variations with different values of j

j= 0.980802

j= 0.984625

j= 0.999814

j= 0.999864

j= 0.999915

1200

1400

1600

1800

2000

2200

0 50 100 150 200 250 300

WDR

Time (hour)

WDR variations with different values of a

a= 12

a= 25

a= 35

a= 43.018

a= 50

64

Figure 5.11: Variation of WDR with different values of b for very high conveyance

channel during VHSC (see Section 4.3)

In order to refine the model results with the change of coefficient values, coefficients a

= 270 and i = -1.7 x 10-5 are used while keeping the values of the other coefficients the

same as shown in the Table 5.1. The results are shown in Figure 5.12. The figure shows

that computed WDR is sensitive to the coefficient values. In this particular application,

a much better model performance is achieved with 5% error. It is evident that computed

WDR is sensitive with the change of coefficient values when all the coefficient values

are changed simultaneously.

1200

1400

1600

1800

2000

2200

0 50 100 150 200 250 300

WDR

Time (hour)

WDR variations with different values of b

b= 100000

b= 112917

b= 120000

b= 130000

b= 150000

65

Figure 5.12: Variation of WDR with time after applying modified coefficients

In another application, the model is applied at the mouth of Baleswar estuary during

cyclone SIDR. In this particular application, refined coefficient values of a = 270 and i

= -1.7 x 10-5 are used. Time series of measured non-dimensional bed shear force is

shown in Figure 5.13. Using this bed shear force and reference geometrical shape

factor, variation of WDR as a function of non-dimensional bed shear force is shown in

Figure 5.14. Computed time series of WDR is shown in Figure 5.15 with 4% error from

the measurements.

1800

1900

2000

2100

2200

2300

0 50 100 150

WDR

Time (hour)

Measured Value

Model Value with coefficients from Table 4.6

Model Value with a = 270 and i = -1.7 x 10-5

0

2

4

6

8

10

0 20 40 60 80 100 120

F/Fo

Time (hour)

Measured bed shear force variation:Baleswar mouth

66

Figure 5.13: Time series of measured non-dimensional bed shear force at the mouth of

Baleswar estuary during cyclone SIDR

Figure 5.14: Variation of WDR with non-dimensional bed shear force at the mouth of

Baleswar estuary. The results show both the model values and the measurements.

Figure 5.15: Comparison of time series of WDR between the model and the

measurements at the Baleswar mouth. The model shows 4% error.

550

570

590

610

630

650

0 2 4 6 8 10

WD

R

F/Fo

Measured_WDR

Model_WDR

550

570

590

610

630

650

0 20 40 60 80 100 120

WDR

Time (hour)

WDR variations during cyclone SIDR: Baleswar mouth.

Measured_WDR

Model_WDR

67

5.4 Application of the Semi-Analytical Model without the Application of Delft 3D

Model

Application of the semi-analytical model as presented in Section 5.3 shows that

a specific model application depends on the computed shear force from the Delft 3D

model. This section presents how the model could be applied in situations when bed

shear force is computed from analytical expressions. These specific applications will

show a wider scope of application of the semi-analytical model. In this case, the

semi-analytical model is applied in the Bishkhali estuary mouth. The mouth is 3km

wide with a depth of 9 m. With this specific width and depth of the channel and by

using Equation (3.8), geometric shape factor of the channel is computed as 116357.

With this geometric shape factor and using the channel classification as shown in

Tables 4.3 and 4.4, the channel is classified as a very high conveyance channel. Instead

of using Delft 3D model results, bed shear force is computed in three different ways:

a) When water depth and depth average flow velocity are known: In this

case, bed shear stress is computed by applying Equations (4.4) and (4.5) which uses

water depth and depth average flow velocity during computation of bed shear stress.

Resulting bed shear force per unit length of the channel (F) is computed by multiplying

the bed shear stress with the wetted perimeter (P) of the channel (Equation 4.3). For

larger value of widths, wetted perimeter is approximately equal to the channel width

(Hickin, 1995). Steps of application are presented in Figure 5.16. For a particular water

depth, variation of bed shear stress as computed by using Equations (4.4) and (4.5) with

depth average velocity is shown in Figure 5.17. Reference bed shear force (Fo) is

calculated by applying Equation (3.10) and reference geometrical shape factor (Go) is

calculated by applying Equation (3.21) by using the coefficients values of respective

channel conveyance. Change of channel morphology due to cyclone is computed by

computing WDR by applying Equation (3.25). Model result (with legend WDR_1) with

this approach is shown in Figure 5.20.

Computation of bed shear stress: u, H known 휏 = 휌 푓 푢 and 푓 = .

Compute bed shear force: F By multiplying the wetted perimeter with bed shear

force.

Calculate reference geometric shape factor and reference bed shear force: Go and Fo

퐺 = 푎(푊퐷푅) + 푏 and 퐹 = 훾퐴푆

68

Figure 5.16: Model application when water depth and depth average velocity are

known.

b) When only velocity of flow is known: From the observed bed shear stress

and depth average velocity for the 140 scenarios, variation of bed shear stress is plotted

as a function of depth average velocity as shown in Figure 5.17.

Figure 5.17: Variation of bed shear stress as a function of depth average velocity.

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Bed

shea

r str

ees (

N/m

2)

Depth average velocity (m/s)

푊퐷푅 =1푎 퐺 푖

퐹퐹 + 푗 − 푏

Applying the semi analytical model:

Change of WDR: Morphological changes due to cyclone

69

When only depth average velocity from a specified distance above the bed is known,

bed shear stress can be calculated by using the von Karman-Prandtl law of velocity

distribution (Bergeron and Abrhams, 1992) as:

푢 = ∗ ln ............ (5.1)

where, u* = shear velocity, z = distance above the bed, zo= roughness height, k = von

Kármán constant = 0.41.

푢∗ = ............ (5.2)

Now by replacing Eq. (5.2) in Eq. (5.1),

푢 = .

ln ........... (5.3)

by rearranging Eq. (5.3), we get,

휏 = 휌 . ............ (5.4)

By applying Eq. (5.4), bed shear stress can be calculated from the depth average

velocity. Computation of WDR by using Eq. (5.4) is shown in Figure 5.20 (legend

WDR_2).Steps of the model application when only flow velocity is known is specified

in Figure 5.18.

휏 = 휌0.41푢

ln 푧푧

Computation of bed shear stress: u, z known

Compute bed shear force: F By multiplying the wetted perimeter with bed shear

force.

Calculate reference geometric shape factor and reference bed shear force: Go and Fo

퐺 = 푎(푊퐷푅) + 푏 and 퐹 = 훾퐴푆

푊퐷푅 =1푎 퐺 푖

퐹퐹 + 푗 − 푏

Applying the semi analytical model:

70

Figure 5.18: Model application when only velocity of flow is known

c) When no observed data is available: For a specific cyclone event (for

example cyclone SIDR), if no observed data is immediately available, changes of

channel morphology can be computed in the following way:

1. The cyclonic event has to be categorized as either as LSC or MSC or HSC or VHSC

based on the characteristics of the cyclone (see Table 4.5). For cyclone SIDR, it can be

characterized as HSC.

2. Figure 4.8 is used to compute the maximum possible value of non-dimensional bed

shear stress. For cyclone SIDR (HSC category) this value is 12.69.

3. Equation (3.25) is used to have the preliminary estimate of WDR for this specific

cyclone. In this example, the WDR value is found to be 378.01 compared to the

observed value which is 373.61.

푊퐷푅 = 퐺 푖 + 푗 − 푏 .......... (3.25)

4. Computed value of WDR from the model is shown in Figure 5.21(abbreviated as

WDR_Max_F/F0) along with the observed value. Steps of the model application are

presented in Figure 5.19.

Change of WDR: Morphological changes due to cyclone

71

Figure 5.19: Steps of the model application when no data is available

Categorize the cyclonic event as: LSC/MSC/HSC/VHSC

(Based on cyclonic characteristics)

Compute maximum possible value of bed shear force: F/Fo

Based on variation of bed shear force as shown in Figure 4.8

Calculate reference geometric shape factor: Go

Applying the semi analytical model by using Go and F/Fo

Change of WDR: Morphological changes due to cyclone

72

Figure 5.20: Temporal variation of WDR during cyclone SIDR at Bishkhali mouth

Figure 5.21: Variation of WDR with bed shear force during cyclone SIDR at Bishkhali

mouth.

355

360

365

370

375

380

0 20 40 60 80 100 120

WDR

Time (hour)

Measured_WDR

WDR_1

WDR_2

355

360

365

370

375

380

0 2 4 6 8 10 12 14

WDR

F/Fo

Measured_WDR

WDR_Max_F/Fo

73

5.5 Comparison of the Model Results with Measured Cross Section (event:

Cyclone SIDR)

In this case, model result is compared with the measured cross-section at

Bishkhali mouth. By the term ‘measured section’, we mean cross section derived from

the Delft 3D model and the observed planform after cyclone SIDR. The measured

section is the combination of depth (from the Delft 3D model) and width (from the

Landsat image).

Observed planform is computed from the Landsat images collected from open

source (www.glovis.usgs.com). To assess the planform of before the cyclone SIDR,

Landsat image of 27 March, 2007 is used (Figure 5.22a). Landsat image of 1 January,

2008 (Figure 5.22b) is selected for assessment of after the cyclone SIDR. Due to lack of

visibility of images, planform change is computed for a longer time span that may add

additional error in calculation. From the comparison of two images, planform changes

due to cyclone SIDR is computed. The result shows that Bishkhali mouth gets 30.07 m

wider due to cyclone SIDR.

74

Figure 5.22: Change of planform in Bishkhali estuary due to cyclone SIDR

Model WDR is converted into average depth by multiplying the known width of the

channel before the cyclone SIDR. Cross section after the cyclone SIDR is computed by

applying the semi-analytical model (when no observed data is available) and

comparison with the measured cross section is shown in Figure 5.23. Computed WDR

from the semi-analytical model is 378.01 after the cyclone SIDR. Due to lack of

observed data before and after the cyclone SIDR, depths of Bishkhali mouth are taken

from the Delft 3D model. After the cyclone SIDR, observed depth at Bishkhali mouth is

8.03 m. By multiplying the observed depth with the model WDR, width of Bishkhali

mouth after the cyclone SIDR is computed as 3035.85 m. From the semi-analytical

model result, Bishkhali mouth gets 35.85 m wider.

(a) (b)

(d) (c)

(e)

Bank line shifted 30.07 m

75

The comparison of model result with the observed planform is shown in Figure 5.23.

Considering all the uncertainties of the ‘measured value’ (the time of measurement,

effect of tide and effect of floodplain etc), the model reasonably simulates the measured

trend with 5.8% error margin.

Figure 5.23: Comparison of the semi-analytical model result with the observed

planform.

-12

-10

-8

-6

-4

-2

0

2

4

0 500 1000 1500 2000 2500 3000 3500

Bed

leve

l ele

vatio

n (m

)

Distance (m)

Before_Sidr Measurement_After_SIDR Model_after_SIDR

76

CHAPTER SIX

CONCLUSIONS AND RECOMMENDATIONS

6.1 Conclusions

A semi-analytical model is developed to compute changes of channel

morphology due to changes in channel bed shear force. The channel bed shear force is

taken as a measure of hydrodynamic forcing. In this study, hydrodynamic scenario

generated from cyclone generated storm surge is considered as a particular event which

is termed as ‘hydrodynamic shock’. Change of channel morphology is represented by

width depth ratio of the channel cross section. The semi-analytical model is

developed using the basic laws of hydraulics. The geometrical properties of the channel

representing the morphological changes are mathematically related with the

hydrodynamic forcing causing the morphological changes. During the process of model

development, four coefficients appear in the semi-analytical model which is evaluated

numerically. A set of values of the coefficients are suggested that can be used for a

wide range of channel and cyclone categories. Using the suggested model coefficient

values, the semi-analytical model is applied to compute changes in channel morphology

due to several cyclone generated hydrodynamic shocks and the results are compared

with a calibrated & validated numerical model results (Delft 3D morphology and

dashboard model). The performances of the model are found to be within ±0.5% to

±5% of the error margin.

6.2 Limitations of the Model

1. The model does not consider effects of sediment load, change of flow direction

due to flood and ebb tides, exchange of momentum between the main channel

and the floodplain.

2. Bankfull condition of the channel is assumed to compute the reference

geometrical shape factor. However, the bankfull condition alone can initiate

change in channel morphology during flood flow.

3. Information on the ‘history of shock’ is not explicitely included in the model.

77

4. Hydrodynamic shock due to cyclonic event is considered to occur as an

independent event. However, during a cyclone, embankment breach can impose

additional forcing which is not considered in the model.

5. Due to lack of field data during a cyclonic event, an extensive compariosn of the

model results with field measurements were not possible. Comparison with the

numerical model results implicitely contain numerical errors which might

artificially reduce model error.

6.3 Recommendations for Future Study

1. In the present form of the model, coefficient values are determined numerically.

A close observation of the expressions of the coefficients (Equation 3.14, 3.15,

3.22 and 3.23) shows that it is possible to derive analytical expressions of the

coefficients. This will make the model truly analytical in nature and will

improve the performance of the model.

2. As measurement of channel cross section just before and after a hydrodynamic

shock is difficult to take, it is recommended to conduct flume study in a

controlled condition. This will provide realistic data of the event which can be

used to validate the model. This will also provide further insight into the process

and will make it possible to include more drivers in the model that are

responsible to cause morphological changes during a hydrodynamic shock.

78

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Appendix

Appendix-A

= 푖 + 푗 ........ (3.13)

Let Eq. (3.13) is a straight line and it can be expressed as,

푦 = 푖푥 + 푗 .......... (A1)

where, = 푦, = 푥.

The straight line is fitted to the data points (x1, y1), (x2, y2), (x3, y3), ......... (xm, ym).

Let yλ1 be the theoretical value for x1 then

푒 = 푦 −푦

푒 = 푦 − (푖푥 + 푗)

푒 = (푦 − 푗 − 푖푥)

Now we have,

푆 = 푒 + 푒 + 푒 + … … … …

푆 = 푒

푆 = (푦 − 푗 − 푖푥 )

By the principle of least squares, the value of S is minimum therefore,

= 0 .......... (A2)

= 0 .......... (A3)

On solving Eq. (A2) and (A3), and dropping the suffix, we have

∑푦 = 푚푗 + 푖 ∑ 푥 .......... (A4)

∑ 푥푦 = 푗 ∑ 푥 + 푖 ∑ 푥 .......... (A5)

From Eq. (A4),

86

푗 = ∑ ∑ .......... (A6)

By replacing Eq. (A6) in Eq. (A5), we have

∑ 푥푦 = ∑ ∑ ∗ ∑ 푥 + 푖 ∑ 푥

⇒ 푚∑푥푦 = ∑ 푥 ∑푦 − 푖 ∑푥 ∑ 푥 + 푚푖 ∑ 푥

⇒ 푚∑푥푦 −∑푥 ∑푦 = 푚푖 ∑ 푥 − 푖(∑푥)

⇒ 푖 = ∑ ∑ ∑∑ (∑ )

.......... (A7)

⇒ 푖 = ∑

∑ ∑ ∑ ∑ (∑ ) ∑ ∑ ∑ ∑ (∑ )

⇒ 푖 = ∑∑푦 − ∑ ∑ ∑ ∑

(∑ ) ∑ .......... (A8)

Now by replacing the Eq. (A7) in Eq. (A6),

푗 =∑ ∑ ∑ ∑

∑ (∑ ) ∗∑

푗 =∑ ∑ ∑ ∑ ∑ ∑

∑ (∑ )

푗 = ∑ ∑ ∑ ∑ ∑ (∑ )

푗 = ∑ ∑ ∑ ∑ (∑ ) ∑

.......... (A9)

Now replacing = 푦, = 푥 in Eq. (A8) and (A9), we have

푖 =∑ /

∑ − ∑ / ∗∑ ( / ∗ / ) (∑ / ) ∗∑ /(∑ / ) (∑ / )

.......... (3.14)

푗 = ∑ / ∑ ( / ∗ / ) (∑ / ) ∑ /(∑ / ) (∑ / )

.......... (3.15)

87

Appendix-B Expansion of (퐵 + 2퐷) : From Equation 3.14, (퐵 + 2퐷) = 퐵 + − + − + − + … … … …

By applying 3.14 for various value of width and depth of channel, values of (퐵 + 2퐷)

is computed and presented in Table A1. It shows that ignoring the terms containing n

≥2 will not affect the values of (퐵 + 2퐷) . Here, n represents exponent of D.

Table A1. Expansion of (퐵 + 2퐷)

Width B (m)

Depth D (m) 1st term

2nd term

3rd term

4th term

5th term

6th term

7th term

(퐵 + 2퐷) Upto 7 term

Upto 2 term

500 1 62.996 0.168 -1.120E-

04

1.991E-07

-4.646E-

10

1.239E-12

-3.579E-

15

63.16 63.16

500 5 62.996 0.840 -2.800E-

03

2.489E-05

-2.904E-

07

3.871E-09

-5.592E-

11

63.83 63.84

1000 3 100.000 0.400 -4.000E-

04

1.067E-06

-3.733E-

09

1.493E-11

-6.471E-

14

100.40 100.40

1000 5 100.000 0.667 -1.111E-

03

4.938E-06

-2.881E-

08

1.920E-10

-1.387E-

12

100.67 100.67

3000 10 208.008 0.924 -1.027E-

03

3.044E-06

-1.184E-

08

5.260E-11

-2.533E-

13

208.93 208.93

15000 15 608.220 0.811 -2.703E-

04

2.403E-07

-2.803E-

10

3.738E-13

-5.399E-

16

609.03 609.03

30000 20 965.489 0.858 -1.907E-

04

1.130E-07

-8.790E-

11

7.813E-14

-7.524E-

17

966.35 966.35

88

Appendix-C

퐺 = 푎(푊퐷푅) + 푏 ……….

(3.21)

Let Eq. (3.21) is a straight line and it can be expressed as,

푦 = 푎푥 + 푏 .......... (C1)

where, 퐺 = 푦,푊퐷푅 = 푥.

The straight line is fitted to the data points(x1, y1), (x2, y2), (x3, y3), ......... (xmm, ymm).

Let yλ1 be the theoretical value for x1 then

푒 = 푦 −푦

푒 = 푦 − (푖푥 + 푗)

푒 = (푦 − 푗 − 푖푥)

Now we have,

푆 = 푒 + 푒 + 푒 + … … … …

푆 = 푒

푆 = (푦 − 푗 − 푖푥 )

By the principle of least squares, the value of S is minimum therefore,

= 0 .......... (C2)

= 0 .......... (C3)

On solving Eq. (C2) and (C3), and dropping the suffix, we have

∑푦 = 푚푚푏 + 푎∑푥 .......... (C4)

∑ 푥푦 = 푏 ∑푥 + 푎 ∑푥 .......... (C5)

From Eq. (C4),

푏 = ∑ ∑ .......... (C6)

89

By replacing Eq. (C6) in Eq. (C5), we have

푥푦 =∑푦 − 푎∑푥

푚푚 ∗ 푥 + 푎 푥

⇒ 푚푚∑푥푦 = ∑ 푥 ∑푦 − 푎∑푥∑ 푥 + 푚푚푎∑ 푥

⇒ 푚푚∑푥푦 −∑ 푥 ∑푦 = 푚푚푎 ∑푥 − 푎(∑ 푥)

⇒ 푎 = ∑ ∑ ∑ ∑ (∑ )

.......... (C7)

⇒ 푎 = ∑

∑ ∑ ∑ ∑ (∑ ) ∑ ∑ ∑∑ (∑ )

⇒ 푎 = ∑∑푦 − ∑ ∑ ∑ ∑

(∑ ) ∑ .......... (C8)

Now by replacing the Eq. (C7) in Eq. (C6),

푏 =∑푦 −푚푚∑푥푦 −∑ 푥 ∑푦

푚푚∑푥 − (∑푥) ∗ ∑푥

푚푚

푏 =∑푦 −푚푚 ∑푥 ∑푥푦 −∑푥 ∑푥 ∑ 푦

푚푚∑푥 − (∑ 푥)푚푚

푏 =∑푦∑ 푥 −∑ 푥 ∑푥푦푚푚∑푥 − (∑푥)

푏 = ∑ ∑ ∑ ∑(∑ ) ∑

.......... (C9)

Now replacing 푦 = 퐺, 푥 = 푊퐷푅 in Eq. (C8) and (C9), we have

푎 =∑

∑ 퐺 − ∑ ∗∑ ( )( ) ∑ ( ) (∑ )(∑ ) ∑ ( )

.......... (3.22)

푏 = ∑ ∑ ( )( ) ∑ ( ) (∑ )(∑ ) ∑ ( )

.......... (3.23)