Flood Studies Update Technical Research Report Volume III … Research... · 2014-07-16 ·...

Flood Studies Update

Technical Research Report

Volume I Rainfall Frequency

Volume II Flood Frequency Estimation

Volume III Hydrograph Analysis

Volume IV Physical Catchment Descriptors

Volume V River Basin Modelling

Volume VI Urbanised and Small Catchments

Volume III

Hydrograph Analysis Kieran O’Connor, Monomoy Goswami and Duncan Faulkner

Derived from Technical Research Reports by

NUI Galway and JBA Consulting


ii

Abstract

This volume presents methods of constructing the hydrograph to accompany a flood peak of

given return period at gauged and ungauged sites in Ireland. The peak flow is typically

derived by the methods of flood frequency estimation presented in Volume II.

The preferred route to constructing the hydrograph is based on the analysis of hydrograph

widths. Flood hydrographs are made comparable by characterising them by so-called

hydrograph widths. For example, W75 represents the duration in hours over which the flow

exceeds 75% of the peak value.

Flood hydrographs for many rivers in Ireland typically have a relatively complex shape, with

subsidiary peaks and undulations. These reflect the general pattern of successive periods of

heavy rainfall leading to the flood but are also moderated by features of the river network.

The aim of hydrograph width analysis is to construct a simplified flood hydrograph shape that

is characteristic of the catchment. Two approaches are considered. In one, a particular

parametric form is imposed on the hydrograph shape. The shape found most useful is a

modified version of the Gamma distribution. In the other approach, the characteristic

hydrograph is selected by direct analysis (and averaging) of hydrograph widths.

Regression-based expressions allow hydrograph descriptors at ungauged sites to be estimated

from physical catchment descriptors (PCDs). Using the parametric approach, a flood

hydrograph with unit peak is constructed as a continuous curve. This is rescaled by the

relevant peak flow to obtain the required design flood hydrograph.

A standalone software package, with graphical user interface, called HWA (Hydrograph

Width Analysis), was created both as a research tool and as an aid to constructing design

flood hydrographs at any site, ideally based on existing or updated flow data.

Although some variation of hydrograph width (and hence hydrograph shape) was noted, no

systematic pattern of variation with peak flow magnitude, season of occurrence or pre-event

flow value could be established. As expected, arterial drainage was typically found to lead to

narrower and peakier hydrographs.

Urbanised catchments are not well represented in the 89 stations subjected to hydrograph

width analysis. This is one of several areas of application where the Interactive Bridge

Invoking the Design Event Method extends the reach of FSU methods appreciably. The

HWA and IBIDEM software packages are available through the FSU Web Portal.

Research on Flood Event Analysis is briefly summarised in Appendix B.

©Office of Public Works 2014


iii

Further information about the research

FSU Technical Research Reports (TRRs) are available in their original

form for researchers and practitioners who seek additional information

about a method. The original TRRs sometimes document exhaustive

application of a method to many catchments. In others, additional options

are reported.

Inevitably, the relevance of the original TRRs is influenced by OPW

decisions on which methods to implement, and how best to arrange and

support them. Readers who consult the original TRRs will notice editorial

re-arrangements and compressions, and occasional changes in notation and

terminology. These were judged necessary to enhance understanding and

use of the FSU methods amongst general practitioners. More significant

changes are labelled explicitly as editorial notes.


iv

Contents i

Abstract ii

Contents iv

Notation xi

Symbols xi

Subscripts xii

Abbreviations and descriptor names xii

Glossary of terms xiii

1 Introduction 1

1.1 Overview 1

1.2 The goal and premise of hydrograph width analysis 2

1.3 Catchment selection 3

1.4 Physical catchment descriptors (PCDs) 4

1.5 The characteristic hydrograph 5

1.6 HWA software 5

2 Processing the flow data for HWA 6

2.1 Data screening and checking 6

2.1.1 Data handling 6

2.1.2 Missing flow data 6

2.1.3 Scrutiny of annual maximum flood peaks 6

2.1.4 Stations affected by arterial drainage 7

2.2 Defining the time-window of the flood hydrograph 7

2.3 Selection of flood hydrographs 8

2.4 Numbering of flood hydrographs 9

2.5 Seasonal distribution of flood events 9

2.6 Filtering of selected hydrographs 10

2.6.1 Desire for broadly unimodal hydrographs 10

2.6.2 Decoupling the main flood response within a complex flood event 10

2.6.3 Discarding the complex segments 10

3 Deriving the characteristic hydrograph at gauged sites 12

3.1 Standardising the flood hydrographs 12

3.2 Calculation of hydrograph widths at particular exceedance levels 12

3.3 Procedures for constructing the characteristic hydrograph 13

3.4 Split-sample and whole-sample calibration 15

3.5 Deriving the median hydrograph 16

3.5.1 Basic method 16

3.5.2 Anomalies in the derived median hydrograph 17

3.5.3 Improving the derived median hydrograph 17

4 The parametric approach 19

4.1 Objectives 19

4.2 General approach 19

4.3 UPO-Gamma model for the characteristic hydrograph 20

4.3.1 Gamma distribution 20

4.3.2 Peak of Gamma distribution 20


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4.3.3 Gamma model with peak at time zero 20

4.3.4 Gamma model with unit peak at time zero 21

4.3.5 Formulation in terms of hydrograph rise time Tr 21

4.3.6 Families of hydrographs constructed using the model 21

4.3.7 Example application of UPO-Gamma model 22

4.4 UPO-ERR-Gamma model for the characteristic hydrograph 23

4.4.1 Formulation 23

4.4.2 Method of fitting 24

4.5 Method of fitting the parametric model 24

4.5.1 Objective function 25

4.5.2 Optimisation scheme 26

4.5.3 Performance evaluation 27

4.6 Reproduction of flood hydrographs of verification events 28

4.7 Other methods 30

5 Performance of methods at gauged sites 31

5.1 Introduction 31

5.2 Relative performance in verification compared to that in calibration 32

5.3 Complexity of hydrographs at Stations 06011 and 34018 33

5.4 Variability in hydrograph widths at some stations 34

5.5 Attenuated response at some stations 38

5.6 General guidance 38

5.7 Results of whole-sample calibration 39

5.7.1 Derived median hydrograph and its descriptors 39

5.7.2 UPO-ERR-Gamma model and its parameters 40

5.7.3 Stations where the flood hydrograph recedes faster than it rises 43

5.8 Characteristic hydrographs on the River Suir 44

5.9 Hydrograph width analysis at gauged sites – a summary 45

5.10 Flood hydrographs having sustained peaks 46

5.10.1 Where the hydrograph shape reflects the temporal pattern of rainfall 46

5.10.2 Where the hydrograph shape is characteristic of the station 46

6 Constructing the characteristic hydrograph at ungauged sites 48

6.1 Introduction 48

6.1.1 Links with other parts of the FSU 48

6.1.2 Assumptions and difficulties 48

6.2 Selection of dependent variables (DVs) 49

6.3 Selection of independent variables (IVs) 50

6.4 Additional notes 51

6.4.1 Treatment of Gamma shape parameter n 51

6.4.2 Software used for the regression analysis 52

6.5 Correlation studies 52

6.5.1 Inter-correlations between PCDs 52

6.5.2 Individual correlations between DVs and initially selected IVs 56

6.5.3 Choosing a subset of PCDs to use as IVs 56

6.5.4 Checking the Normality of the DVs 57

6.5.5 Final selection of the independent variables; a note on the use of BFI 58

6.6 The regression method used 58

6.7 Illustrative results: Estimating W75 when BFI available 58


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6.7.1 Regression models and their performance evaluation 58

6.7.2 Checking the possible influence of collinearity 60

6.7.3 Checking the logical consistency of the model 60

6.7.4 Additional checks 62

6.8 Recommended models for use at ungauged sites 67

6.8.1 The final models 67

6.8.2 Model performance 69

6.8.3 Additional notes on the regression models 70

7 Ancillary investigations 71

7.1 Variation of hydrograph width with peak flow 71

7.2 Variation of hydrograph width with pre-event minimum flow 73

7.3 Variation of hydrograph width with time of year 74

7.4 Effect of arterial drainage on hydrograph widths 75

8 Constructing the characteristic flood hydrograph 79

8.1 Topics covered 79

8.2 Features of the methods 79

8.3 Allowances in design flood hydrographs for pre-event flow 80

8.3.1 Substitution approach 80

8.3.2 Terminology: baseflow or pre-event flow? 81

8.3.3 Choosing the pre-event flow 81

8.4 Estimation of volume of flow 82

8.4.1 Basic method 82

8.4.2 Non-parametric case 82

8.4.3 Parametric case 82

8.5 Deriving the characteristic hydrograph at a gauged site 83

8.6 Estimating the characteristic hydrograph at an ungauged site 84

8.6.1 Using the UPO-ERR-Gamma model 84

8.6.2 Using the parabolic curves method 84

8.6.3 Using IBIDEM 84

8.7 Parabolic curves method 84

8.7.1 Overview 84

8.7.2 Details of method 85

8.7.3 Examples 86

8.7.4 Application at an ungauged site 86

8.8 Constructing the design flood hydrograph 87

8.9 Software 87

8.10 Selection and use of the pivotal catchment 87

8.10.1 Overview 87

8.10.2 Selection of the pivotal catchment 88

8.10.3 Recommended procedure for data transfer 89

8.10.4 Example 89

8.10.5 Further discussion of choice of method and of pivotal catchment 92

8.10.6 Urbanised catchments 93

9 IBIDEM 94

9.1 The idea of IBIDEM 94

9.1.1 Reminder of hydrograph estimation by FSU methods 94

9.1.2 Hydrograph estimation by the FSR design event method 94


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9.1.3 Basic idea of bridge between the FSR and FSU methods 95

9.2 How IBIDEM fits hydrographs 96

9.3 General approach to the optimisation 97

9.3.1 “First Tp and then SPR” 97

9.3.2 Use of horizontal fitting 98

9.3.3 Deriving Tp by optimising the fit to the FSU flood hydrograph 98

9.3.4 Deriving SPR by matching the required peak flow 100

9.4 Additional IBIDEM options 100

9.4.1 Flood frequency 100

9.4.2 Sensitivity to storm duration 100

9.4.3 Sensitivity to model parameters 100

9.4.4 Sensitivity to changes in urbanisation 101

9.5 Further details of the software 102

9.5.1 Inputs 102

9.5.2 Graphical displays 102

9.5.3 Display options 105

9.5.4 Goodness-of-fit measures 105

9.5.5 Tabular display 107

9.5.6 Export of results 108

9.6 Testing 108

9.6.1 Choice of test sites 108

9.6.2 Estimation of FSU hydrograph shapes 108

9.6.3 Estimation of peak flows 110

9.6.4 Rainfall depth-duration frequency tables 110

9.7 Results 111

9.7.1 Suir at Caher Park 111

9.7.2 Owenboy at Ballea 112

9.7.3 Lagan-Glyde at Aclint 112

9.7.4 Anner at Clonmel 114

9.7.5 Tributary to Tolka at Finglas 115

9.7.6 Illustration of effect of fitting threshold 116

9.7.7 Summary 117

9.8 Additional opportunities provided by IBIDEM 117

9.8.1 Strengths and limitations 117

9.8.2 Urban adjustment to design hydrographs 119

9.8.3 Supplying input hydrographs to river models 119

9.8.4 Allowances for projected land-use change 120

Acknowledgements 121

References 121

Appendices 123

Appendix A Gauges used in Hydrograph Width Analysis 123

Appendix B Précis of UCC research on flood event analysis 128

Appendix C Performance of HWA methods on verification events 130

Appendix D HWA results and their estimates from PCDs 167

Appendix E Application of the HWA software 171


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E1 Troubleshooting the installation 171

E2 Graphical User Interface (GUI) concepts of HWA software 173

Appendix F Further details of IBIDEM 183

F1 Method of optimising Tp 183

F2 Method of fitting SPR 184

F3 Checks and validation of outputs 185

Maps

Map 1.1: Stations used in hydrograph width analysis 4 Map 5.1: Catchment of Station 25014 Silver at Millbrook 37 Map 9.1: Location of test catchments 109

Figures

Figure 1.1: Screen-shot of start-up window of HWA software 5 Figure 2.1: Hydrographs of flood events displayed within a common window of 275 hours 8 Figure 2.2: Time series of flood events at Station 07009 Boyne at Navan Weir 8 Figure 2.3: Seasonal distribution of flood events at Station 07009 Boyne at Navan Weir 9 Figure 2.4: Decoupling the main components of Events 1, 7 and 24 at Station 07009 11 Figure 3.1: Standardised flood hydrographs for Events 1, 5, 7 and 24 at Station 07009 13 Figure 3.2: Methods of constructing a characteristic hydrograph 15 Figure 3.3: Median hydrograph for Station 07009 Boyne at Navan Weir 16 Figure 3.4: Median hydrographs with irregularities 17 Figure 3.5: (a) Smoothed median hydrograph; (b) Truncated median hydrograph 18 Figure 4.1: UPO-Gamma hydrograph for Tr=50 and different values of shape parameter n 22 Figure 4.2: UPO-Gamma hydrograph for n=3 and different values of scale parameter Tr 22 Figure 4.3: UPO-Gamma curve fitted to median hydrograph at Station 07009 23 Figure 4.4: Exponential replacement recession (ERR) for different values of parameter C 24 Figure 4.5: UPO-ERR-Gamma curve fitted to median hydrograph at Station 07009 25 Figure 4.6: Performance of UPO-ERR-Gamma model on verification events, Station 07009 29 Figure 4.7: Verification performance of UPO-ERR-Gamma calibrated in five versions 30 Figure 5.1: Performance of median hydrograph method across 37 Grade A1 stations 31 Figure 5.2: Performance of UPO-ERR-Gamma method across 37 Grade A1 stations 31 Figure 5.3: Comparison of model performance across 37 Grade A1 stations 32 Figure 5.4: Performance in verification compared to that in calibration 33 Figure 5.5: Varied hydrograph shapes at Station 34018 Turlough at Castlebar 34 Figure 5.6: Wide and narrow-peaked hydrographs at Station 24013 Deel at Rathkeale 35 Figure 5.7: Wide and narrow-peaked hydrographs at Station 25006 Brosna at Ferbane 35 Figure 5.8: Wide and narrow-peaked hydrographs at Station 25014 Silver at Millbrook 36 Figure 5.9: Wide and slanted hydrographs at Station 25025 Ballyfinboy at Ballyhooney 36 Figure 5.10: Rainfall-runoff behaviour in 30 June 1986 flood at Station 25014 37 Figure 5.11: Attenuated hydrographs at Station 25017 Shannon at Banagher 38 Figure 5.12: Median hydrograph for Station 07009 Boyne at Navan Weir (whole sample) 39 Figure 5.13: Summary index, s, of hydrograph skewness (89 Grade A1 + A2 stations) 40 Figure 5.14: Characteristic hydrograph for Station 35002 Owenbeg at Billa Bridge 43 Figure 5.15: Characteristic hydrograph for Station 30005 Robe at Foxhill 44 Figure 5.16: Characteristic hydrographs for four stations on the River Suir 44 Figure 5.17: UPO-ERR-Gamma characteristic hydrographs for four stations on the Suir 45 Figure 5.18: Hydrographs and rescaled characteristic hydrograph for Deel at Rathkeale 47 Figure 6.1: Matrix plot of PCDs that in part represent catchment size (89 stations) 55 Figure 6.2: Normality plots of log-transformed width descriptors and model parameters 57 Figure 6.3: Normality plot of standardised residuals for 5-variable model for ℓnW75 62 Figure 6.4: Plot of standardised residuals for 5-variable model for ℓnW75 63 Figure 6.5: Median hydrographs at: (a) Station 15002 and (b) Station 35071 68


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Figure 6.6: Derived and modelled values of W75, W50, n, Tr and C (BFI unavailable case) 69 Figure 7.1: Variation of hydrograph width with peak flow at Station 07009 71 Figure 7.2: Variation of hydrograph width with peak flow at Station 07010 72 Figure 7.3: Patterns of variation of hydrograph width with peak flow (at six stations) 72 Figure 7.4: Slope of W75 trend with peak flow magnitude (Grade A1 stations) 73 Figure 7.5: Variation of hydrograph width with pre-event minimum flow (Station 07009) 74 Figure 7.6: Slope of W75 trend with pre-event minimum flow (Grade A1+A2 stations) 74 Figure 7.7: Plot of flood peak against time of year (Station 07009 Boyne at Navan Weir) 75 Figure 7.8: Circular plot of W50, W75 and W90 against time of year (floods at Station 07009) 75 Figure 7.9: Characteristic hydrographs for four sites affected by arterial drainage 78 Figure 8.1: UPO-ERR-Gamma characteristic hydrograph at St

n 07009 by Table 6.7 models 80

Figure 8.2: As Figure 8.1 but with pre-event flow substituting for first part of hydrograph 81 Figure 8.3: Example of parabolic curves method (Station 07009 treated as ungauged) 85 Figure 8.4: Parabolic hydrographs for four stations on the Suir 86 Figure 8.5: Upper hydrographs transferred from Derrycahill to Rookwood 91 Figure 8.6: Derived median and UPO-ERR-Gamma hydrographs for St

ns 26002 and 26005 92

Figure 9.1: Design inputs to FSR rainfall-runoff method of flood frequency estimation 95 Figure 9.2: Illustration that FSR T-year peak flow varies with Tp as well as with SPR 97 Figure 9.3: Horizontal fitting by comparing hydrograph widths 98 Figure 9.4: Relationship between peak flow Qpeak and peak rapid response qpeak 98 Figure 9.5: Double-peaked hydrograph 99 Figure 9.6: Display of fitted and imported hydrographs 103 Figure 9.7: Display of how a variable changes with return period 103 Figure 9.8: Display of hydrographs for multiple storm durations 104 Figure 9.9: Display of how a variable changes with storm duration 104 Figure 9.10: Display of sensitivity to an increase in URBEXT 105 Figure 9.11: FSR hydrograph fitted to UPO-ERR-Gamma hydrograph 106 Figure 9.12: As Figure 9.11 but with fitting threshold raised to 60% of peak flow 107 Figure 9.13: Example of IBIDEM tabular display 107 Figure 9.14: Suir at Caher Park 100-year hydrograph fit 111 Figure 9.15: Owenboy at Ballea 100-year hydrograph fit 112 Figure 9.16: Lagan-Glyde at Aclint – derived median hydrograph from HWA software 113 Figure 9.17: Lagan-Glyde at Aclint – 100-year hydrograph fits 113 Figure 9.18: Anner at Clonmel 100-year hydrograph fit 114 Figure 9.19: Tributary of Tolka at Finglas 100-year hydrograph fit 115 Figure 9.20: Urban adjustment to hydrograph for Tolka tributary at Finglas test site 119

Figure B.1: Catchment-average unit hydrographs standardised by area 129

Figure C.1: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 06011 130 Figure C.2: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 06012 131 Figure C.3: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 06013 132 Figure C.4: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 06014 133 Figure C.5: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 06026 134 Figure C.6: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 07007 135 Figure C.7: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 07009 136 Figure C.8: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 07010 137 Figure C.9: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 07012 138 Figure C.10: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 09001 139 Figure C.11: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 14004 140 Figure C.12: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 14006 141 Figure C.13: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 14007 142 Figure C.14: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 14011 143 Figure C.15: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 14018 144 Figure C.16: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 15005 145 Figure C.17: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 23002 146 Figure C.18: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 24013 147


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Figure C.19: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25003 148 Figure C.20: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25006 149 Figure C.21: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25014 150 Figure C.22: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25017 151 Figure C.23: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25025 152 Figure C.24: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25027 153 Figure C.25: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 25030 154 Figure C.26: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 26007 155 Figure C.27: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 26008 156 Figure C.28: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 26012 157 Figure C.29: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 26019 158 Figure C.30: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 27002 159 Figure C.31: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 29001 160 Figure C.32: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 29011 161 Figure C.33: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 30004 162 Figure C.34: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 30005 163 Figure C.35: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 34018 164 Figure C.36: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 36010 165 Figure C.37: Verification of median hydrograph + UPO-ERR-Gamma methods at Station 36015 166

Figure E.1: Main application window of the HWA program showing a message-box 174 Figure E.2: Data window for entering data 175 Figure E.3: Data windows for displaying graphical and tabular outputs 176 Figure E.4: A dialog window showing a standard windows file-opening dialog-box 176

Boxes

Box 4.1: The choice between horizontal and vertical fitting 26 Box 4.2: Editorial note on performance measures 28 Box 6.1: Collinearity 49 Box 6.2: The role of ALLUV in the hydrograph-width models 61

Tables

Table 3.1: Widths of exceedance for four floods at Station 07009 Boyne at Navan Weir 14 Table 5.1: Outcome of whole-sample calibration at 89 Grade A1 + A2 stations 40 Table 6.1: Summary statistics of dependent variables (DVs) selected for regression analysis 50 Table 6.2: Some summary statistics of the IVs initially selected 51 Table 6.3: Correlation matrix of selected IVs and DVs at (up to) 89 stations 53 Table 6.4: Stepwise regression results for modelling hydrograph width descriptor ℓnW75 59 Table 6.5: Coefficient and collinearity statistics for selected model for ℓnW75 60 Table 6.6: Recommended models – when BFI available 66 Table 6.7: Recommended models – when BFI unavailable 66 Table 7.1: Some leading PCDs of stations on the River Fane 73 Table 7.2: Stations studied for the effect of arterial drainage on hydrograph widths 76 Table 7.3: Pre- and post-drainage values of hydrograph width descriptors/parameters 77 Table 8.1: Selected PCDs for Suck at Rookwood 89 Table 8.2: Data transfers to Suck at Rookwood using parabolic curves method 91 Table 9.1: Some details of the applications to two ungauged test catchments 109 Table 9.2: Design flows (m

3s

-1) for the five test catchments 110

Table 9.3: IBIDEM input variables for the test catchments 110 Table 9.4: Summary of IBIDEM results for five test catchments (100-year flood case) 116 Table 9.5: Sensitivity to fitting threshold (ungauged site on River Anner) 118

Table A.1: Stations used in Hydrograph Width Analysis 123 Table A.2: Details of the flow data used (see also Table 7.2) 125

Table B.1: Stations subjected to rainfall-runoff analysis 128


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Table D.1: Hydrograph width analysis results for all 89 stations 167

Table E.1: Details of toolbar buttons 182

Table F.1: Example of iteration to find best-fitting value of Tp 184 Table F.2: Checks and outputs 186

Notation

Symbols

≈ Approximately

AF Adjustment factor converting (e.g.) quantile estimates from fixed to sliding duration

ANSF Average non-separated flow (m3s

-1 per km

2)

ARF Areal reduction factor (in estimating design depth of catchment rainfall)

BF Baseflow in FSR rainfall-runoff method (m3s

-1); equivalent to pre-event flow Q0

C Recession parameter of UPO-ERR-Gamma model (hours)

CWI Catchment wetness index (in FSR design event method)

D Duration (in hours) of design storm in FSR design event method

f(x) Probability density function

F(x), F Cumulative distribution function

g Ordinate of Gamma distribution

I(n,x) Incomplete Gamma function

K Scale parameter of Gamma distribution (hours)

ℓn Natural logarithm

m Number of (% of peak flow) levels at which hydrograph width evaluated when fitting

n Shape parameter of Gamma distribution (and of UPO-ERR-Gamma model)

N Number of years of record, sample size

P Precipitation depth (mm)

PR Percentage runoff (in FSR design event method)

Q Flow (m3s

-1)

Q0 Pre-event flow (m3s

-1)

QT T-year peak flow (m3s

-1)

QMED Median annual flood (m3s

-1)

r2 Coefficient of determination

s Hydrograph skewness or eccentricity parameter, e.g. in parabolic curves method

s(t) S-curve (i.e. cumulative response curve)

SPR Standard percentage runoff (in FSR design event method)

T Return period (years)

Tflood Return period of flood (in FSR design event method)

Tr Rise-time (= translation parameter) of UPO-ERR-Gamma model

Train Return period of rainfall (in FSR design event method)

Tp Time-to-peak of unit hydrograph (in FSR design event method)

Tp(0) Time-to-peak of instantaneous unit hydrograph (in FSR design event method)

Vc(p) Semi-dimensionless volume of characteristic hydrograph above p% of peak flow

(hours)

VD(p) Volume of design flood hydrograph above p% of peak flow (m3s

-1 hours; m

3)

Var Variance

w Weighting function

W Hydrograph width (hours)

W50 Hydrograph width (hours) at 50% of peak flow

W75 Hydrograph width (hours) at 75% of peak flow

y Ordinate of Gamma distribution standardised to have a unit peak

Γ(n) Gamma function


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Subscripts

p Value at peak; percentage of peak

I Value at point of inflection

Abbreviations and descriptor names

AEP Annual exceedance probability

ALLUV Proportion of extent of floodplain alluvial deposit

AM Annual maximum

AMRE Average value of mean relative error

AREA Catchment area (km2)

BFI Baseflow index (see Volume IV)

CEH Centre for Ecology and Hydrology

CFRAM Catchment Flood Risk Assessment and Management

CSV Comma-separated values (file format)

DDF Depth-duration-frequency

DMH Derived median hydrograph

DV Dependent variable

ERR Exponential replacement recession

FEH Flood Estimation Handbook

FSE Factorial standard error

FSR Flood Studies Report

FSSR Flood Studies Supplementary Report

FSU Flood Studies Update

GIS Geographic information system

GUI Graphical user interface

HWA Hydrograph Width Analysis; also name of standalone software package for HWA

IBIDEM Interactive Bridge Invoking the Design Event Method

IH Institute of Hydrology, former name of CEH Wallingford

IV Independent variable

LH Left hand

MA Moving average

MRE Mean relative error

NERC (UK) Natural Environment Research Council

NSE Nash-Sutcliffe efficiency

OPW Office of Public Works

PCD Physical catchment descriptor (see Volume IV)

POT Peaks-over-threshold

PR Percentage runoff

RH Right hand

RMSE Root mean square error

SAAR Standard average annual rainfall (mm) – the FSU uses 1961-90 as the standard period

SE, se Standard error

tsf Tab-separated format

UK United Kingdom

UPO Unit peak at origin

URBEXT Urban extent: fraction of catchment classified as urban

WP Work Package (within the FSU research programme)


xiii

Glossary of terms

Term Meaning

Annual

exceedance

probability AEP

Probability of one or more exceedances in a year of a preset rainfall depth (in a

given duration)

Annual

exceedance series

Peak-over-threshold (POT) series comprising the largest N events in N years of

record

Annual maximum

series Time series containing the largest value in each year (12-month period) of record

for a particular duration

Calibration Comparison of a model’s predictions with actual data, and adjustment of its

parameters to achieve a better fit with reality

Characteristic

hydrograph

Semi-dimensionless hydrograph defined to represent the characteristic shape of

flood hydrographs. Ordinates of the characteristic hydrograph are standardised

so that the peak value is 1.0. Abscissae indicate the time (in hours)

Coefficient of

determination r2

Proportion of variation accounted for by (e.g.) a regression model

Confidence

interval Bounds within which a population parameter is estimated to lie with a stated

(usually %) confidence; used to indicate the reliability of an estimate

Easting and

Northing Coordinates of a location expressed as distance eastwards and distance

northwards from a fixed datum (i.e. reference point)

Eccentricity Parameter summarising the skewness of the upper hydrograph

Genetic algorithm An optimisation (or calibration) method based on global or heuristic searching

Geometric mean n

th root of the product of a sample of n values of a positive variable such as

rainfall depth

Growth curve Formula specifying the increase of a defined extreme (e.g. peak flow) with return

period; provides the factor by which the index flood is multiplied to estimate the

T-year flood

Interpolation Any method of computing new data points from a set of existing data points

Location

parameter

Parameter representing value subtracted from or added to a variable x to translate

the graph of its probability distribution along the x-axis. The location of the

UPO-ERR-Gamma model is determined by the time of the peak flow.

Peak-over-

threshold (POT)

series

For a given duration (e.g. 24 hours), a time series of independent events

(abstracted from the period of record) that exceed a preset threshold; the series

retains the magnitudes (in mm) and dates of the peak exceedances, together with

their times of occurrence; successive POT rainfall events must not overlap

Residual Observed value minus the value estimated by a model

Return period T

Average number of years between years with rainfalls exceeding a certain value.

T is the inverse of the annual exceedance probability (AEP). Thus, a 50-year

return period corresponds to an AEP of 0.02. The return period is a basic

component of the depth-duration-frequency model used to calculate a rainfall

depth of the desired frequency.

Scale parameter

Parameter controlling the spread of a distribution; e.g. scale parameter Tr

controls the width of the characteristic hydrograph in the UPO-ERR-Gamma

model

Shape parameter Parameter controlling the shape of a distribution; e.g. shape parameter n controls

the shape of the hydrograph in the Gamma part of the UPO-ERR-Gamma model


xiv

Term Meaning

Skewness

A measure of the departure from symmetry of a distribution; the hydrograph

skewness descriptor s is the mean ratio of the width under the rising limb of the

hydrograph to the total hydrograph width at that level.

Standard

deviation Measure of dispersion (i.e. variation) of values about their mean

Standard error Estimated standard deviation of a sample statistic such as the mean, i.e. the

standard deviation of the sampling distribution of the statistic

Unimodal Having one maximum e.g. on its probability density function or hydrograph

Verification (or

validation)

Assessment or confirmation of a derived model’s performance by reference to

additional data (i.e. data not used in calibration of the model)


1

1 Introduction

1.1 Overview

Need for hydrograph information

Until recent years, practitioners in Ireland have typically used methods of flood frequency

estimation based on the Flood Studies Report (FSR). The Flood Studies Update (FSU)

builds on the methodologies of the FSR (NERC, 1975) by using updated databases of Irish

hydrometric data and by applying GIS tools for the computation of Physical Catchment

Descriptors (PCDs). While the estimation of peak flows (see Volume II) is of general

importance, in a proportion of cases it is also necessary to construct the flood hydrograph

associated with the T-year peak flow. The requirement is clearest where a flooding problem

or a flood alleviation scheme is sensitive to prolonged high flows.

Because of “the relative richness of hydrograph data in Ireland and the relative paucity of

rainfall data” (Reed, pers. comm., 2006), it was not envisaged that rainfall records would be

used in the FSU for flood hydrograph estimation. The hydrological analyses reported here

therefore have the objective of establishing methodologies for estimating design flood

hydrographs from recorded flow data only. PCDs are used to develop regression-based

estimates of such hydrographs so that they can be constructed at ungauged sites.

In many applications, the design flood hydrograph corresponding to a specified return period

is required at a particular site. The site of interest – referred to as the subject site – may be

gauged or ungauged. Whereas the design peak flow of a given return period is obtained in

the case of a gauged site by statistical frequency analysis of flood peak data, complementary

methods are required to produce the characteristic hydrograph to be associated with that peak

flow. In the FSU, the requirement is met by Hydrograph Width Analysis.

Some earlier methods

Reed and Marshall (1999) list three approaches to defining the design hydrograph: adjusting

the FSR rainfall-runoff model parameters, borrowing a standard hydrograph shape from the

FSR rainfall-runoff method, and applying a simplified model of hydrograph shape. The first

two approaches are taken forward in the FSU by development of IBIDEM (see Chapter 9). In

the third approach, the upper part of the hydrograph – beneath a flood peak of the required

return period – is synthesised by a quadratic function of W50 defined as the width of the

hydrograph (measured in hours) at 50% of the peak flow. If required, the lower part of the

hydrograph is sketched subjectively. At gauged sites, W50 is estimated from the analysis of

observed flood hydrographs. At ungauged sites, a regression-based estimate relating W50 to

the unit hydrograph time-to-peak is used. In the FEH method (Reed and Marshall, 1999), the

upper part of the flood hydrograph is constrained to be symmetric about its peak. This

approach is taken forward in the parabolic curves method (see Section 8.7). This exploits

additional hydrograph width information and permits the upper hydrograph to be asymmetric.

Archer et al. (2000) develop a non-parametric method for the synthesis of design flood

hydrographs. This is based on direct analysis of the shape of flood hydrographs observed at a

site. Archer et al. analyse hydrographs for flood events drawn from the annual maximum

series. They note the durations of exceedance of selected percentages of the peak flow,


2

distinguishing the elements before and after the peak flow. For each exceedance percentage

point in turn, the median duration is noted across the N annual maximum events. A

hydrograph is thereby derived which is non-dimensional with respect to discharge. The

resulting characteristic hydrograph is then applied to the peak flow of given return period to

synthesise the required design flood hydrograph. By distinguishing periods before and after

the peak flow, the characteristic hydrograph is not constrained to be symmetric.

Archer et al. suggest that the characteristic hydrograph shape thus derived provides a more

realistic basis for generating a design flood hydrograph. The method is claimed to be simpler

and quicker, and not to require the separate assessment of baseflow and storm runoff (Archer

et al., 2000). However, their method is applicable only at gauged sites.

Approach adopted

The Hydrograph Width Analysis (HWA) reported below takes the Archer et al. method as its

starting point. The method presented in Chapters 2 and 3 is applied to flood hydrographs

from 89 gauging stations. Using physical catchment descriptors (PCDs) developed in

Volume IV, the method is generalised in Chapter 6 to allow synthesis of a characteristic

hydrograph at ungauged sites.

Some notes on the structure of volume

Volume III is largely based on HWA research undertaken at NUI Galway as Work Package

3.1 of the Flood Studies Update. Later chapters discuss the application of methods to design

flood hydrograph construction at gauged and ungauged sites. The IBIDEM software package

(see Chapter 9) developed by JBA Consulting extends both the applicability of the HWA

methods and the case-by-case interpretation of T-year flood estimates developed using

Volume II methods.

Station 07009 Boyne at Navan Weir is used as the primary example in illustrating the HWA

procedures. There was no special reason for choosing this station for demonstration

purposes. Other gauged catchments are used where appropriate to illustrate particular

features of HWA. In addition, testing of IBIDEM considers three gauged and two ungauged

sites.

An overarching requirement was that the HWA methods developed needed to be simple

enough to give scope to generalise their use at ungauged (as well as gauged) sites.

1.2 The goal and premise of hydrograph width analysis

The primary goal of the hydrograph width analysis (HWA) research was to devise a

methodology to “flesh out” the hydrograph beneath a given peak value. The aim was to

define the shape of the design flood hydrograph based on typical flood hydrographs which

have occurred. A subsidiary objective was to investigate the extent to which specific factors

influence the typical shape of the flood hydrograph. Ancillary studies reported in Chapter 7

examine the influence on flood hydrograph shape of the flood magnitude, its season of

occurrence, the pre-event flow and effects arising from arterial drainage works.

The premise of HWA is that hydrographs of floods occurring at a particular station are

broadly similar in character and that the typical shape of the hydrograph of a future flood –


3

embodied in the design flood hydrograph – can be expected to reflect the general features of

those which already occurred. Assessment of similarity is subjective, being largely based on

visual judgement.

It is sometimes found that, because of prolonged rainfall at the peak-inducing intensity, a few

flood hydrographs at a station can exhibit a highly flattened and prolonged peak segment.

Use of the median hydrograph width – as in Archer et al. (2000) – ensures that such atypical

flood hydrographs do not receive undue weight in the analysis. Nevertheless, a statistical

measure is required to summarise the degree of similarity between synthesised and observed

flood hydrographs.

Whereas the shapes of the upper parts of observed flood hydrographs (e.g. the parts with

flows above 50% of the respective peak flows) are often found to be generally similar, those

of the lower parts tend to vary widely. The variation reflects a number of factors including

the occurrence of preceding and/or following floods subsidiary to the main event.

If only the upper part of the hydrograph of the design flood is deemed important, a procedure

to model the lower part is not required. However, in a proportion of applications, the

complete hydrograph is required.

1.3 Catchment selection

Detailed flow data are required for hydrograph width analysis, and flow data at 15-minute

interval were obtained for 90 gauging stations operated by the OPW. Physical catchment

descriptors (PCDs) were not initially available for Station 39008. The study therefore

considered a network of 89 stations.

The stations chosen were selected with regard to the quality of flow data expected. Grade A1

and Grade A2 are the highest categories of rating curve and water level measurement

reliability (see Appendix A1.1 of Volume II). The selected stations comprise 37 stations

graded A1 and 52 graded A2. Their catchment areas range in size from 23 to 7980 km2, with

a median value of 285 km2. The 89 catchments are identified in Map 1.1 and in Table A.1 of

Appendix A.

Hydrograph data were supplied as 15-minute data in a time-series format. Each *.tsf datafile

held the date and time of occurrence, the flow (in m3s

-1) and a quality code against the

measurement. Table A.2 indicates the period of flow data abstracted, the completeness of

15-minute data across that period, the number of annual maximum (AM) values represented,

and the median of the annual maxima (i.e. QMED) across that period. Also shown is the

period during which any arterial drainage works were carried out on the catchment. For

stations affected by drainage works, the main HWA used the post-drainage record only.


4

Map 1.1: Stations used in hydrograph width analysis

1.4 Physical catchment descriptors (PCDs)

Physical catchment descriptors (PCDs) at 216 gauged locations on rivers and lakes in Ireland

were supplied by the OPW. Details are given in Volume IV. That volume includes three

special PCDs developed in the FSU research: FAI, BFIsoil and FLATWET.

The special descriptor FLATWET was available and, in certain circumstances, plays a role in

constructing the characteristic hydrograph at an ungauged site. However, the FAI and BFIsoil

descriptors had not been developed at the time of the hydrograph width research. To allow

0 40 8020 Kilometers

Legend

! Stations considered in the "Hydrograph Width Analysis"

!

!

!

!!

!

!

!

!

!

!!

!

!

!

!

!

!

!

!

!!

!

!

!

!

!

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!!!

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!

!!

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!!! !

!!

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!

9001

7033

70127011

70107009

7007

70067004

7002

6026

60146013

6012

6011

39009

3602736021 36019

36015

3601136010

35071

3500535002

35001

34018

34009

34001

30061

30007

30005

30004

2901129004

29001

2700227001

26022

26021

26019

2601226009

26008

26007

26005

26002

25030 25029

25027

25025

25017

2501625006

2500525003

25001

2408224013

24008

23012

2300223001

22071

19001

1800518004

16009

1600816005

16004

16003

16001

15006

15005

15003

1500214018

14011

1400914007

14006

14004

11001

! Station location

(The boundaries shown

mark the Hydrometric

Areas of Ireland)


5

consideration of soil permeability and other storage effects on hydrograph widths, median

values of the baseflow index (BFI) were supplied for 198 stations. BFI values were

unavailable for ten of the 89 stations selected for HWA. Consequently, Stations 07007,

07011, 14004, 15002, 25017, 26009, 29001, 36010, 36027 and 39009 had to be omitted from

those analyses requiring BFI.

1.5 The characteristic hydrograph

The aim of the research is to allow the user to construct the design hydrograph of a given

return period. The hydrograph represents flows in m3s

-1. Following Archer et al. (2000), the

need is met by defining a semi-dimensionless flood hydrograph. This has time coordinates in

hours but the peak flow is standardised to be 1.0. The terminology adopted in the FSU is to

call this the characteristic hydrograph.

At gauged sites, the characteristic hydrograph is constructed by direct analysis of hydrograph

data observed in large floods, i.e. by hydrograph width analysis. At ungauged sites, the

characteristic hydrograph is synthesised from PCDs by methods presented in Chapter 6.

Typically, the required design hydrograph in m3s

-1 is obtained by scaling up the characteristic

hydrograph by the T-year flood peak estimated using Volume II methods.

1.6 HWA software

Written in Visual Basic and Fortran, the standalone software package HWA provides an

interactive tool for Hydrograph Width Analysis, displaying data and results in tabular and

graphical forms. Outputs can be saved under user-defined filenames for future access and

use. A screen-shot of the HWA start-up window is shown in Figure 1.1. Technical details

appear later in Appendix E. The software is available to practitioners through the data and

software download module of the FSU Web Portal.

Figure 1.1: Screen-shot of start-up window of HWA software


6

2 Processing the flow data for HWA

This chapter describes the processing procedures by which flow data were screened and flood

events selected and filtered for hydrograph width analysis.

2.1 Data screening and checking

2.1.1 Data handling

For gauging stations in the OPW network, river-flow data at 15-minute interval are held in

datafiles having the .tsf filename extension. For many stations, these files contain more than

a million items of data.

Scanning such long data series for the purpose of identifying and selecting flood events is

both tedious and restrictive within commonly used software applications. Prior to

introduction of the 2007 version, Microsoft Excel had a limit of 65,536 rows. Even in the

2007 version, the row limit is too small to accommodate 15-minute data series of 30 years or

longer.

Application-specific programs were therefore written in Fortran to accept data in the .tsf

format and to search the data series for flood events. Visual Basic was used to create a

standalone user-interface for displaying flood hydrographs with interactive graphics.

Additional programs were written to analyse the identified flood hydrographs and to select

and implement generally suitable methods for final adoption. The development resulted in

the HWA software package (see Appendix E).

2.1.2 Missing flow data

The HWA research considered flow data from 89 Grade A1 or A2 stations. There are

occasional data gaps in the 15-minute flow records. A typical reason given is that the chart

was missing. Percentages of missing data are listed in Table A.2 for each station. Eight

stations had more than 10% of data missing but only Stations 25005 and 26021 had more than

20% of data missing. The median proportion of missing data was 2.9%.

Complete hydrograph data were therefore not always available for all flood events. In a few

cases it proved possible to analyse the rising or receding limb of the flood event where the

gap in flow data affected only the opposite limb of the hydrograph.

2.1.3 Scrutiny of annual maximum flood peaks

Annual Maximum (AM) flood peaks were extracted and scrutinised for anomalies. In some

cases, the existence of a very large value in the AM series called for special investigations.

This occasionally led to the discard of doubtful data.

The index flood adopted in the FSU is QMED, the median of the AM floods. The QMED

value corresponding to the period of record used in HWA is given in the penultimate column

of Table A.2 (see Appendix A).


7

2.1.4 Stations affected by arterial drainage

For information, the final column of Table A.2 identifies those of the 89 stations which have

experienced arterial drainage within or prior to their overall period of record. The

hydrological and spatial descriptors of the FSU catchments (see Volume IV) were assembled

relatively recently, and generally reflect the post-drainage characteristics of such catchments.

Consequently, the main HWA for these catchments was carried out using hydrographs from

the post-drainage period only.

Stations 07007, 07010, 23002, 26012 and 30004 had 15-minute flow data available for both

pre and post-drainage periods. These five catchments are used specifically in Section 7.4 to

examine the effect of arterial drainage on the typical shape of flood hydrographs.

2.2 Defining the time-window of the flood hydrograph

The convention adopted was to position the time origin at the peak of the hydrograph. Thus,

each flood hydrograph is presented with its peak occurring at t = 0, with its rising and

receding limbs shown on the LH and RH sides of the peak respectively.

In some instances, due to prolonged rainfall of peak-inducing intensity, an observed flood

hydrograph exhibits a flattened (i.e. sustained or persistent) peak. In such cases, the first

occurrence of the peak flow is considered as the origin of the time axis for the purpose of

hydrograph width analysis. Thus, in the case of sustained peak flow, the receding limb of the

flood hydrograph includes the peak flow over the period during which it persists after its first

occurrence.

The user of the HWA software specifies the start and end of the flood hydrograph by

indicating the time intervals from the peak back to the start of the hydrograph and from the

peak forward to the end of the hydrograph. The sum of these two time intervals defines the

time-base (or window) that embraces the flood peak and the flood hydrograph about it.

It is convenient to adopt a common time-base when displaying a number of flood

hydrographs for a particular station. The user of the HWA software guesses values for the

time intervals (before and after the flood peak). Each of the observed flood hydrographs is

then displayed within a window of common size. Finalising values of the time intervals

requires a number of trials, the objective being to contain all the selected flood hydrographs

within the final common window.

Figure 2.1 provides an example of flood hydrographs for three events displayed within a

common window. For this station, the 275-hour window comprises 50 hourly time-steps on

the rising limb of the hydrograph and 225 hourly time-steps on the receding side. This

reflects that flood hydrographs for Station 07009 Boyne at Navan Weir are generally

observed to rise (from the level of the pre-event flow to the peak) over about two days and to

recede (from the peak to the level of the baseflow) over about nine days.


8

Figure 2.1: Hydrographs of flood events displayed within a common window of 275 hours

2.3 Selection of flood hydrographs

The final selection of flood hydrographs was made by applying a peaks-over-threshold (POT)

criterion. This ensures that the hydrograph width analysis gives due weight to the largest

floods recorded. Where the annual maximum series comprises N floods (i.e. representing N

water-years of record), the criterion applied was to select the N largest flood events from this

period. This special case of a POT series is known as the annual exceedance series.

Figure 2.2 illustrates the annual exceedance series for Station 07009 and shows how it relates

to the annual maximum (AM) series. The AM events are marked by small green circles, with

the broken green line drawn to indicate the QMED of 134.8 m3s

-1. Events in the annual

exceedance series are marked by blue circles.

There are 29 annual maxima at this station. Some 19 of these 29 flood events are in the

annual exceedance series. The annual exceedance series includes ten further floods (from

flood-rich years) in place of the ten smallest annual maxima (in flood-poor years).

The blue line marks the level of the 30th

largest flood in the annual exceedance series and

defines the threshold above which the annual exceedance series has been extracted to yield 29

events in 29 years. [Editorial note: For reasons that are not entirely clear, the 30th

largest

flood has been included in the annual exceedance series at this station. The dates shown

along the x-axis of Figure 2.2 are correct but are not very helpful. The tick-marks are spaced

at an interval of 50675 15-minute periods i.e. about every 528 days.]

Figure 2.2: Time series of flood events at Station 07009 Boyne at Navan Weir


9

An exception was made in two cases where the number of flood events would otherwise have

been very small. Stations 14011 and 25003 had hydrograph data for only five and seven

water-years respectively. The number of events selected in these cases was arbitrarily

doubled: i.e. using ten events at Station 14011 and 14 at Station 25003.

2.4 Numbering of flood hydrographs

As part of the selection process, flood events are numbered according to their ranking in the

annual exceedance series. Thus, Event 1 is the largest flood event and Event 10 is the tenth

largest flood event. The event numbering carries through to the flood hydrographs.

[Editorial note: This is thoroughly effective in ensuring that hydrographs of the largest

floods attract particular attention in analysis. It remains to be seen whether the device leads

to confusion when flow records are updated by the extraction of hydrographs for later events.]

2.5 Seasonal distribution of flood events

The circular plots of Figure 2.3 illustrate the seasonal distribution of flood events at

Station 07009. The angular position denotes the calendar date. Again, the green circles mark

the AM events and the blue circles denote the annual exceedance events. The plots in Figure

2.3 are identical except that the radial axis is marked in m3s

-1 in the LH diagram and in

multiples of QMED in the RH diagram.

The mean time-of-year of floods is found by plotting the centroid (analogous to the centre of

mass) of the data points. The centroids in Figure 2.3 are marked by filled circles: green for

the AM series and blue for the annual exceedance series. The mean time-of-year of flood

events at Station 07009 is seen to be early January.

Figure 2.3: Seasonal distribution of flood events at Station 07009 Boyne at Navan Weir

[Editorial note: Radial positions in Figure 2.3 indicate the magnitudes of the flood events.

Calculation of the mean time-of-year of flooding has been weighted by flood magnitude.]


10

2.6 Filtering of selected hydrographs

2.6.1 Desire for broadly unimodal hydrographs

Essentially unimodal (i.e. single-peaked) flood hydrographs are to be favoured when deriving

the characteristic hydrograph. [Editorial note: The characteristic hydrograph is to be applied

to design flood peaks derived by Volume II methods to yield the T-year flood hydrographs

required in many flood risk assessments. Such design events are hypothetical floods. It is

therefore reasonable to allow the characteristic hydrograph itself to be stylised. In essence,

the aim is to construct a design flood hydrograph that represents the typical catchment flood

response to one heavy rainfall event rather than to a succession of events.]

It was observed that many high-ranking flood events across the 89 stations had complex (i.e.

multi-peaked) hydrographs. At some stations, very few single-peaked floods could be

identified. This precluded the option of deriving the characteristic hydrograph from only

those flood events with broadly one-peaked hydrographs. Techniques for decoupling

complex floods were devised to overcome this difficulty.

2.6.2 Decoupling the main flood response within a complex flood event

A complex flood event is one having multiple peaks. Typically, it represents the catchment

flood response to more than one period of heavy rainfall. Several approaches were

investigated for decoupling (i.e. isolating) the main flood response within a complex event.

One approach constructed a master recession curve from segments of the receding limbs of

single-peaked hydrographs observed for the station. An analogous master rising curve was

similarly constructed from segments of the rising limbs of single-peaked hydrographs at the

station. Whilst dealing with some individual stations adequately, the approach failed to

generalise for use across all stations. There was a specific concern that the approach led to

bias in the characteristic hydrograph.

The approach ultimately adopted was simply to discard the complex segments of the flood

hydrograph: retaining only the broadly unimodal part.

2.6.3 Discarding the complex segments

Only that part of the observed complex hydrograph embracing the largest peak is considered

relevant for deriving a generalised shape of the design flood hydrograph. Parts of the

hydrograph that can be visually associated with flood responses before/after the largest-

peaked flood response are discarded. The decoupling is done subjectively, using interactive

features of the HWA software.

The decoupling is illustrated for three flood events at Station 07009 Boyne at Navan Weir.

Figure 2.4 shows the hydrographs for the largest, 7th

largest and 24th

largest floods analysed.

The cyan-coloured sections of the plotted hydrographs indicate the parts discarded. The grey-

coloured section indicates the decoupled component of the main flood response. This is the

hydrograph used in the subsequent Hydrograph Width Analysis.


11

Figure 2.4: Decoupling the main components of Events 1, 7 and 24 at Station 07009


12

3 Deriving the characteristic hydrograph at gauged sites

Methods are described for deriving the characteristic hydrograph at a gauged site. Two

groups of methods are distinguished: parametric and non-parametric. The non-parametric

approach derives the characteristic hydrograph by a statistical averaging of hydrographs. It is

non-parametric because it does not make any particular assumptions about the shape of the

hydrograph.

In contrast, the parametric approach specifies a formulaic shape for the characteristic

hydrograph. Its basic aim is to represent the hydrograph by a smooth curve expressible in

terms of a small number of parameters. Although other strategies are possible, it was found

most effective to fit the parametric form to the characteristic hydrograph first obtained using

the non-parametric method. The parametric approach is therefore taken up in Chapter 4.

3.1 Standardising the flood hydrographs

The flood hydrographs comprise isolated single-peaked floods and decoupled (unimodal)

segments of more complex flood events (see Section 2.6). Collectively, these might be

termed filtered hydrographs. Hereafter they are chiefly just called flood hydrographs.

The flood hydrographs are standardised by dividing the flow ordinates by the magnitude of

the peak flow. Each standardised flood hydrograph thus has a peak value of 1.0. This

corresponds to the 100th

percentile of the peak flow, in that 100% of the hydrograph is less

than or equal to this flow. [Editorial note: This terminology is correct when applied at the

peak but not otherwise. The authors refer to percentiles of the peak flow when they ought to

refer to percentages of the peak flow. It was not practical for editing to correct the

mislabelling in every case. Users of the HWA package should therefore interpret percentile

of peak flow as meaning percentage of peak flow.]

The ordinate scale of the standardised hydrograph is percentages of the peak flow. The time

scale of the hydrograph is unaltered, with the abscissa in hours. Thus, the standardised flood

hydrograph is semi-dimensionless. As noted previously, the time origin is taken at the time

of the peak flow.

Flow levels at increments of 5% of the peak flow are identified to the extent that a particular

hydrograph allows. Figure 3.1illustrates this for four hydrographs at Station 07009 Boyne at

Navan Weir. Events 1, 7 and 24 are decoupled from complex flood events; Event 5 is an

isolated unimodal hydrograph.

3.2 Calculation of hydrograph widths at particular exceedance levels

The hydrograph width at a given percentage of the peak flow is defined as the time during

which the flow at a station exceeds the flow corresponding to that percentage of the peak

flow. The total width of exceedance is a time in hours. Following Archer et al. (2000), the

width is divided into two components: one on the rising limb and another on the receding

limb. As seen in Figure 3.1, the width component at a particular percentage of the peak flow

is sometimes available on one limb but not on the other.


13

Figure 3.1: Standardised flood hydrographs for Events 1, 5, 7 and 24 at Station 07009

In characterising the hydrographs, the first step is to choose a series of percentages. If the

objective is to derive only the upper part of the characteristic hydrograph, percentages above

and including 50% of the peak flow are considered sufficient. For other purposes, a fuller

description of the hydrograph is required. The research chose to use percentages at 5%

intervals from 95% down to 5%. In addition, some use was made of the width at 98% of the

peak flow.

The precise value of the flow that corresponds to a selected percentage of the peak will not

generally appear in the 15-minute record of flow data for the event. Linear interpolation is

used to compute the time at which a particular percentage of the peak flow occurs. The

required hydrograph widths can then be found.

For many selected events, hydrograph widths at the lower percentages are generally

unavailable. The widths of exceedance at selected percentages are shown in Table 3.1 for the

sample events of Figure 3.1. For Event 24, the width of exceedance at 65% of the peak flow

is 15.49 hours on the rising side but is undefined on the receding side. [Editorial note: The

terms hydrograph width and width of exceedance are used interchangeably. There is an

unexplained discrepancy between Table 3.1 and Figure 3.1 in the hydrograph widths on the

receding limb of Event 1.]

In certain applications it can be helpful to focus on hydrograph widths at one or two fixed

percentages of the peak flow. There is particular interest here in W75 and W50, which denote

the hydrograph widths at 75% and 50% of the peak flow.

3.3 Procedures for constructing the characteristic hydrograph

A major element of the research was to develop procedures for constructing the characteristic

hydrograph. The principal methods considered in the research are summarised in Figure 3.2.

The applicability of a particular procedure depends on whether the subject site is gauged or


14

ungauged and whether the complete characteristic flood hydrograph or only its upper half is

of interest. The methods ultimately recommended are highlighted.

Table 3.1: Widths of exceedance for four floods at Station 07009 Boyne at Navan Weir

Per

cen

tage

Width of exceedance (hours)

Event 1 Event 5 Event 7 Event 24

Ris

ing

Rec

edin

g

Tota

l

Ris

ing

Rec

edin

g

Tota

l

Ris

ing

Rec

edin

g

Tota

l

Ris

ing

Rec

edin

g

Tota

l

98 2.84 2.44 5.29 2.81 3.65 6.45 4.24 2.25 6.49 2.96 7.01 9.97

95 5.23 4.25 9.48 4.36 6.54 10.91 7.77 5.32 13.09 5.39 10.22 15.61

90 8.32 6.60 14.92 6.45 9.60 16.05 9.64 8.44 18.07 8.24 14.41 22.65

85 14.11 8.75 22.86 7.84 12.16 20.00 10.78 11.55 22.33 10.56 18.17 28.73

80 16.63 10.34 26.97 9.02 14.49 23.51 10.94 14.23 25.17 12.41 21.98 34.39

75 18.02 10.04 17.18 27.22 11.60 17.34 28.94 13.89 25.83 39.72

70 19.29 10.79 21.06 31.85 12.67 20.68 33.35 15.49

65 20.37 12.20 26.81 39.01 14.27 23.44 37.72 17.41

60 21.07 12.97 33.67 46.64 15.14 27.12 42.26

55 21.79 13.64 40.54 54.17 15.82 30.84 46.66

50 22.54 14.41 47.18 61.59 17.00 35.80 52.79

45 23.51 15.16 53.70 68.86 18.71 43.59 62.31

40 24.42 15.85 61.55 77.39 22.45 56.43 78.88

35 25.33 16.61 73.71 90.32 72.50

30 26.44 17.50 110.40 127.90 97.82

25 28.50 19.11 136.67 155.78 151.27

20 44.84 22.69 200.38 223.07

15

10

5

The present chapter discusses the non-parametric approach in which a semi-dimensionless

flood hydrograph is derived broadly following Archer et al. (2000). Observed (isolated or de-

coupled) flood hydrographs are selected. The characteristic hydrograph is constructed to be

unimodal and to have exceedance widths before and after the peak that take the average of the

corresponding exceedance widths in the sample hydrographs. In the FSU hydrograph width

research, the recommended approach was to use the median value. The characteristic

hydrograph obtained in this way is referred to as the derived median hydrograph or just the

median hydrograph.


15

Figure 3.2: Methods of constructing a characteristic hydrograph

In the parametric approach, the characteristic hydrograph is obtained by fitting an algebraic

formula to the observed hydrographs or to the characteristic hydrograph previously obtained

by the non-parametric approach. The coefficients and constants in the model form the

parameters. The choice of model structure is a matter of judgement but is aided by an

objective measure of how well the modelled hydrograph fits the characteristic hydrograph

derived by the non-parametric approach. The recommended parametric model is the Gamma

curve with exponential replacement recession. This UPO-ERR-Gamma model is introduced

in Section 4.4.

3.4 Split-sample and whole-sample calibration

The 37 Grade A1 stations were used for testing and comparison of the developed methods.

At each station, three flood hydrographs were reserved for verification, with the remaining

events used in calibration. This procedure is referred to as split-sample calibration. To avoid

bias, one large, one medium and one small event were enrolled as the verification events.

[Editorial note: Other parts of the Technical Research Report refer to validation rather than

verification. The terms are interchangeable.]

As detailed in Section 2.4, the M hydrographs at a station are numbered so that the one with

the largest flood peak is Event 1 and the one with the smallest flood peak is Event M. To

select the three verification events, the M events were divided into three equal or near-equal

groups characterising the ranges of large, medium and small flows. In the case of Station

07009 Boyne at Navan Weir, there are 30 flood events in the annual exceedance series.

Events 1 to 10 are deemed large flood events, Events 11 to 20 are deemed medium events and

Events 21 to 30 are deemed small events. A middle-ranking flood event in each group was

adopted as a verification event. For Station 07009, Events 5, 15 and 24 were thus selected as

verification events. The remaining 27 events were used in calibration.

Gauged site Ungauged site

Non-parametric method based

on widths of exceedance

Parametric method

by curve fitting

Derived

median

hydrograph

Hayashi et

al. (1986)

curve

Gamma

curve

Gamma curve with

algebraic

replacement

recession

Negative

Binomial

curve

Inverse

Gaussian

curve Sketch

subjectively

Construct

parabolic

curves that

respect

required

values of

W75, W50 & s

Apply modified

Gamma model

with parameters

n, Tr and C that

yield required

values of W75,

W50 and s

For upper hydrograph alone

Estimate width parameters

W75 and W50 from PCDs*.

Adopt suitable value of

eccentricity parameter (s)

If complete hydrograph required

Apply Gamma curve with

exponential replacement

recession, estimating parameters

n, Tr and C from PCDs*

Alternate formulations are given.

One version requires BFI. BFIsoil

might be used but was not available

at the time of the HWA research.

Subject site

Fit to

derived

median

hydrograph

Gamma curve

with exponential

replacement

recession

Fit to

derived

mean

hydrograph

Fit to event

hydrographs

individually;

adopt median

parameter values

Fit to event

hydrographs

individually;

adopt mean

parameter values

Fit to event

hydrographs

collectively

Derived

mean

hydrograph


16

In the first phase of analysis, the most promising approaches were identified based on how

well the derived characteristic hydrograph fitted the three verification events. The test was

made across all 37 Grade A1 stations.

Having identified the most suitable non-parametric and parametric methods, these were

applied across the whole set of flood events at all 89 stations in a second phase of analysis.

This procedure is referred to as whole-sample calibration. Ultimately, the final estimates of

the characteristic hydrograph were based on all selected flood events at the particular station.

Two best methods were carried forward: one based on the non-parametric approach and the

other based on the parametric approach.

3.5 Deriving the median hydrograph

3.5.1 Basic method

The preferred method in the non-parametric approach is to take median values of the various

component widths of the standardised hydrographs: the averaging being taken across the

group of events being analysed. As noted earlier, widths are defined at various percentages of

the peak flow, and components before and after the time of peak flow are distinguished.

Component hydrograph widths are not available at all percentages. Thus, the median is taken

across those hydrographs that provide a component hydrograph width at the relevant

percentage of the peak flow.

The characteristic hydrograph is constructed so that its component widths at all percentages

correspond to the relevant median value. The resulting hydrograph is referred to as the

derived median hydrograph. The example in Figure 3.1 is for the split-sample calibration at

Station 07009. Thus the hydrograph is the median of 27 standardised hydrographs. Three of

the 30 flood events at this station have been withheld for use in verification. The embedded

table notes the values of the hydrograph widths at 75%, 50% and 25% of the peak.

Figure 3.3: Median hydrograph for Station 07009 Boyne at Navan Weir

Percentage

of peak

flow

Hydrograph width (hours)

On rising limb On receding limb Total

75% 10.49 17.32 27.81

50% 15.15 38.75 53.90

25% 24.11 135.43 159.54

100

90

80

70

60

50

40

30

20

10

0

Pe

rc

en

tag

e o

f p

ea

k f

low

Time in hours (relative to time of peak f low) -50 -37.5 -25 -12.5 0 56.25 112.5 168.75 225


17

3.5.2 Anomalies in the derived median hydrograph

Unrealistic kinks appear at some lower percentages in the rising/receding limb of the derived

median hydrograph. These appear because of the changing (i.e. reducing) number of events

across which the median is drawn at lower percentages of the peak. In the case of Station

07009, the kinks are barely discernible. But, for many stations, the anomalies are unrealistic

and rather distracting e.g. Station 07007 Boyne at Aqueduct in Figure 3.4a. The kinks reflect

both the non-availability of widths at lower percentages in some events and the wide variation

in those widths that are available at lower percentages.

Figure 3.4: Median hydrographs with irregularities

3.5.3 Improving the derived median hydrograph

Two techniques were applied to moderate irregularities in the derived hydrographs. These

were implemented interactively using options developed within the HWA software.

In some cases, a central 3-term moving-average filter was applied one or more times to

smooth the pattern of variation down the offending limb of the hydrograph. Where

smoothing failed to produce an acceptable hydrograph, the lower parts were simply

discarded. Sometimes the lower parts of the derived median hydrograph were discarded;

sometimes the lower parts were discarded after smoothing.

Three applications of the moving-average filter led to a satisfactory outcome for Station

07007 (see Figure 3.5a). At Station 14006, the best that could be achieved was to truncate the

median hydrograph by discarding parts below 20% of the peak flow (see Figure 3.5b).

There was concern that repeated use of a moving-average filter was unduly arbitrary and

subjective. The primary technique recommended for removing unacceptable features of the

derived median hydrograph is therefore to truncate the hydrograph by simply discarding the

lower parts that exhibit inconsistent widths.

Derived median hydrographs for the 37 Grade A1 stations can be glimpsed in Appendix C.

These are based on the initial split-sample calibration. Final results for the whole-sample

calibration at all 89 Grade A1 + A2 stations are summarised later in Table 5.1.

(a) Station 07007 Boyne at Aqueduct (b) Station 14006 Barrow at Pass Bridge


18

Figure 3.5: (a) Smoothed median hydrograph; (b) Truncated median hydrograph

(a) Station 07007 Boyne at Aqueduct (b) Station 14006 Barrow at Pass Bridge


19

4 The parametric approach

The parametric approach specifies a formulaic shape for the characteristic hydrograph. The

favoured model has three parameters.

4.1 Objectives

Generation of the median hydrograph from observed flood events at a gauged site is relatively

straightforward using the HWA software to implement the non-parametric approach

described in Section 3.5. That the median hydrograph is regularly spaced on the standardised

flow axis rather than on the time axis is a minor inconvenience. This can be overcome by

linear or other interpolation. Where the non-parametric approach is truly limiting is in the

difficulty of generalising the method to allow the characteristic hydrograph to be constructed

at an ungauged site.

In the parametric approach, the characteristic hydrograph is represented by an algebraic form

involving two or three parameters only. This leads to design hydrographs that are smoothly

varying and therefore more likely to be intuitively acceptable. However, the chief prize is

that a parametric form for the characteristic hydrograph gives much greater scope for

generalisation of the model for application at ungauged sites.

The two or three parameters of the algebraic form can be related to physical catchment

descriptors (PCDs) available for all sites: gauged and ungauged. [Editorial note:

Generalisation and automation of procedures can, for example, assist applications in

Catchment Flood Risk Assessment and Management (CFRAM).] A further benefit is that the

functional form makes it possible to define the flood hydrograph in its entirety, including the

low parts at the beginning and end. This aids the calculation of flood volumes and supports

other applications in which the whole hydrograph is required.

4.2 General approach

The general approach taken was to fit parametric curves to the median hydrographs derived in

Section 3.5. The following models were considered in the research:

Cubic polynomials (fitted separately before and after the peak);

The Negative Binomial distribution curve;

The Inverse Gaussian distribution curve;

The Hayashi et al. (1986) curve;

Various formulations and extensions of the Gamma distribution curve.

These models were subject to extensive exploration, although not all methods were applied to

all catchments in the 89-station dataset. In general, the parametric curves were fitted to the

median hydrograph in its native semi-dimensionless form i.e. with flows in percentages of the

peak and times in hours before and after the peak.

In the case of statistical distributions such as the Inverse Gaussian and Gamma, the model is

customarily standardised to have unit volume under the curve rather than a unit peak. It is a

matter of algebraic manipulation to come up with a variant that meets the unit peak criterion.


20

This is now illustrated for the UPO-Gamma curve, which denotes a Gamma curve

reformulated to have a Unit Peak at the Origin (abbreviated to UPO). The parametric model

ultimately recommended is a modification of the UPO-Gamma curve.

4.3 UPO-Gamma model for the characteristic hydrograph

4.3.1 Gamma distribution

The Gamma distribution rises from the origin at x = 0 and encloses a unit volume under the

curve. It has the functional form:

K

xexp

K

x

nΓK

1f(x)g

1n

where x ≥ 0 4.1

The model has two parameters: the shape parameter n and the scale parameter K. Γ(n) is the

Gamma function, defined by standard formulae or tables.

The Gamma distribution has a long history of application in rainfall-runoff modelling as the

Nash-cascade model for the so-called instantaneous unit hydrograph (Nash, 1957), and in

flood routing as the Kalinin-Milyukov routing method (Kalinin and Milyukov, 1957).

Examples appearing later (see Figure 4.1 and Figure 4.2) confirm the hydrograph-like curves

generated by the distribution.

4.3.2 Peak of Gamma distribution

It can be shown that the peak of the Gamma distribution occurs at:

1nKxp 4.2

and, when n > 1, takes the value:

1nexp1nnΓK

1g

1n

p

4.3

The Gamma curve is not hydrograph-like if n ≤ 1. For example, when n = 1, it degenerates to

an exponential recession. Thus, its application here is limited to the case n > 1.

4.3.3 Gamma model with peak at time zero

For the peak to occur at time zero, the distribution needs to be shifted left by xp units, i.e. by

K(n-1). Thus, the Gamma distribution with peak at time zero is given by:

K

1nKxexp

K

1nKx

nΓK

1g

1n

where x + K(n-1) ≥ 0 4.4

This simplifies to:


21

K

x1nexp

K

x1n

nΓK

1g

1n

where x + K(n-1) ≥ 0 4.5

4.3.4 Gamma model with unit peak at time zero

The requirement is for a model that can be fitted to the characteristic hydrograph. Typically,

this will be the median hydrograph derived in Section 3.5. The required model therefore has

a peak of 1.0 at time zero.

Dividing Equation 4.3 by Equation 4.5, we obtain the Gamma distribution with unit peak at

time zero:

K

xexp

1nK

x1ggy

1n

p 4.6

This provides the UPO-Gamma model for the characteristic hydrograph, where UPO denotes

Unit Peak at Origin. y denotes the flow as a proportion of the peak flow. The hydrograph

rises from y = 0 at time x = -K(n-1) to y = 1 at time x = 0, and recedes thereafter.

4.3.5 Formulation in terms of hydrograph rise time Tr

The formulation preferred here replaces K with Tr/(n-1), where Tr denotes the rise time of the

Gamma distribution (see Equation 4.2). The UPO-Gamma model is then:

r

1n

r T

1nxexp

T

x1y 4.7

The model rises from 0 at time x = -Tr to 1 at time x = 0. [Editorial note: The Tr parameter

is sometimes referred to as the hydrograph rise time and sometimes as the translation

parameter. This is because moving the time origin from the beginning of the hydrograph to

the peak of the hydrograph has translated the time axis by Tr units.]

4.3.6 Families of hydrographs constructed using the model

Figure 4.1 shows hydrographs constructed using the UPO-Gamma model that all have a rise

time of Tr = 50 hours. The effect of varying the parameter n is seen and its role as a shape

parameter confirmed.

Figure 4.2 shows hydrographs that all have n = 3. The effect of varying the parameter Tr is

seen and its role as a scale parameter confirmed. The hydrograph rises over time Tr,

measured in hours.

[Editorial note: Some notational changes have been made. HWA uses q to denote the

standardised flow, i.e. the hydrograph with unit peak. This has been changed to y to avoid

clashing with the use of q in IBIDEM to denote the rapid response element of the total

hydrograph in m3s

-1.]


22

Figure 4.1: UPO-Gamma hydrograph for Tr=50 and different values of shape parameter n

Figure 4.2: UPO-Gamma hydrograph for n=3 and different values of scale parameter Tr

4.3.7 Example application of UPO-Gamma model

Figure 4.3 shows the outcome of fitting the UPO-Gamma model to the median hydrograph

for Station 07009 Boyne at Navan Weir derived in Section 3.5. The model has two

parameters: the shape parameter n and the rise-time parameter Tr. The use of only two

parameters limits how well the model can fit a derived hydrograph.

It can be seen in Figure 4.3 that the model fits the rising limb of the median hydrograph at

Station 07009 rather well, and also respects the general shape of the upper hydrograph.

However, it provides a poor representation of the lower part of the receding limb.

Per

centa

ge

of

pea

k f

low

Time in hours (relative to time of peak flow)

Per

centa

ge

of

pea

k f

low



23

Figure 4.3: UPO-Gamma curve fitted to median hydrograph at Station 07009

Experience in applying the model across 89 stations found the behaviour in Figure 4.3 to be

rather typical, with the modelled hydrograph receding too quickly. This limitation was

addressed by developing a version of the model offering an extended recession. This is the

UPO-ERR-Gamma model.

4.4 UPO-ERR-Gamma model for the characteristic hydrograph

The UPO-ERR-Gamma model replaces the lower part of the recession of the UPO-Gamma

model by an exponential recession. ERR denotes Exponential Replacement Recession. An

example is shown in Figure 4.5 below.

4.4.1 Formulation

The UPO-ERR-Gamma model follows the UPO-Gamma model of Section 4.3 until its point

of inflection xI on the receding limb of the hydrograph. It can be shown that the inflection

occurs at:

1nTx rI where n > 1 4.8

Here, x again denotes time relative to the time of peak flow. From Equation 4.7, the

hydrograph ordinate at the inflection point is given by:

1nexp1n

11y

1n

I

4.9

Thereafter, the UPO-ERR-Gamma model replaces the Gamma curve by an exponential

recession. The recession curve is defined by:

100

90

80

70

60

50

40

30

20

10

0 -50 -37.5 -25 -12.5 0 56.25 112.5 168.75 225

Pe

rc

en

tag

e o

f p

ea

k f

low

Time in hours (relative to time of peak

flow)

Median hydrograph

UPO-Gamma model


24

C

xxexpyy I

I 4.10

where parameter C controls the rate of recession. It is the time over which the recession

descends to a proportion e-1/C

of its value. The recession decays to 0.5 of its value over the

time 0.693C, the so-called recession “half-life”.

Figure 4.4 provides an impression of the family of shapes supported by the exponential

replacement recession. The case illustrated is where the point of inflection on the Gamma

curve occurs 15 hours after the peak flow and at 60% of its value.

Figure 4.4: Exponential replacement recession (ERR) for different values of parameter C

The coupling of the exponential recession replacement to the Gamma curve means that

hydrographs constructed using the UPO-ERR-Gamma model exhibit a kink at the join. This

reflects a discontinuity in the derivative of the modelled hydrograph. This undesirable feature

was considered acceptable given the improved performance achieved by the UPO-ERR-

Gamma model in comparison to the UPO-Gamma model. If required, the kink could be

moderated by local smoothing.

4.4.2 Method of fitting

Various methods of fitting the UPO-ERR-Gamma model were explored. That ultimately

favoured was to fit the model to the median hydrograph by optimising the three parameters

(n, Tr and C) simultaneously using a genetic algorithm (see next section). The method is

implemented within the HWA software package. Figure 4.5 shows the outcome for Station

07009 Boyne at Navan Weir.

4.5 Method of fitting the parametric model

Fitting the UPO-ERR-Gamma model to the characteristic hydrograph requires a criterion of

what is considered a good fit and a means of seeking the parameter values that provide the

best fit by this measure. The criterion is the objective function and the means of seeking the

best parameters is the optimisation scheme.

Per

centa

ge

of

pea

k f

low

Shapes of the exponential recession curve for different values of the

parameter C

xo = 15, yo = 60

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300

Time (hr)

Ord

inate

of th

e r

ecessio

n

curv

e (

in p

erc

entil

e)

C = 25

C = 50

C = 75

C = 100

C = 125

C = 150

C = 175

C = 200

C = 225

C = 250

C = 275

C = 300


25

100

90

80

70

60

50

40

30

20

10

0 -50 -37.5 -25 -12.5 0 56.25 112.5 168.75 225

Per

cen

tag

e o

f p

eak

flo

w

Time relative to time of peak flow (hours)

Median hydrograph

UPO-ERR-Gamma model

Kink at join of Gamma and exponential replacement recession

4.5.1 Objective function

The objective function adopted is the so-called least-squares criterion. The best fit is judged

the one that minimises the sum of squared differences between modelled and observed values

of the feature of interest.

Figure 4.5: UPO-ERR-Gamma curve fitted to median hydrograph at Station 07009

For applications in rainfall-runoff modelling, the feature of interest is typically ordinates of

the flow hydrograph along its length. In the HWA research, the feature of interest is the

hydrograph width at various percentages of the peak value. In either application, a weight

can be applied to prioritise a good fit in the part of the hydrograph of most interest. The

model fitting is then said to have been done by weighted least-squares.

In fitting the UPO-ERR-Gamma curve to a standardised hydrograph, the objective is to

optimise its three parameters (n, Tr and C) so as to match the known widths of exceedance as

closely as possible in the least-squares sense. The standardised hydrograph being fitted may

be that of a single flood event or a characteristic hydrograph such as the median hydrograph

derived in Section 3.5.

The objective function used for fitting the UPO-ERR-Gamma curve is the weighted sum-of-

squares:

N

1i

2

iii yywS 4.11

Here, yi is the ith

ordinate of the standardised hydrograph, i is the corresponding ordinate

modelled by the UPO-ERR-Gamma, wi is a weighting factor, and S is the sum of squares of

the differences between yi and i across ordinates 1 to N. The summation takes place across

all reference ordinates for which the hydrograph is defined, the reference ordinates

corresponding to end-points to which the hydrograph width (or a component of the

hydrograph width) at 98%, 95%, 90%, 85%, … 5% of the peak flow is defined. If, for

example, the widths of exceedance on the rising side are available at percentiles 98, 95, 90,

85, 80, 75, 70, 65, 60, 55, 50 and 45 and the widths of exceedance on the receding side are

available at percentiles 98, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35 and 30 then N in


26

Equation 4.11 will be 12 + 1 + 15 = 28. Box 4.1 explains why some users may be puzzled by

this choice of objective function.

Equation 4.11 includes the weight wi. The HWA software supports three weighting systems:

Greater weight to the fitting of the widths at higher percentages of the peak flow, by

setting: wi = (yi)2;

Greater weight to the fitting of the widths at lower percentages of the peak flow, by

setting: wi = (1/yi)2;

Even weighting, by setting: wi = 1.

The first option was adopted in the research, i.e. assigning greater weight to the fitting of

widths at higher percentages of the peak flow.

Box 4.1: The choice between horizontal and vertical fitting

4.5.2 Optimisation scheme

The Genetic Algorithm (GA) was chosen as the optimisation scheme for fitting the UPO-

ERR-Gamma curve. GAs are search algorithms based on the mechanics of natural selection

and genetics. The method was developed by John Holland, colleagues and students at the

University of Michigan (Holland, 1975). The method combines “survival of the fittest among

string structures with a structured yet randomized information exchange to form a search

algorithm with some of the innovative flair of human search” (Goldberg, 1989). The

University of Michigan research aimed to:

Abstract, and rigorously express, the adaptive processes of natural systems;

Design artificial systems that retain the important mechanisms of natural systems.

Editorial note: Models such as the UPO-ERR-Gamma have a defined functional form,

albeit a moderately complicated one. It ought to have been possible to fit the hydrograph

width model using an objective function defined in terms of horizontal departures of the

modelled hydrograph from the observed hydrograph. Instead, the HWA authors chose an

objective function based on vertical fitting of the modelled hydrograph to the observed

hydrograph.

Although the difference may not have changed results very appreciably, it is confusing to

have evaluated the comparative performance of different models (in Section 4.5.3 below)

using a measure based on horizontal departures and yet fitted the hydrograph width

models by minimising vertical departures.

Unsurprisingly, the developers of IBIDEM (see Chapter 9) chose a different course. They

chose an objective function that fitted hydrographs from the FSR rainfall-runoff method to

FSU design hydrographs by minimising horizontal departures.

Practitioners are encouraged to make full use of the HWA and IBIDEM software. Visual

display of hydrographs is integral to both packages and should allow users to obtain

effective results. Researchers are to be encouraged to focus on horizontal fitting in any

further development of hydrograph width analysis.


27

Genetic algorithms aim to be robust and to balance the efficiency and efficacy necessary for

survival in many different environments. In each generation, a new set of artificial creatures

(strings) is created using bits and pieces of the fittest of the old strings. However, the

occasional new part is tried for good measure (Goldberg, 1989). [Editorial note: A few

details of the procedure implemented are given in the original research report but these are

not specific to the particular application. The method is said to be based on Duan (2003).]

In hydrological applications, the chief advantage of the genetic algorithm over more

conventional methods of optimisation is that the search is globally oriented. This can help

when fitting rather complex models to hydrological problems. [Editorial note: If the

“surface” being searched (to find the minimum of the objective function) is irregular, gradient

methods of optimisation may lead the user to parameter values corresponding to a local

minimum of the objective function. In contrast, genetic algorithms are equipped to leap clear

and are more likely to find the parameter values corresponding to the global minimum of the

objective function parameters.] Wang (1991) finds the GA to be a robust and efficient

method for calibrating conceptual rainfall-runoff models.

4.5.3 Performance evaluation

Several measures were considered for judging the relative performance of one method (of

modelling the characteristic hydrograph) over another, including the root mean square error

(RMSE) and the Nash-Sutcliffe efficiency coefficient (Nash and Sutcliffe, 1970). The

measure ultimately adopted was the Mean Relative Error (Elshorbagy et al., 2000). Whereas

the Nash-Sutcliffe efficiency and the RMSE are inflated by squared terms, the range of

variation of the values of the MRE was generally found to be small.

In the application here, the MRE at a given percentage pj of the peak flow is defined as:

j

j

Ni

1i ji,

jji,

j

pW

WW

N

1MRE 4.12

where Wi,j is the exceedance width of the ith

observed hydrograph, j is the exceedance width

given by the model and Nj is the number of observed hydrographs for which the width is

defined. In each case, the subscript j denotes the value relevant at percentage pj of the peak

flow. The measure was evaluated at (up to) 20 percentages of the peak flow, with p1 = 98, p2

= 95, p3 = 90,…, p19 = 10 and p20 = 5. For reasons explained in Section 3.2, not all events

have hydrograph widths defined at all percentages of the peak flow. The lower the value of

MRE, the more efficient is the parametric model at reproducing the observed hydrograph

widths (e.g. the widths of the characteristic hydrograph derived by the Section 3.5 method).

In practice, the quality of model fit at and above a given percentage of the peak flow is of

interest. The Average MRE was therefore defined as:

Mk

1k

ppp jk,jjMRE

M

1MRE AverageAMRE 4.13

where k counts over different percentages of the peak flow at and above pj%. For example,

when the quality of fit at and above 50% of the peak flow is of interest:


28

989590555050 MREMREMREMREMRE11

1AMRE 4.14

To simplify matters a little, assessments focused on three reference percentiles corresponding

to the fit above 75%, 50% and 25% of the peak flow. The lower the value of AMRE75, the

better is the fit of the model to the upper part of the hydrograph above 75% of the peak flow.

Box 4.2: Editorial note on performance measures

4.6 Reproduction of flood hydrographs of verification events

An independent test of the relative merit of competing parametric models was possible by

exploiting the three events reserved for verification at each station (see Section 3.4). Figure

4.6 illustrates the performance achieved with the UPO-ERR-Gamma model for Station 07009

Boyne at Navan Weir. The model reproduces the observed flood hydrographs quite well for

Events 5 and 15, and the fit is especially good above 50% of the peak flow. In the case of

Event 24, only the upper part of the hydrograph was available, this being the main flood

response decoupled from a complex event. The fit of the UPO-ERR-Gamma model is poorer

for this event but considered acceptable given that the flood is not a major one, being only the

24th

largest of the 30 events at Station 07009.

When evaluated across all 37 Grade A1 station, the UPO-ERR-Gamma model was judged to

provide the best overall performance (amongst all the parametric models considered) in

modelling the upper parts of the hydrographs reserved for verification. Modelled and

observed hydrographs for these 111 verification events are shown in Figure C.1 to Figure

C.37 of Appendix C. Fits achieved by the non-parametric approach are also shown.

An array of measures is used to assess performance. Mention of the Nash-Sutcliffe

efficiency (NSE) is perhaps justified by its widespread use in hydrological modelling.

However, it is poorly adapted to the case of modelling hydrograph widths. More aptly, the

root mean square error (RMSE) in hydrograph width estimation is used to good effect in

IBIDEM (see Chapter 9, in particular Section 9.5.4).

The authors’ preference for the Equation 4.12 measure (MRE) is uncomfortable. When

defining the mean relative absolute error, it is more usual for the denominator to be taken

as the minimum absolute value of the terms being differenced in the numerator. The

disadvantage of the Equation 4.12 measure is that it does not treat modelled and observed

values even-handedly. n consequence, large modelled values of the hydrograph width

(i.e. j) degrade the evaluated performance much more than small values do. ndeed,

large values of j can lead to values of MRE (and AMRE) that exceed 1.0.


29

Figure 4.6: Performance of UPO-ERR-Gamma model on verification events, Station 07009

Pe

rc

en

tag

e o

f p

ea

k f

low

100

90

80

70

60

50

40

30

20

10

0

Median hydrograph

UPO-ERR-Gamma model

Event 5 hydrograph

-50 -25 0 56.25 112.5 168.75 225

Time relative to time of peak f low

(hours)

Pe

rc

en

tag

e o

f p

ea

k f

low

100

90

80

70

60

50

40

30

20

10

0

Median hydrograph

UPO-ERR-Gamma model

Event 15 hydrograph

-50 -25 0 56.25 112.5 168.75 225


(hours)

Pe

rc

en

tag

e o

f p

ea

k f

low

100

90

80

70

60

50

40

30

20

10

0

Median hydrograph

UPO-ERR-Gamma model

Event 24 hydrograph

-50 -25 0 56.25 112.5 168.75 225


(hours)


30

4.7 Other methods

The research considered many models, and multiple ways of fitting them. The Gamma-UPO-

ERR parametric model was calibrated extensively. The primary versions assessed were:

v1 Fitting to the derived median hydrograph (as recommended and illustrated above);

v2 Fitting to the derived mean hydrograph;

v3 Taking the median of parameter values obtained when fitting to flood hydrographs for

individual events;

v4 Taking the mean of parameter values obtained when fitting to flood hydrographs for

individual events;

v5 Fitting to the event hydrographs collectively.

Further stratification of the study took the objective function as minimising Average MRE

values calculated above 50% of the peak flow, above 75% of the peak flow and above other

percentages. The reader is referred to the original research report and its many appendices.

[Editorial note: It is the practice in applied research to prune back the number of methods,

and to consider in detail only the most promising sub-variations. Some investigators are,

however, reluctant to judge one method better than another without exhaustive analyses.]

Figure 4.7 provides an example of the richness of material generated in the research. A good

method constructs the upper hydrographs of the verification events with low error. The

performance measure AMRE is the average value of the Mean Relative Error in reproducing

upper hydrograph widths (see Section 4.5.3). The recommended version (v1) is seen to

perform best in verification across the 37 Grade A1 stations; v3 performs next best.

Figure 4.7: Verification performance of UPO-ERR-Gamma calibrated in five versions

0.00.20.40.60.81.01.21.41.61.82.0

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Station no.

MR

E

Gamma I median Gamma I mean Gamma II median Gamma II mean Gamma III

0.00.20.40.60.81.01.21.41.61.82.0

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Station no.

MR

E


v1 v2 v3 v4 v5

v1 v2 v3 v4 v5

AM

RE

50

AM

RE

50

0.00.20.40.60.81.01.21.41.61.82.0

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Station no.

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E



31

5 Performance of methods at gauged sites

5.1 Introduction

The performance of the recommended methods is now examined. The recommended method

in the non-parametric approach is the median hydrograph of Section 3.5. The recommended

method in the parametric approach is the UPO-ERR-Gamma model developed in Section 4.4.

The initial assessment is made across the 37 Grade A1 stations.

It is helpful to assess the methods jointly. Where poor performance is identified, it is then

possible to distinguish whether this arises more from the choice of method or more from the

variable nature of hydrographs at a particular station.

Figure 5.1 and Figure 5.2 summarise the performance of the median hydrograph and UPO-

ERR-Gamma methods in calibration and in verification across the 37 Grade A1 stations. The

measure shown is AMRE50.

AMRE denotes the average MRE. This is a double averaging. The mean relative error

(MRE) in modelling hydrograph widths is averaged across available segments of the

hydrograph above 50% of the peak flow, and is also averaged across the available flood

hydrographs. For the verification results, the averaging is across the three events withheld for

the purpose. For the calibration, the averaging is across the remaining flood hydrographs.

Figure 5.1: Performance of median hydrograph method across 37 Grade A1 stations

Figure 5.2: Performance of UPO-ERR-Gamma method across 37 Grade A1 stations

A small value of AMRE50 indicates that the method typically represents the upper hydrograph

well. An arbitrary reference line AMRE50 = 0.4 is drawn across the figures to aid

discrimination of unusual cases. It is seen that AMRE50 lies below 0.4 at most stations.

Although only just discernible in Figure 5.1 and Figure 5.2, the median hydrograph method

outperforms the UPO-ERR-Gamma method. This is more clearly seen in Figure 5.3.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

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Station no.

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Calibration Verification


AM

RE

50

0

0.2

0.4

0.6

0.8

1

1.2

6011

6012

6013

6014

6026

7007

7009

7010

7012

9001

14004

14006

14007

14011

14018

15005

23002

24013

25003

25006

25014

25017

25025

25027

25030

26007

26008

26012

26019

27002

29001

29011

30004

30005

34018

36010

36015

Station no.

MR

E



AM

RE

50


32

1.21.00.80.60.40.20.0

1.2

1.0

0.8

0.6

0.4

0.2

0.0

AMRE50 for UPO-ERR-Gamma

AM

RE

50

fo

r m

ed

ian

hyd

rog

rap

h

Station 34018

Station 06011

Figure 5.3: Comparison of model performance across 37 Grade A1 stations

In calibration, the median AMRE50 (across the 37 stations) is 0.227 for the median

hydrograph method and 0.246 for the Gamma model. The difference is more noticeable in

verification; the median AMRE50 is 0.200 for the median hydrograph method (better than in

calibration!) and 0.252 for the Gamma model. The superior performance of the median

hydrograph method is to be expected given its greater flexibility to accommodate different

shapes of characteristic hydrographs.

A number of factors influence these results. Some stations exhibit wide variation in

hydrograph shapes across events. These are characterised by relatively high AMRE in

calibration. Prime examples are Stations 06011 and 34018. A further factor is that AMRE is

less well defined at stations for which the flood hydrograph is typically complex. AMRE50

nominally measures the average error in estimating hydrograph widths across the upper half

of the hydrograph. However, in practice, AMRE is evaluated across such widths as are

available after filtering of the hydrograph (see Section 2.6).

5.2 Relative performance in verification compared to that in calibration

The median hydrograph method performs better in verification than in calibration at 23

stations and worse at 13 stations, with Station 07010 too close to call. The UPO-ERR-

Gamma method performs better in verification than in calibration at 21 stations and worse at

15 stations, with Station 34018 too close to call.

As illustrated in Figure 5.4, the improvement in performance is most evident at Stations

06011, 06012, 14006, 14007, 14018, 26007 and 36015 (for both methods) and at Station

26012 (for the median hydrograph method). A deterioration in performance in verification is

most evident at Stations 07012 and 25003 (for both methods) and at Station 25017 (for the

median hydrograph method).


33

4210.50.250.125

4

2

1

0.5

0.25

0.125

36015

36010

34018

30005

30004

29011

29001

27002

26019

26012

26008

26007

2503025027

25025

25017

2501425006

25003

24013

23002

15005

14018

14011

14007

14006

14004

09001

07012

07010

07009

07007 06026

06014

06013

06012

06011

Figure 5.4: Performance in verification compared to that in calibration

[Editorial note: With many events typically used in calibration, there is considerable scope

for wide variation in hydrographs at a particular station to degrade model performance. With

only three events used for verification at each station, improved performance may in part be a

matter of chance. Three samples may show broad conformity to the calibrated model or wide

departures from it. Nevertheless, these are good results, since one would normally expect

performance in verification to be inferior to performance in calibration.

The unexpectedly strong performance in verification evident in Figure 5.4 may reflect that the

selection of verification events (see Section 3.4) was not fully automated. With over 2800

flood events across 89 catchments, the selection was a very demanding task in itself. Stations

occasionally exhibit individual hydrographs of a highly unusual shape. There may have been

reluctance – instinctive rather than conspiring – to allow patently unusual events to join the

select few allocated to the verification set.]

5.3 Complexity of hydrographs at Stations 06011 and 34018

The recommended methods perform poorly at Stations 06011 Fane at Moyles Mill and 34018

Castlebar at Turlough. Other methods considered in the research (see Sections 4.2 and 4.7)

also performed poorly on these catchments. A particular difficulty is that flood hydrographs

at these stations are generally complex. At Station 06011, the total width of exceedance is

undefined below 65% of the peak flow in all the hydrographs studied. The restriction is even

more severe at Station 34018, where none of the hydrographs defines the total width of

exceedance below 80% of the peak flow. The hydrographs of four of the eight largest floods

at this station are illustrated in Figure 5.5.

AMRE50Verif

/ AMRE50Calib

for UPO-ERR-Gamma model

AM

RE

50

Ver

if /

AM

RE

50

Cal

ib

for

med

ian

hy

dro

gra

ph

met

ho

d


34

Figure 5.5: Varied hydrograph shapes at Station 34018 Turlough at Castlebar

A further difficulty is that upper segments of the hydrographs at Stations 06011 and 34018

have a mix of sharp-peaked and rounded shapes. The characteristic hydrographs derived by

the median and UPO-ERR-Gamma methods are gently rounded (see Figure C.1 and Figure

C.35) yet some individual hydrographs have upper segments that are sharp-peaked.

The variability in upper-hydrograph shape is particularly marked at Station 34018 Castlebar

at Turlough (see Figure 5.5). This may reflect special features of the catchment that provide

particular scope for temporal and spatial patterns in rainfall to lead to varied and complex

hydrograph shapes. [Editorial note: The name Castlebar at Turlough suggests that geolog-

ical features may in part account for the complexity and variability of hydrographs at Station

34018. The authors note the large loughs in the catchment and suggest that the layout

increases the sensitivity of response timings to the spatial pattern of rainfall.]

5.4 Variability in hydrograph widths at some stations

Hydrographs at stations such as 24013 Deel at Rathkeale, 25006 Brosna at Ferbane, 25014

Siler at Millbrook and 25025 Ballyfinboy at Ballyhooney exhibit wide variability in widths.

As examples, two relatively wide and two relatively narrow hydrographs at each of these

stations are reproduced in Figure 5.6 to Figure 5.9. In the case of Station 25025, the two

narrower hydrographs are rather curiously slanted.

In the context of such wide variations in the shapes of flood hydrographs, it is desirable that

the reasons be investigated and explanations sought in terms of catchment features and/or the

meteorological conditions leading to the observed floods at these stations. Station 24013 is

investigated further in Section 5.10.2.

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 2 Event 1

Event 6 Event 8


35

Figure 5.6: Wide and narrow-peaked hydrographs at Station 24013 Deel at Rathkeale

Figure 5.7: Wide and narrow-peaked hydrographs at Station 25006 Brosna at Ferbane

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 11 Event 2

Event 20 Event 27

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 4 Event 1

Event 3 Event 31


36

Figure 5.8: Wide and narrow-peaked hydrographs at Station 25014 Silver at Millbrook

Figure 5.9: Wide and slanted hydrographs at Station 25025 Ballyfinboy at Ballyhooney

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 23 Event 7

Event 9 Event 21

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 13 Event 5

Event 2 Event 31


37

Twelve flood events at Station 25014 Silver at Millbrook were studied as part of FSU work

on Flood Event Analysis (see Appendix B). Six events were used to derive an average unit

hydrograph, which was tested on six further events. One of these was the 30 June 1986 flood,

which corresponds to the second part of Event 9 (see lower left diagram in Figure 5.8).

The University College Cork analysis in Figure 5.10 suggests that the catchment responded

particularly quickly to rainfall in this event. DR denotes the direct runoff from rainfall. A

possible explanation for the unusually narrow hydrograph is that the flood arose from heavy

rainfall on part of the lower catchment only. The catchment configuration is somewhat

unusual (see Map 5.1 based on UCC research).

Figure 5.10: Rainfall-runoff behaviour in 30 June 1986 flood at Station 25014

Map 5.1: Catchment of Station 25014 Silver at Millbrook


38

5.5 Attenuated response at some stations

In the case of (e.g.) Station 25017 Shannon at Banagher, the flood hydrographs are

exceedingly attenuated (i.e. dampened or “flat”), with only very slow rises to and recessions

from the peak. The peak segment is maintained for several days, and sometimes represents a

sustained high flow with no outstanding peak. Four such hydrographs are reproduced in

Figure 5.11.

Figure 5.11: Attenuated hydrographs at Station 25017 Shannon at Banagher

For a station characterised by such very flat flood hydrographs, only a very small number of

percentile widths are available for calibrating a model of the characteristic hydrograph. It is

therefore unsurprising that a derived hydrograph produced from such a small number of ill-

defined events may not reproduce the flood hydrograph of a verification event very well.

5.6 General guidance

On the basis of the above, it is concluded that, for reliability in producing a design

hydrograph:

Standardised hydrographs should be derived for as many flood events as possible;

Where these differ widely from event to event, the reasons should be explored on the

basis of the physical characteristics of the catchment and of the flood-producing

rainfall;

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Flo

w (

m3s-1

)

Event 4

Event 1

Event 7

Event 10


39

100

90

80

70

60

50

40

30

20

10

0

Per

cen

tage

of

pea

k f

low

Time relative to time of peak flow (hours) -50 -37.5 -25 -12.5 0 56.25 112.5 168.75 225

A characteristic hydrograph fitted to very varied hydrographs, or one developed from

flood hydrographs that are highly attenuated (i.e. dampened or “flat”), should be

applied with caution when producing design flood hydrographs.

5.7 Results of whole-sample calibration

Having identified “best” non-parametric and parametric methods – i.e. the derived median

hydrograph and the UPO-ERR-Gamma model – based on 37 Grade A1 stations, the methods

were applied to the entire set of 89 stations in the study. All available events were now used:

hence, the term whole-sample calibration.

5.7.1 Derived median hydrograph and its descriptors

Figure 5.12 shows the outcome of the whole-sample calibration for Station 07009 Boyne at

Navan Weir.

Figure 5.12: Median hydrograph for Station 07009 Boyne at Navan Weir (whole sample)

The table embedded in Figure 5.12 notes the values of the hydrograph widths at 75%, 50%

and 25% of the peak. Comparison with Figure 3.3 reveals that, for this station, the median

hydrograph is little changed after inclusion of the three events previously reserved for

verification.

Table 5.1 summarises the outcome of hydrograph width analysis applied to the full set of 89

stations. Three width descriptors are presented in the central columns. Two are the widths of

exceedance W75 and W50 at 75% and 50% of the peak flow. Hydrographs are insufficiently

defined to establish these width descriptors for Stations 30061 and 34018; additionally, W50 is

undefined for Stations 06011, 25017 and 34001.

The third width descriptor is the mean ratio, s, of the width on the rising side to the total

width. This average value is calculated across all available widths of all the available flood

hydrographs. The ratio s summarises the skew of the hydrograph, with a value of 0.5

indicating broad symmetry about the peak. Figure 5.13 shows the histogram of values of s

Percentage

of peak

flow

Hydrograph width (hours)

On rising limb On receding limb Total

75% 10.46 17.29 27.75

50% 14.94 39.20 54.14

25% 23.38 136.67 160.05


40

across the 89 stations analysed. It is seen that s is appreciably less than 0.5 at most stations.

This reflects that floods typically rise more quickly than they fall. For Station 07009,

s = 0.345.

1.00.90.80.70.60.50.40.30.20.10.0

7

6

5

4

3

2

1

0

s = mean ratio of width before peak to total hydrograph width

Fre

qu

en

cy

<-- s = 0.5 (symmetric)

Figure 5.13: Summary index, s, of hydrograph skewness (89 Grade A1 + A2 stations)

[Editorial note: Ratios (such as s) should be averaged by taking the geometric mean not by

taking the arithmetic mean. Although not of great significance here, the difference can be

important in particular hydrological applications.]

5.7.2 UPO-ERR-Gamma model and its parameters

The UPO-ERR-Gamma was applied to the entire set of 89 stations, fitting the model by

optimisation using the genetic algorithm (see Section 4.5.2) to the derived median hydrograph

for the particular station. The optimised parameter values appear in the final three columns of

Table 5.1. These are values of the shape parameter n, the rise-time or translation parameter Tr

and parameter C of the exponential replacement recession.

The C parameter could not be calibrated for Station 30061. The Gamma curve fitted to the

derived median hydrograph for this Grade A2 station implies a point of inflection on the

receding limb at 71% of the peak flow, some 30 hours after the peak. For this station, the

median hydrograph does not define after-the-peak hydrograph widths below 90% of the peak

flow. Thus, it was not possible to fit the exponential replacement recession.

Table 5.1: Outcome of whole-sample calibration at 89 Grade A1 + A2 stations

Station

number

Station

grade

Median hydrograph method UPO-ERR-Gamma model

W75 W50 s n Tr C

06011 A1 114.35 N/A 0.374 1.300 29.690 360.834

06012 A1 136.25 243.02 0.325 2.457 93.311 280.948

06013 A1 41.99 70.87 0.354 7.782 59.989 102.855

06014 A1 95.87 154.30 0.394 3.014 89.910 113.849

06026 A1 82.47 146.16 0.390 4.998 102.176 140.966

07001 A2 18.36 34.20 0.377 5.006 23.309 38.360

07002 A2 46.74 93.14 0.351 2.770 32.736 151.959

07004 A2 110.14 171.87 0.382 3.014 101.979 116.780


41

Station

number

Station

grade


W75 W50 s n Tr C

07006 A2 15.42 30.38 0.331 7.782 20.874 58.149

07007 A1 26.22 52.53 0.355 3.745 26.837 69.875

07009 A1 27.75 54.14 0.345 5.276 33.040 95.526

07010 A1 30.42 119.06 0.348 3.458 25.784 222.317

07011 A2 108.21 170.42 0.344 2.988 92.964 116.780

07012 A1 27.75 49.10 0.375 6.111 36.407 88.197

07033 A2 46.41 84.10 0.372 6.111 60.818 105.054

09001 A1 11.21 22.64 0.394 8.399 21.751 22.970

11001 B 7.54 10.84 0.456 26.356 25.241 5.380

14004 A1 48.17 74.35 0.447 5.406 66.484 53.751

14006 A1 57.46 83.02 0.487 4.710 75.828 41.292

14007 A1 9.34 17.14 0.487 21.412 31.787 11.243

14009 A2 26.27 46.20 0.378 3.884 27.746 46.422

14011 A1 45.96 89.57 0.361 5.276 54.734 116.780

14018 A1 65.08 121.78 0.350 2.944 57.728 116.780

15001 A2 15.74 28.49 0.434 9.417 30.458 23.703

15002 A2 8.12 19.23 0.428 17.635 24.966 21.504

15003 A2 5.77 8.79 0.489 10.541 12.422 6.113

15005 B 60.06 114.00 0.417 5.267 83.234 106.520

15006 A2 19.95 35.64 0.517 13.829 53.250 22.970

16001 A2 30.61 46.41 0.359 5.554 40.156 39.826

16002 A2 58.04 102.32 0.411 8.338 91.266 114.581

16003 A2 39.53 77.32 0.216 2.527 16.148 188.604

16004 A2 63.79 102.80 0.429 6.390 90.244 99.191

16005 A2 13.76 21.02 0.541 28.192 51.750 5.380

16008 A2 88.08 146.96 0.243 3.153 44.158 410.670

16009 A2 39.50 92.10 0.360 6.111 49.988 163.685

18004 A2 38.18 73.27 0.327 4.998 43.894 105.054

18005 A2 15.63 26.35 0.427 24.604 52.750 15.641

19001 A2 26.34 44.94 0.245 2.788 12.675 112.383

22071 A2 96.29 190.22 0.348 1.883 50.563 243.571

23001 A2 6.98 11.84 0.442 12.536 16.654 5.380

23002 A1 5.81 9.27 0.528 30.265 22.999 3.182

23012 A2 11.67 18.29 0.474 18.226 32.131 11.243

24001 A2 18.24 27.88 0.360 4.441 19.161 35.429

24008 A2 19.08 30.54 0.363 3.884 19.404 28.100

24013 A1 19.66 28.77 0.570 12.333 48.750 6.846

24082 A2 18.66 27.51 0.316 5.137 21.420 38.360

25001 A2 15.51 29.51 0.460 9.452 31.941 35.429

25003 A1 15.38 29.57 0.343 4.302 16.506 50.087

25005 A2 14.00 33.17 0.314 4.998 13.136 69.875


42

Station

number

Station

grade


W75 W50 s n Tr C

25006 A1 35.86 63.91 0.396 5.276 42.419 94.060

25014 A1 17.63 30.05 0.393 8.965 30.830 36.162

25016 A2 20.26 36.19 0.332 3.884 18.404 62.546

25017 A1 231.91 N/A 0.442 1.500 109.750 374.759

25025 A1 85.33 187.22 0.285 4.136 111.286 222.317

25027 A1 7.66 14.25 0.438 19.409 23.416 19.305

25029 A2 15.87 29.50 0.416 8.886 28.700 50.087

25030 A1 70.22 122.12 0.395 4.223 81.857 94.060

26002 A2 118.67 163.98 0.462 6.581 186.500 39.826

26005 A2 136.04 209.83 0.418 3.597 148.511 84.533

26007 A1 156.97 257.02 0.445 3.040 159.806 107.985

26008 A1 106.69 206.81 0.419 3.875 124.500 177.610

26009 A2 26.52 38.47 0.486 8.469 49.000 14.175

26012 A1 177.27 285.94 0.400 3.849 195.500 257.496

26019 A1 72.81 114.01 0.432 3.362 71.390 70.608

26021 A2 52.68 179.79 0.275 3.484 24.799 527.933

26022 A2 41.75 74.82 0.404 4.998 53.640 66.943

27001 A2 14.87 20.26 0.385 4.998 17.722 11.243

27002 A1 270.72 493.96 0.430 5.276 429.250 187.871

29001 A1 49.94 86.19 0.429 5.328 74.750 46.422

29004 A2 76.87 130.05 0.526 2.770 79.500 76.471

29011 A1 138.65 242.46 0.458 4.014 182.750 114.581

30004 A1 44.33 68.49 0.453 5.302 59.439 46.422

30005 A1 39.87 56.46 0.562 7.399 77.000 22.970

30007 A2 38.52 59.31 0.549 6.111 67.750 20.771

30061 A2 N/A N/A 0.447 2.910 41.901 N/A

34001 A2 95.52 N/A 0.416 2.788 58.347 829.752

34009 A2 19.67 26.03 0.559 9.095 39.699 8.312

34018 A1 N/A N/A 0.315 1.274 35.584 187.871

35001 A2 103.62 154.99 0.435 3.875 116.937 105.787

35002 A2 7.62 11.39 0.577 17.765 24.011 0.25

35005 A2 38.18 85.88 0.340 4.998 36.804 187.871

35071 A2 123.67 210.68 0.321 4.223 99.464 456.843

36010 A1 75.15 155.52 0.440 3.040 73.102 152.692

36011 B 316.02 613.41 0.371 2.214 295.250 229.646

36015 A1 40.08 67.19 0.485 6.189 68.000 35.429

36019 A2 295.51 491.91 0.421 2.483 254.500 302.202

36021 A2 3.11 4.90 0.462 14.698 7.655 2.449

36027 A2 332.71 539.54 0.376 2.605 300.500 213.522

39009 A2 45.10 86.66 0.348 9.104 74.098 115.314


43

[Editorial note: The parameter values of Table 5.1 reveal some unusual features of the

optimisation. Excessive decimal places are shown to confirm that parameter n takes certain

preferential values, with n = 4.998 at six stations and n = 6.111 at a further four stations.

Parameter C also has preferential values, with C = 116.780 at four stations and the values

5.380, 11.243, 27.970, 35.429, 46.422 and 187.871 each appearing at three stations. While

the fits achieved are fully satisfactory, the preferential values suggest that results obtained

with the genetic algorithm are not always fully optimised.]

5.7.3 Stations where the flood hydrograph recedes faster than it rises

Flood hydrographs at Station 35002 Owenbeg at Billa Bridge typically fall more steeply than

they rise. In consequence, the derived median hydrograph in Figure 5.14 also has this feature.

The station has the most skewed hydrograph (s = 0.577) of any in the 89-station dataset.

Reference to Figure 4.1 indicates that this is not a shape that the Gamma family of curves can

accommodate. When forced to do so, the exponential replacement recession in the adopted

UPO-ERR-Gamma is unreasonably steep, with C = 0.25 hours (see Figure 5.14). [Editorial

note: In essence, the ERR part of the model is attempting to compensate for overestimation

(by the Gamma curve) of the hydrograph width component that occurs after the peak.]

Figure 5.14: Characteristic hydrograph for Station 35002 Owenbeg at Billa Bridge

Station 30005 Robe at Foxhill also exhibits hydrographs that typically fall more steeply than

they rise. However, the feature is less pronounced and the UPO-ERR-Gamma model might

be considered just about acceptable (see Figure 5.15).

Overall, the UPO-ERR-Gamma curve was found to model the characteristic hydrograph

adequately at most of the 89 stations. One station having a somewhat unusual characteristic

hydrograph shape is Station 16008 Suir at New Bridge, investigated in the next section.


100

90

80

70

60

50

40

30

20

10 -25 -18.75 -12.5 -6.25 0 18.75 37.5 56.25 75

Per

cen

tage

of

pea

k f

low

Median hydrograph

UPO-ERR-Gamma model


44

Figure 5.15: Characteristic hydrograph for Station 30005 Robe at Foxhill

5.8 Characteristic hydrographs on the River Suir

Multiple gauging stations allow one to see how the characteristic hydrograph changes down

the river system. Figure 5.17 presents the outcome of applying the recommended methods to

four stations on the Suir. The timescale is the same in each graph. Of particular interest is

that the width of hydrographs does not appear to widen appreciably as floods pass down the

river system, except around New Bridge. The steepening of the rising limb is particularly

noticeable at New Bridge and Caher Park.

Figure 5.16: Characteristic hydrographs for four stations on the River Suir

The period of record used in the HWA is substantial. The analysis spans 1954 to 2000 at all

four sites, and somewhat longer periods at Stations 16008 and 16009 (see Table A.2). The

effects evident in Figure 5.17 are therefore not thought to be an artefact of the data samples.

Per

cen

tag

e o

f p

eak

flo

w


Median hydrograph

UPO-ERR-Gamma model

100

90

80

70

60

50

40

30

20

10 -75 -56.25 -37.5 -18.75 0 43.75 87.5 131.25 175

Median hydrograph

UPO-ERR-Gamma model

Median hydrograph

UPO-ERR-Gamma model

Median hydrograph

UPO-ERR-Gamma model

Median hydrograph

UPO-ERR-Gamma model

16004 Thurles

229 km2

16002 Beakstown

486 km2

16008 New Bridge

1090 km2

16009 Caher Park

1583 km2


45

The UPO-ERR-Gamma model represents well the steepening of the rising limb (see Figure

5.17). However, the model has difficulty with the unusual shape of the median hydrograph at

Station 16008 Suir at New Bridge. Small values of n and Tr are needed to represent the rising

limb and the UPO-ERR-Gamma model cannot accommodate the appreciable “hunch” on the

receding limb.

The Suir example provides a strong reminder of the very substantial hydrograph records held

for many Irish rivers, and the scope for hydrograph width analysis to complement the

statistical analysis of flood peaks in Volume II.

216192168144120967248240-24-48-72-96

1.00

0.75

0.50

0.25

0.00


Ch

ara

cte

risti

c h

yd

rog

rap

h

16004 Suir at Thurles

16002 Suir at Beakstown

16008 Suir at New Bridge

16009 Suir at Caher Park

Figure 5.17: UPO-ERR-Gamma characteristic hydrographs for four stations on the Suir

5.9 Hydrograph width analysis at gauged sites – a summary

Table 5.1 has summarised the hydrograph width analysis (HWA) undertaken for the 89 Grade

A1 + A2 stations. The results presented comprise:

Three hydrograph-width descriptors (W75, W50 and s) summarising the upper part of

the median hydrograph derived using the recommended non-parametric method;

Three parameters (n, Tr and C) of the UPO-ERR-Gamma model, which is the

recommended parametric model for the characteristic hydrograph.

The design flood hydrograph of required return period can be produced by scaling up the

ordinates of the characteristic hydrograph by the relevant peak flow derived by Volume II

methods.

It is desirable that the HWA results are updated and extended as new data become available.

Hydrograph width analysis is assisted by provision of the HWA software (see Section 1.6 and

Appendix E). It is anticipated that users will upload their HWA results to the FSU Web

Portal: both to facilitate their own applications and to share the hydrograph-width descriptors

and parameters values obtained at gauged sites with the wider community.


46

5.10 Flood hydrographs having sustained peaks

Sometimes flood hydrographs at a station are observed to have a sustained crest segment in

which the flow varies little around the peak. Such flood hydrographs may or may not be

representative of the typical flood hydrographs occurring at a station. Two cases are

discussed.

5.10.1 Where the hydrograph shape reflects the temporal pattern of rainfall

During a storm event, the continuation of heavy rainfall at the peak-inducing intensity for a

considerable period of time may cause the resulting flood hydrograph to exhibit a sustained

peak. [Editorial note: This behaviour may arise when a rain-producing weather system

becomes relatively fixed, e.g. with moist air continually fed into a particular zone where

topography induces heavy rainfall. The weather system is sometimes termed a “seeder-feeder

mechanism”. The topographic effect is referred to as “orographic enhancement”.] Although

these situations can give rise to a flood of unusually large volume, such events are unlikely to

be a regular occurrence at any particular station.

The premise of hydrograph width analysis is to represent only the characteristic shape of the

hydrograph. Where only one or two events exhibit the sustained hydrograph peak, it is proper

that they do not unduly influence the characteristic hydrograph. This is the case for the

recommended non-parametric method, which takes the median (rather than the mean) of

hydrograph widths.

5.10.2 Where the hydrograph shape is characteristic of the station

At some stations, relatively flat-peaked flood hydrographs are a characteristic feature

attributable to floodplain storage or other features upstream. A prime example is Station

24013 Deel at Rathkeale. A floodplain effect is inherently threshold-sensitive, so it is prudent

to study actual hydrographs (in m3s

-1) as well as standardised hydrographs.

Filtered hydrographs for all 31 events at Station 24013 are overlain in Figure 5.18. The

hydrographs have been translated to synchronise their peaks but not otherwise adjusted. It is

seen that a slowly rising crest segment is indeed typical of flood hydrographs at this site. The

characteristic hydrographs shown in the figure have been scaled up by multiplying the median

standardised hydrograph and the UPO-Gamma standardised hydrograph by the median

hydrograph peak of 116.75 m3s

-1.

The non-parametric method is seen to perform well, with the thick blue line in Figure 5.18

representing the tendency for the crest segment of Deel at Rathkeale flood hydrographs to rise

slowly to a peak before dropping away. The UPO-Gamma model is incapable of representing

this effect.

[Editorial note: Confusingly, the thick black line in Figure 5.18 shows the UPO-Gamma

model rather than the recommended UPO-ERR-Gamma. As explained in Section 5.7.3, the

exponential replacement recession can compensate a little for the intrinsic unsuitability of the


47

Gamma curve in cases where the characteristic hydrograph falls more rapidly than it rises.

The relevant recession is marked by the black broken line superposed on Figure 5.18.]

Figure 5.18: Hydrographs and rescaled characteristic hydrograph for Deel at Rathkeale


48

6 Constructing the characteristic hydrograph at ungauged sites

6.1 Introduction

A major part of research was to generalise Hydrograph Width Analysis (HWA) to allow the

characteristic hydrograph to be constructed at ungauged sites. The original research report

provides a very detailed description of the work. A précis is presented here. Holder (1985)

provides a primer on the use of multiple regression in hydrology.

6.1.1 Links with other parts of the FSU

The generalisations are based on the physical catchment descriptors (PCDs) presented in

Volume IV. There is some commonality with the Volume II work on generalising a model of

the index flood QMED. Both studies use multiple regression analysis, and develop linear

models between logarithmic transforms of the variable of interest and logarithmic transforms

of the PCDs. Individual researchers favour particular notations, terminology and refinements

of the basic techniques. Editing has sought to unify the descriptions.

Whereas the flood frequency research generalises one variable only (QMED), the HWA

research considers three descriptors (W75, W50 and s) and three model parameters (Tr, n and

C). A generic term is needed and these six are referred to below as the dependent variables

(DVs) of the regression study. Having adopted this terminology, it is natural to refer to the

PCDs as the independent variables (IVs).

6.1.2 Assumptions and difficulties

The following standard assumptions of multiple linear regression are noted:

The relationship between the DV and the IVs is linear;

The expected value of the arithmetic mean of the errors is zero (i.e. unbiased);

The error variance is constant across the range of values of the IVs (i.e. homo-

scedasticity);

The errors associated with one set of IV values are uncorrelated with those of another

(i.e. independence);

The errors are normally distributed with zero mean and constant variance (i.e.

normality) – while normality is necessary for the t-tests to be valid, estimation of the

model coefficients requires only that errors be identically and independently

distributed;

The model is properly specified (i.e. all relevant IVs are included and all irrelevant

ones discarded).

Other issues to be considered are:

The avoidance of over-determination. An over-determined or “over-parameterised”

model is one which fits too many free parameters in relation to the number of data

samples available. An adequately determined model is needed if the derived model is

to generalise sensibly to estimate the DV at ungauged sites.


49

Checking that individual observations do not exert undue influence on the model.

Checking for collinearity amongst the IVs (see Box 6.1). If IVs are highly

correlated, the regression coefficients are unlikely to be robust; values are likely to be

unduly sensitive to changes such as the addition of a station to the calibration dataset.

It can readily be appreciated that, in hydrological applications, complete satisfaction of the

assumptions and full resolution of the above issues cannot be achieved. Indeed, some of the

assumptions are expressly contradicted:

Some subsets of the PCDs are known to exhibit high collinearity;

The sample size of stations is unlikely to be large enough to be able to generalise a

model that includes all factors thought physically relevant;

The homogeneity and representativeness of samples is often difficult to ascertain.

Box 6.1: Collinearity

6.2 Selection of dependent variables (DVs)

Regression models are developed for three hydrograph-width descriptors (W75, W50 and s)

and three model parameters (Tr, n and C). These respectively characterise the recommended

non-parametric and parametric approaches to HWA. These six hydrograph descriptors are

the dependent variables (DVs) of the regression analyses.

Four of the variables W75, W50, Tr and C are times in hours. The other two are dimensionless,

with the mean ratio s taking values between 0 and 1 and n being a real number > 1.0. Values

of the six DVs obtained at 89 gauging stations are given in Table 5.1 and form the basic

HWA data used. These data are further summarised in Table 6.1.

For reasons noted in Section 5.7, values of W75, W50 and C could not be derived for a few

stations. The six variables were ℓn-transformed prior to the main model-building, where ℓn

denotes the natural logarithm.

Collinearity refers in a strict sense to the presence of exact linear relationships within a set

of variables. Typically, these are a set of candidate explanatory (i.e. predictor) variables in

a regression-type model. In statistical usage, collinearity also refers to near-collinearity,

i.e. when variables are close to linearly related.

In a multiple regression with collinearity, least-squares regression coefficients are highly

sensitive to very minor changes in the input data. The least-squares problem or the dataset

is said to be ill-conditioned. Some or all of the regression coefficients are likely to be

meaningless.

A typical approach to overcoming collinearity is to simplify the problem, e.g. by retaining

only one of the subset of variables that are highly correlated. Relatively arbitrary

decisions – as to which variables to retain and which to remove – are sometimes

unavoidable and inevitably influence the final model achieved.


50

Table 6.1: Summary statistics of dependent variables (DVs) selected for regression analysis

Dependent

variable Unit

No. of

stations Minimum Median Maximum

Geom.

mean

Arith.

mean CV

W75 h 87 3.11 39.87 332.71 38.70 63.31 1.09

W50 h 84 4.90 72.07 613.41 65.07 106.36 1.11

s – 89 0.22 0.40 0.58 0.40 0.41 0.18

n – 89 1.27 5.00 30.27 5.44 7.04 0.86

Tr h 89 7.66 49.99 429.25 49.38 69.16 1.00

C h 87 2.45 84.53 829.75 63.46 116.04 1.14

6.3 Selection of independent variables (IVs)

In principle, some 36 PCDs might have been considered as independent variables (IVs) in the

regression analysis. Those available included such items as the Eastings and Northings of the

station location and of the catchment centroid. It was judged prudent to use only a selection

of them in order to minimise the expected effects of collinearity (see Box 6.1).

The number of stations for which the dependent variable is available (i.e. 84 to 89 in this

research) is a limiting factor on the number of IVs that can be effectively supported in a

model. Tabachnick and Fidell (2001) and Brace et al. (2003) are amongst those putting

forward rules of thumb for the maximum number of IVs that should be considered when

searching for a “best” model. The limit adopted here was to allow no more than 12 Vs in the

main model-building.

Table 6.2 presents a brief description and some summary statistics for the 19 PCDs

considered initially. Eighteen of these are explicitly discussed in Volume IV and need no

further introduction here. The additional PCD was CGDIST: the distance in km from

catchment centroid to catchment outlet (i.e. the station location). When used in conjunction

with other measures of catchment size, CGDIST can help to represent catchment shape.

Some aspects of hydrograph shape are expected to reflect catchment shape.

[Editorial note: The flood attenuation index FAI and the permeability descriptor BFIsoil were

unavailable at the time of study. The omission of FAI is unfortunate, given that upper

hydrograph shape is expected to be influenced by floodplain effects. Non-availability of

BFIsoil was dealt with here by developing model variants according to whether a gauged BFI

value is available. It will be noted from Volume IV that BFIsoil coincides with gauged BFI at

the 166 stations used in its calibration. Of the two indices of arterial drainage, ARTDRAIN

was favoured over ARTDRAIN2. The opposite choice was made in modelling QMED in

Volume II, so it is important for FSU users to distinguish the two descriptors of arterial

drainage. Both S1085 and TAYSLO definitions of mainstream slope were retained but

S1085 ultimately proved the more useful.]

The 19 PCDs were ℓn-transformed prior to the main model-building, where ℓn denotes the

natural logarithm. Where the lower range of a particular descriptor can take a value of zero,

1.0 is added to the value prior to the ℓn-transformation. This applies to the fractions

ALLUV, ARTDRAIN, FOREST, PASTURE, PEAT and URBEXT.


51

Table 6.2: Some summary statistics of the IVs initially selected

Notation Brief description Unit # of

stns Min Median Max Mean CV

ALLUV Alluvial fraction – 89 0.0029 0.0349 0.0977 0.0370 0.53

AREA Catchment area km2 89 23.41 292.67 7980.41 624.76 1.60

ARTDRAIN

Fraction of area mapped as

benefiting from arterial

drainage

– 89 0.00 0.0015 0.3669 0.0576 1.45

BFI Baseflow index – 79 0.27 0.61 0.83 0.60 0.20

CGDIST Distance from catchment

centroid to gauging station km 89 4.83 11.72 54.19 13.86 0.58

DRAIND NETLEN/AREA km/

km2

89 0.39 0.96 1.81 0.99 0.29

FARL Index of flood attenuation by

reservoirs and lakes – 89 0.66 1.00 1.00 0.94 0.09

FOREST Forested fraction – 89 0.0161 0.0751 0.5619 0.0934 0.87

FLATWET Wetness index – 89 0.54 0.62 0.73 0.63 0.07

MSL Mainstream length km 89 13.92 38.14 214.61 47.65 0.64

NETLEN Length of upstream network km 89 23.99 293.54 6428.92 580.01 1.47

PASTURE Pasture fraction 89 0.2319 0.8134 0.9738 0.7737 0.22

PEAT Peat fraction 89 0.00 0.0527 0.4826 0.0994 1.09

SAAPE Average annual potential

evapotranspiration mm 89 449.60 503.96 546.98 498.22 0.05

SAAR Average annual rainfall mm 89 783.26 1023.31 2101.83 1068.66 0.19

STMFRQ Number of segments in

upstream river network – 89 7.00 288.00 5490.00 576.66 1.48

S1085 Mainstream slope (excluding

top 10% and bottom 15%) m/km 89 0.00021 0.00206 0.01867 0.00277 1.02

TAYSLO Taylor-Schwarz stream slope m/km 89 0.00001 0.00106 0.01308 0.00175 1.25

URBEXT Urban fraction – 89 0.00 0.0064 0.0553 0.0081 0.99

6.4 Additional notes

6.4.1 Treatment of Gamma shape parameter n

One of the six DVs – the shape parameter n – is required to take a value >1 if the Gamma

distribution is to provide a hydrograph that rises to a peak rather than immediately decays.

This case did not arise in fitting the UPO-ERR-Gamma at any of the 89 stations analysed.

The minimum value found was 1.29. Most of the modelling used the DV in the form ℓn(n).

However, it was prudent in the final modelling to use the DV in the form ℓn(n-1). This

guaranteed that hydrographs generated by the model at ungauged sites always rise to a peak

before decaying.


52

6.4.2 Software used for the regression analysis

A one-sentence summary of the goal of multiple regression is “to identify the fewest IVs

necessary to predict a DV where each IV predicts a substantial and independent segment of

the variability in the DV” (Tabachnick and Fidell, 2001). The SPSS statistical software

package was used for: exploring inter-correlations, developing regression equations,

assumption-checking and making additional diagnostic checks. Details and examples are

given in books such as Pallant (2001), Tabachnick and Fidell (2001) and Brace et al. (2003).

6.5 Correlation studies

Correlations amongst the PCDs were examined, both in their native form and after

logarithmic transformation. Those most strongly correlated were examined further. The

correlation matrix of the 19 IVs and six DVs is given in Table 6.3. This shows the ordinary

(Pearson) correlation coefficient for the ℓn-transformed variables.

6.5.1 Inter-correlations between PCDs

Matrix plots showing pairwise scatter-plots were extensively examined. Figure 6.1 illustrates

the extent to which AREA, MSL, NETLEN, STMFRQ and CGDIST compete to represent

catchment size. These strong correlations are understandable. [Editorial note: STMFRQ

denotes the number of streams in the catchment. This is one greater than the number of

stream junctions. Larger catchments tend to have more stream junctions. Thus, STMFRQ in

the FSU is correlated with catchment size. In contrast, the FSR (NERC, 1975) defined

STMFRQ as the number of junctions per unit area.]

Using a Pearson correlation with absolute value greater than 0.6 as an arbitrary guide, other

strong correlations evident in Table 6.3 are briefly discussed.

The strong inverse correlation between mainstream slope (represented by ℓnS1085) and

variables indicative of catchment size (e.g. ℓnAREA, ℓnMSL and ℓnCGDIST) is principally a

function of topography: steep catchments are inevitably rather small. [Editorial note: Such

correlations reflect both physical properties and the available network of stations. When all

≈134,000 FSU ungauged catchments are considered, the inverse correlation between ℓnS1085

and ℓnAREA is weaker, with r = -0.41 (as opposed to r = -0.66 in Table 6.3). Many small

catchments in Ireland have mild stream-slopes but the majority are not sufficiently important

to be gauged.]

Another grouping of PCDs is PASTURE, PEAT and SAAR. The strong inverse correlation

(r = -0.84) between ℓn(1+PASTURE) and ℓn(1+PEAT) appears straightforward. Catchments

dominated by more peaty formations tend to have fewer managed pastures. Also, the land-

cover classifications are mutually exclusive; in cases where most of a catchment is classed as

pasture, there is little available to be classed as peatlands. The evolution of peatlands in the

form of blanket and raised bogs is typically attributed to high rainfall combined with poor

drainage. In the Irish context, it is therefore understandable that a high value of ℓn(1+PEAT)

is often associated with a high value of ℓnSAAR (r = 0.54), as well as with a low value of

ℓn(1+PASTURE). The strong inverse correlation between ℓn(1+PASTURE) and ℓnSAAR

(r = -0.70) is consistent with drier areas being more readily put to pasture.


53

Table 6.3: Correlation matrix of selected IVs and DVs at (up to) 89 stations

PCD

or variable

AR

EA

MS

L

NE

TL

EN

ST

MF

RQ

DR

AIN

D

CG

DIS

T

FA

RL

AR

TD

RA

IN

S1085

TA

YS

LO

FL

AT

WE

T

SA

AR

SA

AP

E

UR

BE

XT

FO

RE

ST

PE

AT

PA

ST

UR

E

AL

LU

V

BF

I

ℓn AREA 1

Row above uses abbreviated names; full name is in first column ℓn MSL 0.94 1

ℓn NETLEN 0.96 0.93 1

ℓn STMFRQ 0.88 0.85 0.97 1 Red denotes Pearson correlation ≤ -0.6 or ≥ 0.6

ℓn DRAIND -0.14 -0.04 0.15 0.32 1 Orange indicates other correlations significant at 1%

ℓn CGDIST 0.83 0.89 0.80 0.71 -0.11 1

ℓn FARL -0.24 -0.26 -0.28 -0.33 -0.14 -0.15 1 Green indicates correlations significant at 5%

ℓn(1+ARTDRAIN) 0.22 0.22 0.21 0.16 -0.02 0.26 0.01 1

ℓn S1085 -0.66 -0.65 -0.56 -0.44 0.36 -0.60 0.21 -0.18 1

ℓn TAYSLO -0.25 -0.23 -0.22 -0.18 0.11 -0.23 0.07 -0.11 0.44 1

ℓn FLATWET -0.03 0.05 0.03 0.10 0.23 0.03 -0.48 0.00 -0.13 -0.10 1

ℓn SAAR -0.15 -0.06 0.02 0.19 0.59 -0.12 -0.41 -0.20 0.32 0.12 0.59 1

ℓn SAAPE -0.02 -0.09 -0.01 0.01 0.03 -0.09 0.39 -0.02 0.28 0.10 -0.83 -0.24 1

ℓn(1+URBEXT) -0.05 -0.10 -0.08 -0.08 -0.11 -0.02 -0.04 0.18 0.06 -0.01 -0.13 -0.08 0.15 1

ℓn(1+FOREST) -0.25 -0.18 -0.14 -0.07 0.36 -0.21 0.04 -0.26 0.37 0.21 0.09 0.49 -0.05 -0.26 1

ℓn(1+PEAT) -0.03 -0.02 0.01 0.06 0.14 -0.12 -0.22 -0.05 -0.04 -0.05 0.52 0.54 -0.43 -0.02 0.42 1

ℓn(1+PASTURE) 0.11 0.10 0.04 -0.07 -0.23 0.18 0.27 0.16 -0.16 -0.12 -0.49 -0.70 0.30 0.06 -0.58 -0.84 1

ℓn(1+ALLUV) 0.07 0.04 0.12 0.08 0.16 0.03 0.38 0.13 0.28 0.08 -0.58 -0.26 0.56 0.03 0.06 -0.41 0.40 1

ℓn BFI 0.42 0.38 0.29 0.23 -0.45 0.38 -0.39 0.22 -0.49 -0.24 0.08 -0.27 -0.16 0.08 -0.48 -0.14 0.15 -0.19 1

ℓn W75 0.33 0.32 0.24 0.22 -0.31 0.23 -0.64 -0.16 -0.49 -0.31 0.41 0.04 -0.40 -0.09 -0.31 0.07 -0.09 -0.48 0.63

ℓn W50 0.32 0.31 0.22 0.20 -0.32 0.22 -0.63 -0.15 -0.48 -0.36 0.36 0.00 -0.35 -0.10 -0.32 0.01 -0.04 -0.44 0.67

ℓn s -0.05 0.00 -0.04 -0.03 0.01 -0.06 0.14 -0.13 0.04 0.05 0.16 0.09 -0.22 -0.12 0.19 0.22 -0.15 -0.17 -0.36

ℓn n -0.26 -0.22 -0.19 -0.16 0.22 -0.23 0.53 -0.09 0.35 0.26 -0.32 -0.02 0.29 -0.14 0.30 -0.04 0.03 0.32 -0.48

ℓn Tr 0.24 0.26 0.16 0.16 -0.27 0.12 -0.43 -0.27 -0.42 -0.25 0.36 0.04 -0.39 -0.13 -0.20 0.10 -0.11 -0.47 0.47

ℓn C 0.37 0.32 0.30 0.30 -0.22 0.32 -0.56 0.04 -0.40 -0.22 0.28 -0.01 -0.26 0.04 -0.32 -0.02 -0.04 -0.27 0.74


54

(This page is intentionally blank.)


55

Figure 6.1: Matrix plot of PCDs that in part represent catchment size (89 stations)

[Editorial note: From Table 6.2, PASTURE is seen to be the dominant classification, with a

mean of 77.4% of catchment land-cover as opposed to 9.9% for PEAT and 12.7% to other

classifications. When all ≈134,000 FSU ungauged catchments are considered, the mean

values of PASTURE, PEAT and “other” are 57.3%, 23.8% and 18.9% respectively. The

corresponding mean values for SAAR are 1069 mm for the 89 catchments studied and 1293

mm for the ≈134,000 FSU ungauged catchments. Thus there appears to be a bias towards

gauging drier and more agriculturally productive catchments than is the Irish norm. This

emphasises the importance of the research undertaken to generalise methods of estimating the

characteristic hydrograph that take full account of catchment properties.]

The strong inverse correlation (r = -0.83) between ℓnSAAPE and ℓnFLATWET reflects that

these descriptors derive respectively from standardised estimates – based on climate data – of

potential evaporation and soil moisture. FLATWET is the proportion of the time for which

soils can be expected to be typically quite wet. FLATWET is expected to be greater in areas

where rainfall is high but the potential for evaporation (indexed by SAAPE) is relatively low.

[Editorial note: SAAR is the pre-eminent climatological descriptor in many hydrological

applications. The lack of correlation between ℓnSAAR and the hydrograph-width variables

(see bottom six rows of Table 6.3) is striking.]

ℓn AREA

ℓn MSL

ℓn NETLEN

ℓn STMFRQ

ℓn CGD ST

ℓn ℓn ℓn ℓn ℓn

AREA MSL NETLEN STMFRQ CGDIST

Width W75

CGDISTDRAINDSTRMFRQNETLENMSLAREA

Wid

th

W75

CG

DIS

TD

RA

IND

ST

RM

FR

QN

ET

LE

NM

SL

AR

EA

Width W75


Wid

th

W75

CG

DIS

TD

RA

IND

ST

RM

FR

QN

ET

LE

NM

SL

AR

EA

Width W75


Wid

th

W75

CG

DIS

TD

RA

IND

ST

RM

FR

QN

ET

LE

NM

SL

AR

EA

Width W75


Wid

th

W75

CG

DIS

TD

RA

IND

ST

RM

FR

QN

ET

LE

NM

SL

AR

EA


56

The strong inverse correlation between ℓnS1085 and ℓnCGD ST (r = -0.60) is more

inscrutable. It may reflect that streams tend to be steeper on catchments where the drainage

pattern is fan-shaped (with a more compact catchment) than when the drainage pattern is

elongated (with a relatively large CGDIST).

Interestingly, the correlation between ℓnS1085 and ℓnTAYSLO is not especially high

(r = 0.44), indicating that these are rather different measures of mainstream channel slope.

6.5.2 Individual correlations between DVs and initially selected IVs

The correlations between each of the six DVs and the 19 initially selected IVs are shown in

the bottom rows of Table 6.3. There are two stand-out sets of associations:

ℓnW75 and ℓnW50 are highly negatively correlated with ℓnFARL;

ℓnW75, ℓnW50 and ℓnC are highly correlated with ℓnBFI.

These are consistent with physical interpretations that:

Lakes and other water bodies (consistent with a smaller value of ℓnFARL) attenuate

the flood passing down the river system, tending to lead to hydrographs that are more

prolonged than otherwise (consistent with larger values of ℓnW75 and ℓnW50);

Catchments that are relatively permeable (consistent with a larger value of ℓnBFI)

tend to lead to hydrographs that are more prolonged than otherwise (consistent with

larger values of ℓnW75 and ℓnW50).

6.5.3 Choosing a subset of PCDs to use as IVs

In view of the strong correlations (see Section 6.5.1) amongst various groups of PCDs, it was

decided that a subset would suffice for the main modelling. For reasons discussed in

Section 6.3, the main regression study would use no more than about 12 IVs.

The most suitable IVs in each of three competitive groups were chosen by favouring those

most strongly correlated with the six DVs under study. The relevant correlations are shown

in the bottom six rows of Table 6.3.

From inspection, it can be seen that:

The magnitudes of the correlations associated with ℓnAREA are generally a little

larger than those associated with ℓnMSL, ℓnNETLEN, ℓnSTMFRQ or ℓnCGDIST;

The magnitudes of the correlations associated with ℓn(1+PASTURE) and

ℓn(1+PEAT) are larger than those associated with ℓnSAAR;

The magnitudes of the correlations associated with ℓnFLATWET are evenly

balanced with those associated with ℓnSAAPE.

Accordingly, ℓnAREA, ℓn(1+PASTURE) and ℓnFLATWET were selected as the

representative variables, and the seven other PCDs discarded. This achieved the target of

allowing no more than 12 IVs in the regression modelling.


57

6.5.4 Checking the Normality of the DVs

The log-transforms yield DVs that are acceptably Normal, satisfying one of the requirements

for linear regression (see Section 6.1.2). The Gamma shape parameter n is somewhat less

convincing than the others in this respect (see Figure 6.2).

Figure 6.2: Normality plots of log-transformed width descriptors and model parameters

Reading across the 4th-last row of Table 6.3, the hydrograph width descriptor ℓn s is seen to

be no more than weakly correlated with the available IVs. Although an attempt was made to

model this index of hydrograph skewness, the best that could ultimately be achieved was to

adopt a fixed value of s = 0.40. From Table 6.1 it is seen that this is very close to both the

arithmetic and geometric means of s, i.e. to the arithmetic means of s and ℓn s. It proved

possible to develop useful regression models for the other five DVs.

ℓnW75 ℓnW50

ℓn s ℓn n

ℓnTr ℓn C

Observed value Observed value



E

xp

ecte

d v

alu

e

Ex

pec

ted

va

lue

E

xp

ecte

d v

alu

e

(i

f N

orm

all

y d

istr

ibu

ted

)

(if

No

rma

lly

dis

trib

ute

d )

(

if N

orm

all

y d

istr

ibu

ted

)


58

6.5.5 Final selection of the independent variables; a note on the use of BFI

The 12 variables finally selected as IVs were (in no particular order):

ℓnAREA, ℓnDRAIND, ℓnFARL and ℓn(1+ARTDRAIN);

ℓnS1085, ℓnTAYSLO, ℓnFLATWET and ℓn(1+URBEXT);

ℓn(1+FOREST), ℓn(1+PASTURE), ℓn(1+ALLUV) and ℓnBFI.

BFI is not strictly a PCD. Rather, it is a hydrological index derived by the analysis of daily

mean flow data. At the time of the hydrograph width research, the mechanism by which BFI

would be modelled at ungauged sites was unclear. Accordingly, two sets of generalisations –

of the hydrograph width variables W75 and W50 and the UPO-ERR-Gamma model parameters

n, Tr and C – were developed according to whether a BFI value is/isn’t available.

6.6 The regression method used

Various forms of multiple regression are possible. That adopted here was stepwise linear

regression. In stepwise regression, IVs are introduced into the regression model one variable

at a time. At each step, the IV offering the greatest reduction in the objective function (least-

squares or weighted least-squares) is added into the model. But IVs already included in the

model “may also be deleted at any step where they no longer contribute significantly to

regression” (Tabachnick and Fidell, 2001). The stepwise method results in a parsimonious

model i.e. one frugal in its use of parameters. The default settings in SPSS were used in

respect of the statistical criteria for including or removing an IV. Accordingly, the thresholds

used were 0.05 (5% significance) for inclusion of an IV and 0.10 (10% significance) for

removal of an IV, the F-test statistic being used to assess the significance of the departure

from the null hypothesis (that there is no linear relationship between the IV and the DV).

[Editorial note: For datasets of the moderate size considered here, computer power is

typically such that “best subsets” regression rather than stepwise regression can be used.

Indeed, the best subsets approach is adopted for the Volume II modelling of QMED. Many

researchers feel more comfortable with the stepwise approach, believing it to provide more

defined safeguards against over-determination of models. An over-determined model is one

which fits too many free parameters in relation to the number of data samples available. In

many cases, the different techniques lead to the same final model.]

6.7 Illustrative results: Estimating W75 when BFI available

Generalisation of the hydrograph width descriptor W75 provides an insight into the methods.

The regression is based on linear least-squares, with ℓnW75 taken as the DV. The stepwise

regression analysis is summarised in Table 6.4, which reports intermediate results for 1, 2, 3,

and 4-variable models as well as the final 5-variable model.

6.7.1 Regression models and their performance evaluation

r2 indicates the proportion of variation explained by the regression model (i.e. by the IVs). It

is often termed the coefficient of determination. There is progressive improvement in r2 as

additional IVs are allowed into the model. The final 5-variable model explains about 72% of

the variability in ℓnW75. Explaining this much of the variability is regarded as quite good.


59

It is inevitable that r2 increases as additional IVs are allowed into the model. By this

criterion, a model using all 12 available IVs would be judged best.

To avoid over-determination, it is necessary to examine the adjusted r2. The adjustment takes

into account the number of “degrees of freedom” consumed by having to fit additional

parameters in the linear least-squares regression. The adjusted r2 provides a reasonable

estimate of how well the regression model might be expected to fit another dataset drawn

from the same population. The adjusted r2 value of 0.701 indicates that the 5-variable model

provides a reasonably good fit.

Table 6.4: Stepwise regression results for modelling hydrograph width descriptor ℓnW75

No.

of

IVs

No. of

catchments IV added

IV

removed r

2

Adjusted

r2

Standard

error of

estimate

(SEE)

Factorial

standard

error of

estimate

(FSE)

1 77 ℓnBF .399 .391 .788 2.20

2 77 ℓn(1+ALLUV) – .575 .564 .668 1.95

3 77 ℓnFARL – .643 .629 .616 1.85

4 77 ℓn(1+ARTDRA N) – .686 .669 .581 1.79

5 77 ℓnS1085 – .721 .701 .552 1.74

The standard error of estimate (SEE) is the standard deviation of the residuals or errors in

predictions by the model: in this case, in the estimates of ℓnW75. This means that – on the

assumption that the model residuals are normally distributed – the actual value of ℓnW75 is

expected to lie within 0.552 of the predicted value in about 68% of cases.

Because our principal interest is in estimating W75 rather than ℓnW75, the factorial standard

error (FSE) is generally more relevant. The FSE is just the exponential of the SEE. For the

final (5-variable) model, the FSE is e0.552

= 1.74. This means that (in about 68% of cases) the

actual value of W75 is expected to lie within the factorial range 0.57 75 to 1.74 75 where

75 is the estimated value of the width descriptor W75 obtained from the regression model

and 0.57 is the reciprocal of 1.74. This confidence interval is considered reasonably good.

For the scenario when BFI is available, the recommended model is:

ℓnW75 = 3.548 + 1.861 ℓnBFI – 12.199 ℓn(1+ALLUV) – 3.946 ℓnFARL

– 3.324 ℓn(1+ARTDRA N) – 0.246 ℓnS1085 6.1

Exponentiating both sides of the equation, the model can be written:

W75 = 34.74 BFI1.86

(1+ALLUV)-12.20

FARL-3.95

(1+ARTDRAIN)-3.32

S1085-0.25

6.2

Table 6.5 confirms that all coefficients are significant at the 0.05 level (│t statistic│> 1.96).

The standardised coefficients (β in the table) highlight the relative contribution of each

descriptor to explaining the variation in ℓnW75. ℓnBF is seen to be the most important

predictor. This vindicates the decision to develop models for the case when this variable is

available.


60

Table 6.5: Coefficient and collinearity statistics for selected model for ℓnW75

Term/regressor Coefficient

Standard

error of

coefficient

β

value

t

statistic Tolerance

Variance

inflation

factor

(VIF)

Constant 3.548 0.68 5.20

ℓnBFI 1.861 0.34 0.43 5.53 0.660 1.52

ℓn(1+ALLUV) -12.199 3.82 -0.23 -3.19 0.767 1.30

ℓnFARL -3.946 0.94 -0.30 -4.20 0.751 1.33

ℓn(1+ARTDRAIN) -3.324 0.92 -0.24 -3.62 0.903 1.11

ℓnS1085 -0.246 0.08 -0.22 -2.95 0.708 1.41

6.7.2 Checking the possible influence of collinearity

In order to assess the possible impact of collinearity (see Box 6.1), the variance inflation

factor (VIF) was also studied. This statistic is the reciprocal of the tolerance, which in turn

denotes the proportion of the variance in a given catchment descriptor that cannot be

explained by the other regressors.

High VIF values (i.e. small tolerances) indicate that a large amount of the variance in one

regressor can be explained by the other regressors. VIF thus indexes the impact of

collinearity (amongst the regressors) on the stability of the multiple regression model. VIF

values are (by definition) greater than or equal to 1. Whilst only a guide, VIF values greater

than 10 are often regarded as indicating serious problems of collinearity. In weaker models,

values above 2.5 may sometimes be a cause for concern.

It is seen from the final column of Table 2.7 that VIF is less than 1.6 for all regressors.

Collinearity is therefore judged not to be a problem with the selected model.

6.7.3 Checking the logical consistency of the model

Logical consistency is often the overriding factor in the final choice of a regression model. Is

the model consistent with what we know about catchment flood behaviour? The 5-variable

model for ℓnW75 appears credible in this respect:

W75 increases with permeability and storage (indicated by a larger value of BFI);

W75 decreases with larger values of FARL (a larger value of FARL is associated with

reduced attenuation of flood water by storage elements such as lakes and reservoirs;

flood hydrographs in such a catchment can be expected to have a higher peak and a

narrower width);

W75 decreases with larger values of ARTDRAIN, consistent with a flashier response

after arterial drainage works (i.e. a flood hydrograph with a higher peak and a

narrower width);

W75 decreases with larger values of S1085, indicating a flashier response from steeper

catchments;

W75 decreases when the proportion of land-cover classed as alluvial (ALLUV) is

larger (more alluvium in a catchment indicates a lower potential of the catchment for


61

accepting rainfall; the resulting flood response is therefore expected to be faster, with

the flood hydrograph expected to be narrower than that in a catchment having less

alluvium).

The last feature is not wholly convincing, because of the high magnitude of the exponent of

1+ALLUV in the Equation 6.2 model for W75. The role of ALLUV in the hydrograph-width

models is discussed further in Box 6.2.

Box 6.2: The role of ALLUV in the hydrograph-width models

Editorial note: Discussion is warranted of an uncomfortable feature of the Equation 6.2

model for W75. This is the high magnitude (-12.20) of the exponent of 1+ALLUV.

ALLUV denotes the proportion of the catchment classed as alluvium in the Teagasc

classification of soils (see Volume IV).

The effect might conceivably reflect that alluvial areas lie close to the river network and

tend to contribute runoff quickly. However, the attribution of physical effects to results

obtained by regression is often hazardous.

From Table 6.2 it is seen that alluvial fractions for the 89 catchments studied range from

0.00 to 0.10. Thus, the modelled factorial effect of the alluvium on W75 ranges from

1.00-12.20

= 1.000 (when ALLUV = 0.00) to 1.10-12.20

= 0.313 (when ALLUV = 0.10).

This may just be reasonable.

PCDs for ungauged sites were not available at the time of the hydrograph width research.

98.3% of the ≈134,000 ungauged catchments supported by the FSU have a value of

ALLUV within the range 0.00 to 0.10. However, 0.25% of catchments are classified as

having ALLUV ≥ 0.20. For these cases, the W75 model (Equation 6.2) implies that

classification of land as alluvium reduces W75 by a factor of more than 9, since

(1+0.20)-12.20

= 0.108 ≈1/9. This does not seem reasonable.

The urban fraction (URBEXT) is the only classification of land cover to play a major role

in the Volume II procedure for estimating the T-year flood peak at an ungauged site. It is

notable that ALLUV plays no role. Thus, an ungauged catchment classified as having an

unusually large alluvial fraction will be modelled as generating hydrographs that are

exceedingly narrow but not especially high-peaked. This appears physically unrealistic.

Should the catchment under study be mapped as having an unusually large alluvial

fraction, it will be prudent for the user to make special checks.

The Equation 6.2 model for W75 has not in fact been implemented. The models

implemented through the FSU Web Portal are shown later in Table 6.7. Only one of these

– the model for estimating Tr – includes the 1+ALLUV term. Moreover, the exponent of

1+ALLUV in that model is somewhat less severe (-8.83) than for the Equation 6.2 model.

Users are nevertheless to be encouraged to make special checks should they be using the

model to estimate Tr on a catchment for which ALLUV≥0.20.

The role of ALLUV in the hydrograph-width models may warrant further exploration.


62

6.7.4 Additional checks

Additional checks were made on the sensitivity of the 5-variable model to the inclusion of

particular catchments in the calibration. The statistics examined include a leverage statistic

(to identify catchments whose observed values of the selected DV influence the regression

model more than others) and Cook’s distance (which measures how much the model

coefficients change when a particular catchment is dropped from the analysis). Some weak

evidence was found that Station 26021 Inny at Ballymahon might have undue influence.

However, rules of thumb indicated that this was not so marked as to warrant its exclusion.

The model residuals (i.e. prediction errors) were tested for normality. The probability-

probability (P-P) plot shown in Figure 6.3 shows some departure from a perfect 1:1 line but

not enough to judge the model inadequate.

Figure 6.3: Normality plot of standardised residuals for 5-variable model for ℓnW75

Model residuals were also tested for homoscedasticity. This requires that the standard

deviations of errors of prediction are approximately equal for all predicted values of the DV.

Homescedastic derives from the Greek for equal scatter. Homoscedasticity is exhibited

when the plot of residuals displays a cloud of dots and the band enclosing the residuals is

approximately equal in width at all values of the predicted DV.

A lack of homoscedasticity (i.e. heteroscedasticity) is characterised by a pattern such as a

funnel shape, indicating greater errors associated with larger predicted values. This may arise

when there is an interaction between an IV and a variable not in the regression model, or

when some IVs are skewed while others are not. No serious violation of the assumption of

homoscedasticity is evident in the Figure 6.4 plot of standardised residuals against the

standardised predicted values. The 5-variable model for ℓnW75 is therefore considered

acceptable.

Observed cumulative probability

Exp

ecte

d v

alu

e

(if

Norm

all

y d

istr

ibu

ted

)


63

Figure 6.4: Plot of standardised residuals for 5-variable model for ℓnW75

Reg

ress

ion

sta

nd

ard

ised

pre

dic

ted

va

lue

Regression standardised residual


64



65



66

Table 6.6: Recommended models – when BFI available

Hydrograph

descriptor

# of

stations

Adj.

r2

FSE Stations identified as possible

outliers* Recommended model

Eqn

#

W75 77 0.701 1.74 26021 W75 = 34.74 BFI1.86

FARL-3.95

(1+ALLUV)-12.20

(1+ARTDRAIN)-3.32

(S1085/1000)-0.25

6.3

W50 75 0.735 1.70 None W50 = 63.05 BFI2.11

FARL-4.55

(1+ALLUV)-10.24

(1+ARTDRAIN)-3.17

(S1085/1000)-0.25

6.4

n 79 0.377 2.02 06011, 11001, 14007, 16005,

18005, 25027, 34018 n = 1 + 2.90 BFI

-1.12 FARL

4.37 6.5

Tr 79 0.493 1.77 26021 Tr = 54.98 BFI1.32

(1+ALLUV)-13.08

(1+ARTDRAIN)-3.70

(S1085/1000)-0.20

6.6

C 77 0.630 2.16 16005 C = 310.75 BFI3.44

FARL-4.88

6.7

*Assignment based on a test of

standardised deleted residuals

Table 6.7: Recommended models – when BFI unavailable

Hydrograph

descriptor

# of

stations

Adj.

r2

FSE Stations identified as possible

outliers* Recommended model Eqn #

W75 87 0.675 1.79 15002, 35071 W75 = 31.28 DRAIND-0.88

FARL-5.85

(1+FOREST)-2.86

(1+ARTDRAIN)-2.92

FLATWET3.12

(S1085/1000)-0.27

6.8

W50 84 0.675 1.80 35071 W50 = 34.02 DRAIND-0.95

FARL-6.59

(1+FOREST)-2.83

(1+ARTDRAIN)-2.60

FLATWET2.44

(S1085/1000)-0.29

6.9

n 89 0.412 1.99 06011, 11001, 14007, 34018 n = 1 + 4.78 DRAIND0.63

FARL5.46

(1 + FOREST)2.46

6.10

Tr 89 0.213 2.03 26021, 30061 Tr = 13.85 DRAIND-0.48

FARL-2.54

(1+ARTDRAIN)-3.16

(S1085/1000)-0.25

(1+ALLUV)-8.83

6.11

C 87 0.485 2.42 16008, 23002, 35071 C = 11.78 DRAIND-0.97

FARL-7.65

(1+FOREST)-3.70

AREA0.26

6.12

*Assignment based on a test of

standardised deleted residuals


67

6.8 Recommended models for use at ungauged sites

6.8.1 The final models

The techniques of Sections 6.6 and 6.7 were applied to develop models for the hydrograph

width measures/parameters: W75, W50, n, Tr and C. The recommended models are presented

in Table 6.6 (for the case when BFI is available) and Table 6.7 (for the case when BFI is

unavailable). These models (see tables on previous page) are now jointly discussed:

When judged by the factorial standard error (FSE), the models using BFI (Table 6.6)

generally outperform those that do not (Table 6.7). This shows the value of BFI in

helping to model hydrograph shape. (Precise comparisons are inhibited because of

the somewhat different datasets used in Table 6.6 and Table 6.7. BFI values were

available for only 79 of the 89 stations.)

The likely importance of storage attenuation and the effectiveness of FARL in its

characterisation are highlighted by the appearance of the descriptor in all but one of

the ten models.

Mainstream slope S1085 appears in the models of the three main characteristic times

W75, W50 and Tr. The exponent of S1085 is reassuringly similar in all cases.

[Editorial note: For a reason known only to the research contractor, values of S1085

were divided by 1000 prior to the regression modelling of hydrograph widths. This

explains why the term S1085/1000 appears in the models for W75, W50 and Tr shown

in Table 6.6 and Table 6.7. This led to difficulties for the contractor testing IBIDEM

at two ungauged sites (see Sections 9.7.4 and 9.7.5) but should have no impact for the

user.]

When BFI is unavailable, the importance of FARL is heightened and DRAIND also

becomes indispensable. Both descriptors appear in all five models. FOREST also

then proves helpful (appearing in four of the models). The exponents of DRAIND

and FOREST indicate that hydrographs are narrower when drainage and forest cover

are more extensive. This likely reflects the faster conveyance of water, noting that

afforestation is often accompanied by drainage works such as ditching.

There is reassuring consistency in the models derived for W75 and W50. The same

terms appear in both models. Moreover, the exponents are broadly comparable.

Except for parameter C, the FSEs are in the range 1.7 to 2.0. This is a moderately

good performance by hydrological standards. [Editorial note: The excellent

performance achieved in estimating QMED on rural catchments (FSE = 1.37, see

Volume II) suggests that the task of modelling typical peak flows on an ungauged

catchment is rather easier than that of modelling typical hydrograph widths. This

likely reflects the highly attenuated nature of many flood hydrographs in Ireland. It

may also reflect the varied duration and often complex pattern of rainfalls that give

rise to flooding.]

The term least well-estimated is parameter C of the UPO-ERR-Gamma model. This

determines the rate of decay of the exponential replacement recession. The poor

performance in modelling C is neither surprising nor especially worrying. The

parameter has no influence on the peak segment of the hydrograph.

The model for C in the BFI unavailable case is the only occasion on which a PCD

indicative of catchment size appears in the hydrograph width modelling. It is also

notable that general wetness indexed by SAAR does not appear in any model.


68

However, the wetness descriptor FLATWET proves useful in modelling W75 and W50

in the BFI unavailable case.

The analyses identify a number of stations that are possible outliers. Those implicated

in estimation of the parameters of the UPO-ERR-Gamma model may not warrant

much concern. It is inevitable that the limited family of hydrograph shapes supported

by the UPO-ERR-Gamma model (see Figure 4.1, Figure 4.2 and Figure 4.4) will not

suit all stations.

The sites implicated as possible outliers in the modelling of W75 and W50 are Stations

15002, 26021and 35071. These are all Grade A2 stations. Station 26021 had by far

the largest proportion of missing flow data of any of the 89 stations analysed (see

Table A.2). The poor performance of the PCD-based models at Stations 15002 and

35071 may warrant further investigation. The characteristic hydrographs at these

stations (see Figure 6.5) are relatively well defined and, in the case of Station 15002

Nore at John’s Bridge, rather finely shaped.

Figure 6.5: Median hydrographs at: (a) Station 15002 and (b) Station 35071

Per

cen

tag

e o

f p

eak

flo

w

100

90

80

70

60

50

40

30

20

10

0

Median hydrograph

-150 -112.5 -75 -37.5 0 75 150 225 300 Time in hours (relative to time of peak flow)

(b) Station 35071 Lareen at L. Melvin

Percen

tag

e o

f p

eak

flo

w

100

90

80

70

60

50

40

30

20

10

0

Median hydrograph

-50 -37.5 -25 -12.5 0 50 100 150 200 Time in hours (relative to time of peak flow)

(a) Station 15002 Nore at John’s Bridge


69

6.8.2 Model performance

The quality of performance achieved by the regression models in the BFI unavailable case is

encapsulated in Figure 6.6. The plots show “observed” and predicted values of the width

descriptors (W75 and W50) and the UPO-ERR-Gamma parameters (n, Tr and C) for the 89-

station dataset. The supporting data are presented in Table D.1 of Appendix D.

Figure 6.6: Derived and modelled values of W75, W50, n, Tr and C (BFI unavailable case)

Note the logarithmic scale of the plots. The factorial standard error (FSE) provides a one-

number summary of the performance achieved. While many values are predicted within a

factor of two, some for the C parameter are seen to be in error by up to a factor of ten.

C (hours) Tr (hours)

n

W75 (hours) W50 (hours)

FSE = 1.79 FSE = 1.80

FSE = 2.42 FSE = 2.03

FSE = 1.99


70

It is confirmed that the generalisation for application at ungauged sites is more successful for

the width descriptors W75 and W50 than for parameters of the UPO-ERR-Gamma model.

It is concluded that, for the BFI unavailable case, the UPO-ERR-Gamma model may not be

sufficiently reliable to construct the characteristic flood hydrograph at ungauged sites. An

alternative is to use the parabolic curves method (see Section 8.7) with the width descriptors

W75 and W50 estimated by Equations 6.8 and 6.9. This synthesises the upper hydrograph

only.

In view of the better performance of the regression models derived for the BFI available case,

consideration might be given to using any or all of the models from Table 6.6 at ungauged

sites by substituting BFIsoil for BFI. This possibility is discussed in Section 8.6.

6.8.3 Additional notes on the regression models

The Gamma shape parameter n is dimensionless. Both FARL and BFI are themselves

dimensionless. So it is encouraging that the regression model is dimensionally correct in the

BFI available case (Equation 6.5).

The other four hydrograph descriptors (W75, W50, Tr and C) are all characteristic times in

hours. None of the PCDs available to the generalisation research had a dimension involving

time. Thus, it is not possible for the regression models to be strictly dimensionally correct.


71

7 Ancillary investigations

The research checked for systematic variations in the shape of the flood hydrograph with:

The magnitude of the peak flow;

The pre-event minimum flow;

Season;

Arterial drainage in the catchment.

7.1 Variation of hydrograph width with peak flow

The variation of hydrograph width with peak flow was checked for all 89 stations studied.

Figure 7.1 presents a typical outcome for Station 07009 Boyne at Navan Weir. There is no

particular trend evident towards wider or narrower hydrographs according to the magnitude

of the flood peak.

[Editorial note: The broken lines connect widths for different events. This is to help visual

detection of any underlying trend. Formal tests for linear trend were also undertaken using

ordinary least-squares regression.].

Figure 7.1: Variation of hydrograph width with peak flow at Station 07009

For a few stations (e.g. Station 07010 Blackwater at Liscartan shown in Figure 7.2), the

graphs display generally positive slopes. However, for most other stations, the parts of the

graphs corresponding to the two or three highest recorded floods actually show negative

slopes, in contrast to the positive slopes for the points corresponding to the floods of lower

magnitudes. Some examples of such inconsistently varying slopes are shown in Figure 7.3.

A composite trend-line of the form y = mx + c was fitted to the plots of hydrograph width

against the magnitude of the peak flow, y being the total width (in hours), x the peak flow (in

m3s

-1), m the slope and c the intercept. At each station in turn, trends were examined across

all hydrograph widths collectively, and for the reference widths W75 and W50 individually.

Peak flow (m3s

-1)

Wid

th o

f ex

ceed

an

ce (

hou

rs)

Labels mark % of peak flow at which width abstracted


72

Figure 7.2: Variation of hydrograph width with peak flow at Station 07010

Figure 7.3: Patterns of variation of hydrograph width with peak flow (at six stations)

Wid

th o

f ex

ceed

an

ce (

ho

urs

) Station 24013 Deel at Rathkeale Station 36015 Finn at Anlore

Peak flow (m3s

-1) Peak flow (m

3s

-1)

Station 06026 Lagan-Glyde at Aclint Station 09001 Ryewater at Leixlip

Wid

th o

f ex

ceed

an

ce (

ho

urs)

Peak flow (m3s

-1) Peak flow (m

3s

-1)

Wid

th o

f ex

ceed

an

ce (

ho

urs

) Station 14004 Figile at Clonbulloge Station 14011 Slate at Rathangan

Peak flow (m3s

-1) Peak flow (m

3s

-1)


Wid

th o

f ex

ceed

an

ce (

ho

urs

)

Peak flow (m3s

-1)



73

Checks for trend were extensive but generally inconclusive. Figure 7.4 shows the slope of

the trend in W75 for the 37 Grade A1 stations. The stations are arranged by catchment size,

with the smallest (Station 34018) on the left and the largest (Station 25017) on the right.

While there is some variation, no marked pattern with catchment size is evident.

Figure 7.4: Slope of W75 trend with peak flow magnitude (Grade A1 stations)

Although the pattern of trend was not generalised, some weak support was found to suggest

that hydrographs may tend to become narrower in larger events on steep catchments (e.g.

high S1085) with fewer lakes (i.e. high FARL) than otherwise. The opposing slopes of the

trends at Stations 06011 (Fane at Moyles Mill) and 06012 (Fane at Clarebane) evident in

Figure 7.4 were explored. The reason for the marked difference is unclear, although the

mainstream slope (S1085) is indeed much lower at the downstream site (see Table 7.1),

suggesting that the intervening area is rather flat.

Table 7.1: Some leading PCDs of stations on the River Fane

Station # Station name Location

AREA S1085 FARL

km2 m/km –

06012 Fane at Clarebane Upstream 162.8 0.0052 0.874

06011 Fane at Moyles Mill Downstream 229.2 0.0027 0.831

7.2 Variation of hydrograph width with pre-event minimum flow

The variation of hydrograph width with peak-event minimum flow was checked for all 89

stations. For the purpose of HWA, the pre-event minimum flow is taken as the minimum

flow on the rising side of the flood hydrograph that lies within the time-window defined in

Section 2.2.

Figure 7.5 presents the outcome for Station 07009 Boyne at Navan Weir. No particular trend

is evident towards wider or narrower hydrographs according to the magnitude of the pre-

event flow. No systematic trend or pattern in the variation of hydrograph widths with pre-

event minimum flow could be identified across the 89 stations.

Although no pattern of trend could be generalised, some weak support was found to suggest

that hydrographs may tend to become wider in sparser river networks (i.e. with lower values

of DRAIND) or more permeable catchments (i.e. with higher values of BFI) when the pre-

event minimum flow is high than when it is low. A more obscure effect was a possible

tendency for hydrographs to become narrower – when the pre-event minimum flow is high –

in catchments where the alluvial fraction (ALLUV) is higher (see Figure 7.6). In the figure,

Slope m of the trend-line Y=mX+c fitting the available total w idths at 75 percentile of selected flood events plotted against the respective peak

flows for each station

-25

-20

-15

-10

-5

0

5

10

15

20

34018

14007

25027

29001

6026

25025

14011

25014

6012

36015

9001

6011

30005

26019

14004

6014

25030

26008

6013

29011

15005

25003

24013

7007

26012

27002

23002

30004

7010

36010

14006

26007

25006

7009

7012

14018

25017

Station no.

Slo

pe m

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Catc

hm

en

t are

a

(km

2)

Slo

pe

of

tren

d-l

ine

(ho

urs

/m3s-1

) Catchment area (km2)

Station #

9000 8000

7000

6000 5000

4000

3000 2000

1000

0


74

the 89 Grade A1+A2 stations are ordered according to the fraction of the catchment mapped

as alluvium. See also the discussion of ALLUV in Section 6.7.3.

Figure 7.5: Variation of hydrograph width with pre-event minimum flow (Station 07009)

Figure 7.6: Slope of W75 trend with pre-event minimum flow (Grade A1+A2 stations)

7.3 Variation of hydrograph width with time of year

The variation of hydrograph width with time of year was checked for all 89 stations using

both regular and circular plots. The seasonal distribution of floods at Station 07009 Boyne at

Navan Weir is illustrated in Figure 7.7. It can be seen that most floods occur in the winter

half-year from October to March, with the three largest in November to January. However,

floods sometimes occur in the summer half-year.

The circular plot of Figure 7.8 indicates that wider hydrographs at this station are generally

associated with the winter half-year (right half of diagram).

-8

-6

-4

-2

0

2

4

6

8

10

12

29

00

4

35

00

1

14

00

4

60

12

26

02

2

60

11

35

07

1

27

00

2

30

00

5

26

00

9

34

00

9

16

00

1

25

02

5

70

02

70

04

70

33

29

01

1

30

00

7

26

02

1

70

11

29

00

1

30

00

4

34

00

1

27

00

1

26

00

2

26

00

7

70

01

26

00

5

36

01

1

18

00

5

35

00

5

15

00

3

36

01

5

26

01

9

22

07

1

16

00

2

39

00

9

70

10

36

01

9

36

01

0

23

01

2

70

12

26

00

8

70

07

35

00

2

70

09

23

00

2

16

00

4

25

03

0

14

00

6

70

06

14

01

1

15

00

5

14

00

9

36

02

7

15

00

2

60

14

15

00

6

11

00

1

16

00

8

25

01

4

16

00

9

60

26

25

01

6

16

00

5

90

01

60

13

24

01

3

15

00

1

14

01

8

23

00

1

25

00

6

19

00

1

18

00

4

16

00

3

25

02

7

25

02

9

25

00

1

24

00

8

25

00

3

24

00

1

24

08

2

25

00

5

14

00

7

Station No.

TR

EN

D_

SL

OP

EW

75_

QP

reM

in

0

2

4

6

8

10

12

14

16

AL

LU

V

ALLUV

TREND_SLOPEW75_QPreMin

Pre-event minimum flow (m3s

-1)

Wid

th o

f ex

ceed

an

ce (

ho

urs

)


ALLUV

Station #

Slo

pe

of

tren

d-l

ine

(hou

rs/m

3s-1

)

0.16

0.14

0.12

0.10

0.08

0.06

0.04 0.02

0.00


75

Figure 7.7: Plot of flood peak against time of year (Station 07009 Boyne at Navan Weir)

Figure 7.8: Circular plot of W50, W75 and W90 against time of year (floods at Station 07009)

However, a systematic pattern could not be established across the 89 stations studied. In

essence, the widest flood hydrographs tend to be in winter but this is in any case the season

where large floods are most prevalent.

7.4 Effect of arterial drainage on hydrograph widths

According to Table A.2, catchments associated with 19 of the 89 stations have undergone

arterial drainage. The drainage schemes were carried out over different periods for different

catchments. Of the 19 stations, 13 are Grade A1 and six are Grade A2. Only data for the

post-drainage periods have been used in the main HWA reported earlier. An ancillary study

investigated the effect of arterial drainage on the shape of the flood hydrographs of the

affected stations.

Radial scale marks

hydrograph width in hours

Station 07009 Boyne

at Navan Weir

Pea

k f

low

(m

3s-1

)

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep


76

Hydrograph data for the pre-drainage periods of five of the 13 Grade A1 stations were used.

The stations selected and periods considered are listed in Table 7.2, together with gauged

values of the index flood, QMED.

It is seen that the effect of arterial drainage is to increase QMED appreciably. This is to be

expected in the post-drainage period because of the improved conveyance characteristics of

the channel network. The one exception highlighted in Table 7.2 is that QMED is virtually

unchanged for Station 23002.

[Editorial note: Judging from the relevant PCDs, arterial drainage on the Feale is not at all

extensive (ARTDRAIN = 0.001 and ARTDRAIN2 = 0.002). The results for this station

therefore appear irrelevant to exploring the effect of arterial drainage on hydrograph widths,

and further discussion is omitted. As noted in Volume II, Catchment 23002 generates some

of the largest floods ever gauged in Ireland. The Feale has been studied by Martin et al.

(2000) amongst others.]

Table 7.2: Stations studied for the effect of arterial drainage on hydrograph widths

Pre-drainage Post-drainage

Station Period #

years

QMED

(m3s

-1)

# events

used Period

#

years

QMED

(m3s

-1)

# events

used

07007 Boyne

at Aqueduct

01/10/1969

to

30/09/1972

3 23.72 7*

09/04/1979

to

05/04/2004

25 35.41 25

07010

Blackwater

at Liscartan

14/11/1952

to

30/09/1981

29 50.40 29

08/12/1986

to

21/05/2003

17 69.61 17

23002 Feale

at Listowel

18/10/1946

to

30/09/1958

12 373.74 12

01/10/1959

to

06/01/2006

46 371.84 46

26012 Boyle

at Tinacarra

01/10/1957

to

30/09/1981

24 36.95 24

01/01/1991

to

22/01/2002

11 46.72 11

30004 Clare

at Corrofin

04/08/1951

to

30/09/1957

6 43.54 14**

01/10/1964

to

01/10/2005

41 89.83 41

* Event 4 discarded at Station 07007

** Events 2 and 9 discarded at Station 30004

The procedures recommended in Chapters 3 and 4 were applied to derive characteristic

hydrographs for flood hydrographs drawn from the pre-drainage period. Resulting values of

the width descriptors (W75 and W50) and UPO-ERR-Gamma model parameters (n, Tr and C)

are shown in Table 7.3, together with the corresponding results for the post-drainage period

(taken from HWA results and their estimates from PCDs

Table D.1).


77

Table 7.3: Pre- and post-drainage values of hydrograph width descriptors/parameters

Pre-drainage Post-drainage

Station W75 W50 n Tr C W75 W50 n Tr C

07007 67.00 N/A 2.20 48.56 70.61 26.22 52.53 3.74 26.84 69.88

07010 76.77 158.23 1.85 44.96 217.82 30.42 119.06 3.46 25.78 222.32

26012 287.76 N/A 1.72 182.25 211.32 177.27 285.94 3.85 195.50 257.50

30004 100.49 213.04 2.76 110.75 140.97 44.33 68.49 5.30 59.44 46.42

The resulting characteristic hydrographs are shown in Figure 7.9. Note that the pre-drainage

and post-drainage hydrographs are drawn to the same timescale but that this differs from

station to station.

Generally, the width descriptors are smaller in the post-drainage period, indicating narrower

flood hydrographs. This corresponds to a quicker passage of flood flow and is consistent

with the expected impact of arterial drainage, which Bhattarai and O’Connor (2004)

summarise as having the objective of achieving a reduction of the extent and duration of

flooding, by inducing faster runoff in the river channel, with higher peaks and shorter

recessions of the discharge hydrograph.

Values of the Gamma shape parameter n are found to increase in all cases after arterial

drainage. As illustrated in Figure 4.1, higher values of n correspond to a peakier hydrograph.

Values of the Gamma rise-time parameter Tr are expected to be shorter after drainage. This

is very much the finding at Stations 07007, 07010 and 30004. However, the post-drainage

period yields a somewhat larger value of Tr at Station 26012. [Editorial note: Reference to

part (c) of Figure 7.9 indicates that the increased value of Tr at Station 26012 is a product of

parameter interaction. The pre-drainage value n = 1.72 leads to an abrupt start to the

modelled hydrograph whereas the post-drainage value n = 3.85 provides a gentler (and

consequently earlier) start. The value of Tr has changed in compensation.]

The research confirms that the effect of arterial drainage is generally to yield peakier

hydrographs of reduced width. The swifter response ties in with the basic requirements of

drainage schemes.


78

Figure 7.9: Characteristic hydrographs for four sites affected by arterial drainage

Pre-drainage period Post-drainage period

-50 -25 0 56.25 112.5 168.75 225

Time in hours relative to time of peak flow

-50 -25 0 56.25 112.5 168.75 225


(a) Station 07007 Boyne at Aqueduct

-75 -37.5 0 56.25 112.5 168.75 225

Time in hours relative to time of peak flow -75 -37.5 0 56.25 112.5 168.75 225


-175 -87.5 0 125 250 375 500


(b) Station 07010 Blackwater at Liscartan

(c) Station 26012 Boyle at Tinacarra

-175 -87.5 0 125 250 375 500


(d) Station 30004 Clare at Corrofin

-125 -62.5 0 87.5 175

Time in hours relative to time of peak flow -125 -62.5 0 87.5 175



79

8 Constructing the characteristic flood hydrograph

8.1 Topics covered

This chapter provides guidance in constructing the characteristic flood hydrograph. The

material covers a number of topics including:

Recommended methods at gauged sites;

Motivation for and description of the parabolic curves method of constructing the

upper hydrograph (Section 8.7);

Recommendations at ungauged sites;

Recommendation to use the pivotal catchment approach (Section 8.10).

The chapter explains the methods chosen for implementation through the FSU Web Portal.

The parabolic method was devised by NUI Galway as part of their HWA research. Its

description here is simplified.

The characteristic hydrograph is typically needed to construct a design hydrograph to

accompany the T-year (peak) flood estimate derived by Volume II methods. The design

flood hydrograph is obtained by scaling up the ordinates of the characteristic flood

hydrograph by the T-year flood flow, QT. In effect, the methods paint in a hydrograph below

the flood peak. Aspects of the synthesis of the T-year design flood hydrograph are therefore

also discussed.

8.2 Features of the methods

The non-parametric and parametric approaches to constructing the characteristic hydrograph

have strengths and weaknesses. It is helpful to recognise these to understand the methods

chosen for implementation. Some difficulties can be circumvented by use of the IBIDEM

method presented in Chapter 9.

Non-parametric method

Incompleteness of the lower part of the characteristic hydrograph generated using the non-

parametric approach presents a problem in some applications. Many flood analysts use

hydraulic modelling techniques that require a complete hydrograph as input. The FSU

recommendation is to sketch in the lower part of the hydrograph subjectively or to use

IBIDEM (see Chapter 9).

Parametric method

The recommended parametric method is the UPO-ERR-Gamma model of Section 4.4. The

characteristic hydrograph generated in this way is continuous and complete. A minor

unrealistic feature is that the gradient of the receding limb of the hydrograph changes

abruptly at the point where the Exponential Replacement Recession takes over from the

Gamma curve (e.g. Figure 8.1). Local smoothing of the hydrograph around the join is

recommended should the feature be found troublesome.


80

It must be recognised that the UPO-ERR-Gamma model performs poorly for unusual sites at

which the flood hydrograph characteristically falls more steeply than it rises.

967248240-24

100

75

50

25

0


Pe

rce

nta

ge

of

pe

ak

flo

w

Figure 8.1: UPO-ERR-Gamma characteristic hydrograph at St

n 07009 by Table 6.7 models

A more general defect is that the UPO-ERR-Gamma portrays the flood hydrograph as rising

from a pre-event flow of zero (e.g. Figure 8.1). This is unrealistic for Irish rivers. Ways of

incorporating a non-zero pre-event flow are now discussed.

8.3 Allowances in design flood hydrographs for pre-event flow

8.3.1 Substitution approach

The approach recommended by NUI Galway for inclusion of pre-event flow is to:

Step 1 Estimate an appropriate pre-event flow, Q0 (see Section 8.3.3);

Step 2 Substitute Q0 for any ordinate of the design flood hydrograph that falls below Q0.

This substitution approach has not been implemented through the FSU Web Portal, where the

general recommendation is to use IBIDEM (see Chapter 9). However, the substitution

approach may be useful in some applications, especially those focused on a specific site.

Figure 8.2 shows an example where the pre-event flow represents 10% of the peak flow. The

substitution approach tends to lead to design hydrographs that rise abruptly from the pre-

event flow. However, the approach has the merit that the modelled hydrograph widths are

unchanged by the adjustment. Some hydraulic modelling may not cope well with the abrupt

change of gradient at the start of the flood hydrograph. Should the feature be found

troublesome, the user can deal with this by local smoothing of the hydrograph around the

join.


81

8.3.2 Terminology: baseflow or pre-event flow?

The pre-event flow is denoted here by Q0. Many users will refer to this as the baseflow

allowance. However, this terminology can lead to misunderstanding. In the absence of

heavy rainfall, baseflow decays with time rather than remains constant.

967248240-24

100

75

50

25

0


Pe

rce

nta

ge

of

pe

ak

flo

w

Figure 8.2: As Figure 8.1 but with pre-event flow substituting for first part of hydrograph

Additionally, there is scope for the less experienced user to confuse the baseflow allowance

with the baseflow index (BFI). BFI is an index of catchment permeability and storage

developed from daily mean flow data. It is defined as the proportion of the long-term river

flow deriving from subsurface flows or from other delayed responses to rainfall. BFI takes a

value between 0 and 1. Further details of BFI are given in Volume IV.

Obscure terminology is nothing new. When formulating a procedure for constructing design

flood hydrographs, the FSR (NERC, 1975) coined the term average non-separated flow

(ANSF) to represent baseflow. The FSR decision to model ANSF in units of m3s

-1 per km

2

(i.e. as a standardised baseflow) rather than in m3s

-1 added to confusion.

The description in this chapter refers chiefly to the pre-event flow. The FSU advocates use of

IBIDEM (see Chapter 9), which builds a bridge between FSU and FSR methods. Inevitably,

IBIDEM adopts the FSR terminology of referring to the pre-event flow as the baseflow. The

two terms should therefore be treated as synonymous.

8.3.3 Choosing the pre-event flow

The FSU has not researched pre-event flows. An approach possible at gauged sites will be to

fix the pre-event flow at the median of pre-event flows noted for past flood events. However,

the complexity of hydrographs at some stations may defy definition of a pre-event flow.

An alternative is to estimate pre-event flow using elements of the FSR rainfall-runoff method.

IBIDEM (see Chapter 9) specifically accommodates this and is applicable at ungauged as

well as gauged sites.


82

When arbitrary choices are made, it is prudent to check sensitivities. The user is therefore

urged to test the sensitivity of results to the pre-event flow assumed. Flood risk assessments

and the design of flood alleviation works ought not to be greatly impacted by the detail of the

lower part of the hydrograph. If the final results are found to be sensitive to the pre-event

flow assumed, this may reflect weaknesses in the hydraulic modelling.

8.4 Estimation of volume of flow

Having derived the characteristic hydrograph, the widths of exceedance at given percentages

of the peak flow of a design flood are known. The flow volume above a given percentage of

the peak of a design flood can be calculated if required.

8.4.1 Basic method

The design flood hydrograph is produced by scaling the ordinates of the characteristic flood

hydrograph by the design peak flow QT of return period T. The volume VD of the design

flood hydrograph above any given flow Q can be estimated by:

Step 1 Expressing the flow Q as a percentage p of the peak flow;

Step 2 Evaluating the semi-dimensionless volume Vc of the characteristic hydrograph

above percentage p of the peak flow; remarkably, Vc is typically measured in hours;

Step 3 Multiplying the semi-dimensionless volume Vc by QT to obtain the volume VD of

the design flood hydrograph above percentage p of the peak flow; VD is typically

measured in m3s

-1 hours or in m

3.

8.4.2 Non-parametric case

In the non-parametric approach, a numerical method such as Simpson’s rule can be used to

integrate the relevant area (i.e. above the flow of interest and below the flood hydrograph) to

obtain the required volume of flow. Surprisingly, it can be convenient to work out the

volume in horizontal slices, using the widths that define the hydrograph. Where necessary,

the hydrograph width is taken to vary linearly between percentages of the peak flow at which

the width is expressly tabulated. The HWA software provides this option.

8.4.3 Parametric case

In the parametric approach, theoretical expressions can be derived for the volume represented

by the area under the UPO-ERR-Gamma curve and above a given flow. When Equation 4.1

is used as an instantaneous unit hydrograph, the cumulative area under the Gamma defines

the so-called S-curve response (Nash, 1957):

s(t) = I(n, t/K) 8.1

where I(n, x) is the Incomplete Gamma function defined by:

x

0

1nv dvvenΓ

1xn,I 8.2


83

and Γ(n) is the Gamma function. Numerical algorithms for the Gamma and Incomplete

Gamma functions are available in standard packages. The volume under the hydrograph

between particular times is obtained as the difference between the S-curve ordinates at those

times, appropriately rescaled.

The volume of flow sometimes has to be computed in two parts: before and after the point of

inflection at which the exponential replacement recession becomes active in the UPO-ERR-

Gamma model. The relevant formulae are incorporated in the HWA software. [Editorial

note: Unless the HWA software is being applied, it is likely to be more convenient to

evaluate volumes using a numerical method such as Simpson’s rule.]

8.5 Deriving the characteristic hydrograph at a gauged site

The non-parametric approach of Chapter 3 is recommended for producing the characteristic

hydrograph at a gauged site with long records of 15-minute flow data. The steps to be

followed are now summarised. The HWA software supports many of these steps. Further

detail is presented in Chapters 2 and 3 above.

Step 1 A set of single-peaked flood hydrographs is extracted from the entire record at a

gauged site. The number of flood hydrographs abstracted is a matter of judgement

but use of the annual exceedance series – i.e. a Peaks-Over-Threshold (POT) series

yielding an average of one event per year – is recommended.

Step 2 At some stations, many of the flood hydrographs will be found to be multi-peaked,

and a sufficient number of isolated single-peaked floods cannot be identified. In such

cases, some complex floods must be decoupled. In essence, the hydrograph is filtered

to retain only the unimodal part at its core. The procedure is described in Section 2.6.

Step 3 In some cases, either because of error in the flow data or peculiarity in the flow

generation process for the particular event, it may not be possible to identify a usable

filtered hydrograph. Such problematic events are best discarded.

Step 4 Each extracted hydrograph is standardised by dividing the flow ordinates by the flood

peak. The standardised hydrograph thereby attains a peak value of 1.0.

Step 5 For each of a number of reference percentages of the peak flow, the widths of

exceedance on the rising and receding limbs of the hydrograph are abstracted. The

widths are measured in hours. The reference percentages of the peak flow used in the

HWA research are: 98, 95, 90, 85, 80, …, 10 and 5%. All such widths are abstracted

where available. In some cases, the width at (e.g.) 75% of the peak flow is available

on one limb of the hydrograph but not on the other.

Step 6 At each reference percentage of the peak flow, the medians of the widths on the rising

and receding sides are separately calculated.

Step 7 The two median widths (at each reference percentage of the peak flow) are plotted as

horizontal lines on a graph on either side of the peak, with width as the abscissa and

percentage of peak flow as the ordinate. The time origin of the graph is set at the time

of the peak flow. [Editorial note: The occurrence of flat-topped hydrographs

sometimes presents a problem. The HWA software adopts the first of exactly equal

peak ordinates as the peak of the hydrograph. If required, users can subvert this

convention by increasing the value of the most central ordinate (of a number of

exactly equal peak ordinates) by a very small amount.]

Step 8 The median hydrograph is constructed as a segmented line passing through the LH

extremities of the horizontal lines, passing through the peak of 1.0 at time 0.0, and


84

passing through the RH extremities of the horizontal lines. The median hydrograph

thus defined is adopted as the characteristic hydrograph of the station.

8.6 Estimating the characteristic hydrograph at an ungauged site

8.6.1 Using the UPO-ERR-Gamma model

Based on the research reported in Chapters 4 and 6, the UPO-ERR-Gamma model can be

used to estimate the characteristic hydrograph at an ungauged site. The steps required are:

Step 1 Abstract the relevant PCDs.

Step 2 Estimate the curve descriptors n, Tr and C using the equations given in Table 6.7.

Step 3 Construct the characteristic hydrograph using Equations 4.7 to 4.10. The graph can be

drawn in Microsoft Excel or other such application software. It is a unit peak at origin

(UPO) model, i.e. the hydrograph is constructed to have a peak value of 1.0 at time

0.0. Thus the time origin is at the time of the hydrograph peak.

Station 07009 Boyne at Navan Weir is again used as the example. The characteristic

hydrograph shown in Figure 8.1 is that derived from PCDs using the equations of Table 6.7.

[Editorial note: This agrees almost perfectly with that derived earlier by HWA (Figure 4.5).

The exceptionally good performance is not typical of that achieved on the 89 catchments as a

whole. Estimation from PCDs is generally prone to considerable error, as evidenced by the

FSEs shown in Table 6.7.]

Experienced users may wish to consider at Step 2 the alternate models given in Table 6.6

which require a value of the baseflow index. The default at an ungauged site is to adopt

BFIsoil as the estimate of BFI.

8.6.2 Using the parabolic curves method

If only the upper hydrograph is required, it is possible to use the parabolic curves method.

This is introduced in Section 8.7.

8.6.3 Using IBIDEM

IBIDEM (described in Chapter 9) is capable of constructing the design flood hydrograph in

full. The package can be guided to match the characteristic hydrograph derived using the

UPO-ERR-Gamma model or that obtained by the parabolic curves method.

8.7 Parabolic curves method

8.7.1 Overview

The parabolic curves method provides a way of estimating the upper hydrograph based on

values of W75 and W50 derived in the non-parametric approach. The method is one of a

number of techniques developed by NUI Galway and can be applied at ungauged as well as


85

gauged sites. The method is more sophisticated than the equivalent FEH technique (Reed

and Marshall, 1999). The parabolic curves method uses hydrograph widths at both 50% and

75% of the peak flow. Moreover, the upper hydrograph is not constrained to be symmetric

about the peak flow. An example is shown in Figure 8.3.

60483624120-12-24-36-48

1.00

0.75

0.50

0.25

0.00


Flo

w a

s p

rop

ort

ion

of

pe

ak

flo

w

Figure 8.3: Example of parabolic curves method (Station 07009 treated as ungauged)

The method is defined by three descriptors: the widths at 75% and 50% of the peak flow (i.e.

W75 and W50 measured in hours) and the eccentricity parameter s. The eccentricity (or

skewness) parameter is a coefficient defining the proportion of the width that occurs before

the time of the peak flow. For the case illustrated in Figure 8.3, s = 0.40; this is the default

value for applications at ungauged sites.

8.7.2 Details of method

The description here differs from that given by NUI Galway. The upper hydrograph is

synthesised in two parts by parabolas passing through the peak flow at (0, 1). The relevant

equations can be written:

y = 1 + bx + cx2 on rising limb 8.3

and:

y = 1 + Bx + Cx2 on receding limb 8.4

The coefficients b, c, B and C are determined from W75, W50 and s.

At first, it appears that the problem is underspecified, with four unknown coefficients and

only three hydrograph descriptors. However, the eccentricity applies at both 75% and 50% of

the peak flow. The solution is therefore fully determined.

NUI Galway adopted a root-solving approach. However, an explicit solution is possible:

W75

W50

Hydrograph descriptors

W75 = 36.69 hours

W50 = 68.65 hours

s = 0.40 (i.e. 40% of width occurs before peak)


86

2

50755075

2

5075

50755075

2

50

2

75 xWWWW4s

W2Wx

WWW4sW

W2W1y

on

rising

limb

8.5

and

2

50755075

2

5075

50755075

2

50

2

75 xWWWWs14

W2Wx

WWWWs14

W2W1y

on

receding

limb

8.6

8.7.3 Examples

Stations on the Suir provide a convenient example of the range of shapes that the parabolic

method supports. The values of W75, W50 and s used are taken from the HWA results

summarised in Table D.1 of Appendix D. The upper hydrographs yielded by the parabolic

curves method are shown in Figure 8.4. The unusual shape for Station 16009 arises because

W75 is less than half W50.

216192168144120967248240-24-48-72-96

1.00

0.75

0.50

0.25

0.00


Flo

w a

s p

rop

ort

ion

of

pe

ak

flo

w

16004 Suir at Thurles

16002 Suir at Beakstown

16008 Suir at New Bridge

16009 Suir at Caher Park

Figure 8.4: Parabolic hydrographs for four stations on the Suir

These characteristic hydrographs can be compared with those given earlier: for the full non-

parametric method (in Figure 5.16) and for the UPO-ERR-Gamma model (in Figure 5.17).

8.7.4 Application at an ungauged site

Based on the research reported in Chapters 3 and 6, the parabolic curves method can be used

to estimate the upper half of the characteristic hydrograph at an ungauged site. The steps

required are:

Step 1 Abstract the relevant PCDs.


87

Step 2 Estimate the hydrograph width descriptors W75 and W50 using the equations given in

Table 6.7.

Step 3 Construct the upper half of the characteristic hydrograph using Equations 8.5 and 8.6.

The graph can be drawn in Microsoft Excel or other such application software. The

hydrograph is constructed to have a peak value of 1.0 at time 0.0. Thus the time origin

is at the time of the hydrograph peak.

Figure 8.3 (shown earlier) reports the outcome for Station 07009 Boyne at Navan Weir,

treating it as an ungauged site. Note that – at an ungauged site – the eccentricity (i.e.

skewness parameter) takes the fixed value s = 0.40.

Experienced users may wish to consider at Step 2 the alternate models given in Table 6.6

which require a value of the baseflow index. The default at an ungauged site is to adopt

BFIsoil as the estimate of BFI.

8.8 Constructing the design flood hydrograph

In principle, the design flood hydrograph for a given T-year peak flow (derived using

Volume II methods) is obtained by scaling up the ordinates of the characteristic flood

hydrograph by the appropriate factor. If only the upper part of the design flood hydrograph is

required, the procedure is complete.

Where the complete design flood hydrograph is required, the user has a number of options:

To sketch in the lower part of the design hydrograph subjectively;

To use IBIDEM (see Chapter 9);

To adopt the parametric method of constructing the characteristic hydrograph, i.e.

using the UPO-ERR-Gamma model of Section 4.4 (but see notes in Section 8.2).

8.9 Software

Implementation gives the user access to the extensive features of the HWA and IBIDEM

packages. These packages are supplied for use offline to the FSU Web Portal. Some

technical details of the HWA software are given in Appendix E. IBIDEM is presented in

Chapter 9 with further details in Appendix F.

Experienced users will be able to consider and develop additional options for constructing the

design flood hydrograph in particular applications.

8.10 Selection and use of the pivotal catchment

8.10.1 Overview

The concept of a pivotal catchment is introduced in Volume II. The pivotal catchment is the

gauged catchment judged to be most relevant to the specific flood estimation problem at an

ungauged site. The concept is fundamental to application of FSU methods at ungauged sites.


88

The FSU Web Portal is designed to steer all users to select and use a pivotal catchment. This

is fundamental to applying Volume II methods for estimating the index flood QMED at an

ungauged site.

Less experienced users may wish to become familiar with the pivotal catchment concept by

exploring its use in QMED estimation in Volume II. In principle, the pivotal catchment

approach is followed whenever the characteristic hydrograph is needed at an ungauged site.

Selection and use of a pivotal catchment promotes the effective use of gauged flood data,

even at ungauged sites. The summary description is as follows. First, the performance of the

ungauged method of Section 8.6 method is assessed by checking how it performs for the

pivotal catchment. Second, the correction factor required to make the ungauged method

perform well at the pivotal site is transferred (fully or partially) to adjust the estimate at the

ungauged site. The overall procedure is referred to as a data transfer.

8.10.2 Selection of the pivotal catchment

The user assesses the most appropriate data transfer by making a reasoned selection of a

pivotal catchment. This is the gauged catchment judged to be most relevant to the specific

flood estimation problem.

The pivotal catchment is the user’s assessment of the most relevant catchment on which to

base a data transfer. Where flood data are available from a gauge sited upstream or

downstream of the subject site, this will often be selected as the pivotal catchment. In other

cases, the selection is likely to be more precarious and will hinge on the user’s judgement of

catchment similarity.

An algorithmic judgment of catchment similarity is likely to give weight to differences in a

few leading factors – e.g. catchment size (represented by AREA), catchment wetness

(indexed by SAAR) and catchment permeability (indexed by BFI or BFIsoil) – and to neglect

all other factors. This is not a safe approach.

A particular feature present in one catchment and absent from another may lead to strong

differences in their flood behaviour. Arterial drainage (indexed by ARTDRAIN or

ARTDRAIN2) is perhaps the most notable such feature. Volume II reports evidence that

BFIsoil and ARTDRAIN2 are important in characterising the post-drainage flood response of

a catchment, whilst the descriptors DRAIND and S1085 are more important in characterising

the response of undrained catchments. These findings may help the experienced user to

judge which PCDs to examine closely when judging hydrological similarity for the purpose

of selecting the pivotal catchment.

Other notable features to consider when assessing catchment similarity are the extent of

urbanisation (indexed by URBEXT) and the presence of large lakes (indexed by FARL).

Research reported in Volume II endorses the recommendation to favour geographical

closeness – as well as similarity in key PCDs such as FARL – when selecting a pivotal

catchment for use in a particular flood estimation problem.


89

8.10.3 Recommended procedure for data transfer

Selection of the pivotal catchment is a demanding task that calls for reasoning and

judgement. Some judgements will be unsettling because of the impact that the data transfer

has on the final results.

In some cases – not least on small catchments – the pivotal catchment selected may not be

wholly convincing. This is not a reason to abandon making a data transfer. However, it may

justify making only a partial transfer. An approach to making a partial transfer is included in

Step 4 of the procedure now illustrated by worked example.

8.10.4 Example

The methodology for estimating the characteristic hydrograph at an ungauged site is

illustrated for the Suck at Rookwood. This corresponds to Station 26002 but is treated here

as an ungauged site. The following provides a broad guide to deriving an estimate of the

characteristic hydrograph at this location.

The worked example is for use of the parabolic curves method. The same principles apply to

use of the UPO-ERR-Gamma model. However, with three parameters to consider, data

transfers are likely to be rather complicated to execute for that model.

Step 1 Confirm location: It is important to confirm the location of the subject site and to

check the centroid of its catchment. The site location determines the PCDs extracted

in Step 2. The centroid is relevant to judging the nearness of the subject catchment to

available gauged catchments, when the user is undertaking the important task of

selecting the pivotal catchment (see Section 8.10.5). t is the user’s responsibility to

check that the FSU digital data provide a fair representation of the real conditions.

Step 2 Derive catchment descriptor information: Table 8.1 lists the PCDs needed in the

version of the parabolic curves method illustrated here. The PCDs derive from the

digital datasets made available with the FSU.

Table 8.1: Selected PCDs for Suck at Rookwood

PCD value unit PCD value unit

AREA 641.45 km2 FOREST 0.080 –

DRAIND 0.799 km/km2 FARL 0.979 –

S1085 0.500 m/km FLATWET 0.690 –

ALLUV 0.025 mm ARTDRAIN 0.000 –

Step 3 Apply hydrograph width models: From Table 6.7 we have for the parabolic curves

method:

W75 = 31.28 DRAIND-0.88

FARL-5.85

(1+FOREST)-2.86

(1+ARTDRAIN)-2.92

FLATWET3.12

(S1085/1000)-0.27

W75 = 31.28 (0.799)-0.88

(0.979)-5.85

(1.081)-2.86

(1.0002)-2.92

(0.690)3.12

(0.500/1000)-0.27

= 84.42 h


90

W50 = 34.02 DRAIND-0.95

FARL-6.59

(1+FOREST)-2.83

(1+ARTDRAIN)-2.60

FLATWET2.44

(S1085/1000)-0.29

= 34.02 (0.799)-0.95

(0.979)-6.59

(1.081)-2.83

(1.0002)-2.60

(0.690)2.44

(0.500/1000)-0.29

= 142.30 h

[Editorial note: The estimates of W75 and W50 differ very slightly from those shown

in the centre-right columns of Table D.1 of Appendix D. This is because, in the

recommended models, the exponents have been rounded to 2 decimal places.]

Step 4 Transfer data from gauged locations to improve model prediction at subject site:

The general procedure is to infer an adjustment factor, AdjFac, by reference to the

performance of the PCD-based model at a nearby gauged site. Thus, the adjustment

factor for W75 would be:

PCD75,

gauged75,

WW

WAdjFac

75 8.7

The adjustment is then partially or fully transferred to the subject site:

PCD75,

h

Wadj75, WAdjFacW75

8.8

The typical procedure is to apply a full transfer by setting the exponent h to 1.0. If

W75 is found to be 20% greater than the PCD-based estimate, it is assumed that the

model will be similarly in error at the subject site. Thus, the estimate of W75 at the

subject site is adjusted by multiplying by 1.20.

The exponent h can be thought of as the hardness of the data transfer. h = 1 denotes a

full (or “hard”) transfer. A partial (or “softer”) transfer might set h = 0.5. In this case,

if W75 is found (at the donor site) to be 20% greater than given by the PCD model, the

estimate of W75 at the subject site is adjusted by multiplying by a factor of 1.200.5

or

1.095.

Much skill attaches to deciding which of several possible donor catchments is pivotal to

improving estimation at the subject site. With gauged sites upstream (Station 26006) and

downstream (Station 26005) of the subject site, the choice might not be clear-cut for the Suck

at Rookwood. However, it transpires that HWA has not been undertaken for Station 26006

Suck at Willsbrook. Thus, the data transfer illustrated here is from Station 26005 Suck at

Derrycahill, which drains an area 69% greater than that at Rookwood.

Table 8.2 summarises the data transfer from the Suck at Derrycahill (Station 26005) to the

Suck at Rookwood. It is seen that hydrograph widths are appreciably underestimated at the

donor site. Use of a hard data transfer assumes that the same relative error will occur when

applying the PCD models at Rookwood and adjusts the hydrograph widths accordingly.

When HWA results for the Suck at Rookwood itself are examined (lighter-shaded rows in

Table 8.2), it is found that the PCD method does indeed underestimate hydrograph widths

there. However, it transpires that, the data transfer from Derrycahill is too strong. In this

instance, a soft transfer with h = 0.5 would work better (see RH column of table). However,

the user will not know this for a subject site that is truly ungauged! The upper hydrographs


91

transferred (see Figure 8.5) are somewhat “pointy” in comparison to the notably flat-topped

hydrograph (black curve) that the parabolic method yields directly at Rookwood.

Table 8.2: Data transfers to Suck at Rookwood using parabolic curves method

Method

Data

transfer

from

HWA PCD Implied

factorial

adjustment

Hydrograph width

HWA

Hard

transfer

with h = 1

Soft

transfer

with h = 0.5

hours hours

Width at 75% of hydrograph peak (W75)

No data

transfer 84.42

Downstream

donor

Station

26005 136.04 86.15 1.58 133.4 106.1

Analysis of

gauged data

Station

26002 118.7

Width at 50% of hydrograph peak (W50)

No data

transfer 142.30

Downstream

donor

Station

26005 209.83 147.63 1.42 202.1 169.6

Analysis of

gauged data

Station

26002 163.98

19214496480-48-96-144

1.00

0.75

0.50

0.25

0.00


Pro

po

rtio

n o

f p

eak

flo

w

HWA at 26002

Soft transfer (26005 to 26002)

Hard transfer (26005 to 26002)

Parabolic curves method

Figure 8.5: Upper hydrographs transferred from Derrycahill to Rookwood


92

[Editorial note: Station 26002 Suck at Rookwood provides an example where the parabolas

fitted to the rising and receding limbs have turning points just before and just after the

nominal peak value of 1.0. This feature is detectable in Figure 8.5 by close scrutiny of the

crest segment of the hydrograph shown in black. Where the feature arises, it is reasonable to

reduce any ordinate that exceeds 1.0 to the peak value of 1.0, thereby producing a flat-topped

hydrograph.]

For completeness, HWA results for the two catchments are shown in Figure 8.6. The

characteristic hydrograph at Derrycahill (Station 26005) is relatively smoothly represented by

the derived median hydrograph (of Section 3.5), which in turn is especially well modelled by

the UPO-ERR-Gamma (of Section 4.4). It is confirmed that hydrographs at Rookwood are

rather narrower than at Derrycahill, although the difference is almost entirely in the receding

limb.

Figure 8.6: Derived median and UPO-ERR-Gamma hydrographs for Stns

26002 and 26005

8.10.5 Further discussion of choice of method and of pivotal catchment

While the pivotal catchment principle applies to transferring a characteristic hydrograph in

much the same as it does to transferring a gauged value of QMED in Volume II, a number of

important differences arise in practice:

In the index flood case, there is the one flood measure QMED to be evaluated and

transferred. In the characteristic hydrograph case there are several possibilities.

There is the choice between use of the UPO-ERR-Gamma model (with three

parameters open to adjustment) and use of the parabolic curves method (with two

width descriptors open to adjustment). The use of IBIDEM (see Chapter 9) brings

additional options.

In the index flood case there is essentially the one PCD-based method of estimating

QMED, albeit with important adjustments for urbanised catchments. In the

characteristic hydrograph case, there is a choice between models that use BFI and

models that do not.

The suitability of a donor reflects many factors. Donors on the same river system are likely

to be most suitable. However, the typical width and shape of hydrographs will be influenced

by any notable feature that intervenes between the subject site and the donor site. The most

obvious features are lakes or reservoirs, which are likely to modify the width and shape of

hydrographs appreciably. This is confirmed by the appearance of FARL in all ten PCD

models presented in Table 6.6 and Table 6.7.


93

Different users will make different judgements. Some will argue that the presence of FARL

in the models allows the transfer to proceed. Others may argue that site-specific features

mean that the lake has a stronger effect than represented in the necessarily generalised model.

Confidence in the relevance of the data transfer is weakened if a special feature intervenes

that is not represented in the model, e.g. if a significant tributary of wholly different character

joins the river between the donor and subject sites. If it is the most suitable donor available,

the pragmatist will allow the data transfer in part: e.g. setting h to 0.5 (or less).

Finally, it should be noted that it may be appropriate or necessary to choose one gauged site

as the pivotal catchment in QMED estimation and another in estimation of the characteristic

hydrograph.

8.10.6 Urbanised catchments

Large-scale urbanisation affects flood magnitudes and catchment response times very

appreciably. Flood magnitudes are generally increased and flood response times (and

hydrograph widths) are compressed, often markedly. Great care is therefore required in

making data transfers to a subject catchment that is heavily urbanised. In similar vein, a

notably urbanised catchment should not normally be chosen as the pivotal station if the

subject catchment itself is largely rural.

Experienced users may find it helpful to apply IBIDEM. This allows the merit of particular

data transfers to be interpreted in terms of the parameters of the FSR rainfall-runoff method

and the urban adjustments to that method presented in FSSR16 (IH, 1985).


94

9 IBIDEM

9.1 The idea of IBIDEM

IBIDEM stands for Interactive Bridge Invoking the Design Event Method. The idea is to

provide a bridge between the FSU method of estimating a design flood hydrograph and the

FSR design event method that it replaces. Two parameters of the FSR rainfall-runoff model

(time to peak and standard percentage runoff) are chosen by optimisation so that the design

hydrograph synthesised by the FSR method matches that produced by the FSU procedures.

This chapter explains how IBIDEM is structured and illustrates its use on five example

catchments. The tests indicate that IBIDEM is helpful in assessing design flood hydrographs

produced using the FSU procedures and can help the experienced user to judge whether a

design hydrograph is consistent with the properties expected of the particular catchment.

IBIDEM is supplied as a standalone software package downloadable through the FSU Web

Portal. Some technical details are given in Section 9.5 and Appendix F. The package was

developed by JBA Consulting.

9.1.1 Reminder of hydrograph estimation by FSU methods

The T-year peak flow is typically estimated as the product of an index flood and a growth

curve. The methods are described in Volume II. The required design hydrograph is

constructed around the peak flow by applying a hydrograph shape taken from the HWA

presented in earlier chapters. There are two main methods:

At gauged sites, the characteristic hydrograph is built up using widths extracted from

observed hydrographs at given percentages of the peak flow. This is the non-

parametric approach of Chapter 3, and can be executed using the HWA software.

At ungauged sites, the parametric approach of Chapter 4 can be applied. Parameters

of the UPO-ERR-Gamma model are estimated from PCDs using the equations

presented in Chapter 6. Application of the parabolic curves method of Section 8.7 is

also supported.

IBIDEM also provides the user with a number of additional options.

9.1.2 Hydrograph estimation by the FSR design event method

Some users may not be very familiar with the FSR design event method. A brief summary is

attempted here. The relevant volume of the Flood Estimation Handbook provides further

details (Houghton-Carr, 1999).

The T-year design hydrograph is constructed as the output to the “unit hydrograph/losses”

rainfall-runoff model. The FSR design event method combines four inputs: the temporal

profile, duration, and rarity of the rainfall event and the pre-event catchment wetness. The

first three define the rainfall input (to the rainfall-runoff model), whilst the fourth defines the

initial condition (of the rainfall-runoff model). These inputs take specific values according to

particular rules (see Figure 9.1). The rules reflect some of the general properties of the

catchment and its climate.


95

Figure 9.1: Design inputs to FSR rainfall-runoff method of flood frequency estimation

It is necessary to adopt suitable values for the parameters of the rainfall-runoff model itself.

For the FSR unit hydrograph/losses model, the parameters are:

The standard percentage runoff, SPR;

The unit hydrograph time-to-peak, Tp;

The standardised baseflow, known as the “average non-separated flow”, ANSF.

On all but highly permeable catchments, the last parameter tends to be relatively unimportant.

Two other factors play a role in the model: the catchment area (AREA), and the areal

reduction factor (ARF). ARF is applied to estimate the design catchment rainfall from the

design rainfall depth at a typical point within the catchment. In application here, the rainfall

depth-duration-frequency model is taken from Volume I rather than from FSR methods.

9.1.3 Basic idea of bridge between the FSR and FSU methods

The aim of IBIDEM is to link the FSU method of T-year hydrograph estimation to the FSR

rainfall-runoff method it replaces. The Tp and SPR parameters of the rainfall-runoff model

are chosen so that the design hydrograph synthesised by the FSR method matches that

produced by the FSU procedures. The approach offers several gains:

Whereas the HWA methods of Chapter 3 construct only the upper parts of the design

hydrograph, IBIDEM synthesises the entire hydrograph. This allows the user to look

at runoff volumes (e.g. for assessing flood storage) and to “route” flood hydrographs,

as they do when using the FSR rainfall-runoff method.

A link with rainfall is made. By noting the percentage runoff (PR) and the rainfall

duration (D) implied by IBIDEM, the user is able to check whether the FSU design

hydrograph has properties consistent with that expected of the catchment.

Those with particular experience of the FSR design event method are able to interpret

the Tp and SPR parameters of the rainfall-runoff model to which the FSU design

hydrograph is said to be equivalent. Based on experience or further guidance, users

can vary these values to test sensitivities and to investigate the possible effects of

catchment change on the design flood hydrograph.

Rainfall profile Rainfall duration Pre-event wetnessRainfall rarity

Profile = constant D = D (SAAR, Tp) Train = Train ( Tflood) CWI = CWI (SAAR)

Rainfall profile Rainfall duration Pre-event wetnessRainfall rarity

Profile = constant D = D (SAAR, Tp) Train = Train ( Tflood) CWI = CWI (SAAR)


96

9.2 How IBIDEM fits hydrographs

IBIDEM fits an FSR rainfall-runoff hydrograph to match the shape and peak flow of an

imported FSU design hydrograph. The fitting is achieved by adjusting the time to peak (Tp)

and standard percentage runoff (SPR) parameters of the FSR rainfall-runoff method.

IBIDEM implements all parts of the FSSR16 version of the rainfall-runoff method (IH,

1985), other than estimation of Tp and SPR from catchment characteristics. Values of Tp

and SPR are instead derived by fitting the implied FSR hydrograph to the imported FSU

hydrograph.

In running the rainfall-runoff method, IBIDEM undertakes the following steps:

Step 1 Imports the physical catchment descriptors AREA, SAAR and URBEXT; URBEXT

is needed for the urban adjustment to the percentage runoff.

Step 2 Finds values of SPR and Tp by optimisation. In some options, adjustments are made

by the user.

Step 3 Selects an appropriate data interval T based on Tp, adopting a convenient value

such as 0.25 hours or 1 hour.

Step 4 Calculates the design rainfall duration D from Tp and SAAR, and evaluates the areal

reduction factor (ARF) from AREA and D.

Step 5 Constructs a triangular unit hydrograph with time-to-peak Tp.

Step 6 Evaluates the design rainfall depth from D and a user-supplied flood return period (or

set of return periods). The user-supplied flood return period (Tflood) is linked to a

rainfall return period (Train) according to the FSR design package used. [Editorial

note: The design package is a prescribed a set of rules to be followed when using the

FSR rainfall-runoff method. One package corresponds to winter conditions and is

typically applied on catchments that are largely rural.]

Step 7 IBIDEM requires the rainfall depth for a typical (i.e. average) point in the catchment.

The depth is multiplied by ARF (Step 4) to obtain the catchment-average rainfall (P)

of required return period. [Editorial note: The user obtains rainfall depths for a set

of durations and return periods through the FSU Web Portal. These are supplied to

IBIDEM in the form of a table of rainfall depths, with durations (0.25 to 600 hours)

in rows and return periods (2 to 200 years) in columns. IBIDEM calculates the

required rainfall depth by interpolation, using linear interpolation between durations

and logarithmic interpolation between return periods.]

Step 8 Distributes the rainfall depth according to a standard temporal profile taken from the

FSR. The most commonly used profiles are the so-called 75% winter and 50%

summer profiles. To meet the project specification, the default setting in IBIDEM is

to use the 75% winter rainfall profile: even on an urbanised catchment. The

alternative summer profile can be chosen by the user.

Step 9 Calculates the percentage runoff PR from SPR, rainfall depth P and the catchment

wetness index CWI, applying an urban adjustment if necessary. The urban

adjustment is amended to use URBEXT from the FSU rather than URBAN from the

FSR. The relevant formula is:

PR = PRrural (1.0 – 0.47 URBEXT) + 70 (0.47 URBEXT) 9.1

(The factor 0.47 arises as the product of 0.30 and 1.567. The factor 1.567 back-

converts URBEXT to be compatible with the URBAN index used in the FSR.)


97

Step 10 Applies the PR to the total rainfall profile to obtain the net rainfall profile, i.e. the

portion of rainfall that generates rapid response runoff.

Step 11 Convolves the unit hydrograph with the net rainfall profile to give the rapid response

hydrograph.

Step 12 Adds baseflow to give the total runoff hydrograph. Baseflow is calculated from

AREA, SAAR and CWI using a standard equation from FSSR16.

9.3 General approach to the optimisation

9.3.1 “First Tp and then SPR”

The two parameters to be fitted (Tp and SPR) affect the hydrograph in distinct ways. SPR

affects the magnitude of the flows but does not have any effect on timings. In cases where

baseflow forms only a minor element, the flood magnitude is roughly proportional to SPR

(see the example in Figure 9.2).

The Tp parameter affects both the timing and the magnitude of the flows. A shorter Tp alters

the T-year flood magnitude in three ways:

It forces an increase in the peak of the unit hydrograph (to maintain the same volume

of flow in a shorter time);

It shortens the design storm duration, hence increasing the rainfall intensity for a

given return period;

The resulting change in the design rainfall depth affects the percentage runoff via the

DPRRAIN term (see Section F2 of Appendix F).

Figure 9.2 provides an example of the kind of effect that Tp and SPR have on the peak of the

design flood hydrograph in the FSR rainfall-runoff method.

Figure 9.2: Illustration that FSR T-year peak flow varies with Tp as well as with SPR

Because SPR has no effect on hydrograph timings, it is convenient to optimise Tp first. SPR

is adjusted in a later step to give a peak flow that exactly matches the peak of the imported

FSU design hydrograph. For rather intricate reasons – with advantages outweighing

disadvantages – this strategy is in fact preferable to that of optimising SPR and Tp jointly.

0

5

10

15

20

25

0 2 4 6 8 10

Tp (hours)

Peak f

low

(m

3/s

)

SPR = 20%

SPR = 40%

25

20

15

10

5

0

0 2 4 6 8 10 Tp (hours)

T-y

ear

pea

k f

low

(m

3 s

-1)

SPR = 20%

SPR = 40%


98

9.3.2 Use of horizontal fitting

IBIDEM fits the FSR rainfall-runoff hydrograph – standardised so that its ordinates are

expressed as percentages of the peak flow – to the characteristic hydrograph derived by FSU

methods. The process uses horizontal fitting, in which differences in hydrograph widths are

minimised between the FSU and FSR representations. This is in contrast to the conventional

vertical fitting of hydrographs in terms of differences in flows.

The set-up is illustrated in Figure 9.3. The FSU hydrograph is built up from median

hydrograph widths at various percentages of the peak flow, using the non-parametric

approach of Chapter 3. [Editorial note: IBIDEM refers to this as the empirical approach.]

Fitting is carried out for the portion of the hydrograph above a threshold. This accommodates

the feature that FSU hydrograph does not cover the full range of flows down to zero.

Figure 9.3: Horizontal fitting by comparing hydrograph widths

9.3.3 Deriving Tp by optimising the fit to the FSU flood hydrograph

Tp is obtained by optimising the shape of the FSR rainfall-runoff hydrograph so that it best

matches the FSU characteristic hydrograph. These semi-dimensionless hydrographs are

expressed as a percentage of the peak flow.

A complication is that baseflow (in the FSR rainfall-runoff method) is defined as a fixed

amount in m3s

-1 rather than as a proportion of the peak flow. The difficulty is overcome by

fitting the widths of the rapid response parts of the hydrographs, i.e. after subtracting the

(fixed) baseflow BF from the FSU hydrograph (Figure 9.4).

Figure 9.4: Relationship between peak flow Qpeak and peak rapid response qpeak

FSU hydrograph Sample FSR hydrograph

Flo

w (

m3

s-1

)

Time (hours)

qpeak

BF

Qpeak

Threshold for fitting Threshold for fitting


99

The detailed procedure is:

Step 1 Calculate the baseflow BF (in m3s

-1) from the FSSR16 method [Editorial note:

FSSR16 provides an equation for ANSF, defined as the baseflow per unit area i.e. in

m3s

-1 per km

2. Thus, BF = ANSFAREA.]

Step 2 Subtract BF from the FSU hydrograph. The peak flow Qpeak is thereby reduced to the

response peak qpeak.

Step 3 Express the threshold for fitting as a % of qpeak:

%qthreshold = %Qthreshold - 100(BF/Qpeak)

This meets the IBIDEM requirement that the user specifies the fitting threshold as a

percentage of the total peak flow, %Qthreshold. The user is prompted to raise the

threshold should the percentage first entered yield a threshold flow that is less than or

equal to BF.

Step 4 Calculate a set of m widths WFSU of the FSU response hydrograph for percentage

flows between %qthreshold and 100%, at an interval of 1% (see LH side of Figure 9.3).

Step 5 Run the FSR rainfall-runoff method with an arbitrary (fixed) SPR and an initial guess

for Tp.

Step 6 Calculate a set of widths WFSR of the FSR response hydrograph at the same

percentages as in Step 4 (see RH side of Figure 9.3).

Step 7 Evaluate the objective function: Σ[WFSU(i) - WFSR(i)]2 for i = 1 to m.

Step 8 Vary Tp and repeat Steps 5 to 7 until the objective function is minimised (see

Section F1 of Appendix F for details of the optimisation method).

The non-parametric method of Chapter 3 may sometimes produce hydrographs with more

than one peak (Figure 9.5). Within IBIDEM, these cases are treated by excluding the time

when flow is below the relevant percentage of the peak when evaluating the width of the

hydrograph. This pragmatic approach ensures that IBIDEM represents the total duration of

the hydrograph but without being unduly affected by the separation of the peaks. The output

from IBIDEM is always a single-peaked hydrograph.

Figure 9.5: Double-peaked hydrograph

IBIDEM discounts this portion of

the total width of the hydrograph


100

9.3.4 Deriving SPR by matching the required peak flow

After Tp has been optimised, the FSR hydrograph is scaled to fit the relevant peak flow,

which will typically have been derived by Volume II methods. SPR is calculated by working

out the factor by which the hydrograph has to be multiplied to match the FSU peak flow.

The details of how IBIDEM does this are given in Section F2 of Appendix F.

9.4 Additional IBIDEM options

The IBIDEM software provides a number of additional options. The principal ones are now

summarised. Graphical displays are illustrated later, chiefly in Section 9.5.2.

9.4.1 Flood frequency

The Flood frequency option allows users to optimise a set of hydrographs for different return

periods. To allow maximum flexibility of options, users are required to import a separate

FSU flood hydrograph for each return period. IBIDEM allows up to seven return periods to

be analysed together. A separate pair of Tp and SPR values is fitted at each return period,

using the method described in Sections 9.2-9.3.

9.4.2 Sensitivity to storm duration

The terms design rainfall and design storm are used interchangeably. The Sensitivity to storm

duration option – and further options – are made available once IBIDEM has performed the

hydrograph fit for a single return period. The fitted values of Tp and SPR are retained (i.e. no

further optimisation is carried out) and the FSR rainfall-runoff method is re-run for five trial

storm durations. A feature of the FSR rainfall-runoff method is that the volume of the flood

hydrograph increases as the storm duration increases.

Default durations for the trials are 0.5D, 0.5D, D, 2D and 2D where D is the duration

resulting from the Tp value found in the optimisation. The user can change the trial durations

if desired.

In addition to testing sensitivities, this option may be helpful in river modelling applications

(see Volume V) where a longer-than-normal storm is being applied to a tributary catchment

in order to generate a T-year flood further down the river system.

9.4.3 Sensitivity to model parameters

The Sensitivity to model parameters option allows the user to re-run the rainfall-runoff

method (after the initial optimisation stage), with altered values of the parameters Tp and/or

SPR. If Tp is altered, the storm duration is automatically updated. If SPR is altered, PR is

updated. Other settings remain unchanged.

The option allows the user to explore the possible impact of land-use change, by adjusting Tp

and/or SPR to represent conditions before and after the change. An implicit assumption is

that the user trusts application of the FSR rainfall-runoff method to represent the particular

land-use change (such as agricultural drainage or tree planting) adequately.


101

9.4.4 Sensitivity to changes in urbanisation

The Sensitivity to changes in urbanisation option allows the user to re-run the rainfall-runoff

method for an altered value of URBEXT. IBIDEM calculates revised values for Tp and PR

to reflect the change in URBEXT. Because of the joint use of newer and older technologies,

the procedure is rather intricate.

Back-converting URBEXT

The first step is to back-convert the revised URBEXT to the equivalent FSR descriptor of

urban extent (URBAN). This is done using:

URBAN = 1.567 URBEXT 9.2

In the FSR rainfall-runoff method method, URBAN affects Tp, PR and the choice of design

event package (winter or summer).

Choice of design package

Were IBIDEM to choose the design package automatically based on the degree of

urbanisation, it would be possible for a small increase in URBEXT to lead to an abrupt

change from use of a winter design event to use of a summer design event, with potentially a

large change in the design flood hydrograph. To avoid this possibility – and to allow greater

flexibility – the choice of design event package is set manually by the user.

Effect on PR

IBIDEM calculates a new PR from SPR using the urban adjustment (Equation 9.1) from Step

9 of the Section 9.2 procedure.

Effect on Tp

Tp for the base condition will have been found during the initial run. IBIDEM updates this

for the revised value of URBAN by invoking part of the FSSR16 model for estimating Tp(0).

The factor representing the urban effect on response times in the FSSR16 model is the term

(1+URBAN)-2.2

.

The Tp value obtained in the initial run of IBIDEM is therefore updated for the altered level

of urbanisation using:

2.2

2.2

revisedrevised

URBAN)(1

)URBAN(1 Tp(0) =0Tp

9.3

Tp is converted to and from Tp(0) as required, using: Tp = Tp(0) + ΔT/2 where ΔT is the data

interval (see Section 9.2). Equation 9.2 is used as required to convert current and projected

values of URBEXT to the corresponding values of URBAN.

Summary

Although intricate, this option allows users to investigate the impacts of urban development

on design flood hydrographs and peak flows.


102

9.5 Further details of the software

9.5.1 Inputs

The IBIDEM software requires the following inputs in all cases:

Catchment descriptors AREA, SAAR and URBEXT: typed in on the first screen

(the FSU descriptor of urbanisation is the fractional urban extent URBEXT, and takes

a value between 0 and 1);

Design flood hydrograph derived from FSU procedures: supplied as a CSV file

(this gives pairs of time and flow values);

Rainfall frequency information from FSU procedures: supplied as a CSV file

giving a table of design rainfall depths at an average point in the catchment (the

tabulated depths are for a standard set of durations and return periods);

Return period associated with the FSU hydrograph (default is 2 years);

Threshold flow to be used in fitting: expressed as a percentage of the peak flow

(default is 50%).

These data are validated during the input process and the user notified of any exceptions (see

Section F3 of Appendix F. In particular, the user is warned if:

The FSR baseflow exceeds part of the imported FSU hydrograph. In this case,

the user needs to import a hydrograph with a higher minimum flow (e.g. by removing

the first or last few values) or to adjust the baseflow.

The threshold falls below the lowest flow value in the rising/receding limb of the

imported FSU hydrograph. In this case, the user needs to raise the threshold flow

used for the fitting or to import a more complete hydrograph.

Additional inputs are required for some of the optional functionality:

For the flood frequency option: Hydrographs for multiple return periods;

For the option to vary baseflow: Value for baseflow;

For the sensitivity to model parameters option: New value for Tp or SPR or both;

For the sensitivity to changes in urbanisation option: New value for URBEXT.

9.5.2 Graphical displays

IBIDEM displays the hydrograph fit, showing the imported FSU hydrograph, the fitted FSR

hydrograph and the threshold flow used for fitting. Figure 9.6 provides an example. The two

hydrographs are aligned so that they peak at the same time.

When the flood frequency option is selected, the user can choose the return period for which

the fit is displayed. Alternatively, it is possible to display a graph showing how a particular

variable changes with return period. The user can select any one of peak flow, percentage

runoff, SPR, Tp, rainfall depth or runoff volume. The example in Figure 9.7 shows how the


103

runoff volume – expressed as a depth in mm across the catchment – changes with return

period.

Figure 9.6: Display of fitted and imported hydrographs

Figure 9.7: Display of how a variable changes with return period

When the sensitivity to storm duration option is selected, the user can plot either a graph

showing multiple hydrographs – i.e. one for each duration plus the imported FSU hydrograph

(e.g. Figure 9.8) – or a graph showing how a particular variable changes with return period.

The example in Figure 9.9 shows how the peak flow varies with the design storm duration.

This provides a way of identifying the critical duration that the bridge to the FSR rainfall-

runoff method implies for the catchment. The figure also illustrates the manner in which

FSU derived

median hydrograph

FSR hydrograph

fitted by IBIDEM


104

options are selected on-screen in IBIDEM. Q denotes the peak flow, PR the percentage

runoff, P the rainfall depth and V the hydrograph volume.

Figure 9.8: Display of hydrographs for multiple storm durations

Figure 9.9: Display of how a variable changes with storm duration

When the sensitivity to model parameters or the urbanisation option is selected, IBIDEM

plots the imported FSU hydrograph, the original fitted FSR hydrograph and the altered FSR

hydrograph resulting from the changed parameter(s). Figure 9.10 illustrates this for a case

where URBEXT increases from 0.00 to 0.20.


105

Figure 9.10: Display of sensitivity to an increase in URBEXT

9.5.3 Display options

Various options are provided for graph layout and units (the option name is in italics):

Hydrographs can be plotted with the vertical axis showing either % of peak flow

(default) or m3s

-1.

Hydrographs can be plotted with the time origin either at the peak (default) or at the

start of the FSR hydrograph.

Flow units can be either m3s

-1 (default) or mm/hr.

Runoff volume units can be either mm equivalent of catchment runoff (default) or m

3

or cumec-hours. A cumec-hour is the volume represented by a flow of 1 m3s

-1

sustained for one hour, i.e. 3600 m3.

Plots of variables against return period can have a horizontal axis showing the

Gumbel reduced variate, the Logistic reduced variate or the natural logarithm of

return period. In each case, a subsidiary axis shows the return period in years. These

are return periods on the annual maximum scale. Thus, the 50-year event corresponds

to a value with an annual exceedance probability of 0.02. [Editorial note: Frequency

statements should be treated with some degree of caution. Although the peak of the

FSU flood hydrograph is nominally of the stated frequency, the frequency assignment

does not strictly transfer to quantities (such as the flood volume) derived by invoking

the bridge to the FSR rainfall-runoff method.]

9.5.4 Goodness-of-fit measures

IBIDEM summarises the goodness of fit – of the FSR rainfall-runoff hydrograph to the FSU

design hydrograph – in two measures: the root mean square error (RMSE) and the Nash-

Sutcliffe efficiency (NSE). These are calculated in quite different ways:


106

RMSE is calculated as part of the IBIDEM fitting process. It is the root mean square

error in terms of hydrograph width (measured in hours) for the upper portion of the

hydrograph over which the fitting is carried out. It indicates how well the FSR and

FSU hydrographs match in terms of their widths. A small value of RMSE indicates a

good fit. The RMSE obtained using IBIDEM is always the minimum possible given

the shape of the imported FSU hydrograph and the family of shapes that the FSR

rainfall-runoff hydrograph can take.

NSE is a dimensionless measure of hydrograph fit calculated in the conventional (i.e.)

vertical direction. It is a measure of the goodness of fit in terms of flow over the

duration of the imported FSU hydrograph. Values close to 1.0 indicate an excellent

fit. Negative values of NSE indicate that a better fit could be achieved using the mean

flow. The statistic is calculated independently of the fitting done by IBIDEM, and

will not usually take the minimum possible value.

[Editorial note: The Nash-Sutcliffe efficiency is used to good effect in generalising a model

for the baseflow index BFI (see Volume IV). However, NSE is problematic to interpret in

some of the cases arising in IBIDEM. Because it gives no special weight to the quality of fit

around the peak, NSE is not ideal for evaluating the match to the upper hydrograph. The

measure has the minor merit of being independent of the method of fitting used in IBIDEM.]

In the case of Figure 9.11, the fit of the FSR hydrograph is judged to be very poor, with

NSE = -0.70. The difficulty arises largely because the receding limb of the FSR hydrograph

is much steeper than that of the FSU hydrograph once the inflection point four hours after the

peak has been passed. Beyond that time, there is a long period when the FSR hydrograph is

much lower than the FSU hydrograph. The recession limb of the imported hydrograph has

less influence on the IBIDEM fit if the threshold used is raised from 50% to 60% (see Figure

9.12). The NSE becomes a respectable +0.70.

Figure 9.11: FSR hydrograph fitted to UPO-ERR-Gamma hydrograph

Characteristic

hydrograph by

UPO-ERR-Gamma

FSR hydrograph

fitted by IBIDEM

NSE = −0.70

NSE evaluated

across this period


107

Figure 9.12: As Figure 9.11 but with fitting threshold raised to 60% of peak flow

[Editorial note: The take-home messages are: (i) Give greater weight to the RMSE measure

than NSE, (ii) Consider the sensitivity of IBIDEM fits to the threshold chosen and (iii) Fitting

horizontally rather than vertically has real merit in hydrograph width modelling!]

9.5.5 Tabular display

Below the graph, IBIDEM tabulates the parameter values and other variables (as shown in

Figure 9.13). After the hydrograph fitting is carried out, the variables shown are: flow return

period, rainfall return period, baseflow (BF), fitted Tp, fitted SPR, PR (based on SPR and

other terms including URBEXT), time-step, storm duration (calculated from Tp and SAAR),

rainfall depth (calculated from storm duration and return period), peak flow (taken from the

imported FSU hydrograph), runoff volume, RMSE and Nash-Sutcliffe efficiency.

Figure 9.13: Example of IBIDEM tabular display

NSE

across

here NSE = +0.70


108

Slightly different versions of the table appear in some options. For example, it is not

appropriate to show the goodness-of-fit statistics within the Sensitivity to storm duration

option. The order of the rows in each version of the table remains the same but the variable

that the user has changed (between columns) is highlighted to aid interpretation. For

example, the row containing the flow return period is highlighted in Figure 9.13. Another

feature is that variables not changing between columns are indicated in grey. Baseflow does

not vary with return period, so the BF row is shaded grey in this example.

9.5.6 Export of results

IBIDEM allows export of a summary report in .CSV format, including a record of the FSU

and FSR hydrographs, PCDs used in the calculations, fitted parameters and measures of the

goodness of fit. A different version of the report is available in the Sensitivity to storm

duration option.

9.6 Testing

9.6.1 Choice of test sites

IBIDEM has been tested on a range of catchments and a variety of FSU hydrographs. Design

hydrographs on gauged catchments will usually be based on hydrograph width analysis, with

the characteristic hydrograph derived by the non-parametric method of Chapter 3. At

ungauged sites, the characteristic hydrograph is likely to be based on the UPO-ERR-Gamma

model of Section 4.4 or the parabolic curves method of Section 8.7.

The five test catchments (see Map 9.1) are:

Station 16009 Suir at Caher Park – a large rural catchment (1602 km2);

Station 19001 Owenboy at Ballea – a small to medium-sized rural catchment

(103 km2);

Station 06026 Lagan-Glyde at Aclint – a medium-sized rural catchment (144 km2);

An ungauged site on a medium to large-sized rural catchment (443 km2) on the Anner

(a tributary of the Suir which it joins at Clonmel);

An ungauged site on a small urbanised catchment (8 km2) on a tributary of the Tolka

at Finglas.

9.6.2 Estimation of FSU hydrograph shapes

For the three test sites with flow data, the HWA software was applied to derive the

characteristic hydrograph by the non-parametric method of Chapter 3.

At the two ungauged sites, the characteristic hydrograph was constructed using a version of

the Chapter 6 procedure, i.e. estimating parameters of the UPO-ERR-Gamma model from

PCDs. The alternative method of constructing the upper hydrograph by the parabolic curves

method was also tested. Some details are reported in Table 9.1.

[Editorial note: Testing of IBIDEM was undertaken before HWA recommendations were

finalised, and before it was possible to estimate BFI at ungauged sites using the BFIsoil model


109

of Volume IV. It was therefore necessary to borrow BFI values: from Station 15001 for the

Anner ungauged site and from Station 08005 for the Tolka tributary. The differences in

technique are not thought to compromise the integrity of the testing of IBIDEM.]

Map 9.1: Location of test catchments

Table 9.1: Some details of the applications to two ungauged test catchments

Variable Unit River Anner Tributary of Tolka at Finglas

Physical catchment descriptors

BFI (see editorial note above) – 0.51 0.52

FARL – 0.999 1.000

ALLUV – 0.047 0.000

ARTDRAIN – 0.000 0.014

S1085 m/km 3.4 16.1

Parameters of the UPO-ERR-Gamma model

n – 7.35 7.23

Tr hours 9.68 12.62

C hours 30.80 32.77

Width descriptors for use of the parabolic curves method

W75 hours 4.18 4.90

W50 hours 7.03 7.57

s (eccentricity parameter) – 0.40 0.40


110

9.6.3 Estimation of peak flows

For the test sites with flow data, QMED was estimated as the median of the annual maximum

flows. At the two ungauged test sites, QMED was estimated from PCDs. [Editorial note:

Testing of IBIDEM was undertaken before the Volume II model for estimating QMED from

PCDs was finalised. Indeed, feedback from IBIDEM testing on the tributary of the Tolka led

to changes in the urban adjustment model finally recommended for QMED estimation.]

Design flows for other return periods were estimated by applying a flood growth curve based

on the FSR regional growth curve for Ireland. Due adjustment was made – by dividing the T-

year flood growth factor by the 2-year flood growth factor – for the different index variable

used in the FSR method. The design flows are shown in Table 9.2. It should be noted that

applications of IBIDEM will generally use design flows estimated by Volume II procedures.

Table 9.2: Design flows (m3s

-1) for the five test catchments

Catchment Return period (years)

2 5 50 100 200

16009 Suir at Caher Park 162 204 303 334 366

19001 Owenboy at Ballea 15.4 19.4 28.8 31.7 34.7

06026 Lagan-Glyde at Aclint 12.9 16.3 24.2 26.6 29.2

Anner at Clonmel 61.5 77.6 115 127 139

Tributary of Tolka at Finglas 1.62 2.05 3.03 3.34 3.66

9.6.4 Rainfall depth-duration frequency tables

IBIDEM requires a table of design rainfall values for a typical point in the catchment. The

user will obtain this through the FSU Web Portal. For the purpose of testing, tables of values

based on the Volume I rainfall frequency procedure were transferred to IBIDEM in CSV files

supplied by Met Éireann. In each case (i.e. for each of the test catchments in turn) the table

of design rainfall depths was supplied for a 2-km grid point close to the catchment centroid.

Table 9.3 summarises the main input variables used in the IBIDEM testing.

Table 9.3: IBIDEM input variables for the test catchments

Catchment AREA

(km2)

SAAR

(mm) URBEXT

Characteristic

hydrograph

Approx. centroid

Easting Northing

Suir at

Caher Park 1602 1079 0.009

Derived median

hydrograph of

Chapter 3

200000 146000

Owenboy

at Ballea 106 1176 0.018 162000 62000

Lagan-Glyde

at Aclint 144 1072 0.007 310000 224000

Anner

at Clonmel 443 986 0.003 UPO-ERR-Gamma

model (Section 4.4

+ pilot of Chapter 6)

224000 134000

Tributary of

Tolka at Finglas 8 734 0.527 321000 240000


111

The heavily urbanised nature of the tributary of the Tolka at Finglas is to be noted.

9.7 Results

The sections below discuss the hydrograph fit obtained with IBIDEM for each of the test

catchments in turn. Although testing considered a range of return periods, the examples

shown are for the 100-year flood. Results are summarised later in Table 9.4.

9.7.1 Suir at Caher Park

For Station 16009 Suir at Caher Park, the HWA used hydrographs from 54 flood events. For

this catchment, the prescribed baseflow by the FSR rainfall-runoff method was 51.0 m3s

-1.

This was slightly lower than the minimum flow in the imported hydrograph. After IBIDEM

provided a warning, the baseflow was reduced to 50 m3s

-1 to overcome the difficulty.

The IBIDEM 100-year hydrograph is shown in Figure 9.14, based on the default fitting

threshold of 50% of the peak flow. The FSU hydrograph has a rapid rising limb but a much

slower recession limb. The FSR rainfall-runoff method results in only a limited range of

hydrograph shapes, and cannot capture this feature of the FSU hydrograph. However, the

RMSE criterion used by IBIDEM to optimise the fit ensures that the widths of the two

hydrographs are broadly similar, on average, for flows above the threshold.

The RMSE for this site is 12.7 hours: the largest for any of the test sites (see Table 9.4). This

reflects the propensity of the catchment to produce flood hydrographs of long duration.

Those interested in the Suir should also refer to Section 5.8. It is notable that the FSR

hydrograph overestimates widths near the peak and underestimates widths at lower flows.

The Nash-Sutcliffe efficiency (NSE) is 0.50, indicating a fairly good fit in terms of flow.

The fitted Tp is 52.8 hours and the SPR is 36.7%. These values seem reasonable for this

large catchment of moderate permeability (BFI = 0.63).

Figure 9.14: Suir at Caher Park 100-year hydrograph fit

Derived median

hydrograph

IBIDEM

hydrograph RMSE = 12.7 hours

NSE = 0.50


112

9.7.2 Owenboy at Ballea

For Station 19001 Owenboy at Ballea, the HWA used hydrographs from 35 flood events.

The IBIDEM 100-year hydrograph is shown in Figure 9.15, based on the default fitting

threshold of 50% of the peak flow. As for the Suir at Caher Park, the FSU hydrograph is

more skewed than the FSR one, in that it rises rapidly and falls more slowly.

The RMSE for this site is 6.1 hours. The Nash-Sutcliffe efficiency is -0.48. The poor

performance in terms of NSE arises because the statistic is calculated as an average over the

duration of the FSU hydrograph, i.e. from about 10 hours before the peak to 55 hours after.

The statistic could be improved by entering a higher value for baseflow (BF) or by raising the

threshold used in fitting.

The fitted Tp is 31.1 hours and the SPR is 29.9%. These values seem reasonable for this

moderate-sized catchment of moderate permeability (BFI = 0.64), although the Tp is perhaps

rather long, as can be seen from the hydrograph plot. However, a shorter Tp would give a

narrower hydrograph and hence a poorer fit in terms of hydrograph widths.

Figure 9.15: Owenboy at Ballea 100-year hydrograph fit

9.7.3 Lagan-Glyde at Aclint

Station 06026 Lagan-Glyde at Aclint used hydrographs from 31 flood events and provides an

example of a case where basic use of HWA yields a derived median hydrograph with “time

reversals”. One of those on the rising limb is at quite a high level, between 70 and 75% of

the peak flow (see Figure 9.16). Optionally, these can be removed using interactive features

within the HWA software.

The fitting method used in IBIDEM can in fact cope with such time reversals, as shown in the

LH plot of Figure 9.17. However, users may be reluctant to present a hydrograph in which

time appears to run backwards! The anomaly can be avoided by editing the FSU hydrograph

within the HWA software or en route to IBIDEM.

Derived median

hydrograph

IBIDEM

hydrograph RMSE = 6.1 hours

NSE = -0.48


113

Figure 9.16: Lagan-Glyde at Aclint – derived median hydrograph from HWA software

Figure 9.17: Lagan-Glyde at Aclint – 100-year hydrograph fits

Incompleteness of the imported hydrograph prompts IBIDEM to issue a warning where

appropriate. A typical message is: “Threshold flow is less than 100 yr input hydrograph

start/end values, please adjust”. Many users would instinctively raise the fitting threshold

from the default value of 50% to 75%. However, as shown in the RH plot of Figure 9.17, it is

permissible to adopt an intermediate threshold at which the hydrograph width (in the

imported FSU hydrograph) is defined on one limb of the hydrograph but not the other. This

allows the fitting to exploit the width information on the receding limb between 70 and 75%

of the peak flow.

IBIDEM gives a good fit to the rising and falling limbs of the FSU hydrograph, above the

threshold value used for fitting. The RMSE is 11.6 hours and the Nash-Sutcliffe efficiency is

0.64, indicating a moderately good fit in terms of flow.

The fitted Tp is 97.3 hours. This is a surprisingly long time-to-peak (of the unit hydrograph)

given the modest size of the catchment (144 km2). The typically slow flood response may in

part reflect the influence of loughs in the catchment (FARL is 0.91).

The fitted SPR is 48.8%. The BFI for this catchment is 0.66, indicating a moderately

permeable catchment. The fitted SPR value is surprisingly high for such a catchment. The

high value of SPR is partly explained by the long time-to-peak which tends to produce a

subdued hydrograph with a relatively low peak. IBIDEM has increased SPR in

compensation, in order to ensure that the FSU peak flow is matched.

Time reversal

DMH edited to

remove time reversal

Derived median

hydrograph

IBIDEM

hydrograph IBIDEM

hydrograph


114

9.7.4 Anner at Clonmel

Two sets of calculations were carried out for this ungauged catchment: one with the

characteristic hydrograph constructed using the UPO-ERR-Gamma model and the other using

the parabolic curves method. These are shown in the Figure 9.18, along with hydrographs

fitted by IBIDEM.

The FSR hydrograph fitted by IBIDEM to the FSU hydrograph in UPO-ERR-Gamma form is

shown in the left-hand side of Figure 9.18. The fit is seen to be fairly good, the main defect

being that the FSR rainfall-runoff method cannot reproduce the sudden change of gradient on

the falling limb when the Gamma curve is replaced by the exponential recession. The RMSE

is 1.9 hours. The Nash-Sutcliffe efficiency is a very poor -0.70. This reflects the departure

of the IBIDEM and UPO-ERR-Gamma hydrographs in the early and (especially) later part of

the period over which the fitting is made. (As explained in Section 9.5.4, NSE is evaluated

from vertical differences throughout the period for which the FSU hydrograph exceeds the

fitting threshold.)

Figure 9.18: Anner at Clonmel 100-year hydrograph fit

IBIDEM provides a very good fit to the FSU hydrograph in parabolic form (see RH side of

Figure 9.18), with RMSE = 1.0 hours and NSE = 0.85.

Interpretation of the Tp and SPR values fitted by IBIDEM is revealing for this catchment.

The fitted Tp is 2.8 hours for the parabolic hydrograph and 7.1 hours for the Gamma

hydrograph. These times to peak (particularly 2.8 hours) seem unreasonably short for this

medium to large rural catchment of 443 km2. Fitted SPR values are 0.4% for the parabolic

hydrograph and 2.3% for the Gamma hydrograph. IBIDEM helpfully warns that these SPR

values are suspiciously low. An SPR of 0.4% is unreasonably low, because it implies

virtually none of the storm rainfall typically becomes rapid response runoff. The very small

value is probably due in part to the need to compensate for the excessively small value of Tp.

IBIDEM has had to decrease SPR in order to ensure that the FSU peak flow is matched.

[Editorial note: Multipliers in the PCD-based models – for the hydrograph width parameter

Tr and the descriptors W75 and W50 – supplied for testing were much too small due to the use

of non-standard units for the mainstream slope descriptor S1085. A feature of the FSR

rainfall-runoff method is that underestimation of Tp leads to underestimation of SPR also. It

is helpful that IBIDEM helpfully warns the user when SPR values are suspiciously low. See

also the editorial note in Section 9.7.5.]

UPO-ERR-Gamma

hydrograph

Parabolic curves

hydrograph IBIDEM

hydrograph

IBIDEM

hydrograph


115

9.7.5 Tributary to Tolka at Finglas

Two sets of calculations were carried out for this urbanised but ungauged catchment: one

with the characteristic hydrograph constructed using the UPO-ERR-Gamma parametric

model and the other using the width descriptors W75 and W50 and the parabolic method.

These are shown in the Figure 9.18, along with hydrographs fitted by IBIDEM.

Because this small catchment is heavily urbanised, the urban catchment design package was

applied within IBIDEM. This means that the 100-year return period rainfall was used to

synthesise the 100-year flood hydrograph, and the 50% summer rainfall profile was adopted.

As on the River Anner, the fitted hydrograph matches the FSU shape fairly well for the UPO-

ERR-Gamma hydrograph and very closely for the parabolic hydrograph. RMSE and NSE

values can be seen in the final columns of Table 9.4, which summarises results for all five

test catchments.

Figure 9.19: Tributary of Tolka at Finglas 100-year hydrograph fit

Fitted Tp values are 9.3 hours for the UPO-ERR-Gamma hydrograph and 4.2 hours for the

parabolic hydrograph. These values seem suspiciously long for a small heavily urbanised

catchment.

For reasons explained in Section 9.3.1, there is interaction between the Tp and SPR

parameters that IBIDEM obtains when fitting the FSR rainfall-runoff method to the design

flood hydrograph that the user has derived by FSU methods. IBIDEM always respects the

peak flow of the imported FSU hydrograph. Whilst the parabolic curves method appears

preferable to the UPO-ERR-Gamma model in terms of the Tp values resulting for this

catchment, this preference is reversed when the SPR values are considered (see final columns

of Table 9.4). The fitted SPR for the parabolic hydrograph is 6.3% which is unusually low.

[Editorial note: As discussed in the editorial note in Section 9.7.4, the developer was

supplied with incorrect multipliers in the models for the hydrograph width parameter Tr and

the descriptors W75 and W50. Because the PCD-based models had grossly underestimated

hydrograph width at both sites used in testing (i.e. the Anner and the Tolka tributary), the

IBIDEM developers understandably cast around for a possible explanation. Indeed they

expressed surprise that none of the regression models for Tr, W75 or W50 includes a term that

reflects catchment size. Such PCDs were considered in the generalisation research of

Parabolic

hydrograph IBIDEM

IBIDEM

hydrograph UPO-ERR-Gamma

hydrograph


116

Chapter 6 but found useful only once: AREA appears in the regression model for parameter

C of the UPO-ERR-Gamma model in the case where BFI is unavailable (see Table 6.7).

A characteristic feature of flood response times in Ireland and Great Britain is that catchment

size often plays a much smaller role than the hydraulically-minded expect. Although

mainstream length (MSL) appeared in the FSSR16 model for Tp(0), it did so only to a

modest exponent of 0.23. This means that the estimated value of Tp(0) doubles only if the

mainstream is 20 times longer. Catchment size is a very poor guide to flood response time!

It is reiterated that the poor results obtained in IBIDEM testing on the Anner and the Tolka

tributary arose largely because the developers had been supplied with PCD models for Tr,

W75 and W50 that had faulty multipliers.]

Table 9.4: Summary of IBIDEM results for five test catchments (100-year flood case)

Variable Suir Owenboy Lagan Anner

* Tolka

*

Gamma Parabolic Gamma Parabolic

Rainfall return

period (years) 140 140 140 140 140 100 100

BF (m3s

-1) 50 3.69 4.56 12.85 12.85 0.13 0.13

Tp (hours) 52.8 31.1 97.3 7.1 2.8 9.3 4.2

SPR 36.7 29.9 48.8 2.3 0.4 25.3 6.3

PR 46.8 40.2 60.7 10.9 6.2 38.1 22.1

Time-step

(hours) 1 1 1 1 0.25 1 0.25

Storm duration

(hours) 111 69 203 15 5.75 17 7.25

Rainfall depth

(mm) 122.2 126.9 149.4 102.1 70.8 85.2 64.8

Peak flow

(m3s

-1)

334.0 31.7 26.6 126.9 126.9 3.3 3.3

Volume (mm

of catcht

runoff)

84.6 69.9 141.3 15.0 5.9 24.4 10.7

RMSE (hours) 12.68 6.09 11.58 1.88 1.02 1.69 0.48

NSE 0.50 -0.48 0.64 -0.70 0.85 0.03 0.88

Editorial note: *

Test results for the Anner and Tolka catchments are in error due to incorrect

multipliers in the PCD-based models originally supplied for Tr, W75 and W50

9.7.6 Illustration of effect of fitting threshold

Tests were carried out using a wide range of thresholds. The effect of varying the threshold

is illustrated for the ungauged site on the River Anner, for an FSU hydrograph constructed

using the UPO-ERR-Gamma model of hydrograph width. The fitting threshold is marked on

each plot in Table 9.5, and a commentary provided.


117

[Editorial note: The option to vary the fitting threshold is an exceedingly valuable feature of

IBIDEM. It allows the user to focus on the hydrograph features most relevant to their

application. In some cases, only the upper hydrograph may be relevant; in others, the entire

hydrograph is important. It is important that the user inspects and interprets values of Tp and

SPR thoroughly. Otherwise, a more hydrologically-informed analyst may later judge the

choice of fitting threshold to have been made as a matter of convenience.]

9.7.7 Summary

The tests led to improvements in IBIDEM and to timely feedback to other parts of the FSU

research. IBIDEM gave broadly sensible results on the three gauged catchments. Tp and

SPR values were within expected ranges on the Suir and Owenboy. The inferred Tp was

longer than expected for the Lagan-Glyde, with SPR taking on a high value in compensation.

As noted above, results for the two ungauged catchments were undermined by the supply of

PCD-based models for Tr, W75 and W50 with incorrect multipliers.

Even when the correct models are used for estimating the characteristic hydrograph from

PCDs, users will find cases where the Tp and SPR values – inferred when IBIDEM fits the

FSR rainfall-runoff method to the imported FSU hydrograph – are unrealistic with perceived

properties of the catchment. There is no simple recipe to deal with such cases. It is largely a

matter of experience.

It is further emphasised that the FSU recommendation is to base flood estimates wherever

possible on data transfers rather than on PCDs alone. Implementation of the FSU research

stresses the importance of choosing a pivotal catchment so that estimates at ungauged sites

gain from knowledge of flood behaviour at gauged sites. Section 8.10 discusses the

selection and use of the pivotal catchment in the context of estimating the characteristic

hydrograph at an ungauged site.

9.8 Additional opportunities provided by IBIDEM

9.8.1 Strengths and limitations

IBIDEM provides a way of assessing FSU outputs using a structured model of hydrograph

formation. The test results above illustrate that the software can help in detecting hydrograph

shapes or peak flows that appear to be inconsistent with properties of a catchment.

A limitation is that IBIDEM relies on the assumptions made in the FSR design event

approach. These may not always be appropriate. The design event method derives a flood

hydrograph from a single combination of inputs (rainfall depth, rainfall duration, rainfall

profile and catchment wetness index). This combination does not always result in a

hydrograph peak of the required return period. Thus, the design event used by IBIDEM may

not always be relevant to the supplied FSU design hydrograph. The implication for users is

that, while IBIDEM can provide a useful diagnostic test of the FSU design hydrograph, the

method is not a cure-all.


118

Table 9.5: Sensitivity to fitting threshold (ungauged site on River Anner)

Threshold

used in

fitting

Hydrograph plot Performance

statistics Comment

90%

of peak flow

RMSE = 0.31 hr

NSE = -1.29

Good fit to widths for

small segment above

threshold

70%

of peak flow

RMSE = 0.19 hr

NSE = -1.42

Very good fit to widths

above threshold (hence

small RMSE)

50%

of peak flow

RMSE = 1.88 hr

NSE = -0.70

Larger RMSE indicates

inferior fit to widths but

smaller NSE indicates

better fit in terms of

flow

30%

of peak flow

RMSE = 5.80 hr

NSE = -0.50

Continuation of trends

noted above ( when

50% of peak flow used

as threshold)

Threshold

Threshold

Threshold

Threshold


119

9.8.2 Urban adjustment to design hydrographs

The options described in Section 9.4 provide additional functionality. A potential further

application of IBIDEM is in estimating improved design hydrographs on urban catchments.

One possibility is to use FSU methods to derive the design flood hydrograph as if the

catchment were entirely rural, by omitting the urban adjustment to QMED. The hydrograph

would then be imported to IBIDEM, with URBEXT set to zero. After carrying out the

fitting, the user would select the option to test sensitivity to urbanisation, and enter the correct

value of URBEXT. The adjusted FSR hydrograph obtained is this way provides an

alternative allowance for urbanisation. A potential advantage of this approach is that it

adjusts the hydrograph widths for urbanisation, not just the peak flow. This is possible

because the FSR rainfall-runoff method incorporates an urban adjustment to both Tp and PR.

Figure 9.20 illustrates the outcome for the heavily urbanised ungauged tributary of the Tolka

at Finglas considered in Section 9.7.5. The adjusted hydrograph has a peak flow over four

times larger than the original one, and the time to peak is much shorter. The increase in peak

flow is caused by two effects: the increase in percentage runoff and the decrease in time to

peak (and consequently storm duration). The increase in peak flow thus synthesised is much

greater than that provided by the Volume II urban adjustment to QMED. [Editorial note:

Details of this example may have been compromised by the supply of PCD-based models for

Tr, W75 and W50 with incorrect multipliers.]

Figure 9.20: Urban adjustment to hydrograph for Tolka tributary at Finglas test site

9.8.3 Supplying input hydrographs to river models

IBIDEM also has potential in deriving inflows for hydrodynamic river models, which often

require hydrographs resulting from design storms with durations different from the critical

Imported FSU hydrograph

Calculated FSR hydrograph

Adjusted FSR hydrograph


120

duration of the particular subcatchment. These hydrographs can be generated using the

option to test sensitivity to storm duration.

Hydrographs generated by IBIDEM are likely to be useful for flood storage and flood routing

studies because they cover the full range of flows. Although the non-parametric method of

Chapter 3 is strongly recommended for use at gauged sites, the characteristic hydrograph it

produces does not extend all the way down to zero flow. IBIDEM provides a structured

alternative to sketching in the lower part of the hydrograph by hand.

9.8.4 Allowances for projected land-use change

IBIDEM provides a route to assessing the effect of future changes in urbanisation or other

land use by varying the parameters of the rainfall-runoff method. The relevant options have

been discussed in Sections 9.4.3 and 9.4.4.


121

Acknowledgements

The hydrograph width analysis was undertaken at the Department of Engineering Hydrology

in the National University of Ireland Galway, principally by Kieran O’Connor and Monomoy

Goswami. Samiran Das undertook some testing of the methods.

IBIDEM was developed by JBA Consulting: principally by Zoë Whiteman and Duncan

Faulkner.

The flood event analysis summarised in Appendix B was undertaken at University College

Cork.

The help of organisations and individuals who gather and curate hydrograph data is gratefully

acknowledged. Peter Newport of OPW is especially thanked for supplying extensive data.

Volume III was edited by Duncan Reed of DWRconsult.

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123

Appendices

Appendix A Gauges used in Hydrograph Width Analysis

Table A.1: Stations used in Hydrograph Width Analysis

Station River Name Station

grade Area (km

2) River Basin District

06011 Fane Moyles Mill A1 229.2 Eastern

06012 Fane Clarebane A1 162.80 Eastern

06013 Dee Charleville A1 309.1 Eastern

06014 Glyde Tallanstown A1 270.4 Eastern

06026 Lagan (Glyde) Aclint A1 148.4 Eastern

07001 Tremblestown Tremblestown A2 151.3 Eastern

07002 Deel Killyon A2 285.0 Eastern

07004 Kells Blackwater Stramatt A2 245.7 Eastern

07006 Moynalty Fyanstown A2 177.5 Eastern

07007 Boyne Aqueduct A1 441.2 Eastern

07009 Boyne Navan Weir A1 1658.2 Eastern

07010 Blackwater Liscartan A1 699.7 Eastern

07011 Kells Blackwater O’Daly’s Br A2 281.7 Eastern

07012 Boyne Slane Castle A1 2460.3 Eastern

07033 Kells Blackwater Virginia Hatchy A2 124.9 Eastern

09001 Ryewater Leixlip A1 209.6 Eastern

11001 Owenavorragh Boleany B 155.1 South-Eastern

14004 Figile Clonbulloge A1 268.9 South-Eastern

14006 Barrow Pass Bridge A1 1063.6 South-Eastern

14007 Stradbally Derrybrock A1 118.6 South-Eastern

14009 Cushina Cushina A2 68.4 South-Eastern

14011 Slate Rathangan A1 162.3 South-Eastern

14018 Barrow Royal Oak A1 2419.4 South-Eastern

15001 Kings Annamult A2 444.3 South-Eastern

15002 Nore John’s Br A2 1644.1 South-Eastern

15003 Dinin Dinin Br A2 299.2 South-Eastern

15005 Erkina Durrow Foot Br B 379.4 South-Eastern

15006 Nore Brownbarn A2 2418.3 South-Eastern

16001 Drish Athlummon A2 135.1 South-Eastern

16002 Suir Beakstown A2 485.7 South-Eastern

16003 Clodiagh Rathkennan A2 243.2 South-Eastern

16004 Suir Thurles A2 228.7 South-Eastern

16005 Multeen Aughnagross A2 84.0 South-Eastern


124


grade Area (km


16008 Suir New Bridge A2 1090.3 South-Eastern

16009 Suir Caher Park A2 1582.7 South-Eastern

18004 Awbeg Ballynamona A2 310.3 Southern

18005 Funshion Downing Br A2 378.5 Southern

19001 Owenboy Ballea A2 103.3 Southern

22071 L. Leane Tomies Pier A2 557.7 Southern

23001 Galey Inch Br A2 191.7 Mid-Western

23002 Feale Listowel A1 646.8 Mid-Western

23012 Lee (Kerry) Ballymullen A2 61.6 Mid-Western

24001 Maigue Croom A2 770.2 Mid-Western

24008 Maigue Castleroberts A2 806.0 Mid-Western

24013 Deel Rathkeale A1 438.8 Mid-Western

24082 Maigue Islandmore A2 762.8 Mid-Western

25001 Mulkear Annacotty A2 647.6 Shannon

25003 Mulkear Abington A1 399.1 Shannon

25005 Dead Sunville A2 192.6 Shannon

25006 Brosna Ferbane A1 1162.8 Shannon

25014 Silver Millbrook A1 164.4 Shannon

25016 Clodiagh Rahan A2 275.2 Shannon

25017 Shannon Banagher A1 7980.4 Shannon

25025 Ballyfinboy Ballyhooney A1 161.2 Shannon

25027 Ollatrim Gourdeen A1 118.9 Shannon

25029 Nenagh Clarianna A2 292.7 Shannon

25030 Graney Scarrif A1 280.0 Shannon

26002 Suck Rookwood A2 641.5 Shannon

26005 Suck Derrycahill A2 1085.4 Shannon

26007 Suck Bellagill A1 1207.2 Shannon

26008 Rinn Johnston’s Br A1 280.3 Shannon

26009 Black Bellantra Br A2 98.2 Shannon

26012 Boyle Tinacarra A1 519.9 Shannon

26019 Camlin Mullagh A1 253.0 Shannon

26021 Inny Ballymahon A2 1098.8 Shannon

26022 Fallan Kilmore A2 61.9 Shannon

27001 Claureen Inch Br A2 46.7 Mid-Western

27002 Fergus Ballycorey A1 564.3 Mid-Western

29001 Raford Rath-gorgin A1 115.5 Western

29004 Clarinbridge Clarinbridge A2 121.4 Western

29011 Dunkellin Kilcolgan A1 354.1 Western


125


grade Area (km


30004 Clare Corrofin A1 699.2 Western

30005 Robe Foxhill A1 237.8 Western

30007 Clare Ballygaddy A2 469.9 Western

30061 Corrib Estuary Wolfe Tone Br A2 3136.1 Western

34001 Moy Rahans A2 1974.8 Western

34009 Owengrave Curraghbonaun A2 117.1 Western

34018 Castlebar Turlough A1 95.4 Western

35001 Owenmore Ballynacarrow A2 299.4 North-Western

35002 Owenbeg Billa Br A2 88.8 North-Western

35005 Ballysadare Ballysadare A2 639.7 North-Western

35071 L. Melvin Lareen A2 247.2 North-Western

36010 Annalee Butlers Br A1 771.7 North-Western

36011 Erne Bellahillan B 320.5 North-Western

36015 Finn Anlore A1 153.1 North-Western

36019 Erne Belturbet A2 1491.8 North-Western

36021 Yellow Kiltybarden A2 23.4 North-Western

36027 Woodford Bellaheady A2 333.8 North-Western

39009 Fern O/L Aghawoney A2 1974.8 North-Western

Table A.2: Details of the flow data used (see also Table 7.2)

Station Flow data studied % of 15-min

data missing

# of AM

events

QMED

(m3s

-1)

Period of

arterial drainage

works From To

06011 01/10/1972 01/02/2001 1.6 29 15.45

06012 01/10/1972 11/01/2004 0.7 32 12.5

06013 29/10/1975 21/12/2004 1.5 30 27.75

06014 23/10/1975 22/10/2002 2.2 28 21.06 1950-57

06026 01/01/1972 01/02/2001 1.6 29 12.33 1950-57

07001 21/05/1975 30/09/2001 3.7 26 19.95 1971-73

07002 01/10/1970 01/09/2004 17.4 30 18.88

07004 26/10/1982 30/09/2005 0.9 23 22.56

07006 05/11/1956 01/10/2005 9.8 46 19.8

07007 09/04/1979 05/04/2004 2.1 25 35.41 1973-78

07009 05/11/1976 03/10/2005 0.8 30 144.91

07010 08/12/1986 21/05/2003 2.7 17 69.61 1982-86

07011 21/12/1983 30/09/1998 2.9 15 31.95 1980-82

07012 01/10/1986 01/01/2006 0.5 20 261.05 1969-86

07033 10/01/1980 01/10/2005 0.9 26 13.32

09001 15/10/1956 01/01/2006 5.8 50 33.77


126


data missing

# of AM

events

QMED

(m3s

-1)

Period of

arterial drainage

works From To

11001 07/03/1972 17/11/2005 4.2 34 45.7

14004 01/01/1972 01/07/2001 0.1 29 21.7

14006 01/01/1972 02/01/2006 0.4 34 78.34

14007 01/02/1980 01/10/2001 1.5 22 15.21

14009 01/01/1980 01/11/1999 2.7 20 6.78

14011 27/09/2000 12/11/2004 3.0 5 11.08

14018 01/01/1972 10/10/2005 1.5 34 147.91

15001 01/01/1972 01/08/2005 1.9 33 84.51

15002 01/10/1965 24/08/2001 1.3 36 198.19

15003 01/01/1972 01/05/2005 3.2 33 145.27

15005 01/01/1972 21/03/2005 1.3 33 27.68

15006 01/01/1972 01/01/2006 0.6 34 294.38

16001 01/10/1972 28/04/2005 7.2 33 15.41

16002 01/10/1954 21/11/2001 1.4 48 53.14

16003 01/10/1954 21/11/2001 1.4 48 29.07

16004 01/10/1954 13/06/2000 1.5 46 21.03

16005 01/10/1954 30/09/2001 16.0 47 20.4

16008 01/10/1954 01/06/2005 4.3 51 92.02

16009 14/01/1940 30/09/2004 0.5 64 163.63

18004 01/01/1972 23/04/2005 1.1 33 31.02

18005 01/01/1972 29/07/2002 0.2 30 54.83

19001 01/10/1972 01/01/2005 3.7 33 15.47

22071 01/10/1973 30/09/2004 5.2 31 105.20

23001 01/01/1960 20/12/2004 2.8 45 105.04

23002 01/10/1959 06/01/2006 7.6 46 371.84 1951-59

23012 04/04/1974 31/12/1991 4.6 18 15.88

24001 21/10/1976 01/01/2006 0.9 30 107.84 1975-76

24008 28/11/1973 01/01/2006 6.2 33 117.24

24013 01/10/1972 23/04/2003 4.9 31 108.99

24082 26/10/1977 21/02/2001 6.2 25 138.93 1975-76

25001 20/10/1977 01/01/2004 7.5 27 125.27

25003 03/04/1995 01/01/2002 4.2 7 66.71

25005 01/10/1972 01/04/1999 65.1 11 29.17

25006 05/09/1953 26/09/2005 1.7 52 81.04 1948-53

25014 01/10/1972 19/09/2005 3.2 33 16.52 1948-56

25016 01/10/1951 29/05/2005 3.1 54 24.31 1948-53

25017 02/01/1989 20/03/2003 2.1 14 481.44


127


data missing

# of AM

events

QMED

(m3s

-1)

Period of

arterial drainage

works From To

25025 01/10/1972 17/08/2003 6.9 31 9.85

25027 01/01/1972 15/01/2002 2.9 30 23.5 1955-65

25029 01/01/1972 01/01/2005 9.7 33 52.81

25030 01/10/1972 15/10/2005 4.3 34 41.66

26002 01/10/1972 01/11/2005 7.0 34 55.14

26005 01/10/1954 01/01/2003 1.7 49 94.56

26007 01/10/1972 13/08/2003 2.6 31 85.95

26008 26/09/1979 08/08/2003 3.7 24 23.69

26009 01/10/1972 18/02/2002 0.4 30 13.02

26012 01/01/1991 22/01/2002 3.0 11 46.72 1982-92

26019 16/09/1953 21/01/2002 4.4 49 21.04

26021 01/10/1972 31/07/2003 73.0 10 64.84

26022 01/01/1972 22/01/2002 10.1 30 6.35

27001 01/10/1972 23/04/2003 8.1 31 20.03

27002 03/05/1954 31/12/2005 1.8 52 32.22

29001 07/10/1957 01/01/2001 20.0 36 13.03

29004 10/07/1973 02/01/1986 1.8 13 11.24

29011 11/02/1983 06/01/2003 2.6 20 29.26

30004 01/10/1964 01/01/2005 9.9 41 89.83 1958-64

30005 01/10/1978 31/12/2004 10.3 26 37.89 1973-78

30007 20/11/1974 30/06/2005 3.6 31 64.13

30061 01/10/1950 12/02/2004 6.1 54 228.44

34001 01/10/1972 01/01/2006 1.8 37 174.27 1960-71

34009 01/01/1972 01/01/2000 4.5 28 28.05

34018 12/08/1976 27/04/2004 3.6 28 11.51 1960-71

35001 08/11/1955 01/10/1997 3.7 43 31.34

35002 19/01/1972 12/11/2002 3.1 31 52.88

35005 01/01/1946 30/09/2004 17.2 51 74.92

35071 04/12/1974 15/01/2003 4.0 29 26.69

36010 01/10/1972 01/11/1998 0.3 27 61.61

36011 01/10/1972 01/07/1998 2.1 26 18.32

36015 29/10/1956 01/02/2001 0.9 45 22.41

36019 19/12/1597 01/09/1998 0.3 41 88.75

36021 14/03/1978 01/12/1999 0.6 22 23.59

36027 08/08/1974 23/10/1992 0.5 19 25.12

39009 05/09/1972 09/01/1982 0.0 10 43.24


128

Appendix B Précis of UCC research on flood event analysis

University College Cork (UCC) analysed rainfall-runoff behaviour for a range of Irish

catchments. The research was intended to remind FSU users that – whilst river floods in the

temperate climate of Ireland generally arise from heavy rainfall – there are important

differences between catchments in the conditions that give rise to flooding.

Some details of the 12 catchments studied are given in Table B.1. Nine of the catchments are

listed in ascending order of size. The remaining three form a nested set on the Munster

Blackwater. The catchments range in size from 15 km2 for the Dripsey at Coachford to 1605

km2 for the Nore at John’s Bridge. Mainstream slopes (S1085) range from 0.32 m km

-1 for

the Fergus at Ballycorey to 10.3 m km-1

for the Dripsey. Average annual rainfalls range from

913 mm for the Boyne at Trim to 1470 mm for the Dripsey.

[Editorial note: Brune (2007) expands the work by considering a further ten catchments,

chiefly in the north-west and in the greater Dublin area.]

Table B.1: Stations subjected to rainfall-runoff analysis

Station AREA

(km2)

S1085

(m

km-1

)

SAAR

(mm)

Sites from which

hourly rainfall data

taken

Comment

Dripsey at

Coachford†

15 10.3 1470 Dripsey Upland

19001 Owenboy at

Ballea 106 3.79 1248 Cork Airport 100% rural

25014 Silver at

Millbrook 165 5.55 992 Birr Rural

07002 Deel at

Killyon 285 12.72 960 Mullingar

1975, post-

drainage

06013 Dee at

Charleville Weir 307 2.37 1096

Dundalk +

Bailiborough

27002 Fergus at

Ballycorey 562 0.32 1252 Shannon Airport

Karst +

minor lakes

16008 Suir at

Newbridge 1120 0.96 1030 Bansha

* + Dundalk

*

07005 Boyne at

Trim 1282 0.43 913 Mullingar + Navan

1975, post-

drainage

15002 Nore at

John’s Bridge 1605 0.85 979

Kilkenny + Coon +

Oakpark Up to 2002

18050 Blackwater

at Duarrigle 245 3.9 1456 Millstreet + 32

**

Nested

(upper)

18048 Blackwater

at Dromcummer 881 2.7 1356

Millstreet +

Freemount + 32**

Nested

(middle)

18006 Blackwater

at Mallow 1186 2.1 1303

Millstreet + Free +

Mallow + 32**

Nested

(lower) †

UCC research catchment, subcatchment of Station 19028 Dripsey at Dripsey *

Daily data only **

Special network of 32 raingauges in Blackwater catchment, monitored by UCC for 2005-2006


129

Volume IV presents physical catchment descriptors (PCDs) developed for general use in the

FSU. UCC attempted a more detailed description of the catchments. The overall goal was to

illustrate rather than codifying flood event analysis in Ireland.

Twelve flood events were analysed for each of the 12 catchments. The times series data

analysed are river flows and rainfall depths drawn from several years of record. The main

flood event analysis undertaken was based on the unit hydrograph method but did not

consider volumetric aspects of the rainfall-runoff response to any great degree. The main

output was discussion of the catchment-average unit hydrographs (UHs) derived for the 12

catchments. The UHs shown in Figure B.1 have been standardised by dividing by catchment

area to facilitate inter-catchment comparisons.

Figure B.1: Catchment-average unit hydrographs standardised by area

The 12 catchments were tentatively allocated to five catchment types:

Type 1 The lowest UH peak magnitude and longest UH duration response was for the Fergus

at Ballycorey, with an area-normalised UH peak of ≈1.510-3

m3s

-1 mm

-1 km

-2 and a

UH timebase (i.e. the duration of flood response to a unit net rainfall) of ≈12 days;

Type 2 The second lowest UH peak magnitude (≈710-3

m3s

-1 mm

-1 km

-2) and a timebase of

≈36 to 60 hours, as in the four rivers: the Deel, the Suir, the Dee and the Boyne;

Type 3 The third lowest UH peak magnitude (≈1510-3

m3s

-1 mm

-1 km

-2) and a timebase of

≈12 to 30 hours, as in the four rivers: the Dripsey, the Owenboy, the Silver and the

Blackwater at Mallow;

Type 4 The fourth lowest UH peak magnitude (≈2010-3

m3s

-1 mm

-1 km

-2) and a timebase

of ≈24 hours, as in the two rivers: the Nore and the Blackwater at Dromcummer;

Type 5 The highest UH peak magnitude (≈2710-3

m3s

-1 mm

-1 km

-2) and a timebase of ~18

hours, as in the Blackwater at Duarrigle.

Some consideration was also given to artificial neural network (ANN) analysis, and to the

potential application of ANN models in flood warning.


130

Appendix C Performance of HWA methods on verification events

Figure C.1: Verification of median hydrograph + UPO-ERR-Gamma methods at Station

06011


131


06012


132


06013


133


06014


134


06026


135


07007


136


07009


137


07010


138


07012


139


09001


140


14004


141


14006


142


14007


143


14011


144


14018


145


15005


146


23002


147


24013


148


25003


149


25006


150


25014


151


25017


152


25025


153


25027


154


25030


155


26007


156


26008


157


26012


158


26019


159


27002


160


29001


161


29011


162


30004


163


30005


164


34018


165


36010


166


36015


167

Appendix D HWA results and their estimates from PCDs

Table D.1: Hydrograph width analysis results for all 89 stations

Estimates in the RH columns derive from PCD regression models that do not use BFI, i.e. from the models reported in Table 6.7

From HWA From PCD models of Table 6.7 (no BFI)

Station # River Station Name Width descriptors UPO-ERR-Gamma params Width descriptors UPO-ERR-Gamma params

W75 (h) W50 (h) n Tr (h) C(h) W75 (h) W50 (h) n Tr (h) C(h)

06011 Fane Moyles Mill 114.35 1.30 29.69 360.83 131.72 2.67 99.81 220.11

06012 Fane Clarebane 136.25 243.02 2.46 93.31 280.95 143.58 275.96 2.35 92.91 270.81

06013 Dee Charleville 41.99 70.87 7.78 59.99 102.86 20.32 37.60 5.63 24.52 53.83

06014 Glyde Tallanstown 95.87 154.30 3.01 89.91 113.85 36.71 69.03 4.21 35.31 88.45

06026 Lagan (Glyde) Aclint 82.47 146.16 5.00 102.18 140.97 28.95 53.96 4.43 29.03 67.84

07001 Tremblestown Tremblestown 18.36 34.20 5.01 23.31 38.36 24.88 45.71 5.44 34.50 48.64

07002 Deel Killyon 46.74 93.14 2.77 32.74 151.96 41.90 82.28 4.14 42.49 92.89

07004 Kells Blackwater Stramatt 110.14 171.87 3.01 101.98 116.78 134.85 274.14 2.38 88.18 274.11

07006 Moynalty Fyanstown 15.42 30.38 7.78 20.87 58.15 18.91 33.47 6.51 27.49 36.21

07007 Boyne Aqueduct 26.22 52.53 3.75 26.84 69.88 20.42 40.55 5.86 27.13 56.14

07009 Boyne Navan Weir 27.75 54.14 5.28 33.04 95.53 26.51 52.30 5.41 34.31 91.07

07010 Blackwater Liscartan 30.42 119.06 3.46 25.78 222.32 47.19 89.45 4.08 48.25 119.06

07011 Kells Blackwater O’Daly’s Br 108.21 170.42 2.99 92.96 116.78 123.25 246.43 2.57 85.30 238.80

07012 Boyne Slane Castle 27.75 49.10 6.11 36.41 88.20 33.89 65.87 4.98 40.20 116.29

07033 Kells Blackwater Virginia Hatchy 46.41 84.10 6.11 60.82 105.05 65.21 118.23 3.93 66.92 81.00

09001 Ryewater Leixlip 11.21 22.64 8.40 21.75 22.97 28.54 52.78 5.56 44.47 50.93

11001 Owenavorragh Boleany 7.54 10.84 26.36 25.24 5.38 18.13 34.51 6.52 36.26 35.12

14004 Figile Clonbulloge 48.17 74.35 5.41 66.48 53.75 53.65 100.57 5.04 96.62 65.75

14006 Barrow Pass Bridge 57.46 83.02 4.71 75.83 41.29 27.45 50.07 5.91 49.03 69.84

14007 Stradbally Derrybrock 9.34 17.14 21.41 31.79 11.24 32.10 59.83 5.06 32.68 52.78

14009 Cushina Cushina 26.27 46.20 3.88 27.75 46.42 32.62 59.38 5.84 53.95 35.04

14011 Slate Rathangan 45.96 89.57 5.28 54.73 116.78 61.11 121.30 4.21 86.32 82.24

14018 Barrow Royal Oak 65.08 121.78 2.94 57.73 116.78 46.55 88.89 5.66 68.27 93.39


168




15001 Kings Annamult 15.74 28.49 9.42 30.46 23.70 20.33 35.66 6.87 33.68 42.10

15002 Nore John’s Br 8.12 19.23 17.64 24.97 21.50 31.62 58.18 6.91 60.23 58.77

15003 Dinin Dinin Br 5.77 8.79 10.54 12.42 6.11 14.41 25.68 8.36 41.24 27.00

15005 Erkina Durrow Foot Br 60.06 114.00 5.27 83.23 106.52 36.07 65.31 5.58 54.18 59.22

15006 Nore Brownbarn 19.95 35.64 13.83 53.25 22.97 31.07 56.89 6.73 56.72 68.11

16001 Drish Athlummon 30.61 46.41 5.55 40.16 39.83 28.69 52.40 7.11 69.12 29.22

16002 Suir Beakstown 58.04 102.32 8.34 91.27 114.58 31.72 57.04 6.47 58.76 48.16

16003 Clodiagh Rathkennan 39.53 77.32 2.53 16.15 188.60 18.62 32.01 7.03 27.76 34.51

16004 Suir Thurles 63.79 102.80 6.39 90.24 99.19 28.94 51.57 6.44 49.91 39.89

16005 Multeen Aughnagross 13.76 21.02 28.19 51.75 5.38 10.77 18.20 9.93 26.89 14.46

16008 Suir New Bridge 88.08 146.96 3.15 44.16 410.67 31.21 55.98 6.74 52.23 55.12

16009 Suir Caher Park 39.50 92.10 6.11 49.99 163.69 30.29 54.38 6.92 52.13 57.84

18004 Awbeg Ballynamona 38.18 73.27 5.00 43.89 105.05 23.77 41.61 8.21 41.88 28.22

18005 Funshion Downing Br 15.63 26.35 24.60 52.75 15.64 27.52 47.41 6.73 48.80 41.96

19001 Owenboy Ballea 26.34 44.94 2.79 12.68 112.38 32.67 52.61 6.50 32.46 31.84

22071 L. Leane Tomies Pier 96.29 190.22 1.88 50.56 243.57 103.53 202.15 2.51 67.99 286.23

23001 Galey Inch Br 6.98 11.84 12.54 16.65 5.38 12.30 21.01 9.13 21.59 20.64

23002 Feale Listowel 5.81 9.27 30.27 23.00 3.18 15.08 25.04 10.05 37.07 24.21

23012 Lee (Kerry) Ballymullen 11.67 18.29 18.23 32.13 11.24 14.00 21.82 8.57 24.43 17.01

24001 Maigue Croom 18.24 27.88 4.44 19.16 35.43 20.86 37.55 6.39 22.81 55.25

24008 Maigue Castleroberts 19.08 30.54 3.88 19.40 28.10 21.15 38.13 6.28 23.27 57.71

24013 Deel Rathkeale 19.66 28.77 12.33 48.75 6.85 21.06 37.01 6.75 27.70 43.26

24082 Maigue Islandmore 18.66 27.51 5.14 21.42 38.36 20.76 37.37 6.39 22.70 55.06

25001 Mulkear Annacotty 15.51 29.51 9.45 31.94 35.43 9.48 16.65 10.11 19.85 23.86

25003 Mulkear Abington 15.38 29.57 4.30 16.51 50.09 10.65 18.62 8.96 18.87 25.76

25005 Dead Sunville 14.00 33.17 5.00 13.14 69.88 16.17 28.73 7.11 20.71 31.80

25006 Brosna Ferbane 35.86 63.91 5.28 42.42 94.06 33.85 66.59 4.64 28.77 109.20

25014 Silver Millbrook 17.63 30.05 8.97 30.83 36.16 10.69 19.40 7.27 16.99 29.60

25016 Clodiagh Rahan 20.26 36.19 3.88 18.40 62.55 16.72 31.01 5.68 22.13 52.82

25017 Shannon Banagher 231.91 1.50 109.75 374.76 285.21 2.35 142.58 719.78


169




25025 Ballyfinboy Ballyhooney 85.33 187.22 4.14 111.29 222.32 41.39 74.47 4.98 64.07 58.50

25027 Ollatrim Gourdeen 7.66 14.25 19.41 23.42 19.31 18.66 33.56 6.35 24.45 34.51

25029 Nenagh Clarianna 15.87 29.50 8.89 28.70 50.09 18.27 32.82 6.36 24.67 43.40

25030 Graney Scarrif 70.22 122.12 4.22 81.86 94.06 27.49 52.55 5.74 54.81 46.96

26002 Suck Rookwood 118.67 163.98 6.58 186.50 39.83 84.62 142.63 5.47 87.48 69.54

26005 Suck Derrycahill 136.04 209.83 3.60 148.51 84.53 86.15 147.63 5.46 93.33 80.02

26007 Suck Bellagill 156.97 257.02 3.04 159.81 107.99 88.32 151.33 5.44 94.60 83.12

26008 Rinn Johnston’s Br 106.69 206.81 3.88 124.50 177.61 110.70 200.38 3.61 80.01 115.85

26009 Black Bellantra Br 26.52 38.47 8.47 49.00 14.18 58.62 98.28 4.76 62.44 53.74

26012 Boyle Tinacarra 177.27 285.94 3.85 195.50 257.50 187.00 366.65 2.98 122.83 202.74

26019 Camlin Mullagh 72.81 114.01 3.36 71.39 70.61 64.94 109.55 5.85 72.53 48.30

26021 Inny Ballymahon 52.68 179.79 3.48 24.80 527.93 185.77 397.77 2.47 108.40 384.16

26022 Fallan Kilmore 41.75 74.82 5.00 53.64 66.94 75.77 129.73 4.18 79.86 64.81

27001 Claureen Inch Br 14.87 20.26 5.00 17.72 11.24 10.02 16.57 11.91 33.86 9.06

27002 Fergus Ballycorey 270.72 493.96 5.28 429.25 187.87 153.55 316.40 2.59 139.23 292.53

29001 Raford Rath-gorgin 49.94 86.19 5.33 74.75 46.42 29.52 48.72 7.48 51.37 25.59

29004 Clarinbridge Clarinbridge 76.87 130.05 2.77 79.50 76.47 58.11 99.97 4.70 77.98 60.86

29011 Dunkellin Kilcolgan 138.65 242.46 4.01 182.75 114.58 50.90 88.36 5.18 66.23 65.87

30004 Clare Corrofin 44.33 68.49 5.30 59.44 46.42 49.13 84.48 5.33 46.89 75.02

30005 Robe Foxhill 39.87 56.46 7.40 77.00 22.97 44.37 74.76 5.67 43.71 50.26

30007 Clare Ballygaddy 38.52 59.31 6.11 67.75 20.77 53.24 89.71 5.35 50.11 67.04

30061 Corrib Estuary Wolfe Tone Br 2.91 41.90 1.56 168.16

34001 Moy Rahans 95.52 2.79 58.35 829.75 103.33 3.52 64.53 197.49

34009 Owengrave Curraghbonaun 19.67 26.03 9.10 39.70 8.31 32.28 49.18 7.44 38.86 25.88

34018 Castlebar Turlough 1.27 35.58 187.87 2.43 66.80 196.27

35001 Owenmore Ballynacarrow 103.62 154.99 3.88 116.94 105.79 111.98 188.17 5.12 111.33 61.88

35002 Owenbeg Billa Br 7.62 11.39 17.77 24.01 10.56 15.38 13.72 23.90

35005 Ballysadare Ballysadare 38.18 85.88 5.00 36.80 187.87 69.53 116.80 5.34 68.86 68.27

35071 L. Melvin Lareen 123.67 210.68 4.22 99.46 456.84 28.70 44.00 7.54 42.51 30.62

36010 Annalee Butlers Br 75.15 155.52 3.04 73.10 152.69 107.09 196.64 3.30 76.90 183.22


170




36011 Erne Bellahillan 316.02 613.41 2.21 295.25 229.65 195.91 380.64 2.46 107.26 277.04

36015 Finn Anlore 40.08 67.19 6.19 68.00 35.43 54.95 90.55 4.92 51.43 57.30

36019 Erne Belturbet 295.51 491.91 2.48 254.50 302.20 234.64 468.71 2.20 109.37 540.31

36021 Yellow Kiltybarden 3.11 4.90 14.70 7.66 2.45 5.89 8.84 18.78 22.48 3.67

36027 Woodford Bellaheady 332.71 539.54 2.61 300.50 213.52 233.97 476.48 2.30 112.89 314.24

39009 Fern O/L Aghawoney 45.10 86.66 9.10 74.10 115.31 59.63 102.78 4.04 49.19 81.79

171

Appendix E Application of the HWA software

E1 Troubleshooting the installation

The installation process may fail because of a number of conflicts or inadequacies in the

computer in which the HWA program is to be installed. If that happens, before exiting the

installation process, the installation wizard will display a message informing the user on the

cause of failure to install. The user may then take appropriate action to satisfy the

requirements to successfully install the program. Some of the most likely causes of failure of

the installation process and possible remedies are given below.

E1.1 Lack of storage space

The user’s computer may not have adequate disk space for installing all files required for

running the program. This problem may be solved by creating enough space in the disk either

by removing unnecessary or temporary files and folders, or by adding extra physical disk

space by upgrading to higher spcifications. When enough disk space is available, the

installation may be tried again.

E1.2 One or more files exist in the destination folder

The installation process may fail because of the existence of one or more files in the

destination folder. This problem may be solved by emptying the destination folder, either by

deleting the files, if not useful, or by moving the useful files to some other folder or folders.

The installation process may then be tried again.

E1.3 An out-of-date system file exists in the computer

When the Version of a dll (Dynamic Link Library) file (Oleaut32.dll) is older than that

required by the program for successful installation, the following message appears and the

installation process fails:

Setup cannot continue because some system files are out of date on your system. Click

OK if you would like Setup to update these files now. You will need to restart

Windows before you can run Setup again. Click Cancel to exit Setup without

updating system files.

When the user selects the OK button on the message box thus displayed, the Setup.Exe

program installs a newer version of the required dll file, which is compatible with the

installation program. In order to update the file to the correct version, the operating system

must be restarted by rebooting the computer. After rebooting, the application, the Setup.Exe

program is to be re-run to install.

E1.4 Out-of-date system files exist in the computer (multiple errors)

During installation, the installation program delays the replacement of the in-use system files,

until rebooting takes place, by saving the new files as temporary files in the Temp folder. In

order to replace the existing files with the .tmp files to complete the installation process, the

172

system uses a replacing and renaming operation. If something interferes with this operation,

then the in-use system files are not updated. Hence, once the computer is rebooted and the

installation program is restarted, the same error message appears and the installation process

fails again. The two most common causes for this to happen are that the .tmp files are deleted

or that the Temp folder is on a different drive or partition from the operating system. By

default, the operating system is installed to either the Windows or the Winnt folder.

The following stops may resolve this problem:

a) Copy the TEMP and TMP environment variables to a folder that is in the same drive

partition as the Windows system files. To do this, open a command prompt window and

type the following at the prompt:

Set TMP = C:\TEMP

Set TEMP = C:\TEMP

This will save the TEMP and TMP environment variables to a folder named Temp that

resides on the C: drive. The folder must exist prior to carrying out these steps. Once

these environment variables are set, the application should then install.

b) If the Autoexec.bat file contains the following line (or similar):

If exists c:\temp\*.tmp del c:\temp\*.tmp

this is to be commented out by placing REM in front of it.

c) Disable any antivirus software (or other memory resident programs) and try running Setup

again. Often the best way to accomplish this is to run Setup in Safe Mode. It may also be

necessary to copy all of the Setup files to a temporary folder on the hard drive disk and

run Setup.exe from there.

d) Left-over files from a failed Setup attempt can also cause this problem. If found, delete

the msftqws.pdw subfolder and its contents from the Temp folder. Also look for

Setup1.exe in the Windows or Winnt folder and any *.CAB files from previous installs, and

delete them. This should be done after each failed install.

e) Some logon scripts can cause this problem, so try to run Setup before logging on to the

network if the computer is connected to a network.

E1.5 Existence of out-of-date system files in the computer (on non-upgraded

operating systems)

If the operating system in the user’s machine is out of date, older versions of the system files

may cause problems during installation of the program and the installation process may fail.

The file that causes this problem is Oleaut32.dll. In this case, the same message, as given in

Section E1.3, appears repeatedly during each successive installation attempt even after

carrying out the modifications suggested in Sections E1.3 and E1.4.

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In order to solve this problem, the user has to install the latest Versions of system files in the

computer. Microsoft provides freely downloadable programs called ‘Service Packs’ for this

purpose. These are available in the Download Centre (or the Support Section) of the

Microsoft website (www.Microsoft.com). The user has to download the relevant Service

Pack and install it in his/her computer before installing the HWA program. The Service

Packs replace the older Versions of the system files by the latest (updated) ones, and add

additional components which were not previously available for proper functioning of the

system. It is expected that after successful installation of Service Packs and hence upgrading

of the operating system, the HWA program can be installed properly.

E1.6 The program icon is not created and the program is not listed under the

Program menu

During the last phase of installation of the HWA program, the Installation Wizard may issue a

message saying, An error occurred trying to create a program icon for “HWA”. This

message box displays Abort, Retry, and Ignore buttons. The Abort button terminates the

installation process, the Retry button does not help in resolving the problem, and repeats the

message after each click, while the Ignore button finishes the installation process, and the

message saying the HWA Setup was completed successfully appears. But, while searching for

the HWA Program in the Program list under the Start task bar item, the program may not be

found. This problem may be caused by some error in the required System files. In order to

find a solution for this problem, the user may locate the HWA.EXE application file in the

folder where the program was installed in the user’s hard-disk (usually, by default,

C:\Program Files\HWA). Double clicking the .Exe file in the My Computer pane opens the

HWA program and the program is then expected to work properly. The user may create a

Shortcut to the application file and place the shortcut on the Desktop for quick access to the

program.

E2 Graphical User Interface (GUI) concepts of HWA software

E2.1 Basic GUI components

In the Graphical User Interface (GUI) environment, the user interacts with the HWA Package

using the keyboard, the mouse, the windows, the menus, the tool bar buttons and the

command buttons. A window is usually a facility for entering input information, which is

surrounded by a border and moveable around the screen. The main application window in the

HWA Package is shown in Figure E.1.

As HWA is a Windows-based program, other Windows-based applications may also be

operated at the same time without necessarily closing the HWA program. The main window

of the HWA program can be minimised or maximised or used in its normal size, during

working with other Windows applications. The mouse enables the user to point at and to

select objects to work on, or to perform actions, by clicking the LH mouse button. The

keyboard is used for entering input information for running the HWA program, to move

between various objects, or to perform particular actions. Menus in the menu bar are used to

perform certain actions which may be accessed by clicking with the mouse or pressing the

relevant key on the keyboard. The buttons in the tool bar at the top of a window provide a

visual representation of and quick access to the intended tasks, which the buttons are meant to

http://www.microsoft.com/

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link. Whenever the mouse pointer is placed above a button in the tool bar, a short description

(ToolTip text), briefing the intended task to be performed by the button, is displayed. To

invoke an effect on a button or a menu with the keyboard keys, identical to that produced by

clicking a button or menu with a mouse pointer, the user has to hold down the ALT key and

press the key for the letter (i.e. character) shown underlined (i.e. underscored) in the caption

of the button or menu. The buttons captioned Continue or OK or Close in any window may

be invoked by pressing the Return key on the keyboard, while the buttons captioned Back or

Cancel may be activated by pressing the Esc (Escape) key. A message box – shown in the

window in Figure E.1 – is used to instruct, inform or warn the user as appropriate.

Figure E.1: Main application window of the HWA program showing a message-box

The HWA GUI uses three types of windows. These are:

Main application window

Data window

Dialog window

Some of the important features of these windows are now described.

Menu item

Toolbar

button


Close button

Maximize button

Minimize button

Top title Toolbar Menu bar

Message-box

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The main application window is the one shown in Figure E.1. It appears as soon as the user

starts running the program. This window is comprised of a Multiple Document Interface

(MDI) form which includes a menu, a toolbar, a “child” window area, and a status bar. The

title bar contains the title of the program as well as the maximise, minimise and close buttons.

All other windows required for entering data or displaying outputs reside within this MDI

window.

Data windows

Data windows are the windows containing either data-entry fields or displays of tabular and

graphical outputs. The data window in Figure E.2 contains information labels, six data-entry

boxes, three pairs of “radio” (i.e. option) buttons, one check box and three command buttons

which are to be used to enter input information for running the HWA program.

The data window in Figure E.3 contains information labels, a list-box showing event

numbers, a picture-box exhibiting the hydrograph of the flood event shown highlighted in the

list box, one grid with a vertical scroll bar providing the ordinate number, date, time and

discharge related to the displayed hydrograph in a tabular form, one pair of radio (option)

buttons, two check boxes, 18 command buttons and one frame shown disabled. In the case of

such a data-entry window, the cursor is automatically placed at the topmost data-entry field

when the data window first appears. The user can directly enter data by using the keyboard

and/or mouse. In order to specify data in other fields, the user navigates by using the (Up),

(Down), (Left), and (Right) buttons, by pressing the Tab button on the keyboard, or by

clicking the mouse after placing the cursor into that field where the data is to be entered.

Figure E.2: Data window for entering data

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Figure E.3: Data windows for displaying graphical and tabular outputs

Dialog window

Dialog windows are used in HWA to either request information from the user or provide

information to the user. Usually an ellipsis (…) after the caption of a menu or a button

indicates that invoking the intended action results in a dialog window. A dialog window is

also displayed when some command buttons, e.g. that captioned ‘Browse’, are clicked, or

when a data-entry field that requires a filename is double-clicked. Figure E.4 shows a dialog

window for specifying a filename for storing the results summary.

Figure E.4: A dialog window showing a standard windows file-opening dialog-box

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E2.2 Typical GUI features of the windows displaying hydrographs

In the case of a data-display window containing a hydrograph, different GUI components are

provided for effective display of relevant information. For illustration, some features of the

window displaying flood hydrographs are described below. These features are common to

other data-display windows as well.

i Displaying the hydrograph of an event from a list of selected events: In the

window displaying the observed flood hydrographs, event numbers of all selected

observed floods are provided in a list-box on the left hand side of the window. By

default, one item in the list, usually the first one, is shown highlighted by a blue shade,

and the corresponding hydrograph is displayed in a picture-box provided on the right

hand side of the list-box. The user may scroll through the list using the vertical scroll

bar provided alongside the list-box to choose any item. The list of events can also be

navigated using the (Up) and (Down) keys. When the user clicks on an event

number in the list box, that event number is highlighted and the existing hydrograph is

replaced by that corresponding to the highlighted event number.

ii Displaying hydrograph in different units: By default, time is displayed in hours on

the time-axis, i.e. the abscissa, of the hydrograph. However, given that the OPW data

files hold data in 15-minute time intervals, an option is provided to display time in 15-

minute intervals as well. A pair of radio (option) buttons, one captioned Hour and the

other captioned No. of 15 minute intervals (data interval in OPW data file) is provided

for this purpose. The user can view the hydrograph in either of the two time units by

clicking the respective radio button.

iii Showing data values in a grid: By default, the tabular values are not displayed.

However, a command button captioned Show tabular values of hydrograph is

provided at the bottom on the right hand side of the window. When this button is

pressed, a grid appears on the right hand side of the picture-box and the caption of the

button changes to Hide tabular values of hydrograph. The values related to the

displayed flood hydrograph are shown in that grid in tabular form, using rows and

columns. By default, one of the rows, usually the top one, is shown highlighted by a

yellow shade. When the user clicks on any other row, the highlighter moves to the

row thus clicked. The (Down) and (Up) keys on the keyboard can also be used to

move the highlighter from one row to the next, either downward or upward. The user

may scroll through rows using the vertical scroll bar provided alongside the grid.

iv Showing values on the hydrograph at any data point: When the user clicks on any

point inside the picture-box, an indicator appears at that point as a grey-coloured

vertical line. Note that for some graphical outputs in other windows, e.g. those

displaying derived flood hydrographs, an indicator having a light green colour instead

of grey, is displayed. The picture-box shown in Figure E.3 shows this line at the 62nd

hour, i.e. the 248th

time-step in the 15-minute interval, on the receding side of the

hydrograph. A label having a light yellow background simultaneously appears at the

top right of the window displaying relevant information for the time-step

corresponding to the clicked data point, and a check-box provided on the left hand

side of the label is shown checked. The user can hide the label containing the

information by unchecking the check-box. The user can place the indicator in the

picture-box by clicking at any point for which s/he wishes to see the value.

Alternatively, the ‘’ or the ‘’ keys may be pressed to move the indicator by one

178

time-step at a time, either to the left or to the right, in order to show the values at the

desired data point. If, as described in iii) above, the grid containing the values of the

hydrograph is exhibited, then the highlighter on this grid automatically moves to the

row containing the information related to the data-point, either clicked on the

hydrograph, or reached by pressing the ‘’ or the ‘’ arrow buttons on the keyboard.

When the user double-clicks on the picture-box, the indicator and the label disappears.

v Changing the background colour: If the user wishes to change the background

colour of the hydrograph, for example for the purpose of presentation and/or printing,

the command button BackGround Colour… needs to be clicked. The standard

Windows colour-palette displaying all colours, hues and shades, appears. The user

may choose any colour and press the OK button provided on the palette. The graph is

redrawn with the chosen colour on the background.

vi Copying a graph onto the clipboard: By pressing the command button Copy Graph,

a graph can be copied onto the clipboard. The Graph, thus copied, can then be pasted

in other Windows application programs such as MS-Word or MS-Excel.

vii Copying tabular values onto the clipboard: By pressing the command button Copy

table, the table can be copied onto the clipboard. The values, thus copied, can then be

pasted into other Windows application programs. In the case of MS-Excel, the copied

values are pasted in separate rows and columns; the user can thus carry out any further

analysis or displays using facilities of MS-Excel to augment those provided within the

HWA program.

viii Saving a graph in a picture file: The hydrograph displayed in the picture-box can be

saved as a picture file in bitmap format for later use, e.g. for preparing a report, or for

presentation. This is achieved by clicking the command button Save graph As… when

a standard Windows file-saving dialog box appears. The user can use the controls on

the dialog box, thus displayed, and specify a filename to save the hydrograph as a

bitmap in the chosen folder.

ix Printing a graph using a printer: The hydrograph displayed in the picture-box can

be printed using a printer connected to the user’s computer by clicking on the

command button Print graph…, when a standard Windows printing dialog box

appears. The user can select the desired settings before printing the hydrograph.

In addition to the above-mentioned GUI components, the data-display window showing the

hydrographs of the observed flood events supports other specific features. Some of these are

evident from diagrams presented in the main body of the volume (e.g. Figure 5.18).

E2.3 Options on start-up of the HWA program

When the user clicks the Continue button on the start-up window, a message box appears as

shown in Figure E.1. This message provides information about two options of entering input

information into the program.

Under the first option, the user may enter all relevant input information into data-entry fields

in a window by using keyboard and mouse. Each data-entry field is provided with an

appropriate label to indicate the specific type of data that the field is supposed to receive from

the user. This option is essentially required when the user applies the program to a gauged

station for the first time. In the data-entry window, a data-entry field is provided in which the

user can specify the name of a results summary file. The default filename extension of such a

179

file is *.sum. If no filename is specified, a default filename WP3_1Sys.sum is used to hold the

results summary of the Hydrograph Width Analysis each time the program is run.

The second option can be used only if the HWA program was run at least once before with

the data of the gauged station and the results summary had been saved in a user-specified file.

Under this option, the user has to specify the name of the previously-saved results-summary

file in a data-entry field. In order to do this, s/he can browse for the required file, either by

clicking on the Browse button, or by double-clicking the data-entry field. The resulting

window shows the list of directories and folders which can be searched for the required file,

as in any other Windows-based program. Once the desired file is located, the user can either

select the file by clicking on its name and press the OK button, or double-click on the

filename. The window containing the list of directories and folders automatically closes and

the filename appears in the data-entry field. When the user presses the Continue button,

relevant information is extracted by the program from the specified results summary file and

displayed in the data-entry window. Thus, the user is saved the effort of entering input

information each time the program is re-run with data of a particular station. Of, course, the

user can make changes and deletions in the data-entry fields after these are displayed in the

window, and then run the program with the changed or modified set of information. The

default system filename of WP3_1Sys.sum can be specified if the user wishes to resume the

previous analysis but had omitted to save this in a named file.

E2.4 Menu bar items

As highlighted in Figure E.1, the main application window of the HWA program contains

nine menu items on the menu bar. The menu and sub-menu captions provide a brief

indication of the intended tasks. Although a mouse can be used for pointing to and clicking

on a menu item, the keyboard keys can also be used for invoking a similar effect. In order to

do this, the user has to press the key for the letter (i.e. character) underlined in the caption of

the menu or sub-menu item when the user holds down the ALT key. Some initially disabled

menu bar items are later enabled. For example, the menu items Results summary and

Hydrographs of flood events are enabled once hydrographs of observed flood events have

been extracted by the program from the record of discharge data. Similarly, the Derived

hydrographs menu item is enabled once the derived semi-dimensionless flood hydrographs

are produced by the program. A brief description of the menu bar items is provided below.

‘File’ menu

This menu is activated by clicking File on the menu bar or by keying ALT+F. A list of sub-

menus appears having two enabled items (Set working directory and Open) and three disabled

items.

The sub-menu Set working directory facilitates setting of the working directory in the case

when the user wants to use data files from and store output files into a folder other than the

one in which the HWA Package is installed. When clicked, this menu item brings up a

standard dialog window, showing the list of drives, folders and files, which may be used to

nominate/select the working directory before running a program.

The Open sub-menu has two further sub-menus (Existing file… and New document) which

can be used for either opening an existing file or a new file in ASCII format and for carrying

out editing, printing and saving operations as required. The Save As…, Close and Print…

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sub-menus under the File menu are enabled once the user opens an existing file or a new

document.

‘Analysis options’ menu

This menu is activated by clicking Analysis options on the menu bar or by keying ALT+A.

Sub-menus Start from scratch and Use results file stored during an earlier run then appear.

By clicking the sub-menu Start from scratch, the user can enter relevant input information

into data-entry fields in a window by using the keyboard and mouse (see Section E2.2). The

sub-menu Use results file stored during an earlier run can only be used if the HWA program

was run at least once before, and the data and results summary saved in a user-specified file.

‘Results summary’ menu

This menu is activated by clicking Results summary on the menu bar or by keying ALT+R. It

is enabled after the HWA program extracts the hydrographs of observed flood events from the

record and displays these in a data window. When the user clicks on this menu, a data

window appears showing the summary of results in an ASCII formatted file. It may be noted

that the current version of the HWA program retains all options and procedures developed

and tested in the course of the hydrograph-width research. All outputs of the Hydrograph

Width Analysis are stored in the results summary file, which can be quite large.

‘Hydrographs of flood events’ menu

This menu is activated by clicking Hydrographs of flood events on the menu bar or by keying

ALT+G. It is enabled after the HWA program extracts the hydrographs of observed flood

events from the record and displays these in a data window. If a data window other than that

containing the observed flood hydrographs is shown active within the main application

window, a click on this menu activates and brings to the front the window containing the

flood hydrographs.

‘Derived hydrographs’ menu

This menu is activated by clicking Derived hydrographs on the menu bar or by keying

ALT+D. It is enabled after the HWA program successfully produces the derived median and

mean flood hydrographs as one of the outputs of the Hydrograph Width Analysis. If a data

window other than that containing the derived flood hydrographs is shown active within the

main application window, a click on this menu activates and brings to the front the window

containing the derived flood hydrographs.

‘Modified Gamma hydrographs’ menu

This menu is activated by either clicking Modified Gamma hydrographs on the menu bar or

by keying ALT+y. It is enabled after the HWA program successfully produces the modified

Gamma hydrographs as one of the outputs of the Hydrograph Width Analysis. If a data

window other than that containing the modified Gamma hydrographs is shown active within

the main application window, a click on this menu activates and brings to the front the

window containing the modified Gamma hydrographs.

181

‘Window’ menu

The ‘Window’ menu contains four sub-menus and a list of “child” windows which are open

within the main application window. It can be activated by clicking the menu title or by

keying ALT+W. The first sub-menu is New Window, which allows the user to open a new

document window for creating a new ASCII formatted file, if required. Any number of such

windows can be opened. The other sub-menu items are Cascade, Tile Horizontal and Tile

Vertical, which may be used to arrange a number of opened windows on the screen by any of

the three different styles as available in any standard Windows application. When one or

more child windows are kept opened during a run of HWA, a list (by title) of the windows

appears at the bottom of the Window menu. The user may bring up any of these child

windows by clicking the relevant title.

‘Help’ menu

This menu option is disabled in the current version of the HWA software program.

‘Exit’ menu

In order to close the session, the user can click Exit in the menu bar or key ALT+x. The user

is guided through the closure procedure.

E2.5 Toolbar buttons

As shown in Figure E.1, the main application window of the HWA program contains eleven

buttons on the toolbar. ToolTips provide a brief indication of the intended tasks and appear

when the mouse hovers on the relevant button. Some buttons are disabled during data entry

operations. The toolbar functions are summarised in Table E.1.

E2.6 Closing the HWA program

The expected options are provided to close the HWA program in a number of different ways.

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Table E.1: Details of toolbar buttons

(Letters in red show the relevant keyboard shortcuts when depressed with the ALT key.)

Icon ToolTip text

Menu or sub-

menu item

performing the

task

Status

Set working

directory

File: Set working

directory Enabled throughout.

Open new

document

File: Open:

Existing file… Enabled throughout.

Open existing file

File: Open: New

document Enabled throughout.

Start analysing

from scratch

Analysis options:

Start from scratch

Enabled at the beginning. Disabled when the

option of analysing by entering data on the

screen is chosen by clicking this button.

Enabled again when this option of analysing

is closed.

Use results file

stored during an

earlier run

Use results file

stored during an

earlier run

Enabled at the beginning. Disabled when the

option of analysing by reading data from a

pre-saved results summary file is chosen by

clicking this button. Enabled again when this

option of analysing is closed.

Results summary Results summary

Becomes enabled once hydrographs of

observed flood events are extracted and

displayed.

Hydrographs of

flood events

Hydrographs of

flood events

Becomes enabled once hydrographs of

observed flood events are extracted and

displayed.

Derived

hydrographs

Derived

hydrographs

Becomes enabled once semi-dimensionless

derived hydrographs are produced and

displayed.

Modified Gamma

hydrographs

Modified Gamma

hydrographs

Disabled at the beginning. Becomes enabled

after semi-dimensionless modified Gamma

hydrographs are produced and displayed.

Help Help Disabled throughout in the current version of

the HWA software.

Exit Exit Enabled throughout.

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Appendix F Further details of IBIDEM

F1 Method of optimising Tp

Optimising Tp involves minimising the objective function:

Σ[WFSU(i) - WFSR(i)]2 for i = 1 to m.

With only one variable to adjust, the minimisation is straightforward. IBIDEM adopts a

simple approach based on the method of bisection.

The starting point for the search is an initial guess for Tp. This is set as the time elapsing

from the first ordinate of the input FSU hydrograph to its peak value. It is not necessary to

start with a particularly good guess. The search range is then set as follows:

Minimum = 0.001 hours

Maximum = 10 times initial guess

This range of extreme values is likely to far exceed the realistic range in which the best

parameter value lies. However, with automated calculations, there is little penalty in adopting

such a wide range as a precautionary measure.

At each iteration, IBIDEM considers five trial values of Tp denoted by Tp[1], Tp[2], Tp[3],

Tp[4] and Tp[5]. For the first iteration, the five trial values are:

Tp[1] = 0.001 i.e. the minimum value which will be considered

Tp[2] = (Tp[1] + Tp[3]) /2 i.e. half way between Tp[1] and Tp[3]

Tp[3] = initial guess


Tp[5] = 10 x initial guess i.e. the maximum which will be considered

Each of the five trial values of Tp is used to create an FSR hydrograph shape. The value,

Tp[n], that gives the best fit (i.e. the smallest value of the objective function) is used as the

central value for Tp in the next iteration. Trial values for Tp are reassigned as follows:

Tp[1] = Tp[n-1] i.e. updates lower bound of range in which optimum lies


Tp[3] = Tp[n] i.e. best value from previous iteration


Tp[5] = Tp[n+1] i.e. updates upper bound of range in which optimum lies

The iterative procedure continues until the range within which the optimum value is known to

lie becomes acceptably small. The criterion used is Tp[5] - Tp[1] < 0.01 hours. At that point,

the value giving the best fit is adopted as the optimum value of Tp.

Consider, as an example, the case where the ultimate best-fitting value is Tp = 3.0 hours and

the initial guess is Tp = 5.0 hours. Table F.1 shows the trial values used in the first five

184

iterations. The best-fitting trial value of Tp (shown in red) is adopted as the central value

Tp[3] in the next iteration.

Table F.1: Example of iteration to find best-fitting value of Tp

Iteration First Second Third Fourth Fifth

Tp[1] 0.001 0.001 1.25 2.50 2.81

Tp[2] 2.50 1.25 1.87 2.81 2.96

Tp[3] 5.00 2.50 2.50 3.12 3.12

Tp[4] 27.5 3.75 3.12 3.43 3.27

Tp[5] 50.0 5.00 3.75 3.75 3.43

It is seen that, after five iterations, the Tp value (2.96 hours) is already close to the ultimate

best-fitting value of 3.0 hours.

F2 Method of fitting SPR

Having determined Tp so as to fit the characteristic hydrograph as closely as possible,

IBIDEM calculates SPR by matching the peak of the FSR response hydrograph, qpeak, to the

required response peak from the FSU hydrograph, qFSU

peak, which is found by subtracting BF

from the peak FSU flow.

The calculation of SPR follows from the fact that the response hydrograph is directly

proportional to the percentage runoff, PR. In the general case of a part-urbanised catchment,

PR = PRrural (1.0 – 0.47 URBEXT) + 70 (0.47 URBEXT) F.1

This applies the FSSR16 urban adjustment, but using the FSU index URBEXT rather than the

FSR index URBAN. See Step 9 of Section 9.2.

Simplifying Equation F.1 gives:

PR = PRrural (1 – 0.47 URBEXT) + 32.9 URBEXT F.2

The term PRrural is composed of three parts:

PRrural = SPR + DPRCWI + DPRRAIN F.3

Here, SPR is standard percentage runoff, DPRCWI is dynamic percentage runoff attributable to

catchment wetness and DPRRAIN is dynamic percentage runoff attributable to event rainfall.

The latter two quantities depend solely on catchment descriptors (SAAR, which controls

CWI) and the design rainfall depth, which is a function of storm duration, which can be

determined from Tp.

It is possible to calculate the response hydrograph peak qpeak without carrying out a full

convolution (see Houghton-Carr, 1999), by using the “short-cut” method described in FSSR9

(IH, 1979):

qpeak = RC.(PR/100).(P/D).AREA F.4

185

where:

RC is a routing coefficient which depends on D/Tp (a function of SAAR);

P is the depth of the design storm (after application of ARF);

D is the duration of the design storm.

FSSR9 presents a graph showing how RC varies with D/Tp based on the 75% winter rainfall

profile. A similar graph is presented by Houghton-Carr (1999), which includes a line

corresponding to the 50% summer rainfall profile.

Based on Equations F.2 to F.4, IBIDEM calculates the value of SPR that yields the required

qpeak. It is found from:

RAINCWI

peak

DPR - DPR URBEXT0.47 - 1

URBEXT32.9 - RC.AREA.P

100.D.q

SPR F.5

IBIDEM evaluates RC from a digitised version of the graph in Figure 3.10 of Houghton-Carr

(1999), with the y axis quantities divided by 10 to correct a mistake in the FEH. The fact that

RC is found graphically introduces a slight uncertainty to the calculation of SPR, but this has

been found to be small.

F3 Checks and validation of outputs

IBIDEM checks the outputs and provides error, warning or information messages when

necessary. A list of the checks made is in Table F.2.

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Table F.2: Checks and outputs

Criterion Status Comment Notes

SPR ≤ 0 Error Inferred SPR is

not positive

This could happen, for example, when the peak of

the input hydrograph is unrealistically low and the

catchment is urbanised. After the urban

component of the PR is calculated by IBIDEM, it

is sometimes found necessary to use a negative

SPR in order to match the input peak flow. A

typical cause will be that the imported FSU peak

flow is too low, e.g. due to a failure to incorporate

an adequate urban adjustment in QMED.

Alternatively, the catchment may not be well

represented by the structure of the FSR rainfall-

runoff model or by the composition of the design

event used as the input to the model.

0<SPR≤10 Warning Inferred SPR is

unusually low

This may be valid if the catchment is highly

permeable. But it could otherwise be caused by the

problems mentioned above, e.g. an unrealistically

low input peak flow.

10<SPR≤25 Information

Inferred SPR

implies a notably

permeable

catchment

50<SPR≤60 Information

Inferred SPR

implies a notably

impermeable

catchment

60<SPR≤100 Warning Inferred SPR is

unusually high

This may be valid if the catchment is extremely

impermeable. But it could otherwise be caused by

an unrealistically high imported peak flow.

SPR>100 Error Inferred SPR is

more than 100%

This could happen when the peak of the input

hydrograph is unrealistically high given the nature

and size of the catchment.

Tp≤0 Error Inferred Tp is not

positive

This cannot happen, given the procedure used to

determine Tp. However, the check is still made.

PR ≤ 0 Error Inferred PR is

not positive

This should not happen. PR is back-calculated

using Equation F.4, which should not yield a

negative result as all the other variables in the

equation can only take positive values.

75<PR≤100 Warning Inferred PR is

unusually high

PR>100 Error Inferred PR is

more than 100% This would typically happen only if SPR>100.

Flood Studies Update Technical Research Report Volume III … Research... · 2014-07-16 ·...

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Transcript of Flood Studies Update Technical Research Report Volume III … Research... · 2014-07-16 ·...