Stochastic Runoff Routing Model
Parameter for Design Flood
Estimation using Joint Probability
Approach
Mr. Hitesh D. Patel
Student ID: 16095380
M. Eng. (Hons) Thesis
School of Engineering
University of Western Sydney
November 2010
Principal Supervisor: Dr. Ataur Rahman
Associate Supervisor: A/Prof Chin Leo
DECLARATION
I hereby declare that the work presented in this thesis is solely my own work and that to
the best of my knowledge is original except where otherwise indicated. The material
submitted for this thesis as a whole has not been submitted for a degree in this or any
other university.
Mr. Hitesh Patel
i
ACKNOWLEDGEMENTS
I hereby take this opportunity to thank my supervisor, Dr. Ataur Rahman for giving me
the opportunity to conduct research on my selected topic under his supervision, for his
availability and direction on how to successfully carry out my research and also for
providing me all the help to solve difficulties, moral support and many valuable
suggestions. Without his guidance this would not have been possible. I also acknowledge
the support of my associate supervisor A/Prof Chin Leo.
ii
TABLE OF CONTENTS
ABSTRACT...................................................................................................................... xi
CHAPTER 1 INTRODUCTION ..................................................................................... 1
1.1
BACKGROUND TO THE RESEARCH ........................................................... 1
1.2
OBJECTIVES ..................................................................................................... 6
1.3
OVERVIEW OF THE THESIS.......................................................................... 7
CHAPTER 2 REVIEW OF JOINT PROBABILITY APPROACH TO DESIGN
FLOOD ESTIMATION ................................................................................................. 11
2.1
GENERAL........................................................................................................ 11
2.2
VARIOUS DESIGN FLOOD ESTIMATION TECHNIQUES ....................... 11
2.3
STREAMFLOW BASED METHODS............................................................. 12
2.3.1 Flood Frequency Analysis ............................................................................ 13
2.3.2 Empirical Methods........................................................................................ 14
2.4
RAINFALL EVENT BASED METHODS ...................................................... 14
2.4.1 Design Event Approach ................................................................................ 16
2.4.2 Joint Probability Approach (JPA)................................................................. 21
2.5
DESCRIPTION OF THE JOINT PROBABILITY APPROACH.................... 22
2.5.1 Analytical Methods....................................................................................... 23
2.5.1.1 Methods based on Eagleson’s kinematic runoff model ........................ 23
2.5.1.2 Methods based on geomorphologic unit hydrograph............................ 25
2.5.1.3 Methods based on U. S. Soil Conservation Service’s curve number
procedure............................................................................................................... 28
2.5.1.4 Methods based on other types of rainfall-runoff models ...................... 29
2.5.2 Approximate Methods .................................................................................. 32
2.5.2.1 Discrete methods................................................................................... 32
2.5.2.2 Simulation techniques........................................................................... 34
2.6
STATISTICAL BASIS OF JOINT PROBABILITY APPROACH................. 37
2.6.1 Probability of union ...................................................................................... 37
2.6.2 Conditional probability and joint probability ............................................... 38
2.6.3 Independence of two events.......................................................................... 39
2.6.4 Total Probability Theorem............................................................................ 40
2.6.5 Joint Probability Distributions ...................................................................... 42
2.7
RECENT RESEARCH ON THE JOINT PROBABILITY APPROACH TO
DESIGN FLOOD ESTIMATION ................................................................................ 45
2.8
SUMMARY...................................................................................................... 50
CHAPTER 3 METHODOLOGY.................................................................................. 51
3.1
GENERAL........................................................................................................ 51
iii
3.2
HYDROLOGIC MODELLING FRAMEWORK ............................................ 51
3.2.1 Runoff Production Function - Loss Model ................................................... 52
3.2.2 Transfer Function - Runoff Routing Model.................................................. 52
3.2.2.1 RORB Model Principles ....................................................................... 54
3.2.3 Input Variables in the Monte Carlo Simulation............................................ 57
3.2.4 Stochastic Modelling Framework in the Monte Carlo Simulation ............... 58
3.3
DISTRIBUTION OF KEY MODEL INPUT VARIABLES IN MONTE
CARLO SIMULATION ............................................................................................... 61
3.3.1 Rainfall Event Definition.............................................................................. 61
3.3.2 Complete Storm ............................................................................................ 62
3.3.3 Storm-core..................................................................................................... 64
3.4
DISTRIBUTION OF FLOOD-PRODUCING VARIABLES .......................... 65
3.4.1 Duration ........................................................................................................ 66
3.4.2 Storm-Core Rainfall Intensity....................................................................... 67
3.4.2.1 Development of Storm-Core IFD Curves ............................................. 68
3.4.2.2 Preparation of IFD Table ...................................................................... 70
3.4.3 Storm-Core Rainfall Temporal Pattern......................................................... 72
3.4.4 Initial loss...................................................................................................... 73
3.4.5 Runoff routing model parameter k................................................................ 76
3.5
SIMULATION TECHNIQUE.......................................................................... 77
3.5.1 Number of runoff events generated .............................................................. 78
3.5.2 Steps in Simulation ....................................................................................... 79
3.6
SIMULATION OF DERIVED FLOOD FREQUENCY CURVES................. 83
CHAPTER 4 DESCRIPTION OF STUDY CATCHMENTS .................................... 85
4.1
STUDY CATCHMENTS ................................................................................. 86
4.1.1 Selection criteria for study catchments ......................................................... 86
4.2
DESCRIPTION OF SELECTED STUDY CATCHMENTS ........................... 90
CHAPTER 5 RORB MODEL FORMULATION AND IMPACT OF MODEL
PARAMETER ON DESIGN FLOOD ESTIMATES.................................................. 96
5.1
GENERAL........................................................................................................ 96
5.2
STEPS FOR RORB MODEL DEVELOPMENT............................................. 97
5.3
DATA AND STUDY CATCHMENT.............................................................. 98
5.3.1 Selection of storm events ............................................................................ 100
5.4
RESULTS ....................................................................................................... 101
5.4.1 FIT Runs ..................................................................................................... 101
5.4.2 TEST run..................................................................................................... 106
5.4.3 Sensitivity analysis...................................................................................... 108
5.5
SUMMARY.................................................................................................... 115
iv
CHAPTER 6 RESULTS FROM MONTE-CARLO SIMULATION USING
STOCHASTIC RUNOFF ROUTING MODEL PARAMETER.............................. 116
6.1
STORM ANALYSIS ...................................................................................... 116
6.1.1 Distribution of storm-core durations Dc...................................................... 118
6.1.2 Storm-Core Rainfall Intensity (Ic)............................................................... 120
6.1.3 Storm-Core Temporal Patterns (TPc).......................................................... 123
6.2
LOSS ANALYSIS .......................................................................................... 124
6.3
MODEL CALIBRATION (k, IL, CL)............................................................ 127
6.4
DERIVED FLOOD FREQUENCY CURVE ................................................. 131
6.5
COMPARISON OF DERIVED FLOOD FREQUENCY CURVES WITH
RESULTS OF AT-SITE FLOOD FREQUENCY ANALYSES................................ 133
6.6
COMPARISON OF EXISTING MONTE CARLO SIMULATION
TECHNIQUE WITH UPDATED MONTE CARLO SIMULATION TECHNIQUE143
CHAPTER 7 SUMMARY AND CONCLUSION...................................................... 150
7.1
SUMMARY.................................................................................................... 150
7.2
CONCLUSIONS............................................................................................. 152
7.3
RECOMMENDATIONS FOR FURTHER STUDY...................................... 153
REFERENCES.............................................................................................................. 155
APPENDICES ............................................................................................................... 166
APPENDIX A Output plots for FIT runs (RORB Model)........................................ 166
APPENDIX B Flood Frequency Analysis Result for the Coopers Creek catchment
......................................................................................................................................... 176
APPENDIX C Design run results (RORB model) for the Coopers Creek catchment
......................................................................................................................................... 180
APPENDIX D Distribution of storm-core durations................................................. 189
APPENDIX E Intensity-Frequency-Duration (IFD) tables and Plot ....................... 190
APPENDIX F Storm-core temporal pattern.............................................................. 194
APPENDIX G Distribution of initial loss ................................................................... 196
APPENDIX H Plot of Fitting Results (One Storage model) ..................................... 198
APPENDIX I List Publications from This Research................................................. 205
v
LIST OF FIGURES
Figure 2.1: Various design flood estimation techniques................................................... 12
Figure 2.2: Flood estimation by Design Event Approach (Rahman et al., 2001)............. 19
Figure 2.3: Attributes of Design Event Approach (Beran, 1973) ..................................... 20
Figure 3.1: Overall RORB Runoff Routing Model (Laurenson et al., 2007) ................... 55
Figure 3.2: Monte Carlo Simulation to determine derived flood frequency curve........... 61
Figure 3.3: Rainfall events: complete storms and storm-cores......................................... 64
Figure 3.4: Identification of a storm-core ......................................................................... 65
Figure 3.5: Histogram of storm-core durations (Dc) at Cooper’s creek (Pluviograph ID
58072, NSW) .................................................................................................................... 66
Figure 3.6: Storm-core IFD curves at pluviograph station 58072, Catchment: Cooper’s
Creek, NSW ...................................................................................................................... 71
Figure 3.7: Initial loss for complete storm (ILs) and initial loss for storm-core (ILc)....... 74
Figure 3.8: Schematic diagram of the Updated Monte Carlo Simulation Technique.
Shaded boxes represent stochastic variables..................................................................... 81
Figure 4.1: Location of the selected catchments............................................................... 89
Figure 4.2: Wadbilliga catchment with stream gauge and pluviograph station................ 91
Figure 4.3: Corang River catchment with stream gauge and pluviograph station............ 92
Figure 4.4: Coopers Creek catchment with stream gauge and pluviograph station.......... 93
Figure 4.5: Horton and Moonan Brook catchment with stream-gauge and pluviograph
station................................................................................................................................ 95
Figure 5.1: Catchment boundaries, subareas and channel ................................................ 99
Figure 5.2: Baseflow separations for storm 1981-X1..................................................... 101
Figure 5.3: Example of excellent fit result for 1984-X1 storm....................................... 103
Figure 5.4: Example of reasonable fit result for 1984-X2 storm.................................... 103
Figure 5.5: Example of poor fit result for a storm 1977-X2........................................... 103
Figure 5.6: Frequency distribution of all kc values ......................................................... 105
Figure 5.7: Error (%) in peak flow for the test runs....................................................... 107
Figure 5.8: Approach used to check the sensitivity of model parameters on peak
discharge ......................................................................................................................... 109
vi
Figure 5.9: Comparison of peakflow for various simulations ........................................ 111
Figure 5.10: Comparison of at-site flood frequency analysis (FFA), observed annual
maximum floods and simulation runs with various kc in design run .............................. 114
Figure 6.1: Distribution of storm-core duration (Dc) for Horton River Catchment
(pluviograph station 54138)............................................................................................ 119
Figure 6.2: Distribution of storm-core duration (Dc) for Moonan Brook Catchment
(Pluviograph station 61335)............................................................................................ 119
Figure 6.3: IFD curve for Pluviograph Station 54138 .................................................... 121
Figure 6.4: IFD curve for Pluviograph Station 69049 .................................................... 122
Figure 6.5: Sample observed storm-core temporal patterns for durations greater than 12
hours for Horton River catchment (Pluviograph Station 54138).................................... 123
Figure 6.6: Sample observed storm-core temporal pattern for durations less than 12 hours
for Horton River catchment (Pluviograph Station 54138).............................................. 124
Figure 6.7: Probability Distribution of Initial Loss (ILs) for the Horton River Catchment
......................................................................................................................................... 126
Figure 6.8: Probability Distribution of Initial Loss (ILc) for the Horton River Catchment
......................................................................................................................................... 127
Figure 6.9: Fitting result of Event 2 for Horton River (Qobs is observed hydrograph and
Qcom is computed hydrograph)........................................................................................ 130
Figure 6.10: Fitting result of Event 2 for Coopers Creek catchment (Qobs is observed
hydrograph and Qcom is computed hydrograph) ............................................................. 130
Figure 6.11: Derived flood frequency curve using average k value from calibration run
for Horton River catchment............................................................................................ 133
Figure 6.12: Comparison of DFFC (partial series) and results of at-site FFA for Horton
River catchment.............................................................................................................. 135
Figure 6.13: Comparison of DFFC (partial series) and results of at-site FFA for Coopers
Creek catchment ............................................................................................................. 136
Figure 6.14: Comparison of DFFC (partial series) and results of at-site FFA for
Wadbilliga catchment..................................................................................................... 139
Figure 6.15: Comparison of DFFC (partial series) and results of at-site FFA for Corang
river catchment ............................................................................................................... 140
vii
Figure 6.16: Comparison of DFFC (partial series) and results of at-site FFA for Moonan
brook catchment ............................................................................................................. 141
Figure 6.17: Comparison of simulation runs for all the study catchments ..................... 143
Figure 6.18: Comparison of Old MCST and Updated MCST for Horton River Catchment
......................................................................................................................................... 146
Figure 6.19: Comparison of Old MCST and Updated MCST for Coopers Creek
Catchment ....................................................................................................................... 146
Figure 6.20: Comparison of Old MCST and Updated MCST for Wadbilliga Catchment
......................................................................................................................................... 147
Figure 6.21: Comparison of Old MCST and Updated MCST for Corang River Catchment
......................................................................................................................................... 147
Figure 6.22: Comparison of Old MCST and Updated MCST for Moonan brook
Catchment ....................................................................................................................... 148
Figure 6.23: Comparison of absolute median relative errors of old MCST and updated
MCST for all study catchments considering ARIs of 2 to 100 years ............................. 149
viii
LIST OF TABLES
Table 3.1: An example of class intervals and representative points for storm-core duration
(Dc) for developing IFD curves ........................................................................................ 69
Table 3.2: An example of IFD table used in data generation (pluviograph station 58072,
Catchment: Cooper’s Creek, NSW). Intensities are in mm/h........................................... 71
Table 4.1: Selected catchments and nearby pluviograph station details........................... 89
Table 5.1: Catchment sub-areas and reach lengths........................................................... 99
Table 5.2: Results of the FIT run for selected events ..................................................... 104
Table 5.3: Some important summary statistics of the kc values based on 40 storm events
......................................................................................................................................... 106
Table 5.4: Impacts of various combinations of model parameters on peak flow estimates
......................................................................................................................................... 107
Table 5.5: The percentage differences in peakflows for selected ARIs obtained from
variety of design simulation runs and at-site flood frequency estimates ........................ 110
Table 5.6: Simulation results with variable kc and fixed IL and CL values ................... 113
Table 6.1: Parameters file a54138.psa for rainfall analysis (for Station 54138) ............ 117
Table 6.2: Important output files from program mcsa5.for (for Station 54138)............. 117
Table 6.3: Statistics of storm-core duration (Dc) for all stations .................................... 118
Table 6.4: IFD table for pluviograph station 54138 (rainfall intensities are mm/hr) ..... 121
Table 6.5: IFD table for Pluviograph Station 69049(rainfall intensities are mm/hr)...... 122
Table 6.6: Parameter file ‘b418027.lan’ for Loss Analysis............................................ 126
Table 6.7: Statistics of Initial loss for complete storm (ILs) for all stations ................... 126
Table 6.8: Statistics of Initial loss for storm-core (ILc) for all stations .......................... 127
Table 6.9: Parameter file ‘hocal1.dat’ for runoff routing model calibration.................. 129
Table 6.10: Typical values of parameters from calibration run for all the study catchments
......................................................................................................................................... 129
Table 6.11: Parameter file ‘hocal1.dat’ for model calibration ....................................... 132
Table 6.12: The percentage difference between DFFC and observed floods for Horton
River catchment .............................................................................................................. 135
ix
Table 6.13: The percentage difference between DFFC and observed floods for Cooper’s
creek catchment .............................................................................................................. 136
Table 6.14: The percentage difference between DFFC and observed floods for Wadbilliga
catchment ........................................................................................................................ 139
Table 6.15: The percentage difference between DFFC and observed floods for Corang
river catchment................................................................................................................ 140
Table 6.16: The percentage difference between DFFC and observed floods for Corang
river catchment................................................................................................................ 141
Table 6.17: Absolute median relative error for all simulation run for the study
catchments considering ARIs 1, 2, 5, 10, 20, 50 and 100 years. ................................... 142
Table 6.18: DFFC for Coopers Creek catchment using old MCST and updated MCST 145
x
ABSTRACT
The Design Event Approach is currently recommended rainfall-based flood estimation
method in Australia according to Australian Rainfall and Runoff. However, Design Event
Approach does not account for the probabilistic nature of the key flood producing
variables except for the rainfall depth. This arbitrary treatment of key inputs and model
parameters in Design Event Approach can lead to inconsistencies and significant bias in
flood estimates for a given average recurrence interval. A significant improvement in
design flood estimates can be achieved through a Joint Probability Approach, which is
more holistic in nature that uses probability-distributed input variables/model parameters
and their correlations to obtain probability-distributed flood output. More recently, there
have been notable researches in Australia on Monte Carlo Simulation Technique for
flood estimation based on the principles of Joint Probability that can employ many of the
commonly adopted flood estimation models and design data in Australia. The previous
studies in Australia on Joint Probability Approach/Monte Carlo Simulation Technique
have considered rainfall duration, rainfall intensity, rainfall temporal pattern and initial
loss as random variables in the simulation but the probabilistic nature of runoff routing
model storage delay parameter k has been disregarded, which in many circumstances is
likely to cause under- or over-estimation of design flood peaks. Application of Monte
Carlo Simulation Technique with RORB model, the most widely used hydrologic model
in Australia, has not been well investigated. At present, the RORB model has a limited
capability in terms of implementation of the Monte Carlo Simulation Technique in flood
xi
modeling. In the current RORB modeling, storage delay parameter kc is considered to be
a fixed input.
In this study, the applicability of the Monte Carlo Simulation Technique with RORB
model has been investigated using a large number of selected storm and runoff events
from Lismore catchment in New South Wales. It has been found that the value of kc
exhibits a high degree of variability from event to event, and use of different possible
representative values of kc results in quite different design flood peak estimates and hence
it should be considered as a stochastic variable in modeling under the framework of the
Monte Carlo Simulation Technique.
In this study, the previously developed Monte Carlo Simulation Technique in Australia
(old Monte Carlo Simulation Technique) has been upgraded by incorporating runoff
routing model storage delay parameter (k) as a stochastic variable. The updated Monte
Carlo Simulation Technique has been tested on five catchments in New South Wales. The
derived flood frequency curves from the new Monte Carlo Simulation Technique have
been compared with at-site flood frequency estimates and the old Monte Carlo
Simulation Technique. It has been found that the new Monte Carlo Simulation Technique
provides more accurate design flood estimates as compared to the old Monte Carlo
Simulation Technique.
xii
Chapter 1: Introduction
CHAPTER 1
INTRODUCTION
1.1
BACKGROUND TO THE RESEARCH
Amongst various natural disasters on earth, flood contributes one of the top ones in terms
of economic damage. With Victorian floods in September 2010, Queensland floods in
February 2009 and January 2008, New South Wales East Coast floods in June 2007, it
seems like damaging floods have been in the news very frequent over the last few years.
Each year floods cause millions of dollars of damage across Australia. Annual spending
on infrastructure requiring flood estimation in Australia is about $1 billion. The average
annual cost of flood damage in Australia is estimated to be about $400 million
(MRSTLG, 1999). Due to global climate change (resulting from greenhouse effects), the
severity and frequency of floods and associated damage are expected to increase
significantly in the near future in Australia (similar to other parts of the world) (CSIRO,
2001, Muzik, 2002). Estimation of peak streamflow of a given average recurrence
interval (ARI) (called design flood or flood quantile) is required in many different types
of hydrological and environmental studies. Due to its large economical and
environmental relevance, estimation of design flood remains a subject of great
importance and interest in flood hydrology.
1
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
There are various methods for design flood estimation including streamflow based
methods and rainfall-based methods. To estimate the complete design flood hydrograph,
rainfall-based methods such as runoff routing model and unit hydrograph are generally
adopted. In Australia, runoff routing model is more popular which uses the Design Event
Approach (I. E. Aust., 1987) with industry-based runoff routing models such as RORB
(Laurenson et al., 2007) and URBS (Carroll, 2007).
The Design Event Approach uses a probability-distributed rainfall depth with
representative values of other input variables such as rainfall temporal pattern and initial
loss and assumes that the resulting flood has the same frequency as the input rainfall
depth. The key assumption involved in this approach is that the representative design
values of the input variables/model parameters at different steps can be defined in such a
way that they are “annual exceedance probability (AEP) neutral” i.e. they result in a flood
output that has the same AEP as the rainfall depth input. The success of this approach is
crucially dependent on how well this assumption is satisfied. There are no definite
guidelines on how to select the appropriate values of the input variables/model
parameters that are likely to convert a rainfall depth of a particular AEP to the design
flood of the same AEP. There are many methods to determine an input value, the choice
of which is largely dependent on various assumptions and preferences of the individual
designer.
2
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
Due to non-linearity of the transformation in the rainfall-runoff process, it is generally not
possible to know a priori how a representative value for an input should be selected to
preserve the AEP of the rainfall depth input for flood output. In summary, the current
Design Event Approach considers the probabilistic nature of rainfall depth but ignores the
probabilistic behaviour of other input variables/model parameters such as rainfall
duration and losses. The assumption regarding the probability of the flood output i.e. that
a particular AEP rainfall depth will produce a flood of the same AEP is unreasonable in
many cases. The arbitrary treatment of the various flood producing variables, as done in
the current Design Event Approach, is likely to lead to inconsistencies and significant
bias in flood estimates for a given AEP. This results in either over-design or under-design
of flood structures both of which have important economic consequences.
A significant improvement in design flood estimates can be achieved through rigorous
treatment of the probabilistic aspects of the major input variables/model parameters in the
rainfall-runoff models. This can be done through a Joint Probability Approach, which is
more holistic in nature that uses probability-distributed input variables/model parameters
and their correlation structure to obtain probability-distributed flood output.
While Australian Rainfall and Runoff (ARR) (I. E. Aust., 1987) recommended the
Design Event Approach to rainfall-based design flood estimation, it recognised the
importance of considering the probabilistic nature of the flood- producing input variables.
It thus recommended further investigation into the Joint Probability Approach. Hill and
3
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
Mein (1996) in their study of incompatibilities between storm temporal patterns and
losses for design flood estimation, mentioned, “A holistic approach will perhaps produce
the next significant improvement in design flood estimation procedures”. They found the
error in design flood estimates as high as 40% in some Victorian catchments due to
inconsistencies in design loss and temporal patterns values alone. The Joint Probability
Approach is superior to the currently adopted Design Event Approach because the former
can account for the probabilistic nature of the flood producing variables and their
interactions in an explicit manner and eliminates the subjectivity in selecting the
representative value of a flood producing variables that show a wide variability such as
initial loss.
Rahman et al. (1998) summarised the previous researches (e.g. Eagleson, 1972; Beran,
1973; Russell et al., 1979; Diaz-Granados et al., 1984; Sivapalan et al., 1990) on the Joint
Probability Approaches to flood estimation and found that most of the previous
applications were limited to theoretical studies; mathematical complexity, difficulties in
parameter estimation and limited flexibility generally preclude the application of these
techniques to practical situations. Rahman et al. (2002a) developed a Monte Carlo
simulation technique (MCST) for flood estimation based on the principles of joint
probability that can employ many of the commonly adopted flood estimation models and
design data in Australia. The new technique has enough flexibility for its adoption in
practical situations and has the potential to provide more precise design flood estimates
than the existing Design Event Approach.
4
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
So far, the Joint Probability Approach has been developed and applied for small gauged
catchments (Rahman et al., 2002a, b; Rahman and Carroll, 2004). The Joint Probability
Approach has been tested with industry-based flood estimation model URBS (Rahman et
al., 2002c). Application of the approach to ungauged catchments has been investigated
(e.g. Rahman and Kader 2004). Application of the approach to extreme flood range has
been tested by Nathan and Weinmann (2004). The approach has been tested for larger
catchments with URBS model (e.g. Charalambous et al., 2005).
Kuczera et al. (2006) compared the Joint Probability Approach and design storm in the
case study involving detention basin, which showed that unacceptably large bias can arise
from misspecification of initial conditions in volume sensitive systems. Aronica and
Candela (2007) derived frequency distributions of peak flow by Monte Carlo simulation
procedure using a simple semi-distributed stochastic rainfall-runoff model.
Muncaster and Bishop (2009) investigated the design flood estimates produced by Monte
Carlo framework contained in RORB model for three urban catchments in Victoria and
concluded that the practical applications of RORB Monte Carlo framework aids the
understanding of this approach and identified the need of transition from current Design
Event Approach to more robust Joint Probability based approaches.
5
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
There have been quite a good number of researches on the Joint Probability Approach to
design flood estimation as noted above. The researches by Rahman et al. (2002a, b, c),
Charalambous et al. (2003, 2005) and Rahman and Carroll (2004) have demonstrated
significant promise with the Joint Probability Approach, however, in these studies the
probabilistic nature of the runoff routing model storage delay parameter k has been
disregarded, which in many circumstances is likely to cause under- or over-estimation of
design flood peaks. Hence, the proposed research aims to improve the Joint Probability
Approach/ Monte Carlo Simulation Technique by incorporating k as a random variable.
1.2
OBJECTIVES
The objectives of this thesis are:

To conduct a literature review on rainfall-based design flood estimation techniques
with a particular emphasis on the Joint Probability Approach/ Monte Carlo
Simulation Technique.

To examine the probabilistic nature of the model parameter kc (storage delay
parameter) of the RORB model and its impacts on design flood estimates.
6
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction

To upgrade the previously developed Monte Carlo Simulation Technique in Australia
by incorporating the runoff routing model parameter k (storage delay parameter) as a
random variable.

To compare the performances of the upgraded Monte Carlo Simulation Technique
(which considers k as a random variable) with at-site flood frequency estimates and
old Monte Carlo Simulation Technique (which considers k as a fixed input) for a set
of selected catchments in New South Wales.
1.3
OVERVIEW OF THE THESIS
This thesis consists of seven chapters as outlined below.
The introductory Chapter 1 provides a background of the study. This highlights the
importance of flood research and points out key limitations of the currently recommended
rainfall based design flood estimation method in Australia known as Design Event
Approach. This briefly presents the advantages of the Joint Probability Approach/Monte
Carlo Simulation Technique over the Design Event Approach. This also provides a brief
review of the key researches on the Joint Probability Approach/Monte Carlo Simulation
Technique and identifies scopes of further research. Finally, this chapter points out the
objectives of this thesis.
7
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
Chapter 2 presents a detail review of various rainfall based design flood estimation
techniques. This describes the key components of the Design Event Approach and
highlights its limitations and then discusses how Joint Probability Approach can
overcome the major limitations with the Design Event Approach. Various previous
researches on the Joint Probability are then critically examined. It describes the analytical
methods of the Joint Probability Approach and points out its limitations in relation to its
practical applicability. Various forms of the approximate methods of the Joint Probability
Approach are then discussed. The theoretical aspects of the Joint Probability Approach
are also discussed in this chapter. Various recent researches on the Joint Probability
Approach are then reviewed. Finally, the research questions to be investigated in this
thesis are identified.
Chapter 3 presents detail methodology of the proposed research. This begins with the
modeling principles of the Monte Carlo Simulation Technique. The principles of runoff
routing model RORB is then presented. The stochastic modeling framework in the Monte
Carlo Simulation Technique is described next. The storm event definition is then
presented which follows the detail description of stochastic inputs into the Monte Carlo
Simulation Technique, which includes the specification of the distributions of rainfall
duration, intensity, temporal pattern and initial loss. This chapter also presents a flow
chart illustrating various components of the proposed research methodology.
8
Hitesh D. Patel
Student ID: 16095380
Chapter 1: Introduction
Chapter 4 outlines the data requirements of the proposed research. This presents the
selection criteria of the study catchments. Based on these criteria, a total of 5 study
catchments are selected from NSW. A brief description of these catchments is then
presented. The rainfall and streamflow data are then collated for these catchments.
Chapter 5 presents the development of RORB model for a selected study catchment. This
begins with the description of the steps in formulating the RORB model. The detail steps
in the RORB modeling is then presented i.e. sub-division of the catchment, selection of
storm events, preparation of catchment vector file, preparation of storm event files,
calibration, fit and test runs. This finally examines the probabilistic nature of the RORB
model parameter kc and its impacts on design flood estimates.
Chapter 6 presents the enhancement of the Monte Carlo Simulation Technique. This
presents the results of storm analysis i.e. the identification of the distribution of rainfall
duration, intensity and temporal pattern, initial loss and storage delay parameter k for the
selected study catchments. This also involves the calibration of the runoff routing model
for a large number of selected rainfall and streamflow events. Finally, the derived flood
frequency curves obtained from the updated Monte Carlo Simulation Technique are
compared with the at-site flood frequency estimates and the old Monte Carlo Simulation
Technique which considers k as a fixed input.
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Chapter 1: Introduction
Chapter 7 presents a summary of the study as well as the conclusions derived from this
research. Finally, the recommendations for further research are pointed out.
There are ten appendices. Appendix A presents detail results of the calibration of the
RORB model. Appendix B presents results of at-site flood frequency analysis using LP3
Bayesian method. Appendix C presents detail results of the design runs from the RORB
modeling. Appendices D, E, F and G present results of the distributed input variables for
various study catchments i.e. rainfall duration, intensity, temporal patterns and initial
loss. Appendix H presents results of the calibration of the runoff routing model
parameter. Appendix I presents list of publications from this research.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
CHAPTER 2
REVIEW OF JOINT PROBABILITY APPROACH TO
DESIGN FLOOD ESTIMATION
2.1
GENERAL
This chapter of the thesis reviews design flood estimation methods in general with a
particular emphasis to rainfall-based design flood estimation methods. This presents a
detail review of the design flood estimation methods based on the Joint Probability
Approach.
2.2
VARIOUS DESIGN FLOOD ESTIMATION TECHNIQUES
Design flood estimation methods can be broadly classified into two groups: streamflowbased methods and rainfall-based methods (Lumb and James, 1976, Feldman, 1979,
James and Robinson, 1986, I. E. Aust., 1987) as illustrated in Figure 2.1.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Design
Flood
Estimation
RainfallBased
Methods
Event-Based
Methods
StreamflowBased
Methods
Continuous
Methods
DesignEvent
Approach
Partial
Continuous
Simulation
Joint
Probability
Approach
Complete
Continuous
Simulation
Flood
Frequency
Analysis
Regional flood frequency
analysis for ungauged
catchments
Empirical Methods
for ungauged
catchments
Rational
Method
Regression
Index flood
methods
Figure 2.1 Various design flood estimation techniques
2.3
STREAMFLOW BASED METHODS
Streamflow-based methods can be applied to catchments where there is a long record of
streamflow data available. These catchments are referred to as ‘gauged catchments’.
These catchments are generally large. Streamflow-based methods base their analysis
purely on stream-gauging data. By analysing this streamflow data, estimates of flood
discharges for a given ARI can be provided. The most common streamflow-based
methods are the flood frequency analysis and regional flood frequency analysis. Regional
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
flood frequency analysis can be applied to catchments which have limited streamflow
data or in cases where there is no streamflow data available. In the latter case, streamflow
data from gauged catchments in a homogenous region are used to develop prediction
equations which can be applied to ungauged catchments.
2.3.1
Flood Frequency Analysis
Flood frequency analysis is a method of analysing the statistics of recorded flood data
with the objective of defining the underlying probability distribution of the data for
subsequent use in flood quantile estimation. The most common application of flood
frequency analysis is with the observed flow discharge data, although analysis of flood
depth can often be equally appropriate.
In flood frequency analysis, a unique relationship between a flood magnitude and the
corresponding ARI T is sought. The task is to extract information from flow records to
estimate the relationship between Q and T. Three different models may be considered for
this purpose (Cunnane, 1989). These models are (1) the annual maximum series (AM)
model, (2) the partial duration series (PD) or peaks over a threshold (POT) model, and (3)
the time series (TS) model. In the annual maximum (AM) flow series, only the peak flow
in each year of record is considered. However, the use of an AM series may involve some
loss of information. For example, the second or third peak within a year may be greater
than the maximum flow in other years and yet they are ignored (Kite, 1977; Chow et al.,
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
1988). This situation is avoided in the partial duration (PD) or the peaks over a threshold
(POT) models where all peaks above a certain base value are considered. The base is
usually selected low enough so that the total data length is at least equal to the number of
years of data availability (Kite, 1977). The PD (or POT) model, however, is limited by
the fact that some of the observations may not be independent (Chow et al., 1988).
2.3.2
Empirical Methods
Empirical methods use observed flows to derive one or several coefficients to be
incorporated into an equation representing the rainfall-runoff model (James and
Robinson, 1986). The most common example is the Probabilistic Rational Method (I. E.
Aust., 1987). Such methods are ‘black box’ type of models, that is, they do not
incorporate any hydrologic knowledge in the system but are simply a means of
converting a known rainfall input into a design flood output. These methods are widely
used for ungauged catchments and its application is limited to peak flows only and hence
is not useful particularly when a complete design streamflow hydrograph is required.
2.4
RAINFALL EVENT BASED METHODS
Rainfall-based flood estimation techniques are the most common in hydrologic practice
due to the wide availability of rainfall data. In rainfall-based methods, estimation is based
largely on the analysis and conversion of rainfall data into flood discharges. Such a
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
process typically involves the use of a runoff-routing model or unit hydrograph to convert
a design rainfall event into a flood hydrograph. During this conversion process the runoff
routing model is calibrated with a number of observed rainfall and streamflow events
data.
The Design Event Approach and Monte Carlo Simulation Technique are both rainfall
event based methods. They have common deterministic components. These include a loss
model for computing rainfall excess and a runoff-routing model for converting rainfall
excess into a streamflow hydrograph. However, the techniques differ in the way input
variables are treated with respect to their probabilistic behaviour. A discussion of rainfallbased methods is outlined below. The discussion is based on the two broad categories of
empirical methods, event-based methods and continuous simulation methods.
Event-based methods make use of design rainfall data. Design rainfall in Australia is
based on the intensity-frequency-duration (IFD) data given in Australian Rainfall and
runoff (ARR) (I. E. Aust., 1987). The IFD rainfall data in ARR is derived from a fitted
surface through observed rainfall events across many sites in the region.
Event-based methods can be grouped into two types: the Design Event Approach, which
analyses a single event, and the Joint Probability Approach, which analyses multiple
events. These methods are discussed in detail below.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.4.1
Design Event Approach
According to ARR (I. E. Aust., 1958, 1977, 1987), Beran (1973) and Ahern and
Weinmann (1982), following are the steps involved with the Design Event Approach.
The estimation of design flood of a specified AEP by this method is illustrated in Figures
2.2 and 2.3 and summarised in the following steps:
 Select a number of design storm durations D1, D2, . . . For each of these, obtain a
streamflow hydrograph following the steps, given below.
 Obtain an average rainfall depth from the IFD curve, given the design location,
specified AEP and duration.
 Obtain average catchment rainfall using an empirical areal reduction factor.
 Select a design rainfall temporal pattern.
 Compute gross rainfall hyetograph.
 Select loss parameters and compute rainfall excess hyetograph.
 Formulate catchment response model.
 Select catchment response parameters.
 Select design baseflow.
 Compute streamflow hydrograph and add baseflow with the calculated hydrograph.
 Repeat the above procedure for the selected durations D1, D2, . . .
 The rainfall duration giving maximum peak flood is taken as critical duration, and the
corresponding peak is taken as the design flood of the specified AEP.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
The key assumption involved in this approach is that the representative design values of
the inputs/parameters at different steps can be defined in such a way that they are “AEP
neutral” i.e. they result in a flood output that has same AEP as rainfall input. The success
of this approach is crucially dependent on how well this assumption is satisfied.
There are no definite guidelines on how to select the appropriate values of the
inputs/parameters in the above steps that are likely to convert a rainfall depth of a
particular AEP to the design flood of the same AEP. There are many methods to
determine an input value. A designer is commonly in the situation to select an input value
(e.g. median value from a sample of inputs or fitted parameter values) from a wide range.
For example, in the case of eastern Queensland, the recommended range of initial loss is
0 to 140 mm (I. E. Aust., 1987). Likewise, other inputs to the design such as critical
storm duration, spatial and temporal distributions of the design storm, baseflow values,
etc. can also be determined by many methods, the choice of which is dependent on
various assumptions and preferences of the individual designer. Due to the non-linearity
of the transformation process involved, it is generally not possible to know a priori how a
representative value for an input should be selected to preserve the AEP.
For example, critical storm duration is an important factor in converting rainfall input to a
flood output of design AEP. The critical storm duration of a catchment depends on the
combination of storm factors, loss factors and catchment characteristics, and selection of
inappropriate value for any of these factors and inappropriate combination of these
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
factors will result in different critical durations and consequently the AEP of the rainfall
not being preserved. An example of inappropriate combination could be indicated by an
excessively long critical storm duration for a given catchment size, as found in a number
of studies (e.g. Walsh et al., 1991; Hill and Mein, 1996).
The uncertainties in input values to design can be illustrated by a tree diagram (Figure
2.3) representing a practical design situation where unknown inputs are shown by ranges
of values.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Rainfall: average intensity
(Duration = D, AEP = 1 in Y)
RUNOFF
PRODUCTION
Rainfall: areal reduction factor
Rainfall: areal pattern
Rainfall: temporal pattern
Loss model + parameters
Routing model type/Structure
HYDROGRAPH
FORMATION
Model parameters
Design baseflow
HYDROGRAPH
Design flood hydrograph peak
AEP = 1 in Y
Figure 2.2 Flood estimation by Design Event Approach (Rahman et al., 2001)
For example, the storm duration may be D1, D2, D3, etc., or storm losses may take on
any value L1, L2, L3, etc. Thus, there are various ways in which a design rainfall and
other inputs can be combined to produce a resulting flood. Because of the uncertainty
about the correct value of an input to be used in a design situation, except for the rainfall
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
depth for a given duration which is described by a probability distribution, designers tend
to adopt median or representative values for those inputs, with the hope that this will lead
to a flood estimate of the same probability as that of the design rainfall (Ahern and
Weinmann, 1982 and I. E. Aust., 1987).
Figure 2.3 Attributes of Design Event Approach (Beran, 1973)
In summary, the current Design Event Approach considers the probabilistic nature of
rainfall depth but ignores the probabilistic behaviour of other inputs/parameters such as
rainfall duration, losses, baseflow. The assumption regarding the probability of the flood
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
output i.e. that a particular AEP rainfall depth will produce a flood of the same AEP is
unreasonable in many cases. This is because the design estimate is sensitive to legitimate
but subjective variations in design assumptions (Beran, 1973; Russell, et al., 1979; Ahern
and Weinmann, 1982: Rahman et al., 2002a). The arbitrary treatment of the various
flood-producing variables, as done in the current Design Event Approach, is likely to lead
to inconsistencies and significant bias in flood estimates for a given AEP.
2.4.2
Joint Probability Approach (JPA)
The basic idea underlying this approach is that a particular design flood characteristic
could result from a variety of combination of flood producing factors, rather than from a
single combination, as done in the Design Event Approach. This approach was pioneered
by Eagleson (1972) who used an analytical approach to derive the probability distribution
of peak streamflows from an idealized V-shaped flow plane. This approach has been
advanced and improved in the last two decades (e.g. Rahman et al., 2002, Charalombus et
al., 2003, Rahman and Kader, 2004, Aronica and Candela, 2007, Muncaster and Bishop
2009). Ahern and Weinmann (1982) mentioned that Joint Probability Approach, which
considers the outcomes of events with all possible combinations of input values and, if
necessary, their correlation structure, should lead to better estimates of design flows. The
method is regarded to be theoretically superior to the Design Event Approach and
regarded as an attractive design method (I. E. Aust., 1987). This method is discussed in
more details in the following section.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.5
DESCRIPTION OF THE JOINT PROBABILITY APPROACH
The Joint Probability Approach considers the principal inputs/parameter values to the
design as random variables, and thus attempts to eliminate subjectivity in selecting input
values. In this approach, flood output has a probability distribution instead of a single
value. The method of combining probability distributed inputs to form a probability
distributed output is known as the derived distribution approach. The procedure of
determining a derived flood frequency distribution for a catchment can be thought of as a
combination of deterministic and stochastic hydrologic modelling (Laurenson, 1974;
Laurenson and Pearse, 1991). The stochastic elements are reflected in the adopted
distributions of the input variables and parameters, as well as in the assumed correlation
structure. These are generally determined not only from the data at the site but also from
a broader information base for the region (Weinmann, 1994). The transformation of
catchment inputs into outputs is deterministic in nature and is achieved by means of a
rainfall-runoff model.
A derived probability distribution can be found in two ways: (i) analytical methods and
(ii) approximate methods. The choice of a method to compute a derived distribution from
these options is influenced mainly by the level of analytical skills and the computer
resources available for the task (Weinmann, 1994).
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.5.1
Analytical Methods
There are many examples where an analytical approach has been used for deriving flood
frequency distributions. Bates (1994) and Sivapalan et al. (1996) presented a summary of
these studies. A review of the previous work is presented below with a particular focus on
the results of the studies in relation to practical applicability of the methods. The studies
are grouped here depending on the runoff production/runoff routing method adopted.
2.5.1.1 Methods based on Eagleson’s kinematic runoff model
The derived flood frequency approach was pioneered by Eagleson (1972) who derived
the probability distribution of peak streamflow from a given catchment from the
probability distributions of climatic and catchment characteristics by using a kinematic
model for runoff from an idealised V-shaped flow plane. This approach assumed that
storm characteristics (duration and intensity) are independent random variables with a
joint exponential probability density function. He used the empirical areal reduction
factors to convert point rainfall to catchment-average rainfall. His rainfall-runoff model
utilised a partial area runoff generation model with an infiltration capacity that was
assumed to be constant during an event, as well as across all events. The runoff routing
model utilised kinematic wave equations for both overland flow and channel flow. The
method has only limited practical applicability for reasons such as (i) the assumption of
independence between rainfall duration and intensity is not likely to be satisfied; (ii) the
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
analytical kinematic wave formulation is applicable to simple V-shaped geometry; (iii)
the number of parameters of the derived distributions is large (Wood and Hebson, 1986)
and some (e.g. overland flow surface parameter, stream bed parameter) are difficult to
obtain for a particular catchment; (iv) the lumped roughness/slope parameters used have
no direct physical interpretation; and (v) the mathematical difficulties associated with the
flow equations make analytical derivations very difficult for more complex real
catchments (Hebson and Wood, 1982).
Wood (1976) extended the method of Eagleson (1972) by allowing the infiltration
capacity (which represented random antecedent wetness) to vary between storm events
according to some assumed distribution. He found that the random variability in the
antecedent wetness of the catchment could have a remarkable effect on the predicted
return periods.
Cadavid et al. (1991) applied a derived distribution approach to small urban catchments,
which included Eagleson’s (1972) rainfall model, Philip’s (1957) infiltration equation,
and the kinematic wave model for runoff routing. Their model did not show good fits,
particularly for low AEP floods. It was noted that Eagleson’s (1972) exponential rainfall
model may not be a satisfactory representation of rainfall processes that cause floods and
that the estimation of the rainfall model parameters may have a major effect on the
success of the derived distribution approach.
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Muzik (1994) presented a study illustrating how the physical laws applicable to runoff
affect the probability distribution of peak flows. The analytical solution of the kinematic
wave equations of overland flow from an impervious runoff plane due to uniformly
distributed rainfall was adopted. It was found that the distribution of peak discharge of
elemental runoff approaches the parent distribution of rainfall intensity when the physical
parameters of the runoff plane exceed certain critical values. It was then argued that the
distribution of floods on a natural watershed, when runoff conditions are maximised,
should similarly approach a limiting distribution in its upper tail governed by probability
distributions of rainfall parameters in the region.
2.5.1.2 Methods based on geomorphologic unit hydrograph
Hebson and Wood (1982) and Diaz-Granados et al. (1984), in application of derived
flood frequency distributions, adopted Eagleson’s (1972) rainfall model and runoff
routing model based on the geomorphologic unit hydrograph (GUH) concept (RodriguezIturbe and Valdes, 1979; Gupta et al., 1980; Rodriguez-Iturbe et al., 1982a, b). The GUH
is an instantaneous unit hydrograph derived from considerations of drainage network
structure.
Hebson and Wood (1982) used Eagleson’s (1972) partial area runoff production model
and their runoff routing model was based on the third-order GUH of Rodriguez-Iturbe
and Valdes (1979). They attempted to incorporate the effects of catchment scale and
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
shape into the runoff dynamics, and suggested that the GUH would be more suitable than
Eagleson’s (1972) kinematic wave method to derive the joint probability distribution of
floods. Their procedure was tested on two Appalachian Mountain catchments and the
results compared well with the observed streamflow data.
Diaz-Granados et al. (1984) adopted an infiltration excess runoff generation model
(covering the whole catchment) based on Phillip’s (1957) representation of the infiltration
process. Their runoff routing model was based on a later development of the GUH theory
(Rodriguez-Iturbe et al., 1982a). They tested their procedure against the sample flood
frequency distributions for arid and wet climates and achieved good and reasonable fit,
respectively.
Wood and Hebson (1986) extended the work of Hebson and Wood (1982) to the study of
flood frequency similarity between catchments. The model involved use of dimensionless
rainfall inputs and a dimensionless basin response function. The probability distribution
of the dimensionless areal rainfall was derived assuming a gamma distribution that
incorporated basin size and rainfall areal correlation structure. This is different from the
use of empirically derived areal reduction factor as used by Eagleson (1972).
Moughamian et al. (1987) examined the performance of the derived flood frequency
models of Hebson & Wood (1982) and Diaz-Granados et al. (1984). They applied these
methods on three catchments, and found that both models performed poorly in every
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
catchment when compared to sample distributions. The significant errors in the derived
flood frequency curves resulted from the cumulative effect of a large number of relatively
small errors in the rainfall inputs and rainfall-runoff models. This study suggested that
fundamental improvements are needed before they can be applied in practice with any
confidence (Sivapalan et al., 1990).
Sivapalan et al. (1990) described a derived flood frequency model using a partial area
runoff generation model, based on an extension of TOPMODEL to include Hortonian
runoff generation estimated by the Philip’s (1957) infiltration equation, and a runoff
routing model based on the generalised GUH and consistent with partial area runoff
generation. This work was an extension of the previous work by Hebson and Wood
(1982), Diaz-Granados et al. (1984) and Wood and Hebson (1986). The areal rainfall
intensities were sampled from a gamma distribution that accounted for the effects of areal
averaging similar to the geoclimatic scaling factor of Wood and Hebson (1986). The
method allowed for the variability of antecedent moisture conditions between storms and
the effects of catchment scale both on the rainfall input distributions and in runoff
generation. The work was mainly devoted to provide a greater understanding of the
interrelationships that underlie the storm response of catchments of different scales and
physical characteristics. The results were presented in a dimensionless framework to
study hydrologic similarity of catchments. The approach placed more importance on the
‘production phase’ rather than the ‘transfer phase’ of the rainfall-runoff process, and
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
mainly dealt with ‘scaling and similarity issues’ rather than flood estimation. The
developed flood frequency model was not tested on actual catchments.
Troch et al. (1994) modified the procedure of Sivapalan et al. (1990) in an application to
a catchment in Pennsylvania. The main difference was the use of a width function-based
runoff routing scheme by the former. The application was limited to the investigation of
the sensitivity of flood frequencies to a number of model parameters. The practical
applicability of the method to the design flood estimation problem was not demonstrated.
2.5.1.3 Methods based on U. S. Soil Conservation Service’s curve number
procedure
Using a simple equation from the U. S. Soil Conservation Service (SCS) curve number
method (Soil Conservation Service, 1972) to estimate runoff from rainfall R and
maximum water abstraction S, Haan and Edwards (1988) derived the joint probability
density function of runoff Q and S, from which the marginal distribution of Q was
determined. The equation derived is strictly applicable to the SCS curve number method,
and the derivation procedure becomes much more difficult in situations where a more
complex transformation between rainfall and runoff is required.
Raines and Valdes (1993) modified Diaz-Granados et al.’s (1984) approach where the
SCS curve number procedure was used instead of Philip’s (1957) infiltration equation to
estimate runoff. The new model and those of Hebson & Wood (1982) and Diaz-Granados
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et al.’s (1984) were applied to four catchments in Texas, and it was found that none of the
models was able to fit satisfactorily the observed flood frequency curves. They noted that
rainfall model parameters were the major source of error.
Becciu et al. (1993) adopted a derived distribution technique in flood estimation for
ungauged catchments. A two component extreme value distribution was adopted to
derive the regional growth function and a derived distribution approach was adopted to
estimate the index flood. In the derived distribution the point rainfall was described by a
Poisson distribution; intensity and duration of rainfall were assumed to be mutually
independent random variables with exponential distributions and the spatial reduction of
precipitation over the basin area was accounted for by means of an areal reduction factor.
The approach used a curve number method and linear reservoir cascade theory to model
surface runoff. The application of the methodology to catchments in Northern Italy
showed its capability to satisfactorily reproduce the frequency distribution of the
observed data.
2.5.1.4
Methods based on other types of rainfall-runoff models
Beven (1986) adopted a Joint Probability Approach to flood estimation where he used
rainfall distributions similar to Eagleson (1972), a rainfall-runoff model that combined
the topographically based TOPMODEL with a routing model based on the catchment’s
width function. In this study, Beven (1986) also investigated the change of processes with
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
increasing severity of floods, e.g. the increase of the proportion of saturated area with
decreasing AEP.
Haan and Wilson (1987) presented a methodology for computing runoff frequencies from
the probabilistic behaviour of rainfall and other factors affecting runoff. They considered
two runoff variables: runoff volumes and peak flows. The derived distribution of peak
flows was based on the Rational Method:
(2.1)
Q = CIA
They noted that runoff coefficient (C) reflects many hydrologic factors including
antecedent conditions. If C is calculated from Equation 2.1 from several observed storm
events, C is found to be a random variable reflecting otherwise unquantified variations in
the hydrologic conditions of the drainage area. The probability distributions of C and I
were described by Beta and Extreme Value Type I distributions respectively. They used
numerical integration to obtain derived distribution under the assumption of
independence of C and I. They found that consideration of C as a random variable
provided larger peak flows than that obtained assuming C as a constant, particularly at
higher returns periods. This was in agreement with the earlier observation of Schaake et.
al. (1967) that C may be larger for storms with greater return periods. This has also been
recognised in ARR (I. E. Aust., 1987). Haan and Wilson (1987) demonstrated the
appropriateness of the Joint Probability Approach but did not make any clear
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
recommendation of the use of this approach, and suggested further study before ‘any
sweeping conclusion can be made’.
Bloschl and Sivapalan (1997) investigated the effects of various flood producing factors
(runoff coefficients, antecedent conditions, storm durations and temporal pattern) on
flood frequency curve in a derived distribution frame work. Like Sivapalan et al. (1996),
they used IFD curves for the rainfall model. They found that non-linear runoff generation
(reflected in increasing runoff coefficient with event size), random antecedent soil
moisture (reflected in random runoff coefficients), and non-linear routing (reflected in
faster runoff response with event size) all translate into steeper flood frequency curves
than in the linear case. They argued that this non-linearity may be the reason that flood
frequency curves tend to be much steeper than rainfall frequency curves. It might be
noted that the different slopes and shapes of rainfall and flood frequency curves have
been observed for many catchments. It could be argued from the observation of Bloschl
and Sivapalan (1997) that these differences are an expression of significant non-linearity
in runoff generation and hydrograph formation processes.
They found storm temporal pattern to be of critical importance for the flood frequency
behaviour and the assumption of equal return periods of the input rainfall depth and
output flood associated with the current Design Event Approach “is always grossly in
error”, a finding which has very important implication in design practice. For the two
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study catchments in Austria, the Design Event Approach underestimated flood return
periods by a factor of at least two but “this factor may be as large as ten”.
2.5.2
Approximate Methods
Approximate methods are often used in hydrology to determine derived frequency
distribution. There are two categories of approximate methods:
a) Discrete methods: Total probability theorem is generally used where continuous
distributions of hydrologic variables are discritized.
b) Simulation technique: Random samples are drawn from continuous distribution of
input variables.
2.5.2.1 Discrete methods
Here discrete probability distributions are used to describe hydrologic variable, such as
rainfall duration, antecedent precipitation index, soil moisture deficit, etc. even though
they are really continuous ones. Many researchers e.g. Beran (1973), Laurenson (1974),
Russell et al. (1979), Fontaine and Potter (1993) adopted this method. The accuracy of
the approach depends on the degree of discritization
In discrete methods, the theorem of total probability is normally used to calculate flood
probabilities. Fontaine and Potter (1993) make the simplest application of this. For a
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
given flood, its exceedance probability is the sum of three terms, each being the joint
probability of extreme rainfall and antecedent soil moisture. In SCS curve number
method (Soil Conservation Service, 1972), it is assumed to be represented by three curve
numbers. In fact, this over-simplified assumption is one basic limitation of the proposed
Joint Probability Approach.
The same concept is applied by Russell et al. (1979) to a rainfall-runoff model
represented by three parameters (time of concentration T, infiltration rate I and storage
constant R). Russell et al. (1979) used actual storm rainfall records instead of a synthetic
storm. The Clark rainfall runoff model (Clark, 1945) which provides the basis for the
HEC1 model was used in which rainfall is lagged by a time-area curve and routed
through linear storage. It was assumed that infiltration rate would be constant for any
particular storm.
Laurenson (1974) presented the most general application of total probability, which is
described by ‘transformation matrix’ approach. The method requires division of a design
problem into a sequence of steps, each step transforms an input distribution into output
distributions, which becomes the input to the next step (Laurenson, 1974). In applying the
method, input, transformation relation and output should be expressed in matrix form.
One particular value of the transformation matrix represents the conditional probability of
obtaining an output value given a value of the input. The ‘transformation matrix’ method
provides a wide range of application (Ahern and Weinmann, 1982 and Laurenson and
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Pearse, 1991) when the stochastic nature of the hydrologic system needs to be accounted
for. The above examples demonstrate how the theorem of total probability can be applied
for calculating design flood probabilities. If all the random variables involved in the
design are independent, computation of flood probabilities becomes very simple once
probabilities of those input variables are given. For the case of dependent variables,
application of the theorem becomes relatively difficult.
Beran (1973) presented a procedure that sampled the possible ways in which a storm of a
given ARI could cause floods, and derived their joint probability distributions. The unit
hydrograph method was used as catchment response model. In applying the method,
smoothing of flood probability distributions may be required because of discretizing
continuous distributions into class intervals. Shen et al. (1990) presented numerical
integration to determine the derived distribution. They used a Poisson process for arrival
of storm events, exponential distributions for rainfall intensity and duration, Phillip’s
equation for infiltration capacity, and the kinematic wave equation to formulate a rainfall
runoff model. The results of the study are applicable to given ranges of basin
characteristics only.
2.5.2.2 Simulation techniques
A number of investigators have used simulation methods to determine derived flood
frequency distributions. For example, Durrans (1995) represented a simulation procedure
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
to determine derived flood frequency curve for regulated sites, which has been described
as “an integrated deterministic-stochastic approach to flood frequency analysis.” It was
done in the following steps:
1) Random sampling of unregulated annual flood peak and unregulated flood volume
2) Random sampling of a dimensionless initial reservoir depth and dimensionless gate
opening area
3) Routing the inflow hydrograph through reservoir
4) Replication of steps (1) to (3) N times to obtain N outflow hydrograph peaks. Here N is
in the order of thousands.
Muzik (1993) adopted a modified SCS curve number method in the Monte Carlo
Simulation to obtain a derived distribution of peak discharge. The approach combines
knowledge of physical processes with the theory of probability in that knowledge of the
processes allows putting reasonable limits on the variable values. Here the initial
abstraction and five-day antecedent rainfall values (P5) were assumed to be a random
variable. The steps involved in the simulation are: (i) generation of a random value of P5;
(ii) from the relationship between P5 and S obtaining the maximum potential retention S;
(iii) generation of a random value of the initial abstraction Ia; (iv) generation of a random
value of total rainfall P; and (v) computation of rainfall excess depth. The rainfall excess
depth was then transformed deterministically by means of the unit hydrograph method
into a flood hydrograph.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Sivapalan et al. (1996) and Tavakkoli (1985) adopted a simulation approach to derive
flood frequency curves for an Australian catchment. The method resulted in slight
overestimation of flood peaks, which he mainly attributed to the runoff generation model.
Muzik and Beersing (1989) studied the transformation process of probability distributions
of rainfall intensity for the case of runoff from a uniformly sloping impervious plane.
Here kinematic wave and experimentally derived relations were used to compute the peak
discharge. Beran (1973) adopted a simulation technique in that the sampling produced
lower flood values at smaller ARIs than the expected flood following storms of that same
ARI. This method is not a fully generalised simulation approach; it is a combination of
the approximate method and the simulation technique. Here probability distributions of
storm durations and temporal pattern were based on complete storms and obtained from
the observed data but existing IFD (intensity-frequency-duration) curves based on storm
bursts were adopted for rainfall depth.
Bloschl and Sivapalan (1997) adopted a Monte Carlo simulation method for mapping
rainfall ARIs to runoff ARIs. The simulation consisted of the following steps: (i) Draw
storm durations from an exponential distribution. (ii) Draw precipitation on probabilities
from a uniformly distribution P [0; 1] and calculate precipitation return period from Tp =
1/(1-p)/m where m is the number of events per year; (iii) get rainfall intensities, p, from
the IFD curve using the two previous pieces of information; and (iv) fit temporal pattern
to rainfall, apply runoff coefficient to estimate rainfall excess, simulate streamflow
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
hydrograph from the selected runoff routing model, and note the peaks. At the end, the
flood peaks were ranked which allowed assignment of an ARI to each event by using
plotting positions: Tq = n/j/m where Tq is the return period of the flood, n is the total
number of events, and j is the rank.
2.6
STATISTICAL BASIS OF JOINT PROBABILITY APPROACH
The basic probability concepts as described by Benjamin and Cornell (1970) and Walpole
and Myers (1993) have been used in this study. The basic probability concepts are
explained in this section.
2.6.1
Probability of union
The probability of an event which is the union of two events A and B, i.e. the probability
of the occurrence of either A or B or both, denoted by P(AB), is the sum of their
individual probabilities minus the probability of their joint occurrence (Benjamin and
Cornell, 1970). That is:
P(AB) = P(A) + P(B) - P(AB)
(2.2)
If events A and B are mutually exclusive then P(AB) becomes zero thus Equation 2.2
reduces to:
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Student ID: 16095380
Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
P(AB) = P(A) + P(B)
2.6.2
(2.3)
Conditional probability and joint probability
Conditional probability is a concept of great practical importance, because it provides the
capability of re-evaluating the probability of an event in light of additional information
(Walpole and Myers, 1993). The conditional probability of the event A given that the
event B has occurred, denoted by P(A|B), is defined as the ratio of the probability of the
intersection of A and B to the probability of the event B. That is:
P(A|B) = P(AB)/ P(B)
(2.4)
Here P(AB) is the probability of joint occurrence of the events A and B and called
“joint probability of events A and B”. In application, P(B) and P(A|B) often come from
a study of the problem, whereas actually the joint probability P(AB) is desired; this is
obtained as follows:
P(AB) = P(A|B) P(B) =P(B|A) P(A)
(2.5)
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Student ID: 16095380
Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.6.3
Independence of two events
If two physical events are not related in any way, the measure of the probability of one
will not be changed if it is known that the other has occurred. This intuitive notion leads
to the definition of probabilistic independence. Two events A and B are said to be
independent if and only if
P(A|B) = P(A)
(2.6)
From Equation 2.5 this definition of independence implies that
P(AB) = P(A|B) P(B) =P(A) P(B)
(2.7)
To generalise, if events A, B, C, . . . are mutually independent then their joint probability
of occurrence is
P(ABC . . .) = P(A) P(B) P(C) . . .
(2.8)
This is known as multiplicative rule, and plays an important role in the statistical
hydrology. Expressed in words, if events are independent, the probability of their joint
occurrence is simply the product of their individual probabilities of occurrence.
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Hitesh D. Patel
Student ID: 16095380
Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
In flood hydrology, many of the flood causing components are assumed to be
independent, but in reality, most of these are not completely independent. Without
independence, the mathematical treatment of many hydrological phenomenon becomes
highly complicated.
2.6.4
Total Probability Theorem
If Bi (i varies from 1 to n, where n is a positive integer) represents a set of events which
satisfies the following two conditions: (i) mutually exclusive, i.e. P (B1  B 2  . . .  B n ) =
P(B1) + P(B2) +. . .+ P(Bn) and (ii) collectively exhaustive, i.e. P (B1  B 2  . . .  B n ) = 1,
then the probability of another event A can be determined by using the Total Probability
Theorem. This can be given as:
P(A) = P(AB1) + P(AB2) + P(AB3) + . . . P(ABn)
(2.9)
This theorem represents the expansion of the probability of an event in terms of its
conditional probabilities, conditioned on a set of mutually exclusive, collectively
exhaustive events. It is often a useful expansion in problems where it is desired to
compute the probability of an event A, since the terms in the sum may be more readily
obtainable than the probability of A itself (Benjamin and Cornell, 1970). It is considered
as one of the workhorses in probability applications (Kuczera, 1994).
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Student ID: 16095380
Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
The Theorem of Total Probability, expressed in one dimension by Equation 2.9, can also
be expanded to two or more dimensions. For example, in three dimensions B, C, D, the
theorem is written as follows:
P(A) 
   P(A| B i , C k , D x ) P(B i  C k  D x )
n
m
t
(2.10)
i 1 k 1 x 1
If Bi, Ck, Dx are independent events, Equation 2.10 becomes:
P(A) 
   P(A| B i , C k , D x ) P(B i ) P(C k ) P(D x )
n
m
t
(2.11)
i 1 k 1 x 1
In applying the Theorem of Total Probability to the calculation of flood probability, the
explanations for the terms involved in Equation 2.11 are as follows:
 P(A) is the unconditional probability of a flood (to be exceeded in any given year);
 P(A|Bi) is the conditional probability of a flood given an input Bi that occurs at the
same time as A, not just in the same year;
 P(Bi) is the probability of obtaining a value of Bi for the input B; and
 B, C, D are random variables to the design, for example temporal pattern, losses,
storm duration, etc.
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Student ID: 16095380
Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.6.5
Joint Probability Distributions
Jointly distributed random variables
When two or more random variables are considered simultaneously, their joint behaviour
is determined by a joint probability law, normally described by a joint cumulative
distribution function. When random variables are discrete, a joint probability mass
function (PMF), and when they are continuous, a joint probability density (PDF) function
is used to describe the governing law of their joint behaviour.
Joint Probability Density Function
Consider two random variables X and Y. The probability that X lies between x1 and x2
and Y lies between y1 and y2 is given by:
P[( x1  X  x 2 ) and ( y1  Y  y 2 )] 
 p
x2
x1
y2
X ,Y
( x, y ) dydx
(2.12)
y1
This is the volume under the function pX,Y(x,y) over the region. When the region is not a
simple rectangle, the integration becomes difficult to evaluate, a common problem
encountered in the application of joint probability theory to flood estimation problems.
The joint cumulative distribution function is defined by
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
FX ,Y ( x , y )  P[( X  x ) and (Y  y )] 
  p X ,Y ( x, y)dydx
y
x
(2.13)
 
The density function is a partial derivative of the cumulative function, that is
p X ,Y ( x , y ) 

2
 x y
FX ,Y ( x , y )
(2.14)
Marginal Probability Density Function
In studying the behaviour of one random variable say X, one may eliminate consideration
of the other random variable Y. The behaviour of a particular random variable
irrespective of the other is described by the marginal PDF. The marginal PDF of X is
obtained by integrating the joint density function over all values of Y:
p X ( x) 
p


X ,Y
(2.15)
( x , y ) dy
Conditional Probability Density Function
If the value of one random variable is known, say Y = y0, the relative likelihood of the
other random variable X taking a value in the interval x, x + dx is pX,Y(x,y0)dx. To obtain
a proper density function, these values are normalised by dividing them by their sum:
 p X,Y ( x, y0 )dx  pY ( y0 )

(2.16)

The conditional PDF of X when Y is given is defined by:
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
p X |Y ( x, y) 
p X ,Y ( x, y)
(2.17)
pY ( y)
Normally, the marginal distributions are not sufficient to specify the joint distribution.
The relationship between the conditional and marginal distribution function determines
how much an observation of one variable helps in the prediction of the other (Benjamin
and Cornell, 1970).
Joint Probability Density Function of independent random variables
If the conditional distribution pX|Y(x,y) is identical to the marginal distribution pX(x), X
and Y are said to be independent random variables. That is when X and Y are
independent random variables, their joint probability distribution is the product of their
marginal distributions:
pX,Y(x,y) = pX(x)pY(y)
(2.18)
The assumption of independence allows one to obtain the joint distribution from only the
marginals.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.7
RECENT RESEARCH ON THE JOINT PROBABILITY APPROACH TO
DESIGN FLOOD ESTIMATION
A review of the most recent studies is presented below with a particular focus on the
results of the studies in relation to practical applicability of the Joint Probability
Approach to design flood estimation. Kuczera et al. (2000) represented “KinDog
kinematics model” which was used to route the rainfall to the catchments outlet. This is
based on the “Field-william kinematic model”. It conceptualises rainfall excess as
Hortonian overland flow routed through a non-linear storage into the channel.
Two more analytical attempts to estimate the flood probability distribution with the
derived distribution methodology are by Iacobellis and Fiorentino (2000) and by Goel et
al. (2000). Iacobellis and Fiorentino (2000) assumed that the peak direct flow is
expressed as the product of average runoff per unit area, u(a), and the peak contributing
area, a. They assumed that the probability distribution of u(a) is conditional and is related
to the probability distribution of the rainfall depth occurring in a duration equal to the
characteristic response time.
Goel et al. (2000) used a stochastic rainfall model, which assumes that rainfall intensity is
either positively or negatively correlated to the rainfall duration for the generation of the
rainfall. They modeled rainfall runoff processes using an f-Index infiltration model and a
triangular geomorpho-climatic instantaneous unit hydrograph model.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Weinmann et al. (2002) highlighted some of the theoretical and practical limitations of
the currently used Design Event Approach to rainfall based design flood estimation. They
noted that Monte Carlo simulation has the advantage that it can utilise some of the
models and design data used with the Design Event Approach, which would allow it to
more easily applicable to flood estimation in practical situations.
Rahman et al. (2002a) presented a more holistic approach of design flood estimation
based on the principle of Joint Probability Approach. This Monte Carlo Simulation
Technique based on the Joint Probability Approach offers a theoretically superior method
of design flood estimation as it allows explicitly for the effects of inherent variability in
the flood producing factors and correlations between them.
Rahman et al. (2002c) presented a study illustrating how Monte Carlo Simulation
Technique can be integrated with industry-based model such as URBS. It was found that
the integrated URBS- Monte Carlo Simulation Technique can be used to obtain more
precise flood estimates for small catchments. Rahman et al. (2002b) examines the
variability of initial losses and specification of its probability distribution for use in the
Joint Probability Approach. It was found that the use of a mean value instead of the
probability distribution of initial losses reduces flood magnitudes significantly,
particularly at smaller ARIs.
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Hitesh D. Patel
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
Heneker et al. (2002) represented the ways of overcoming the Joint Probability problem
by allowing design rainfall obtained from Australian Rainfall and Runoff (ARR) to be
directly converted into rainfall excess. They employed a continuous simulation approach
using calibrated stochastic point rainfall, stochastic evaporation and water balance models
to determine rainfall excess exceedance probabilities for various durations.
Charalambous et al. (2003) applied the URBS- Monte Carlo Simulation Technique to two
large catchments in Queensland. They found that the URBS- Monte Carlo Simulation
Technique can easily be applied to large catchments. Although the limited data
availability in their application introduced significant uncertainty in the distributions of
the input variables e.g. IFD curves.
Kuczera et al. (2003) suggested that the current revision of ARR needs to articulate the
shortcomings of the design storm approach, identify calibration strategies, which gives
guidance about its reliability in different application. They also mention that event Joint
Probability methods based on Monte Carlo Simulation are computationally less
demanding but require specification of the probability distribution of initial conditions.
They advocated the development of Joint Probability Approach in preference to Design
Event Approach.
Rahman and Kader (2004) tested the Joint Probability Approach to design flood
estimation for ungauged catchments. They attempted to find out how the distribution of
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
rainfall intensity can be regionalised in the state of Victoria in Australia. They examined
the regional relationship between two types of design rainfalls, ARR and Joint Probability
Approach based data. They found that the regionally predicted JP IFD values to be
linearly correlated with the corresponding ARR IFD values. They also found that ARR
IFD values are generally higher than the corresponding JP IFD values. The developed
regional relationship between JP IFD and ARR IFD values, however did not produce
satisfactory derived flood frequency curves for the ungauged catchments. They
recommended that further development is needed before the method can be applied to
ungauged catchments.
Rauf and Rahman (2004) examined the sampling properties of rainfall events for
constructing intensity frequency duration (IFD) curves in ARR method and Joint
Probability Approach. To examine how frequently the same rainfall spell can appear in
the data series across various durations a term “commonality” was used. They found that
Joint Probability Approach based IFD data are generally smaller than the ARR IFD data.
Kuczera et al. (2006) compared the Joint Probability Approach and design storm in a case
study involving detention basin and illustrated that unacceptably large bias can arise from
misspecification of initial conditions in volume sensitive systems. His study merely adds
to the already considerable evidence that specification of average initial conditions in the
design storm approach is problematic and that design storm approach can be seriously
biased. He also concludes that Joint Probability Approach based on Monte Carlo
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
simulation are computationally less demanding but require specification of the
probability distribution of initial conditions, which may not be easy in many situations.
Aronica and Candela (2007) derived frequency distributions of peak flow by Monte Carlo
procedure using a simple semi-distributed stochastic rainfall-runoff model. They applied
this procedure starting from a simplified and parsimonious description of rainfall and
surface runoff processes to six Sicilian basins which showed that Monte Carlo Simulation
Technique can reproduce the observed flood frequency curves with reasonable accuracy
over a wide range of return period.
Muncaster and Bishop (2009) investigated the design flood estimates produced by limited
Monte Carlo framework contained in the RORB model (Laurenson et al., 2007) for three
urban catchments in Victoria. They examined the performance of the retarding basis and
drainage-related infrastructures using both the ARR87 and locally sampled design
temporal patterns employing the Joint Probability Approach facilities in the current
RORB package. The result of their study highlighted the joint probabilistic nature of the
catchment runoff response, and inherent difficulty in satisfying the assumption of
AEP/ARI neutrality. They concluded that the practical applications of RORB Monte
Carlo framework will aid the understanding of this approach. They identified the need of
transition from current Design Event Approach to more robust Joint Probability event
based approach.
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Chapter 2: Review of Joint Probability Approach to Design Flood Estimation
2.8 SUMMARY
From the literature review it has been found that Joint Probability Approach can
overcome the major limitations with the Design Event Approach to flood estimation. It
has also been found that analytical methods with the Joint Probability Approach is less
attractive than Monte Carlo simulation method to design flood estimation. The previous
applications of Monte Carlo simulation has not considered runoff routing model
parameter as a random variable, which is investigated in this study.
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Chapter 3: Methodology
CHAPTER 3
METHODOLOGY
3.1
GENERAL
The Monte Carlo Simulation Technique (MCST) comprises three principal elements
(Rahman et al., 2002a):
(i) a (deterministic) modelling framework to simulate the flood formation process;
(ii) the key model variables (inputs and parameters), referred to as component variables
henceforth, with their probability distributions; and
(iii) a stochastic modelling framework to synthesise the derived flood distribution from
the distributions of component variables. These elements are described below.
3.2
HYDROLOGIC MODELLING FRAMEWORK
The hydrologic model of the flood formation process involves the same components as
the models most commonly used with the current Design Event Approach to flood
hydrograph estimation: a runoff production function (or loss model), and a runoff transfer
function (or runoff routing model). The design rainfall inputs are converted to a design
flood output in two steps: runoff production and streamflow hydrograph formation.
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Chapter 3: Methodology
3.2.1
Runoff Production Function - Loss Model
A runoff production model (or loss model) is needed to partition the gross rainfall input
into effective runoff (or rainfall excess) and loss. Rahman et al. (2001) have discussed
various loss models that can be used with the Joint Probability Approach. In this study,
the initial loss-continuing loss model has been adopted as it is widely used in Australian
flood estimation practice.
3.2.2
Transfer Function - Runoff Routing Model
A catchment response model is needed to convert the rainfall excess hyetograph
produced by the loss model into a surface runoff hydrograph. Rahman et al. (1998)
reviewed the models commonly used in previous joint probability studies. In Australian
flood design practice, it is common to use a semi-distributed and non-linear type of
catchment response model, referred to as runoff routing model. This type of model, being
distributed in nature, can account for the areal variation of rainfall and losses, and
consider the non-linearity of the catchment routing response. Examples of models in this
group include RORB (Laurenson et al., 2007) and URBS (Carroll, 2007), a further
development of the concepts embodied in RORB. There is a considerable body of
experience available for RORB and similar models on appropriate parameter values for
different types of catchments in Australia. For the single non-linear storage model, the
storage-discharge relationship is expressed by:
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Chapter 3: Methodology
S = kQm
(3.1)
Where S is catchment storage in m3, k is a storage delay parameter in hours, Q is the rate
of outflow in m3/s and m is a non-linearity parameter (taken as 0.8 in this study).
A number of input variables/parameters are involved in the above two steps: (i) design
rainfall data - rainfall duration, average rainfall intensity, rainfall temporal pattern (ii)
loss parameters: initial and continuing losses (iii) runoff routing model parameters and
(iv) baseflow. Design rainfalls needed for the Joint Probability Approach are to be
developed from the pluviograph data at or near the catchment of interest; the losses,
runoff routing model parameters, and baseflow are obtained from observed rainfall and
streamflow data (for gauged catchments) or regional equations (for ungauged
catchments). The input variables/parameters that need to be considered in a probabilistic
fashion are further discussed below.
For hydrograph formation, different categories of runoff-routing models can be
distinguished according to how they deal with particular aspects of representing
catchment characteristics in the model, such as:
1.
Lumped or spatially distributed representation of the catchment’s runoff-routing
characteristics and for distributed (or semi-distributed) representation, the method of
catchment sub-division (topographically-based or isochronal lines);
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Chapter 3: Methodology
2.
Combined or separate modelling of the routing response of different catchment
elements (overland flow, streamflow, natural and artificial storages);
3.
Adoption of a linear or non-linear form of relationship between storage and
discharge;
4.
The ability of the model to deal with special features of the catchment or drainage
network, such as modifications to natural flow characteristics in parts of the
catchment, flow diversion points and various flow control structures.
In Australia, the most commonly applied runoff-routing models fall into the category of
semi-distributed models (node-link models) that use a topographic division into
subcatchments, and a network of routing elements that are typically characterised by a
non-linear power function relationship between storage and discharge as described by
Equation 3.1. This is the form adopted in most routing elements of the RORB, URBS and
WBNM models, and in the overland flow component of the XP-RAFTs model.
3.2.2.1 RORB Model Principles
RORB is a runoff and streamflow routing program used to calculate hydrographs from
rainfall and other channel inputs. It subtracts losses from rainfall to produce rainfall
excess and routes this through catchment storage to produce hydrographs (Laurenson et
al., 2007).
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Chapter 3: Methodology
The way in which RORB develops a streamflow hydrograph is illustrated in Figure 3.1.
The model of the catchment consists of two parts, a loss model and a catchment storage
model. Inputs to the model can consist of rainfall on a catchment area or direct inflow to
the channel system. In the former case, rainfall is operated on by a loss model to convert
rainfall into rainfall-excess, which is then routed through the catchment storage model to
produce the surface runoff hydrograph. In the latter case, channel inflow enters the
catchment storage model directly.
Rainfall
RUNOFF ROUTING MODEL
Loss Model
Catchment
storage model
Rainfall excess
Channel
inflow
Surface Runoff
Hydrograph
Channel outflow
Figure 3.1 Overall RORB Runoff Routing Model (Laurenson et al., 2007)
RORB provides for spatial variability of rainfall and losses by subdividing the catchment
into a number of sub-areas, typically five to fifteen. This is also necessary for the
modeling of the distributed nature of catchment storage. The subdivision is drawn along
watershed lines so that hydrographs calculated at the downstream boundaries of sub-areas
include all of the contributing area upstream. The adopted sub-areas are assumed
homogeneous in hydrologic response i.e., different response surfaces (e.g. urban, rural)
should normally be assigned to separate sub-areas.
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Chapter 3: Methodology
The catchment is divided into subareas and the rainfall on each subarea is adjusted to
allow for the infiltration and other losses. Each subarea contains a stream segment called
its main stream, which may be part of the catchment main stream or of a tributary stream.
The computed rainfall excess of the subarea is assumed to enter the channel network at a
point on the subarea's main stream near the centroid of the subarea. There, it is added to
any existing flow in the channel, and the combined flow is routed through a storage
element by a linear or nonlinear storage routing procedure based on continuity and a
storage function as described by Equation 3.1.
Detailed descriptions of the RORB model parameters k and m can be found in RORB
manual. The overall catchment storage is represented in the model by a network of
storages arranged like the actual stream or channel network. Each model storage between
the two nodes of the channel network represents storage effects along river reaches. The
nodes represent subarea inflow points, stream confluences, inflow points to storage
reservoirs and other points of interest on the catchment or channel network.
Storm rainfall is input to each sub-area at a node located at, or near its centroid, but
generally on a major stream. These sub-areas nodes are also the points where rainfallexcess enters the storage. The depth and temporal pattern of rainfall can be the same on
all sub-areas, or individually different, depending on the data available. Thus, temporal
and spatial variation of rainfall over a catchment is provided for in the model; storm
movement can also be simulated. Two alternative loss models, initial loss-proportional
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Chapter 3: Methodology
loss and initial loss-continuing loss are provided. Both provide for an initial loss, which is
a threshold value of rainfall that must occur before any rainfall-excess is produced. The
model of losses that occur after the initial loss has been satisfied may be either a constant
loss rate or a loss directly proportional to rainfall intensity. Both loss models, therefore,
contain two parameters, one determining the initial loss and the other the remaining loss.
3.2.3
Input Variables in the Monte Carlo Simulation
The major factors affecting storm runoff production are: rainfall duration, rainfall
intensity, temporal and areal patterns of rainfall, and storm losses. Factors affecting
hydrograph formation are the catchment response characteristics embodied in the runoff
routing model (model type, structure, and parameters) and design baseflow. Ideally, all
the variables should be treated as random variables, but for practical reasons,
consideration of a smaller number of variables would be preferable, if it did not result in a
significant loss of accuracy. Given the dominant role of rainfall and loss in the flood
formation process, it might be expected that the incorporation of the probabilistic nature
of these variables would result in significant reduction of bias and uncertainties in design
flood estimates. Although continuing loss (CL) is an important variable in the rainfallrunoff process, it has not been included as a random variable in this study. The main
objective of this study is to upgrade the Joint Probability Approach /Monte Carlo
Simulation Technique method of Rahman et al. (2002a) by including probabilistic runoff
routing model parameter k with the technique. Thus, five variables have been considered
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Chapter 3: Methodology
here for probabilistic representation: rainfall duration, rainfall intensity, rainfall temporal
pattern, initial loss and runoff routing model storage delay parameter k. In contrast to this,
the currently used Design Event Approach treats only rainfall intensity for a given
duration as a probabilistic variable. The input variables or parameters that need to be
considered in a probabilistic fashion are further discussed in Section 3.4.
The areal distribution of rainfall over the catchment is assumed to be uniform, and the
average catchment rainfall intensity is obtained from the point rainfall intensity, using an
areal reduction factor (e.g. Siriwardena and Weinmann, 1996). The continuing loss is
assumed to be a constant; likewise, a constant baseflow is assumed, determined as the
average baseflow at the start of surface runoff generation in observed events. A single set
of parameter values for the runoff-routing model is used here; the calibration procedure
allows the determination of a set of model parameters for a given catchment, which can
be applied with reasonable confidence.
3.2.4
Stochastic Modelling Framework in the Monte Carlo Simulation
The basic idea underlying the proposed new modelling framework is that the distribution
of the flood outputs can be directly determined by simulating the possible combinations
of hydrologic model inputs and parameter values. Two stochastic modelling frameworks
may be used: the deterministic simulation approach and the stochastic or Monte Carlo
simulation approach (Rahman et. al., 1998; Weinmann et. al., 1998). The first approach
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Chapter 3: Methodology
uses a discrete representation of continuous probability distributions, and completes
enumeration of all possible event combinations. Here, we adopted a Monte Carlo
simulation approach for its relative simplicity and flexibility. The method is described
below after Rahman et al. (2001).
For each run of the combined loss and runoff routing model, a specific set of input and
model parameter values is selected by randomly drawing values from their respective
distributions. Any significant correlation between the variables can be allowed for by
using conditional probability distributions. For example, the strong correlation between
rainfall duration and intensity can be allowed for by first drawing a value of duration and
then a value of intensity from the conditional distribution of rainfall intensity for that
duration interval. The results of the run (e.g. the flood peak) are then stored and the
Monte Carlo simulation process is repeated a sufficiently large number of times to fully
reflect the range of variation of input and parameter values in the generated output. The
output values of a selected flood characteristic (e.g. flood peak) can then be subjected to a
frequency analysis to determine the derived flood frequency curve.
The adopted Monte Carlo simulation approach is illustrated in Figure 3.2, and the steps
involved in the modelling process are detailed below:
 draw a random value of duration Di from the identified marginal distribution of rainfall
duration;
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Chapter 3: Methodology
 draw a random value of AEP:
 given the duration Di and AEP, draw a random value of rainfall intensity Ii(Di) from
the conditional distribution of rainfall intensity;
 given the duration Di, draw a random temporal pattern TPi(Di) from the conditional
distribution of temporal pattern ( or the set of observed temporal patterns for duration
Di);
 given the duration Di, draw a random value of initial loss ILi(Di) from the conditional
distribution of initial loss;
 draw a random value of runoff routing model storage delay parameter kifrom the
conditional distribution of model storage delay parameter;
 run the randomly selected variables Di, Ii, TPi, ILi and ki ( with a constant continuing
loss) through the runoff generation and runoff routing models to simulate a flood
hydrograph;
 add the baseflow to the simulated flood hydrograph and note the flood peak Qi;
 repeat the above steps N times (N in the order of thousands, i.e. i=1, 2,…N); and
 use the N simulated flood peaks to determine the derived flood frequency curve using
rank-order statistics.
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Chapter 3: Methodology
Di
Ii (Di)
TPi (Di)
ILi (Di)
CL
S = kQm
Qi
Q
Vi
BF
t
Figure 3.2 Monte Carlo Simulation to determine derived flood frequency curve
3.3
DISTRIBUTION OF KEY MODEL INPUT VARIABLES IN MONTE
CARLO SIMULATION
3.3.1
Rainfall Event Definition
The Design Event Approach treats rainfall intensity as a random variable, and uses a
number of trial rainfall burst durations with fixed temporal patterns to obtain design flood
estimates. In the analysis used to derive the design rainfall data in ARR87, the burst
durations were predetermined rather than random (I. E. Aust., 1987). In contrast, the Joint
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Chapter 3: Methodology
Probability Approach treats all the three rainfall characteristics (i.e. rainfall duration,
intensity and temporal pattern) as random variables. Thus, the new event definition has to
incorporate the random nature of these three rainfall characteristics. It has to capture all
those events that have the potential to produce a flood but, for the sake of simplicity of
representation, include only those parts of an event that will have a significant influence
on the flood response. For this purpose, a ‘complete storm’ and a ‘storm-core’ (the most
intense part of the storm) are defined as described below.
3.3.2
Complete Storm
A complete storm is defined in three steps, illustrated in Figure 3.3 (Hoang, 2001):
 A ‘gross’ storm is a period of rain starting and ending by a non-dry hour (i.e. hourly
rainfall > C1 mm/h), preceded and followed by at least six dry hours.
 ‘Insignificant rainfall’ periods at the beginning or at the end of a gross storm, if any,
are then cut off from the storm, the remaining part of the gross storm being called the
‘net’ storm. [A period is defined as ‘having insignificant rainfall’ if all individual
hourly rainfalls  C 2 (mm/h), and average rainfall intensity during the dry period
 C1 (mm/h)].
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 The net storms, from now on simply referred to as complete storms, are then evaluated
in terms of their potential to produce significant storm runoff. This is performed by
assessing their rainfall magnitudes, i.e. by comparing their average intensities with
threshold intensities. A net storm is only selected for further analysis if the average
rainfall intensity during the entire storm duration (RFID) or during a sub-storm
duration (RFId), satisfies one of the following two criteria:
RFI D  F1 2I D
(3.2)
RFI dmax  F 2  2I d
(3.3)
Where 2ID is the 2-year ARI intensity for the selected storm duration D, and 2Id the
corresponding intensity for the sub-storm duration d. The values of 2ID and 2Id are
estimated from the design rainfall data in Australian Rainfall and Runoff (ARR87).
In the above event definition, the use of appropriate reduction factors F1 and F2 allows
the selection of only those events that have the potential to produce significant storm
runoff. The use of smaller values of F1 and F2 captures a relatively larger number of
events; appropriate values need to be selected such that events of very small average
intensity are not included. In this study, the following parameter values have been
adopted: F1 = 0.4, F2 = 0.5, C1 = 0.25 (mm/h), and C2 = 1.2 (mm/h) as suggested by
previous studies (Rahman et al., 2001).
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Chapter 3: Methodology
3.3.3
Storm-core
The available IFD information in ARR87 is not based on complete storms but on periods
of intense rainfall within complete storms, called bursts. If this existing information is to
be used with the Joint Probability Approach, it is more useful to undertake the design
rainfall analysis in terms of storm bursts. However, as the duration of the bursts in the
ARR87 analysis was predetermined rather than random, it is necessary to consider a new
storm burst definition that will produce randomly distributed storm burst durations. These
newly defined storm bursts are referred to as storm-cores (Rahman et al., 1998).
10
Storm-core
Rainfall intensity, mm/h
9
8
7
End of net storm
6
5
Start of storm
4
End of gross storm
3
2
1
0
1
6
11
16
21
26
Time, h
31
36
41
46
Figure 3.3 Rainfall events: complete storms and storm-cores
For each complete storm, a single storm-core can be identified, defined as “the most
intense rainfall burst within a complete storm”. It is found by calculating the average
intensities of all possible storm bursts, and the ratio with an index rainfall intensity 2Id for
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Chapter 3: Methodology
the relevant duration d, then selecting the burst of that duration which produces the
highest ratio. In Figure 3.4 the storm-core has a duration of 3 hours. For that duration the
ratio with 2I3 is 2.94, compared to a value of 1.43 for 2I1 (duration of 1hour) which is the
most intense rainfall burst within the complete storm.
40
Rainfall intensity, mm/h ,
35
1-h relative intensity = 30/21 =1.43
3-h relstive intensity = 15/5.1 = 2.94
3-h av. intensity
30
25
2
20
Storm-core
I1
15
10
2
5
I3
0
1
2
3
4
5
6
Time, h
Figure 3.4 Identification of a storm-core
3.4
DISTRIBUTION OF FLOOD-PRODUCING VARIABLES
In the Monte Carlo Simulation Approach by Rahman et al. (2002a), four variables were
considered for probabilistic representation. These were rainfall duration, rainfall
intensity, rainfall temporal pattern and initial loss.
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Chapter 3: Methodology
3.4.1
Duration
The storm-cores are selected from the hourly pluviograph data of selected stations and
analysed for storm-core duration (Dc), average rainfall intensity (Ic), and temporal
patterns (TPc). Figure 3.4 shows a typical histogram of the frequencies of different stormcore durations from a pluviograph station, indicating that Dc values are approximately
exponentially distributed. This implies that, at a particular station, there are many more
short duration storm-cores than longer duration ones and that number of storms reduce
exponentially with duration.
Figure 3.5 Histogram of storm-core durations (Dc) at Cooper’s creek (Pluviograph ID
58072, NSW)
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Chapter 3: Methodology
The exponential distribution has one parameter and its probability density function is
given by:
p(Dc)=(1/β)e-Dc / β
(3.4)
where p stands for probability density, Dc is the storm-core duration and β is the
parameter of the exponential distribution. The parameter β can be taken as the mean of
the observed Dc values in a pluviograph station or over a region. The exponential
distribution has a skewness of 2, and its mean and standard deviation are equal. For the
purposes of this study, an exponential distribution of storm-core duration (Dc) has been
adopted.
3.4.2
Storm-Core Rainfall Intensity
In practice, the conditional distribution of rainfall intensity is expressed in the form of the
intensity-frequency-duration (IFD) curves, where rainfall intensity is plotted as a function
of rainfall duration and frequency. In the Joint Probability Approach adopted here, the
IFD curves for storm-core rainfall intensity have been developed in a number of steps, as
described below.
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3.4.2.1 Development of Storm-Core IFD Curves
In practice, the conditional distribution of rainfall intensity is expressed in the form of
intensity-frequency-duration (IFD) curves, where rainfall intensity is plotted as a
function of rainfall duration and frequency. The IFD curves for storm-core rainfall
intensity were developed in a number of steps, as described below following Rahman et
al. (2002a).
(i)
The range of storm-core durations Dc is divided into a number of class intervals
(with a representative or mid point for each class). An example is given in Table 3.1.
(ii)
For the data in each class interval (except the 1h class), a linear regression line is
fitted between log(Dc) and log(Ic). The slope of the fitted regression line is used to adjust
the intensities for all durations within the interval to the representative point using the
following equation. Intensities for other than 6 hours are adjusted to the 6-hour
equivalent. For example, for the 8-hour intensities:
Iadjusted = 10^(log(Ia) + 0.6298*(logDa - logDb))
(3.5)
Where the indices a and b correspond to the two nearest durations from the mid point,
respectively.
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Table 3.1 An example of class intervals and representative points for storm-core duration
(Dc) for developing IFD curves
Class interval (h)
Representative point (h)
1
1
2-3
2
4 -12
6
13 - 36
24
37 - 96
48
(iii) The adjusted intensity values in a class interval form a partial series. An exponential
distribution is fitted to the partial series Ii (i = 1, …, M), where M is the number of data
points in a class. Quantiles are obtained from the following equation:
I(T) = I0 + ln(T)
(3.6)
Where I0 is the smallest value in the series;  =  Ii/M – I0;  = M/N; N is the number of
years of data; and T is the average recurrence interval (ARI) in years. Rahman et al.
(2001) found that an exponential distribution better fitted the partial series rainfall
intensity data than the other candidate distributions for Victorian data and recommended
the adoption of an exponential distribution, which has been followed here. Adopting the
fitted distribution, design rainfall intensity values Ic(T) are computed for ARIs of 2, 5, 10,
20, 50 and 100 years.
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Chapter 3: Methodology
(iv) For a selected ARI, the computed Ic(T) values for each duration range are used to fit
a second degree polynomial between log(Dc) and log(Ic)
log(Ic) = a{log(Dc))2 + b(log(Dc)} + c
(3.7)
where a, b and c are constants.
3.4.2.2 Preparation of IFD Table
The adopted Monte Carlo Simulation Technique begins with the generation of a Dc value
from its marginal distribution. Given this Dc and a randomly generated ARI value, the
rainfall intensity value Ic is then drawn from the conditional distribution of Ic, expressed
in the form of IFD curves. This requires the definition of a continuous distribution
function, ideally in the form of a functional relationship between Dc, Ic and ARI.
However, as it is difficult to derive a functional relationship that suits different
conditions, an IFD table is used with an interpolation procedure to generate Ic values for
any given combination of Dc and ARI. Equation 3.6 and Equation 3.7 are the basis of the
IFD table, used for data generation in the adopted Monte Carlo Simulation Technique. In
an IFD table, Ic values are tabulated for Dc values of 1, 2, 6, 24, 48, 72 and 100 hours,
and ARIs of 0.1, 1, 1.11, 1.25, 2, 5, 10, 20, 50, 100, 500, 1,000 and 1,000,000 years. A
linear interpolation function in the log domain is used between the tabulated values of Dc
and ARI. Table3.2 shows the IFD results for pluviograph station number 58072 in
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Chapter 3: Methodology
Cooper’s Creek catchment in NSW and its storm-core IFD curve is shown in Figure 3.6,
which represents consistent set of IFD curves
Table 3.2 An example of IFD table used in data generation (pluviograph station 58072,
Catchment: Cooper’s Creek, NSW). Intensities are in mm/h.
Duration,
h
1
2
6
24
48
72
100
1
19.2
11.2
5.1
2.1
1.4
1.1
1
2
24.1
14.4
6.7
2.8
1.9
1.5
1.3
5
30.5
18.6
8.9
3.8
2.5
2
1.7
10
35.3
21.8
10.5
4.5
3
2.4
2
ARI, years
20
50
40.1 46.5
24.9
29
12.1 14.2
5.2
6.1
3.5
4.1
2.8
3.3
2.3
2.8
Coopers Creek-58072
1000.0
I c (mm/hr)
100.0
100
51.3
32.1
15.8
6.8
4.6
3.7
3.1
500
62.4
39.3
19.5
8.5
5.7
4.6
3.8
1000
67.2
42.5
21.1
9.2
6.2
4.9
4.1
1000000
114.9
73.3
36.9
16.2
11
8.8
7.4
ARI-1
ARI - 2
ARI - 5
ARI - 10
ARI - 20
ARI - 50
ARI - 100
ARI - 500
ARI - 1000
ARI - 1000000
10.0
1.0
1
10
D c (hours)
100
Figure 3.6 Storm-core IFD curves at pluviograph station 58072, Catchment: Cooper’s
Creek, NSW
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Chapter 3: Methodology
It should be noted here that Ic values for ARIs less than 1 year and greater than 100 years
are of less direct interest in the development of derived flood frequency curves for design
flood estimation up to the limit of the 100 year ARI. However, these extrapolated values
are required to cover the range that might arise in the Monte Carlo Simulation. The part
of the developed IFD curves for ARIs of 100 to 1,000,000 years is subject to very large
estimation errors from rainfall data records of limited lengths (in this study generally less
than 30 years). Where the interest is on rare to extreme floods (ARI greater than 100
years), this part of the curves needs to be adjusted using design rainfall data from some
appropriate regionalization approach, for example the CRC FORGE method
(Nandakumar et al., 1997).
3.4.3
Storm-Core Rainfall Temporal Pattern
A rainfall temporal pattern is a dimensionless representation of the variation of rainfall
depth over the duration of the rainfall event. Following the procedure of Hoang (2001), in
this study the time distribution of rainfall has been characterised by a dimensionless mass
curve, (i.e. a graph of dimensionless cumulative rainfall depth versus dimensionless
storm time with 10 equal time increments).
Rahman et al. (2001) found that temporal patterns of rainfall depth for storm-cores (TPc)
are not dependent on season and total storm depth. This means that dimensionless
temporal patterns from different seasons and for different rainfall depths can be pooled
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Chapter 3: Methodology
together. However, the patterns were found to be dependent on storm duration, yielding
two groups: (1) up to 12 hours duration; and (2) greater than 12 hours duration.
As the rainfall data used in the analysis was only defined at hourly intervals, the
minimum storm-core duration used in the temporal pattern analysis was 4 hours. Storms
with less than 4-hour duration are assumed to have the same patterns as the observed 4 to
12 hour storms.
Design temporal patterns for storm-cores (TPc) could be generated by the ‘multiplicative
cascade model’ as applied by Hoang (2001). However, in the present Monte Carlo
Simulation Technique, historic temporal patterns have been used directly instead of
generated temporal patterns similar to Rahman et al. (2001). That is, observed temporal
patterns (in dimensionless form) were drawn randomly from the observed samples
corresponding to the generated Dc value.
3.4.4
Initial loss
The initial loss for a complete storm (ILs) is estimated to be the rainfall that occurs
prior to the commencement of surface runoff (illustrated in Figure 3.7). The storm-core
initial loss (ILc) is the portion of ILs that occurs within the storm-core. The value of ILc
can range from zero (when surface runoff commences before the start of the storm-core)
to ILs (when the start of the storm-core coincides with the start of the complete storm
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event). Rahman et al. (2002b) proposed following equation to estimate ILc from ILs:
ILc = ILs[0.5 + 0.25log10(Dc)]
(3.8)
Rainfall/Streamflow
Flood hydrograph
Storm-core
IL s
IL c
Time, h
Figure 3.7 Initial loss for complete storm (ILs) and initial loss for storm-core (ILc)
This relationship gives ILc = ILs at Dc = 100 hour, and ILc = 0.50  ILs at Dc = 1 hour. In
the use of the ILs distribution with an adjustment factor, such as the one proposed in
Equation 3.8, is preferable to the use of ILc directly, as ILs is more readily estimated from
data.
Rahman et al. (2002b) also adopted a four-parameter Beta distribution to describe the
distribution of ILs in that the four parameters are estimated from the observed lower
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Chapter 3: Methodology
limit (LL), upper limit (UL), mean and standard deviation of the ILs values.
The four-parameter Beta distribution can be expressed by Equation 3.9 (Benjamin and
Cornell, 1970):
f Y ( y) 
1
( y  a) r 1 (b  y ) t  r 1
t 1
B (b  a)
(3.9)
a  y  b and t > r
(3.10)
where fy(y) is the probability density, a, b, t and r are parameters and B is the beta
function defined below:
B
(r  1)! (t  r - 1)!
(t  1)!
(3.11)
The mean and variance of the Beta distribution are given by:
 Y  a  (b  a )
r
t
Y 2 
(3.12)
(b  a) 2 r (t  r )
t 2 (t  1)
(3.13)
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Chapter 3: Methodology
The parameters of the Beta distribution r and t can thus be determined from known values
of a, b,  Y and  Y , that is, the lower and upper limits, mean and standard deviation
respectively of the observed loss values at a site.
There are a number of possible alternatives to the selected Beta distribution to describe
the variability of initial loss, e.g. the Gamma, Exponential and Truncated Normal
Distributions. The Beta distribution was adopted for its flexibility and because its
parameters lend themselves readily to physical interpretation (Rahman et al., 2002b).
3.4.5
Runoff routing model parameter k
As discussed in Section 3.2.2 a catchment routing model is needed to convert the rainfall
excess hyetograph produced by the loss model into a surface runoff hydrograph. In
Australian flood design practice, it is common to use a semi-distributed and non-linear
type of catchment routing model. There is a considerable body of experience available for
RORB and similar models on appropriate parameter values for different types of
catchments in Australia. Based on its ready adaptability for the purposes of this study the
RORB and a simple runoff routing model have been used. For the single non-linear
storage model, the storage-discharge relationship is expressed by Equation 3.1.
In this study, a four-parameter Beta distribution has been adopted to describe the
distribution of k, and the four parameters are estimated from the observed lower limit
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Chapter 3: Methodology
(LL), upper limit (UL), mean and standard deviation of the k values. The observed k
values have been obtained from the calibration of the model using selected storm and
runoff events.
3.5
SIMULATION TECHNIQUE
‘Monte Carlo Simulation’ refers to a mathematical technique that is used to determine
the outputs from a model represented by a complex set of equations that cannot be
readily solved analytically. In this study, the Monte Carlo Simulation approach is used to
generate a sample of NG (Number Generated) different runoff events from NG different
combinations of rainfall and loss inputs. For each event, a set of values of Dc, Ic, TPc,
and ILc is generated to define the rainfall excess hyetograph. A value of k is then
generated from the fitted Beta distribution, which is then used in routing to produce a
corresponding streamflow hydrograph. A large number of hydrographs (in the order of
30,000 to 60,000) is typically generated and the resulting flood peaks are extracted and
subjected to a frequency analysis to obtain the derived flood frequency curve. The Monte
Carlo Simulation Technique adopted in this study is similar to Rahman et al. (2001) and
is summarised below.
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Chapter 3: Methodology
3.5.1
Number of runoff events generated
The number of separate events to be generated depends on the range of ARIs of interest,
the degree of accuracy required, the number of probability-distributed variables involved
and the degree of correlation between them. For this study, it was found that at least
40,000 rainfall events have to be generated to produce relatively stable estimates of the
derived flood frequency curve in the ARI range from 1 to 100 years.
If the purpose of the Monte Carlo Simulation was to estimate flood events in the extreme
range, or if more random variables were involved, the required number of generated
events would increase by orders of magnitude. It would then be desirable to apply more
efficient Monte Carlo Simulation methods, such as importance sampling (e.g. Thompson
et al., 1997).
The number of partial series flood events to be generated (NG) is obtained from the
following equation:
NG = *NY
(3.14)
where  is the average number of storm-core events per year, and NY is the number of
years of data to be generated. As an example, for  equal to 5, a total of 10,000 data
points has to be generated to simulate 2000 years of data.
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Chapter 3: Methodology
3.5.2
Steps in Simulation
To simplify the Monte Carlo simulation, a total of NG runoff events are first generated
and stored as individual data files for use in the simulation. Each event is defined by
random values of rainfall duration and ARI, which define the average rainfall intensity, a
random temporal pattern, and a random value of initial loss. These values are generated
from the distributions identified in Section 3.4. The steps in enhanced Monte Carlo
simulation are illustrated in Figure 3.8
As a first step, values of storm-core duration, Dc are generated from an assumed
exponential distribution. This has one parameter estimated as the observed mean Dc
value, obtained from the pluviograph data from the catchment of interest. In the second
step, a random value of storm-core rainfall intensity (Ic) for each given value of Dc is
generated, using the IFD table described in Section 3.4.2.1. First, a random ARI value is
selected from the following equation (after Stedinger et al., 1993, equation 18.6.3b):
ARI 
1
ln(1  AEP)
(3.14)
where AEP is the annual exceedance probability, obtained from a uniform distribution U
(0, 1). Since the primary aim is to develop derived flood frequency curves in the range of
annual exceedance probabilities of say 1 in 100 to 1 in 2, the interval U (0,1) is too wide.
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Chapter 3: Methodology
However, to cover a reasonably wide range of rainfall intensities that might arise during
simulation, U was limited to the range 10-6  U  1 – e -. As an example, for an average
number of storm-core events  equal to 5, this results in 10-6  U  0.993; in terms of ARI
(years) this is equivalent to 106  ARI  0.2. For the given Dc and ARI values, an Ic value
is then read from the IFD table for the site of interest, using linear interpolation with
respect to both log(Dc) and log (ARI) in accordance with Rahman et al. (2001).
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Chapter 3: Methodology
Select Storm
events
Identify
distributions of
input variables
Analysis
Simulation
Storm Duration
(DC)
DC
Storm rainfall
Intensity (IC)
IC
Storm temporal
pattern (TPC)
Initial Loss
(ILC)
TPC
ILC
CL
Design loss
analysis:
Continuing loss
Rainfall excess hyetograph
k
Runoff model
calibration
New random
variable
Baseflow (BF)
analysis
Route through runoff
routing model
(constant m=0.8)
Baseflow
Construct derived flood
frequency curve
Peak of simulated
streamflow
hydrograph
Figure 3.8 Schematic diagram of the Updated Monte Carlo Simulation Technique.
Shaded boxes represent stochastic variables (BF = baseflow).
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Chapter 3: Methodology
In the third step to generate a temporal pattern, the adopted simulation method randomly
selects a historic temporal pattern recorded at the site of interest depending on the
generated Dc value. The procedure is repeated NG times to sample NG temporal patterns.
In the fourth step, storm-core initial loss values are derived by first generating a storm
initial loss value from the Beta distribution fitted to the ILs data from the observed events
at the site of interest. The generated ILs value is then converted to a storm-core loss ILc,
using Equation 3.8. The procedure is repeated NG times to generate NG values of ILc.
In the fifth step, storage delay parameter k value is identified from the calibration of
runoff routing model using a good number of rainfall and runoff events. A four parameter
Beta distribution is then fitted to the k data. Now, NG k values are simulated from the
fitted beta distribution.
In addition to these five stochastic inputs, the simulation of streamflow hydrographs
requires the following fixed inputs: (a) catchment area in km2 (for calculation of areal
reduction factor) (b) an estimate of continuing loss (CL) in mm/h and (c) baseflow value.
The peak of each of the NG simulated hydrographs is stored for later analysis to form a
derived flood frequency curve.
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Chapter 3: Methodology
3.6
SIMULATION OF DERIVED FLOOD FREQUENCY CURVES
The NG flood peaks from the simulation are subjected to flood frequency analysis to
derive flood frequency curves. A non-parametric frequency analysis method is used to
construct a derived flood frequency curve from the set of NG simulated flood peaks. As
these flood peaks are obtained from a partial series of storm-core rainfall events, they also
form a partial series. Construction of the derived flood frequency curve from the
generated partial series of flood peaks involves the following steps as outlined in Rahman
et al. (2001):
1. Arrange the NG simulated peaks in decreasing order of magnitude and assign rank 1
to the highest value, 2 to the next one and so on.
2. For each of the ranked floods, compute an ARI from the following equation:
ARI 
NG  0.2 1 NY  0.2
x 
m  0.4 
m  0.4
(3.15)
Where NG is the number of simulated peaks, m is the rank, and  is the average
number of storm-core events per year at the catchment of interest, and NY is the
number of years of simulated data.
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Chapter 3: Methodology
3. Prepare a plot of ARI versus flood peaks that is the plot of the empirical flood
frequency curve defined by the simulated flood peaks.
4. Compute flood quantiles for selected ARIs by fitting a smooth curve through
neighbouring points. (Given the large number of data points, logarithmic interpolation
between the two neighbouring data points, without any smoothing, has been adopted in
this study.)
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Chapter 4: Description of study catchments
CHAPTER 4
DESCRIPTION OF STUDY CATCHMENTS
Three types of data are needed for this study:
(i) Pluviograph data to identify probability distributions of rainfall variables (e.g.,
duration, intensity and temporal pattern).
(ii) Streamflow data (combined with pluviograph data) to identify the probability
distributions of initial loss and the key runoff routing storage delay parameter kc for
RORB model or k (in case of simple one-storage model). Rainfall and streamflow
data for selected flood events are required to calibrate the parameters of the runoff
routing model which forms the basis of identification of probability distributions of k
or kc. Streamflow data is also required to obtain annual maximum flood series which
are then used to construct at-site flood frequency curve.
(iii)Various catchment characteristics data are needed to develop the RORB catchment
sub-division e.g. topographic map, streamlines, stream length and contour lines.
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Chapter 4: Description of study catchments
4.1
STUDY CATCHMENTS
Previous researches on Joint Probability Approach /Monte Carlo Simulation Technique
have been restricted to the state of Queensland and Victoria, Australia. This study aims to
apply Monte Carlo Simulation Technique and attempts to enhance the technique using
the catchments from New South Wales, Australia. This part of south-eastern Australia is
dominated by winter rainfall.
4.1.1
Selection criteria for study catchments
The selection of study catchments are based on the following factors:
(i)
Rural and unregulation: Ideally, the selected streams should be unregulated, since
major regulation affects the rainfall-runoff relationship significantly (storage
effects). Streams with minor regulation, such as small farm dams and diversion
weirs, may be included because this type of regulation is unlikely to have a
significant effect on annual floods. Gauging stations on streams subject to major
upstream regulation were not included in this study.
(ii)
Landuse change: Major landuse changes, such as the clearing of forests or
changing agricultural practices modify the flood generation mechanisms and make
streamflow records heterogeneous over the period of record length. Catchments
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Student ID: 16095380
Chapter 4: Description of study catchments
which have undergone major landuse changes over the period of streamflow records
were not included in this study.
(iii) Catchment area: For one-storage runoff routing model the catchment area should
be smaller than 200 km2 but for the RORB model, there is no upper limit of
catchment area. However, too large catchment should not be used even with the
RORB model as calibration of the model for too large catchment becomes difficult
and hence for the RORB model an upper limit of 2000 km2 is adopted in this study.
(iv) Pluviograph location: The distance between centroid of the streamflow measuring
station and pluvio stations should not be more than 10 km, as a greater distance may
change the areal distribution of rainfall on the catchment remarkably and may not
satisfy the assumption of uniform rainfall throughout the catchment (an assumption
that is made in the runoff routing modeling in this study).
(v)
Record length: The catchments should have reasonably long and readily available
pluviograph and streamflow data, preferably, a minimum of 25 years of streamflow
data, and at least 10 years of concurrent pluviograph and streamflow data.
The length of recorded data is important in an approach such as the Monte Carlo
Simulation Technique. The probability distributions of the key input variables:
storm-core duration, (Dc) and rainfall intensity (Ic) are identified from the storm
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Chapter 4: Description of study catchments
analysis in the form of IFD curves. In addition, the storm analysis is used to prepare
the database of observed Temporal Patterns (TPc). A loss analysis is used to
determine the probability distributions of storm-core initial loss (ILs) which needs
concurrent rainfall and streamflow events data. All these data need a good record
length of both pluviograph and streamflow data.
The record length also plays an important role in validating the derived frequency
distribution curve of flood estimates in the ARI range from 1 to 100 years. For
example, ideally 25 years of data or greater is required to obtain a reasonable
estimate of 50 year flood quantile. The streamflow record should contain at least
one large flood (e.g. 50 year or 100 year flood).
Initially 150 pluviograph stations distributed throughout New South Wales were selected
and the location of nearby streamflow gauging stations and the catchment conditions
were checked for candidate stations. Considering the above factors, five catchments were
finally selected. The locations of the selected catchments are shown in Figure 4.1.
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Chapter 4: Description of study catchments
Figure 4.1 Location of the selected catchments
The mean and median record length of the selected pluviograph stations are 22.6 years
and 23 years respectively. Details of the selected pluviograph and streamflow gauging
stations can be seen in Table 4.1.
Table 4.1 Selected catchments and nearby pluviograph station details
54138
418027
7
Distance
between
61335
210017
6.3
streamgauge and
Pluviograph Catchment pluviograph
ID
ID
(km)
Horton
Moonan
Brook
220
1976
2006
30
103
1969
1980
River name
& location
Catchment
area
(km2)
Date
opened
Date
closed
11
Pluvio
record
length
(years)
69075
218007
7.48
Wadbilliga
122
1974
1988
14
69049
215004
5
Corang
166
1971
2006
35
58072
203002
5
Coopers Ck
62
1975
1998
23
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Hitesh D. Patel
Student ID: 16095380
Chapter 4: Description of study catchments
4.2
DESCRIPTION OF SELECTED STUDY CATCHMENTS
Wadbilliga catchment (Catchment ID 218007): The Wadbilliga River catchment has
an area of approximately 122 km2 which originates from the Wadbilliga national park and
flows down and merges with, first Yowrie River and then with Turross River which
finally ends at Tuross Lake near Tuross head. This is a mountainous catchment with 90%
of area covered with forest which can be seen in Figure 4.2. Streamflow data has been
sourced from gauging station number 218007. Rainfall data has been obtained from the
pluviograph number 69075 located in Yowrie, which is about 7.48 km (measured by
straight line between two points) away from the gauging station. The hourly rainfall
pluviograph data of 14 years starting from 1974 to 1988 is available.
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Student ID: 16095380
Chapter 4: Description of study catchments
Figure 4.2 Wadbilliga catchment with stream gauge and pluviograph station
Corang River catchment (Catchment ID 218007): The Corang River catchment is
located in eastern slopes about 40 km away from the Great Dividing Range. The Corang
River rises in the Budawangs and joins the Shoalhaven River about 5 km west of Nerriga.
About 60% of the river basin lies on flat area. The catchment area is approximately 166
km2. The streamflow data from station number 215004 and the hourly rainfall data of 35
years from station number 69049, located in Nerriga about 5.98 km away from the
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Student ID: 16095380
Chapter 4: Description of study catchments
gauging station, have been available. The mean annual flow from this river is
approximately 62,604 ML/year.
Catchment Name: Corang River
Streamflow station ID: 215004
Pluvio ID: 69049
Figure 4.3 Corang River catchment with stream gauge and pluviograph station
Coopers Creek catchment (Catchment ID 203002): The Coopers Creek catchment is
located in far north east side of New South Wales. The catchment has an area of
approximately 66 km2. The pluviograph is located at Federal Post Office; about 5 km
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Student ID: 16095380
Chapter 4: Description of study catchments
away from the stream gauge number 203002. The concurrent streamflow and pluviograph
data from 1975 to 1998 have been available. The catchment can be seen in the Figure 4.4.
Catchment Name: Coopers Creek
Streamflow station ID: 203002
Pluvio ID: 58072
Figure 4.4 Coopers Creek catchment with stream gauge and pluviograph station
Horton River catchment (Catchment ID 418027): The Horton River is a river in
northern New South Wales. The Horton River drains most of the northern slopes of the
Nandewar Range. The headwaters of the river are located north of the town of Barraba
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Chapter 4: Description of study catchments
(but on the northern slopes of the range, whereas Barraba is on the southern side). The
branches of the Horton River flow generally north and eventually reach the Gwydir River
between the towns of Bingara and Gravesend. The catchment has an area of nearly 220
km2 and the 30 years of hourly rainfall data and streamflow data have been available. The
distance between pluviograph and streamgauge is about 7 km. The catchment experiences
mean annual rainfall of 946 mm. The valley of the Horton River is used for grazing and
some cropping. It is a sparsely populated area with no significant towns. The catchment
can be seen in Figure 4.5.
Moonan Brook catchment (Catchment ID 210017): Moonan Brook River originates
from Barrington Tops and flows in west to Lake Glenbawn. The catchment is surrounded
by mountains and about 80% of the region is covered with moderate forest which can be
seen in Figure 4.5. The catchment experiences good rainfall and has mean annual rainfall
of 1132 mm. The area of catchment is nearly 103 km2 and the rainfall data of 11 years
has been available from pluviograph station number 61335 located in Stewarts Brook,
which is about 6.3 km away from the gauging station number 210017.
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Student ID: 16095380
Chapter 4: Description of study catchments
Figure 4.5 Horton and Moonan Brook catchment with stream-gauge and pluviograph
station
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Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
CHAPTER 5
RORB MODEL FORMULATION AND IMPACT OF MODEL
PARAMETER ON DESIGN FLOOD ESTIMATES
5.1
GENERAL
For estimation of design floods there are several runoff routing models used in Australia;
RORB, URBS, WBNM, RAFTS etc. Based on the previous researches on Monte Carlo
Simulation Technique in Australia, the industry-based software URBS has integrated
Monte Carlo Simulation Technique within the software, which however, needs further
enhancement for applications under a wide range of hydrologic and catchment
conditions. Application of Monte Carlo Simulation Technique with RORB model, the
most widely used hydrologic model in Australia, has not been well investigated. At
present, the RORB model has a limited capability in terms of implementation of the
Monte Carlo Simulation Technique in flood modeling. In the current version of RORB
model the two input variables can be treated in a partial stochastic manner, namely initial
loss and the rainfall temporal pattern. This chapter develops RORB model for a
catchment and examines the impacts of RORB model parameter kc on design flood
estimates.
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
5.2
STEPS FOR RORB MODEL DEVELOPMENT
The overall modelling steps were used as suggested by Laurenson, et al. (2007). The
three functions of fitting, testing and design are associated with three different types of
runs, whose characteristics are summarised below.
(i) On gauged catchments, FIT runs is used first with data for one or more of the available
flood events to evaluate the model’s parameters. From the 40 different storm events used
to calibrate the model in this study, the value of kc would be categorised according to the
goodness-of-fit.
(ii) TEST runs would be used next with data for the remainder of the recorded flood
events to test the model. Three different storm events would be used to validate the key
model parameters.
(iii) If the results of the TEST runs proved to be satisfactory, DESIGN runs would then
be used to estimate design floods.
(iv) To check the sensitivity of the key model parameters obtained from FIT run, design
run with various combinations of key model parameters i.e. kc, IL and CL would be used
to estimate design floods.
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
(v) Peak flood estimate (i.e. the hydrograph peak) for various ARIs obtained from
DESIGN run would be compared with the at site flood frequency estimates (i.e. the
observed flood quantile).
5.3
DATA AND STUDY CATCHMENT
Description of the study catchment (Coopers Creek at Lisomre) is given in Section 4.2.
The subject catchment is situated in temporal pattern Zone 1 (I. E. Aust., 1987).
Streamflow data at the Repentance gauging station has been available since 4th November
1976 to 1st January 2007. The data was obtained from Pinnena 9.2 CD (Department of
Climate and Water, NSW). There are some daily stations in the area; however, as the
network of rainfall stations is not very dense when compared to the size of the catchment,
it might be acceptable to use a uniform rainfall pattern.
The catchment was divided into 9 subareas which centered on streams and bounded by
drainage divides. The drainage network was also subdivided into reaches, each of which
was associated with model storage. The 9 subareas and 10 model storages are shown in
Figure 5.1. The catchment drainage data required to run the model is tabulated in Table
5.1. The subdivision was done on 1:100,000 topographic map and the areas and reach
lengths were also obtained from the same map.
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
Figure 5.1 Catchment boundaries, sub-areas and channel
Table 5.1 Catchment sub-areas and reach lengths
Sub-area
name
A
B
C
D
E
F
G
H
I
Total
Sub-area
( km2)
8.5
8.4
7.9
13.2
3.5
1.8
11.8
7.3
3.5
65.9
99
Reach
1
2
3
4
5
6
7
8
9
10
Length
(km)
3.7
3.6
4.0
5.8
4.9
1.9
7.8
4.9
2.5
2.5
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
5.3.1
Selection of storm events
Storm events of comparatively longer duration and of higher rainfall intensity were
selected from the rainfall data. In the absence of more pluviograph stations in the
catchment, it appears to be reasonable to use uniform rainfall pattern throughout the
catchment. A total of 43 storm events were selected to check the sensitivity of kc on the
design flood estimation. The data for the 43 storms used in the study consist of hourly
rainfall quantities and corresponding hourly discharge at the catchment outlet. Out of
these 43 storm events, 40 are used to calibrate the model in FIT run and 3 storm events
are used to validate the model parameters.
The streamflow data available at the gauging station includes surface runoff from the
catchment. It is necessary to separate the baseflow from the surface runoff volume to
estimate net streamflow resulting from the rainfall. The discharge input in the program is
the net streamflow which is the total discharge recorded in the gauging station minus the
baseflow. The baseflow separation method proposed by Boughton (1987) was adopted in
this study which considers that the rate of increase in baseflow depends on a fraction of
the surface runoff  . That is the rate of baseflow at any time step i (BFi) may be
expressed as equal to the baseflow in the previous time step (BFi-1) plus alpha times the
difference of total streamflow at step i (SFi) and baseflow at step i-1 (BFi-1). That is:
BFi = BFi-1 +  (SFi-BFi-1)
(5.1)
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
At the beginning of surface runoff, the baseflow is assumed to be equal to the streamflow.
The value of α is estimated from the observed streamflow events; the design α value
should provide an acceptable baseflow separation for all the selected storms in the
catchment. The baseflow separation for storm of 1981-X2 is shown in Figure 5.2.
Baseflow separation strom 1981-X2
90
3
Streamflow (m /s)
80
70
60
50
Streamflow
(m3/s)
Baseflow
(m3/s)
40
30
20
10
0
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57
Time (hrs)
Figure 5.2 Baseflow separations for storm 1981-X2
5.4
5.4.1
RESULTS
FIT Runs
The model parameters to be obtained through calibration are: (i) loss parameters, which
involve calculating the rainfall excess from the total rainfall; and (ii) the routing
parameters, which involve the routing of the rainfall excess through the model storages of
the catchment to the outlet. The objective of FIT runs was (i) to find a best fit value of the
model parameter kc using historical streamflow and rainfall events data and (ii) to find the
best fit value of kc by altering IL and kc to match with the observed streamflow
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
hydrograph (as close as possible) while keeping the parameter m constant (the value of m
was assumed to be 0.8).
The kc values of the 40 fit runs were categorised according to their goodness-of-fit. The
results were considered as ‘excellent fit (E)’ if the calculated hydrograph, which is
indicated by red line in the Figure 5.3 closely follows the actual hydrograph indicated by
the blue line in Figure 5.3, as well as the difference in time to peak is negligible.
If the shape of calculated hydrograph was similar to the actual hydrograph but the time to
peak is delayed then it was considered as a ‘reasonable fit (R)’ as can be seen in Figure
5.4. Figure 5.5 shows the fitting result for a storm in which the calculated hydrograph
neither followed the actual hydrograph path nor did the time to peak matched very well.
This type of fit was considered as a ‘poor fit (P)’. The summary of goodness of fit results
is shown in Table 5.2. Results for all the fit runs are shown in APPENDIX A.
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
Figure 5.3 Example of excellent fit result for 1984-X1 storm
Figure 5.4 Example of reasonable fit result for 1984-X2 storm
Figure 5.5 Example of poor fit result for a storm 1977-X2
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Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
Table 5.2 Results of the FIT run for selected events
Storm
kc
(h)
IL
(mm)
CL
(mm/h)
1978
1986
1977-X3
1977-X4
1978-X2
1978-X3
1979-X1
1979-X2
1979-X3
1979-X4
1979-X5
1979-X7
1980-X1
1980-X3
1981-X2
1981-X3
1981-X4
1983-X1
1984-X1
1985-X1
1990
1979
1977-X1
1979-X6
1980-X2
1981-X5
1984-X2
1993-X1
1994-X1
1981
1983
1993
1984
1985
1994
1995
1977-X2
1978-X1
1979-X8
1981-X1
8.55
10.1
10.2
10.22
8
16.5
8.9
5.2
12.95
4.67
9.75
9.45
11.2
2.8
9.6
7.1
8
13.4
9.35
22
11.2
1.72
29.45
15.5
25.5
7
11.1
5.0
27.0
15.55
18.85
22.6
16.85
21.15
27.0
24.0
21
27
38
59
14
31
70
10
10
10
90
2
70
70
5
80
55
5
35
23
23
27
10
10
10
47
30
77
70
66
10
35
22
68.8
5
30
40
15
35
40
20
40
45
80
3.2
0.47
4
6.35
3.58
6.44
1.18
50.33
2.74
0.61
27.97
1.42
1.12
30.55
0.43
0.08
1.65
0.14
6.3
2.34
8.5
3.55
42.89
1.03
0.24
2.8
3.6
1.3
3.21
0.54
4.53
0.62
3.46
1.83
4.4
6.04
4.24
1.6
1.14
2.93
Peak flow Qp
(m3/s)
Cal
Actual
21.71
5.913
114.1
22.5
21.7
9.8
99.9
24.8
42.5
147.8
37.1
100.4
21.2
11.3
33.1
74.1
37.3
12.63
71.2
10.19
66.4
150
1.61
4
5.4
31.8
234.9
52.58
8.06
1.04
19.04
0.5
2.13
4.418
2.16
0.39
17.15
1.9
2.7
0.99
104
21.59
5.891
114.2
22.5
21.6
9.8
100.4
24.9
42.4
147.8
37.1
100.4
21.2
11.3
33.1
74.1
37.2
12.64
71.2
10.14
66.3
149
1.61
4
5.4
31.8
234.9
51.92
8.13
1.04
19.08
0.5
2.13
4.432
2.17
0.38
17.18
1.9
2.8
0.99
Time to peak
(h)
Cal
Actual
13
22
29
9
13
8
14
4
30
29
7
14
17
5
15
13
6
17
42
22
3
59
6
36
28
23
25
15
28
37
87
14
15
47
7
9
21
37
24
80
13
26
30
8
13
11
14
4
30
28
8
14
19
5
15
15
7
18
42
24
2
59
12
34
25
25
22
28
35
36
75
28
13
52
19
27
23
23
33
83
%
difference
in
peakflow
0.556
0.373
-0.088
0.000
0.463
0.000
-0.498
-0.402
0.236
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.269
-0.079
0.000
0.493
0.151
0.671
0.186
0.000
0.000
0.000
0.000
1.271
-0.861
0.000
-0.210
0.000
-0.188
-0.316
-0.461
2.632
-0.175
0.000
-3.571
-0.601
Type
of fit
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
R
R
R
R
R
R
R
R
P
P
P
P
P
P
P
P
P
P
P
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
The distribution of kc values for all the fit runs is shown in Figure 5.6, which shows a
wide variation in obtained kc values. Due to the observed degree of high variation, it
seems to be unreasonable to adopt a median or mean kc value in the design run which can
ensure the probability neutrality in the rainfall runoff modelling as assumed with the
Design Event Approach.
Figure 5.6 Frequency distribution of the kc values
Sensitivity studies of kc showed that as kc was increased, the hydrograph peak decreased
and the time to peak (lag) increased. This is to be expected, since kc is the indicator of the
lag parameter of the storage element as well as the size of storage effects. Also it was
interesting to note that three different fits were obtained for the three different storms in
the same year of 1984 and the kc values differed remarkably for each FIT run. The
variability in the kc values in the FIT run (obtained as above) was very high with the
minimum value being 1.72 hour and the maximum value 59 hours. The distribution of kc
105
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
values (Figure 5.6) shows that nearly 35% of kc values were in the range of 8-12 hours.
Almost 40% of kc values were in the range of 13-30 hours. For only two fit runs the kc
values were greater than 30 hours and both of these hydrographs were having very poor
fit. The mean and median kc values for all the storm events were 15.56 hours and 11.2
hours, respectively. Some important summary statistics of the kc values are shown in
Table 5.3. Since the kc values show a high variability, it is deemed to be important to
check the probabilistic nature of kc and its impacts on design flood estimates. As such
different kc values were used in the TEST run (as discussed below).
Table 5.3 Some important summary statistics of the kc values based on 40 storm events
Index
1
2
3
4
5
6
5.4.2
Statistics
Average from all storms
Median from all storms
Average from excellent fit
Median from excellent fit
Average from excellent and reasonable fit
Median from excellent and reasonable fit
kc (h)
15.56
11.2
9.96
9.6
11.43
9.75
IL (mm)
35.9
30.5
31.4
23
35.07
27
CL (mm/h)
6.23
2.87
7.59
2.74
7.52
2.8
TEST run
The representative model parameters determined in the FIT run, namely the value of kc
from Table 5.2 and m = 0.8 were verified using three other storms, which were of single
burst storms. Here, representative loss values from Table 5.2 as determined from the FIT
runs were used. The results of the TEST run for various combinations of the model
parameters are summarized in Table 5.4 and the percentage errors in peak flows are
plotted in Figure 5.7. It is observed that for storm 1984-T2 all the considered kc and IL
106
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
values provided poor predictions where the prediction error was as high as 46% and
nearly 70% of predictions were below the actual peak flow.
When using the value of kc selected from the FIT runs for its use in a design run, a high
level of uncertainty is associated with it. However, when validating the kc and IL values
obtained from FIT runs as recommended by the RORB manual on the three independent
storm events, there was as high as 46% difference in peak flow estimation. The errors for
predictions were in the range of + 20% to - 46 % (shown in Figure 5.7). These results
demonstrate the difficulty in selecting an appropriate set of parameter values for design
purpose with confidence.
30
20
0
R18
R17
R16
R15
R14
R13
R12
-10
R11
R10
R9
R8
R7
R6
R5
R4
R3
R2
R1
Error (%)
10
Error (% )
-20
-30
-40
-50
Test run
Figure 5.7 Error (%) in peak flow for the test runs (Runs R1, R2,… are defined in
Table 5.4)
Table 5.4 Impacts of various combinations of model parameters on peak flow estimates
Storm
kc (h)
IL
(mm)
1987-T1
1987-T1
15.56
11.2
35.9
30.5
Peak flow Qp (m3/s)
Time to peak (h)
CL
(mm/h)
Calculated
Actual
Calculated
Actual
4.85
4.85
382.1
476.1
436.6
436.6
4.8
4.8
7.8
7.8
107
Error
in peak
flow
(%)
-12.48
9.05
Test
Run
R1
R2
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
1987-T1
1987-T1
1987-T1
1987-T1
1984-T2
1984-T2
1984-T2
1984-T2
1984-T2
1984-T2
1984-T3
1984-T3
1984-T3
1984-T3
1984-T3
1984-T3
5.4.3
9.96
9.6
11.43
9.75
15.56
11.2
9.96
9.6
11.43
9.75
15.56
11.2
9.96
9.6
11.43
9.75
31.4
23
35.07
27
35.9
30.5
31.4
23
35.07
27
35.9
30.5
31.4
23
35.07
27
4.85
4.85
4.85
4.85
7.34
7.71
7.34
7.71
7.34
7.71
6.51
6.51
6.51
6.51
6.51
6.51
513.1
525.1
469.8
520
30.5
39.6
43.3
41.5
39
41.1
46.5
60.4
66.2
68.1
59.5
67.3
436.6
436.6
436.6
436.6
56.6
56.6
56.6
56.6
56.6
56.6
71
71
71
71
71
71
4.8
4.8
4.8
4.8
3.8
5.1
3.8
5.1
3.8
5.1
1.3
1.3
1.3
1.3
1.3
1.3
7.8
7.8
7.8
7.8
3.8
5.1
3.8
5.1
3.8
5.1
1.3
1.3
1.3
1.3
1.3
1.3
17.52
20.27
7.6
19.1
-46.11
-30.04
-23.5
-26.68
-31.1
-27.39
-34.51
-14.93
-6.76
-4.08
-16.2
-5.21
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
Sensitivity analysis
In practice, a user is most likely to select any combination of the parameter values which
are presented in Table 5.3. To examine the effects of key model parameters on flood
estimates, a variety of combinations of the representative values of kc, IL and CL (from
Table 5.3) were used to estimate the flood peaks. Figure 5.8 illustrates the approach used
in this study to check the sensitivity of the model parameters on flood estimates. The
steps involved in this approach are summarized below:
(1) select a random value of representative kc obtained from the FIT runs listed in Table
5.3;
(2) select a random value of representative IL obtained from the FIT run listed in Table
5.3;
(3) select a random value of representative CL obtained from the FIT run listed in Table
5.3;
108
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
(4) use these randomly selected representative parameters to run the RORB model for the
same design condition; and
(5) note the peak discharge for selected ARI and compare with the at-site flood frequency
estimates.
kc (h)
kc1,
kc2,
kc3,
kc4,
kc5,
kc6
CL (mm/h)
IL (mm)
CL1,
CL2,
CL3,
CL4,
CL5,
CL6
IL1,
IL2,
IL3,
IL4,
IL5,
IL6
Randomly select value of kc, IL, CL obtained from FIT run
eg. kc1, IL3, CL5
Runoff
routing
model
RORB
Peak flow
Surface hydrograph
Discharge
(m3/s)
Time (hr)
Figure 5.8 Approach used to check the sensitivity of model parameters on peak discharge
Hitesh D. Patel
109
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood Estimates
Table 5.5 The percentage differences in peakflows for selected ARIs obtained from variety of design simulation runs and at-site flood
frequency estimates
Simulation
run
Combination of model
parameter
kc/IL/
CL
ARI
1y
%
Error
ARI
2y
%
Error
ARI
5y
%
Error
ARI
10y
%
Error
ARI
20y
%
Error
ARI
50y
%
Error
ARI
100y
%
Error
S1
Median kc from E fit
Median IL from E and R fit
Average CL from Excellent fit
9.6
27
7.59
83.9
471.6
136.7
-0.2
223.4
-8.7
274.6
-13.6
345.8
-10.4
428.4
-8.8
501.7
-5.2
Average kc from E and R fit
Average IL from all storm
11.43
35.9
102
594.9
162.3
18.6
244.9
0
295.9
-6.9
367.4
-4.8
449.3
-4.3
521.7
-1.4
Median CL from E and R fit
2.8
S3
Median kc from all storm
Median IL from excellent fit
Median CL from all storm
11.2
23
2.87
119.3
712.7
180.6
31.9
266.3
8.8
317.3
-0.1
385.4
-0.1
466.3
-0.7
538.3
1.8
S4
Median kc from all storm
Median IL from excellent fit
Median CL from excellent fit
11.2
23
2.74
120.8
723.1
182.3
33.1
268.2
9.6
319.4
0.5
387.5
0.5
468.8
-0.2
540.8
2.2
S5
Median kc from all storm
Average IL from all storm
Median CL from E and R fit
11.2
35.9
2.8
103.7
606.6
165
20.5
249.1
1.8
300.8
-5.3
373.3
-3.2
455.9
-2.9
529
0
S6
Average kc from all storm
Average CL from all storm
Average IL from all storm
15.56
6.23
35.9
59.1
302.8
97.1
-29.1
153.7
-37.2
190.2
-40.1
245.9
-36.3
308.3
-34.4
365.6
-30.9
S7
Median kc from Excellent fit
Median CL from Excellent fit
Median IL from Excellent fit
9.6
2.74
23
138
840.2
206.7
50.9
300.9
22.9
356.2
12.1
429.8
11.4
515.2
9.7
591.3
11.8
S8
Median kc from E and R fit
Median CL from E and R fit
Median IL from E and R fit
9.75
2.8
27
132.9
805.1
198.4
44.9
292.6
19.5
347.9
9.5
421.9
9.4
507
7.9
581.8
10
S2
110
Hitesh Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
700
500
At-site
FFA
S1
400
S2
3
Discharge(m /s)
600
S3
300
S4
S5
200
S6
S7
100
S8
0
1
2
5
10
20
50
100
ARI (years)
Figure 5.9 Comparison of peakflow for various simulations
A total of 288 design runs were conducted with all the possible combinations of kc, IL
and CL (results have been given in APPENDIX C) and peakflow were estimated. The
peak flow for selected ARIs obtained from design run were then compared with at-site
flood frequency estimates and percentage errors were calculated. An LP3 distribution was
used for at-site flood frequency analysis (FFA) as shown in APPENDIX B. Table 5.5
shows the percentage difference in peakflows for selected ARIs obtained from variety of
design simulation runs and at-site flood frequency estimates.
Design run results for the model parameters combinations which showed the lowest error
relative to at-site flood frequency estimates are shown in bright green color in Table 5.4
111
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
and shown in Figure 5.9. Simulation run S1 (represented by median value of kc from
excellent fit, median value of IL from excellent and reasonable fit and average CL from
excellent fit) provided quite accurate result for 2 years ARI but grossly underestimated
the peakflow value by as much as 14% for ARI greater than 2 years. Simulation S2
(represented by average value of kc from excellent and reasonable fit, average value of IL
from all the storms and median kc from excellent and reasonable fit) overestimated the
peakflow for 2 years ARI by 19% but performed quite well for 5 years ARI. Whereas, the
same set of parameters underestimated peakflow by as much as 7% for ARIs greater than
5 years. Simulation run S3 (represented by median kc value from all the storms, median
IL value from excellent fit and median CL value from all the storms) provided the best
result for ARI greater than 5 years. It quite accurately predicted the peakflow for 10 and
20 years ARIs whereas the error of prediction for 50 and 100 years ARI was as low as
2% relative to at-site flood frequency estimates.
In RORB manual (Laurenson et al., 2007) it is recommended to use a representative
value of model parameters kc, IL and CL e.g. mean or median obtained from the fit runs.
The simulation run S6 with average values of model parameters as recommended in
RORB manual (Laurenson et al., 2007) grossly underestimated the peakflow values and
the error of prediction was quite high with the range of - 26 to - 41% relative to at-site
flood frequency estimates. Even the simulation run with median value of model
parameters from excellent fit (S7) and excellent and reasonable fit (S8) overestimated the
peakflow values by 51% and 45% respectively.
112
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
Sensitivity of kc values was also checked by various design simulation runs with fixed IL
and CL. Table 5.6 shows the results of various simulation runs with fixed median IL (23
mm) value from excellent fit and median CL value from all the storms (2.87 mm/h). The
estimated peak flows for various combinations of kc values with fixed IL and CL values
are shown in Figure 5.10.
Table 5.6 Simulation results with variable kc and fixed IL and CL values
Simulation
run
SF1
SF2
SF3
SF4
SF5
SF6
kc values
from variety of fit
Average kc from all storms
Median kc from all storms
Average kc from E fit
Median kc from E fit
Average kc from E and R fit
Median kc from E and R fit
kc (h)
15.56
11.2
9.96
9.6
11.43
9.75
113
ARI
1y
90.7
119
132
136
117
135
ARI
2y
137.5
180.6
198.9
204.7
177.5
202.3
Flood peak (m3/s)
ARI
ARI ARI
5y
10y
20y
204.2 244.3 298.3
266.3 317.3 385.4
291.2 345.6 417.8
298.8 354.1 427.6
262.1 312.4 379.7
295.6 350.7 423.5
ARI
50y
365.7
466.3
502.1
512.6
459.9
508.2
Hitesh D. Patel
Student ID: 16095380
ARI
100y
424.8
538.3
577.3
588.7
531.3
584
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
900
800
Lower 90% CL
(at-site FFA)
At-site FFA
700
Uper 90% CL
(at-site FFA)
Observed flow
500
3
Q m /s
600
SF1
400
SF2
300
SF3
SF4
200
SF5
100
SF6
0
1
10
100
ARI (years)
Figure 5.10 Comparison of at-site flood frequency analysis (FFA), observed annual
maximum floods and simulation runs with various kc in design run
The flood frequency curve (SF1) obtained using average kc value from all the 40
calibrated storm events provided notable underestimation at higher ARIs but quite good
estimation at smaller ARIs up to about 3 years. The flood frequency curves SF4
(represented by median kc value from all the excellent fit run storms), SF3 (represented
by average kc value from all the excellent fit run storms) and SF6 (represented by median
kc value from all the excellent and reasonable fit run storms) showed notable
overestimation. The flood frequency curve SF5 (represented by average kc value from all
the excellent and reasonable fit run storms) showed the best fit for ARIs greater than 3
years.
114
Hitesh D. Patel
Student ID: 16095380
Chapter 5: RORB Model Formulation and Impact of Model Parameter on Design Flood
Estimates
5.5
SUMMARY
It is found that selection of representative model parameter kc for RORB model is quite
difficult. The number of events used in calibration, calculation of representative values
(e.g. median or mean) and types of fit (e.g. excellent, good, reasonable, poor) affect the
magnitude of flood peak estimate remarkably. Also, selection of kc value cannot be made
independent of loss values. It is thus suggested that kc should be considered as a random
variable in flood modeling using the joint probability approach/Monte Carlo simulation.
Hence, it may be suggested that RORB model should be enhanced so that it can consider
kc as a random variable.
115
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
CHAPTER 6
RESULTS FROM MONTE-CARLO SIMULATION USING
STOCHASTIC RUNOFF ROUTING MODEL PARAMETER
6.1
STORM ANALYSIS
The first step in applying the Monte Carlo simulation is to carry out storm analysis in
which hourly pluviograph data at a given pluviograph station is analysed to select stormcore rainfall events in order to identify the probability distributions of storm-core
duration (Dc), storm-core rainfall intensity (Ic) in the form of IFD curves and storm-core
temporal patterns (TPc).
For rainfall analysis, a FORTRAN program called mcsa5.for is used. The basic input data
are (i) Hourly pluviograph data; and (ii) Design rainfall intensity data and skewness from
ARR (I. E. Aust., 1987) Volume 2, which are used to select the significant rainfall events.
The input to the program is given via a parameter file e.g. a54138.psa. An example of
parameter file for Pluviograph Station 54138 (Horton River) is shown in Table 6.1. The
important output files from program mcsa5.for are listed in Table 6.2
116
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Table 6.1 Parameters file a54138.psa for rainfall analysis (for Station 54138)
Program
Parameter
file
Parameter
a54138
mcsa5.for
a54138.psa
Description
Pluviograph station ID
P54138.dat
6
Hourly pluviograph data file, rainfall in mm
Zero rainfall period between successive complete storm events, hours
0.4
f1, Reduction factor to identify significant complete storm events
0.5
f2, Reduction factor to identify significant complete storm events
2
30.88
i1, Log-normal design rainfall intensity, 2 years ARI-1 hour duration, mm
6.38
2
i12, Log-normal design rainfall intensity, 2 years ARI-12 hour duration, mm
1.65
2
i72, Log-normal design rainfall intensity, 2 years ARI-72 hour duration, mm
50
62.35
i1, Log-normal design rainfall intensity, 50 years ARI-1hour duration, mm
11.61
50
i12, Log-normal design rainfall intensity, 50 years ARI-12 hour duration, mm
3.25
0.38
50
i72, Log-normal design rainfall intensity, 50 years ARI-72 hour duration, mm
G, Skewness
220
Catchment area, km2
418027B.txt
Hourly streamflow data file, streamflow in m3/s
Table 6.2 Important output files from program mcsa5.for (for Station 54138)
Output
a54138.dit
a54138.dcs
a54138.cdr
a54138.tpo
a54138.ifd
Description
Duration, intensity and total rainfall for complete storm
Duration of complete storm
Storm-core duration
Output file for temporal pattern analysis
IFD table
117
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
6.1.1
Distribution of storm-core durations Dc
One of the primary outputs of the storm analysis, and primary input for the Monte Carlo
Simulation Technique is the mean value of storm-core duration Dc for a particular rainfall
station. The mean value of Dc is β, which is the parameter of the exponential distribution
(exponential distribution is explained in Section 3.4.1). The exponential distribution has a
skewness of 2, and its mean and standard deviation are equal. The statistics of storm-core
durations Dc are listed in Table 6.3. The observed distributions of the rainfall station’s
storm-core durations are illustrated in APPENDIX D. Distributions of storm-core
duration (Dc) for Horton River catchment and Moonan Brook Catchment are shown in
Figure 6.1 and Figure 6.2 respectively.
Table 6.3 Statistics of storm-core duration (Dc) for all stations
Catchment
name
Station
No.
No. of
Events
Range
(h)
Mean
(h)
Median
(h)
Horton
Corang
Wadbilliga
Coopers
Moonan
54138
69049
69075
58072
61335
149
77
34
72
75
1 to 72
1 to 71
2 to 72
1 to 108
1 to 72
13.08
15.13
23.12
17.43
11.85
6
6
17
8.5
8
118
Std.
Deviation
(h)
16.19
18.55
22.82
21.06
13.55
Skewness
(h)
1.76
1.61
0.93
1.97
2.14
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Figure 6.1 Distribution of storm-core duration (Dc) for Horton River Catchment
(Pluviograph Station 54138)
Figure 6.2 Distribution of storm-core duration (Dc) for Moonan Brook Catchment
(Pluviograph Station 61335)
119
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
6.1.2
Storm-Core Rainfall Intensity (Ic)
The conditional distribution of storm-core rainfall intensity to storm-core duration
(Ic/Dc) is represented in the form of intensity-frequency-duration (IFD) tables, generated
from the selected rainfall station. From the IFD table, the IFD curve can be plotted. The
IFD curves of selected 5 pluviograph stations were obtained using the method as
explained in Section 3.4.2. The IFD values for station 54138 and station 69049 are shown
in Table 6.4 and Table 6.5 respectively and the corresponding IFD plots are shown in
Figure 6.3 and Figure 6.4 respectively. These plots revealed that the obtained IFD curves
were consistent in that they do not intersect each other. The IFD tables for the all the
study catchments are provided in APPENDIX E.
120
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.4 IFD table for Pluviograph Station 54138 (rainfall intensities are mm/h)
1
19.2
11.2
5.1
2.1
1.4
1.1
1.0
1.11
20.0
11.7
5.3
2.2
1.5
1.2
1.0
1.25
20.8
12.2
5.6
2.3
1.6
1.3
1.1
2
24.1
14.4
6.7
2.8
1.9
1.5
1.3
5
30.5
18.6
8.9
3.8
2.5
2.0
1.7
10
35.3
21.8
10.5
4.5
3.0
2.4
2.0
ARI, years
20
40.1
24.9
12.1
5.2
3.5
2.8
2.3
50
46.5
29.0
14.2
6.1
4.1
3.3
2.8
100
51.3
32.1
15.8
6.8
4.6
3.7
3.1
500
62.4
39.3
19.5
8.5
5.7
4.6
3.8
1000
67.2
42.5
21.1
9.2
6.2
4.9
4.1
1000000
114.9
73.3
36.9
16.2
11.0
8.8
7.4
Horton-Station 54138
1000
Ic (mm/hr)
Duration, h
1
2
6
24
48
72
100
100
10
1
1
10
D c (hours)
100
Figure 6.3 IFD curve for Pluviograph Station 54138
121
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.5 IFD table for Pluviograph Station 69049 (rainfall intensities are mm/h)
1
1.11
1.25
2
5
12.0
8.0
4.1
1.7
1.0
0.8
0.6
12.9
8.5
4.3
1.8
1.1
0.9
0.7
13.9
9.1
4.6
1.9
1.3
1.0
0.8
18.1
11.3
5.6
2.5
1.7
1.4
1.2
26.2
15.8
7.7
3.7
2.7
2.3
2.0
Corang River ARI, years
10
20
50
32.3
19.2
9.3
4.5
3.4
2.9
2.7
38.5
22.6
10.9
5.4
4.1
3.6
3.3
46.6
27.0
13.0
6.5
5.0
4.5
4.1
100
500
1000
1000000
52.7
30.4
14.6
7.3
5.8
5.1
4.8
66.9
38.3
18.3
9.3
7.4
6.7
6.3
73.0
41.6
19.9
10.2
8.1
7.4
6.9
134.0
75.3
35.7
18.6
15.2
14.0
13.4
Corang-69049
1000
100
I c (mm/hr)
Duration, h
1
2
6
24
48
72
100
10
1
1
0.1
10
100
D c (hours)
Figure 6.4 IFD curve for Pluviograph Station 69049
122
Hitesh D. Patel
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Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
6.1.3
Storm-Core Temporal Patterns (TPc)
The observed storm-core rainfall temporal patterns (TPc), in the form of dimensionless
mass curves, are determined for each selected pluviograph station from the storm analysis
program mcsa5.for with output extension of a54138.tpo for Horton River catchment. The
program mcdffc3k.for creates two database files of the observed dimensionless temporal
patterns from the study pluviograph station with upto 12 hours (e.g. a54138.L12) and
greater than 12 hours durations (e.g. a54138.g12). The typical observed temporal patterns
for durations greater than 12 hours and durations less then 12 hours from Horton River
catchment is shown in Figure 6.5 and Figure 6.6 respectively. The temporal patterns for
all the study catchments are shown in APPENDIX F.
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Period
Figure 6.5 Sample observed storm-core temporal patterns for durations greater than 12
hours for Horton River catchment (Pluviograph Station 54138)
123
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Period
Figure 6.6 Sample observed storm-core temporal patterns for durations less than 12
hours for Horton River catchment (Pluviograph Station 54138)
6.2
LOSS ANALYSIS
To identify the probability distribution of storm-core initial loss (ILc) and probability
distribution of initial loss for complete storm (ILs), a FORTRAN program called
losssca.for is used. The basic data input to this program are concurrent hourly streamflow
and hourly rainfall data. The required input data are provided through a parameter file
(with extension .lan, which stands for loss analysis). Table 6.6 shows the parameter file
for Horton River catchment. The important output files generated from this program are
(1) a54138.ics (initial loss values for complete storm, ILs) and (2) a54138.isc (storm-core
initial loss values, ILc). Figure 6.7 shows the probability distribution of initial loss for
124
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
complete storm and Figure 6.8 shows the initial loss for storm-core for Horton River
catchment. The initial loss histograms for all the study catchments are shown in
APPENDIX G.
Loss analysis for all the study catchments was carried out and Table 6.7 shows the
statistics of initial loss for complete storm (ILs). The statistics of initial loss for stormcore considering all the study catchments is shown in Table 6.8. The analysis of the
output shows that for the Coopers Creek catchment the range of observed ILs is very high
(0 mm to 523 mm). The standard deviation is almost 50% higher than the mean initial
loss value. The initial loss value of greater than 100 mm seems to be unreasonable and
further data checking of streamflow and pluviograph data was done. It was found that
during year 1975 to 1976 no streamflow data was recorded which means that all the
rainfall occurred during that period has been calculated as loss by the program, resulting
in higher initial loss range. The error code in streamflow data was 255. It also highlights
the stepwise nature of the approach - how quality checking in each step is just as
important as undertaking the modelling itself. This initial loss value of 523 mm is
ignored. A four parameter Beta distribution was fitted to the initial loss data. The four
parameters are lower limit, upper limit, mean and standard deviation of initial loss values.
125
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Table 6.6 Parameter file ‘b418027.lan’ for Loss Analysis
Program
Parameter file
Parameter
a54138
losssca.for
b418027.lan
Description
Pluviograph station ID
220
P54138.dat
Catchment area, km2
Hourly pluviograph data file, rainfall in mm
418027B.txt
Hourly streamflow data file, streamflow in m3/s
Table 6.7 Statistics of initial loss for complete storm (ILs) for all stations
Catchment Station
name
No.
Horton
Corang
Wadbilliga
Coopers
Moonan
54138
69049
69075
58072
61335
No. of
Events
Range
(mm)
Mean
(mm)
149
77
34
72
75
0 to 111
0 to 81
0 to 148
0 to 523
0 to 73
35.83
29.97
36.03
49.63
22.50
Std.
Median
Skewness
Deviation
(mm)
(mm)
(mm)
31.27
18.99
1.173
26.18
16.47
0.708
32.87
28.70
1.897
27.67
76.92
3.987
21.60
15.34
0.894
Figure 6.7 Probability distribution of initial loss (ILs) for the Horton River Catchment
126
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Table 6.8 Statistics of initial loss for storm-core (ILc) for all stations
Catchment
name
Station
No.
No. of
Events
Range
(mm)
Mean
(mm)
Horton
Corang
54138
69049
69075
149
77
34
0 to112
0 to 72
0 to 147
31.78
25.82
30.24
58072
61335
72
75
0 to 274
0 to 63
38.50
19.91
Wadbilliga
Coopers
Moonan
Std.
Median
Skewness
Deviation
(mm)
(mm)
(mm)
28.72
18.31
1.34
22.29
15.97
0.74
26.56
28.13
2.34
22.84
17.68
57.63
13.89
2.47
0.90
Figure 6.8 Probability distribution of initial loss (ILc) for the Horton River Catchment
6.3
MODEL CALIBRATION (k, IL, CL)
To determine the derived flood frequency curve for a particular catchment, the runoff
routing model needs to be calibrated for the catchment. In Monte Carlo Simulation
Technique (as described in Section 3.2.2) single non-linear storage model with a storage
discharge relationship of the form S = kQm with the exponent (m) fixed at a value of 0.8
127
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
used in this study.
The objective of model calibration is to determine a value of k that results in satisfactory
fit for a range of recorded rainfall and runoff events at the catchment outlet. The
calibration of the adopted model is similar to the techniques used for other runoff routing
models such as RORB. However, in this study a four parameter beta distribution is used
to define the storage delay parameter k to obtain derived flood frequency curve (DFFC).
The calibrated values are also used to carry out the sensitivity analysis of k.
A FORTRAN program called Cali4.for is used to calibrate runoff routing model. The
required input data are provided through a parameter file, with extension .dat (e.g.
hocal1.dat). Table 6.9 shows the parameter file for Horton River catchment. The
important output files generated from this program are (1) aHorEv1.rpf (routing plot file
to plot observed streamflow and computed streamflow) and (2) aHorEv1.bff (baseflow
file for plotting streamflow vs. baseflow) and (3) aHorEv1.rre (Routing results, errors
etc.). Typical values of parameters from calibration run for all the study catchments are
summarised in Table 6.10 and the quality of fit for Event 2 for Horton River catchment
and Coopers Creek catchment is shown in Figure 6.9 and Figure 6.10, respectively. The
plot of fit run for all the study catchments is shown in APPENDIX H. Because of the
short record of concurrent streamflow and pluviograph data for two catchments namely
Corang and Moonan only two and one storm events respectively, were identified for
model calibration.
128
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Table 6.9 Parameter file ‘hocal1.dat’ for runoff routing model calibration
a
Ev1
Cali4.for
hocal1.dat
Description
Catchment name, which will be prefixed to all output files from this
program
Run sequence to distinguish simulation runs (a,b,c,...)
Identification of rainfall-streamflow event number (eg. Ev1, Ev2...)
0.005
Baseflow separation parameter, Alpha
220
Catchment area, km2
Event1calib.txt
Rainfall-streamflow event data file name
49.65
Initial loss value IL, mm
3.2
Continuing loss value CL, mm/h
10
Runoff routing model storage delay parameter k, h
0.8
Runoff routing model non-linearity parameter m (assumed 0.8)
Program
Parameter file
Parameter
Horton
Table 6.10 Typical values of parameters from calibration run for all the study catchments
Catchment Event
name
no.
Wadbilliga
Horton
Corang
Coopers
Moonan
Ev1
Ev2
Ev3
Ev4
Ev1
Ev2
Ev3
Ev4
Ev1
Ev2
Ev1
Ev2
Ev3
Ev4
Ev1
Storm start
(y/d/m/h)
1976/25/10/16
1978/14/06/03
1984/25/01/20
1977/25/02/01
1977/22/01/22
1977/20/02/13
1978/04/11/07
1977/13/05/19
1976/29/06/20
2000/07/03/20
1977/01/03/19
1979/29/07/01
1985/08/07/02
1989/22/01/23
1979/14/07/10
IL
CL
(mm) (mm/h)
k (h)
30
20
38.5
30
49.65
98
10
50
23
25
37
70
30
30
10
44
25
43
16.35
10
22.7
22
15.6
23.45
33.5
17.8
14
11.56
17.5
58.6
129
3.5
1.2
3.62
2
3.2
1.1
4
0.1
1.9
2.5
3.5
3
16
0.5
6
Difference
in peak
(%)
-0.72
-0.52
0.21
-1.5
0.59
-0.11
0.44
-0.06
-0.09
0.03
-0.21
0.2
-0.16
-0.12
0.00
Difference
in volume
(%)
-10.46
-5.29
17.89
-10.1
26.45
-2.3
26.6
12.1
16.14
-44.73
-22.74
17.48
-12.37
7.73
-35.15
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
200
Horton 418027_Ev2
Qobs
180
Qcom
160
Discharge, m/s
140
3
120
100
80
60
40
20
0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
Time, hours
Figure 6.9 Fitting result of Event 2 for Horton River (Qobs is observed hydrograph and
Qcom is computed hydrograph)
50
Coopers 203002_Ev2
Qobs
45
Qcom
40
3
Discharge, m /s
35
30
25
20
15
10
5
0
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81
Time, hours
Figure 6.10 Fitting result of Event 2 for Coopers Creek catchment (Qobs is observed
hydrograph and Qcom is computed hydrograph)
130
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
6.4
DERIVED FLOOD FREQUENCY CURVE
The Monte Carlo Simulation Technique has been applied to the five study catchments
listed in Table 4.1. As discussed in Section 3.4.1 the method assumes that storm-core
durations have exponential distribution and the complete storm initial loss (IL) and model
storage delay parameter (k) have four parameter Beta distribution. The existing
FORTRAN program (Rahman et al., 2002a) has been upgraded to consider k as a random
variable in Monte Carlo Simulation Technique framework. The upgraded FORTRAN
program called mcdffc3k.for has been used to obtain derived flood frequency curve.
The required input data are provided through a parameter file, with extension .par (e.g.
xhoka1.par). Table 6.11 shows the parameter file to obtain derived flood frequency curve
for the Horton River catchment. The important output files generated from this program
are (1) e.g. a54138.gdc (generated storm-core rainfall durations) (2) e.g. a54138.gic
(generated storm-core rainfall intensities) (3) e.g. a54138.glc (generated storm-core initial
loss values) (4) e.g. a54138.gkv (generated storage delay parameter k values) (5) e.g.
a54138.gsp (generated streamflow hydrograph peaks and ARI) and (6) e.g. a54138.ffc
(derived flood frequency curve).
The derived flood frequency curve for the Horton River catchment is shown in Figure
6.11. The values of k namely mean, standard deviation, upper limit and lower limit,
which are obtained from calibration run (shown in Table 6.10) have been used. Similar
131
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
derived flood frequency curves for all the study catchments were obtained which are
shown in Section 6.4.
Table 6.11 Parameter file ‘xhoka1.par’ to obtain derived flood frequency curve
Program
Parameter file
Parameter
Horton
a
40000
13.08
220
a54138.ifd
lista.cop
0.3
111.53
35.82
18.99
10
2.1
0.8
10
22.7
17.58
5.9
1.05
2000
mcdffc3k.for
xhoka1.par
Description
Catchment name, which will be prefixed to all output files from this
program
Run sequence to distinguish simulation runs (a,b,c,...)
Number of streamflow events to be simulated
Mean of storm-core duration (hours)
Catchment area, km2
Intensity-frequency duration table
Temporal pattern database file name
Complete storm initial loss (IL) lower limit, mm
Complete storm initial loss (IL) upper limit, mm
Complete storm initial loss (IL) mean value, mm
Complete storm initial loss (IL) standard deviation, mm
Interval in temporal mass curve, generally 10
Continuing loss (CL), mm/h
Runoff routing model non-linearity parameter m (assumed 0.8)
Runoff routing model storage delay parameter (k) lower limit, hours
Runoff routing model storage delay parameter (k) upper limit, hours
Runoff routing model storage delay parameter (k) mean value, hours
Runoff routing model storage delay parameter (k) standard deviation,
hours
Design Baseflow value, m3/s
Length of simulation, years (used 2000 years in this study)
132
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
DFFC Horton-418027
500
450
400
350
3
Q, m /s
300
250
200
150
100
50
0
0.1
1
ARI,years
10
100
Figure 6.11 Derived flood frequency curve using average k value from calibration run
for Horton River catchment
6.5
COMPARISON OF DERIVED FLOOD FREQUENCY CURVES WITH
RESULTS OF AT-SITE FLOOD FREQUENCY ANALYSES
The Monte Carlo Simulation Technique has been applied to the selected five study
catchments shown in Table 4.1. For each catchment, the value of k obtained from
calibration run was used to derive flood frequency curve, where the range of k value is
used as the upper limit and lower limit. The mean and standard deviation values of k were
also obtained from the calibration results. For the Horton River, Coopers Creek and
Wadbilliga catchments four storm events were used for calibration from which the four
parameter values of k can be reasonably defined. For the Moonan Brook and the Corang
River catchment only one and two storm events respectively was identified due to low
133
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
quality and short concurrent pluviograph and streamflow data. For these catchments the
upper limit (UL) and lower limit (LL) of k values is obtained by increasing and
decreasing the observed at-site mean k value by 20%. The four parameter values of initial
loss (lower limit, upper limit, mean and standard deviation) are obtained from the output
file with extension of .slp (e.g. a54138.slp for Horton River catchment). The fixed
variables used in the simulation of streamflow hydrograph were observed at-site mean
continuing loss value obtained from model calibration, design baseflow and non linearity
parameter (m) as 0.8. To generate the peak floods for 2000 years, 40,000 simulations run
were used.
The effect of k on derived flood frequency curve was examined by simulating hydrograph
by decreasing all the four parameter values of k (lower limit, upper limit, mean and
standard deviation) by 20%, 40%, 60% and 70%. The resulting derived flood frequency
curves (partial series) for the Horton River, Coopers Creek, Wadbilliga, Corang River
and Moonan Brook catchments are compared in Figures 6.12, 6.13, 6.14, 6.15 and 6.16
respectively with the results of frequency analyses of the partial flood series available at
the sites (following the empirical distribution approach using Cunnane’s plotting position
formula). The percentage difference between derived floods (partial series) and observed
flood (partial series) for the above five catchments are presented in Tables 6.12, 6.13,
6.14, 6.15 and 6.16.
134
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.12 The percentage difference between DFFC and observed floods for Horton River catchment
DFFC-a
(obs. k,
m3/s)
131.4
182.9
222.3
262.4
319.9
370.4
%
diff
(abs)
24.3
37.2
29.7
41.9
37.1
35.7
36.4
%
diff.
-24.3
-37.2
-29.7
-41.9
-37.1
-35.7
DFFC-b
(80% of
obs. k,
m3/s)
158
217.3
265.9
314.1
374.7
438.1
%
diff.
-9
-25.4
-15.9
-30.5
-26.3
-24
DFFC-c
(60% of
obs. k,
m3/s)
196
269.1
324.2
385.4
464.3
545.7
%
diff
(abs)
9
25.4
15.9
30.5
26.3
24
24.7
%
diff.
12.9
-7.6
2.5
-14.7
-8.6
-5.3
%
diff
(abs)
12.9
7.6
2.5
14.7
8.6
5.3
8.1
DFFC-d
(40% of
obs. k,
m3/s)
260.9
350.4
420
497.5
624.2
742.7
%
diff.
50.3
20.4
32.8
10.2
22.8
28.9
DFFC-e
(30% of
obs. k,
m3/s)
313.4
418.3
498.8
601.2
762.5
855.1
%
diff
(abs)
50.3
20.4
32.8
10.2
22.8
28.9
25.9
%
diff.
80.5
43.7
57.8
33.1
50
48.4
DFFC Horton-418027
1000
900
Observed flow
800
DFFC-a (obs.
k)
700
600
DFFC-b (80%
of obs. k)
3
Q, m /s
ARI,
years
2
5
10
20
50
100
Obs.
flow,
m3/s
174
291
316
452
508
576
Median
500
DFFC-c(60%
of obs. k)
400
DFFC-d (40%
of obs. k)
300
200
DFFC-e (30%
of obs. k)
100
0
1
10
ARI, years
100
Figure 6.12 Comparison of DFFC (partial series) and results of at-site FFA for Horton River catchment
135
Hitesh Patel
Student ID: 16095380
%
diff
(abs)
80.5
43.7
57.8
33.1
50
48.4
49.2
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.13 The percentage difference between DFFC and observed floods for Cooper’s Creek catchment
DFFC-a
(obs. k,
m3/s)
110
141.6
166.6
196.6
227.6
256.6
%
diff.
-28.4
-44.9
-45
-43.7
-50.5
-47.8
%
diff
(abs)
28.4
44.9
45
43.7
50.5
47.8
45
DFFC-b
(80% of
obs. k,
m3/s)
130.1
166.8
196.8
229.9
265.9
303.7
% diff.
-15.4
-35.1
-35
-34.1
-42.1
-38.3
% diff
(abs)
15.4
35.1
35
34.1
42.1
38.3
35.1
DFFC-c
(60% of
obs. k,
m3/s)
159.5
205.5
239.8
279.7
325.4
382.4
%
diff.
3.7
-20.1
-20.8
-19.9
-29.2
-22.3
%
diff
(abs)
3.7
20.1
20.8
19.9
29.2
22.3
20.5
DFFC-d
(40% of
obs. k,
m3/s)
207.7
267.2
311.7
363.7
433
503.1
DFFC-e
(30% of
obs. k,
m3/s)
245.8
319.5
375.6
438.8
533.2
594.1
%
diff.
59.9
24.3
24
25.7
16
20.8
Observed flow
600
DFFC-a (obs. k)
500
3
%
diff.
35.1
3.9
2.9
4.2
-5.8
2.3
%
diff
(abs)
35.1
3.9
2.9
4.2
5.8
2.3
4.1
DFFC Coopers creek-203002
700
Q, m /s
ARI,
years
2
5
10
20
50
100
Obs.
flow,
m3/s
154
257
303
349
460
492
Median
400
DFFC-b (80%
of obs. k)
300
DFFC-c(60% of
obs. k)
200
DFFC-d (40%
of obs. k)
100
DFFC-e (30%
of obs. k)
0
1
10
ARI, years
100
Figure 6.13 Comparison of DFFC (partial series) and results of at-site FFA for Coopers Creek catchment
136
Hitesh Patel
Student ID: 16095380
%
diff
(abs)
59.9
24.3
24
25.7
16
20.8
24.2
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
The results for the Horton river Catchment are presented in Figure 6.12 which shows
that derived flood frequency curve obtained using the observed at-site mean k value of
17.58h, standard deviation (std dev) of 5.9h, UL and LL k values of 22h and 10h
respectively, significantly underestimates flood peaks compared to the observed floods.
A reduction of 20% (80% of observed k values) of all the four parameter k values
increases the derived flood frequency curve by 12% but still underestimates the derived
flood frequency curve where the absolute median relative error is estimated at 24.7%
compared to at-site flood frequency analysis considering ARIs of 1, 2, 5, 10, 20, 50 and
100 years. The best match between derived flood frequency curve and observed floods is
obtained by decreasing the observed four parameter k values by 40% (LL = 6h, UL =
13.62h, mean = 10.55h and std dev = 3.54h) for which the absolute median relative error
is as low as 8.1%.
For Coopers Creek catchment flood peaks derived by using observed four parameters k
values (LL = 11.56h, UL = 17.8h, mean = 15.22h and std dev = 2.99h) and 80% of the
observed four parameters k values (LL = 9.25h, UL = 14.24h, mean = 12.77h and std
dev = 2.39h) grossly underestimates flood peaks by 45% and 35% respectively. The
DFFC-d (represented by 40% of observed k values) as shown in Figure 6.13 gives very
close match for ARI greater than 2 years with absolute median relative error in the range
of 2.3% to 5.8%. The derived flood frequency curve obtained by using 30% of the
observed k values grossly overestimates the peak flood by as much as 24%.
137
Hitesh Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
Comparison of derived flood frequency curve (partial series) and results of at-site flood
frequency analysis for Wadbilliga catchment is shown in Figure 6.14 below. For this
Catchment, the observed four parameter k value (LL = 16.35h, UL = 44h, mean = 32.9h
and std dev = 13.65h) gives very close result for ARI greater than 5 years whereas the
same parameters overestimates the peak floods for 2 and 5 years ARI significantly. A
further decrease in observed four parameter values of k by 20%, 40%, 60% and 70%
increases the derived floods by 3%, 17%, 44% and 66% respectively.
138
Hitesh Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.14 The percentage difference between DFFC and observed floods for Wadbilliga catchment
DFFC-a
(obs. k,
m3/s)
178.7
237.5
283.4
337.4
409.9
460.9
%
diff.
101
17.4
-5.5
-20.8
-5.7
4.7
%
diff
(abs)
101
17.4
5.5
20.8
5.7
4.7
11.5
DFFC-b
(80% of
obs. k,
m3/s)
207.2
274.1
320.5
379.8
463.9
518
%
diff.
133.1
35.5
6.8
-10.9
6.7
17.7
%
diff
(abs)
133.1
35.5
6.8
10.9
6.7
17.7
14.3
DFFC-c
(60% of
obs. k,
m3/s)
246.5
320.1
377.6
441.5
531.6
579.5
%
diff.
177.2
58.2
25.9
3.6
22.2
31.6
%
diff
(abs)
177.2
58.2
25.9
3.6
22.2
31.6
28.7
DFFC-d
(40% of
obs. k,
m3/s)
303.1
389.7
454.8
528.5
623.2
700.1
%
diff.
240.9
92.6
51.6
24
43.3
59
%
diff
(abs)
240.9
92.6
51.6
24
43.3
59
55.3
DFFC-e
(30% of
obs. k,
m3/s)
343
443.8
519.1
596.7
689.8
806.5
%
diff.
285.7
119.3
73
40
58.6
83.2
DFFC Wadbilliga-218007
1000
900
Observed flow
800
3
Q, m /s
ARI,
years
2
5
10
20
50
100
Obs.
flow,
m3/s
88.9
202
300
426
435
440
Median
700
DFFC-a (obs.
k)
600
DFFC-b (80%
of obs. k)
500
DFFC-c(60%
of obs. k)
400
DFFC-d (40%
of obs. k)
300
DFFC-e (30%
of obs. k)
200
100
0
1
10
ARI, years
100
Figure 6.14 Comparison of DFFC (partial series) and results of at-site FFA for Wadbilliga catchment
139
Hitesh Patel
Student ID: 16095380
%
diff
(abs)
285.7
119.3
73
40
58.6
83.2
78.1
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.15 The percentage difference between DFFC and observed floods for Corang River catchment
DFFCa (obs.
k)
98.7
138
165.1
196
236
275.1
%
diff.
-41.8
-52.9
-47.7
-42.2
-47.2
-45.9
%
diff
(abs)
41.8
52.9
47.7
42.2
47.2
45.9
46.5
DFFC-b
(80% of
obs. k,
m3/s)
116.8
160.4
191
223.9
271.3
306.8
%
diff.
-31.1
-45.2
-39.4
-33.9
-39.3
-39.6
%
diff
(abs)
31.1
45.2
39.4
33.9
39.3
39.6
39.4
DFFCc(60% of
obs. k,
m3/s)
142
192.2
228.5
271.7
322.9
367.9
%
diff.
-16.2
-34.4
-27.6
-19.8
-27.7
-27.6
%
diff
(abs)
16.2
34.4
27.6
19.8
27.7
27.6
27.6
DFFC-d
(40% of
obs. k,
m3/s)
183.3
242.2
293
344.8
419.7
466.1
%
diff.
8.1
-17.3
-7.1
1.7
-6.1
-8.3
DFFC-e
(30% of
obs. k,
m3/s)
215.8
285.7
339.8
398.4
486.9
573.7
%
diff
(abs)
8.1
17.3
7.1
1.7
6.1
8.3
7.6
%
diff.
27.3
-2.4
7.7
17.6
9
12.9
%
diff
(abs)
27.3
2.4
7.7
17.6
9
12.9
10.9
DFFC Corang 215004
600
Observed flow
500
DFFC-a (obs.
k)
400
DFFC-b (80%
of obs. k)
300
DFFC-c(60%
of obs. k)
200
DFFC-d (40%
of obs. k)
3
Q, m /s
ARI,
years
2
5
10
20
50
100
Obs.
flow,
m3/s
170
293
316
339
447
508
Median
DFFC-e (30%
of obs. k)
100
0
1
10 ARI, years
100
Figure 6.15 Comparison of DFFC (partial series) and results of at-site FFA for Corang River catchment
140
Hitesh Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model Parameter
Table 6.16 The percentage difference between DFFC and observed floods for Corang river catchment
DFFC-a
(obs. k,
m3/s)
10.9
14.7
17.3
20.3
23.6
27.6
%
diff.
-45.4
-78.8
-85.2
-83.6
-82.8
-81.2
%
diff
(abs)
45.4
78.8
85.2
83.6
82.8
81.2
82
DFFC-b
(80% of
obs. k,
m3/s)
13.8
18.6
21.9
25.7
30.3
34.8
%
diff.
-30.8
-73.2
-81.3
-79.2
-77.8
-76.3
%
diff
(abs)
30.8
73.2
81.3
79.2
77.8
76.3
77.1
DFFC-c
(60% of
obs. k,
m3/s)
18.6
25.3
30
34.6
42.2
48.1
%
diff.
-6.2
-63.4
-74.3
-72
-69.2
-67.3
%
diff
(abs)
6.2
63.4
74.3
72
69.2
67.3
68.2
DFFC-d
(40% of
obs. k,
m3/s)
28.2
38.2
45.2
52.4
64.2
72.4
%
diff.
42.1
-44.8
-61.3
-57.6
-53.1
-50.8
%
diff
(abs)
42.1
44.8
61.3
57.6
53.1
50.8
51.9
DFFC-e
(30% of
obs. k,
m3/s)
37.5
50.8
60.2
69.5
86
97.8
%
diff.
88.8
-26.5
-48.6
-43.7
-37.2
-33.5
%
diff
(abs)
88.8
26.5
48.6
43.7
37.2
33.5
40.5
DFFC Moonan 210017
200
Observed flow
180
DFFC-a (obs.
k)
160
140
120
DFFC-b (80%
of obs. k)
100
DFFC-c(60%
of obs. k)
Q, m3/s
ARI,
years
2
5
10
20
50
100
Obs.
flow,
m3/s
19.9
69.1
117
124
137
147
Median
80
DFFC-d (40%
of obs. k)
60
DFFC-e (30%
of obs. k)
40
20
0
1
10 ARI, years
100
Figure 6.16 Comparison of DFFC (partial series) and results of at-site FFA for Moonan brook catchment
141
Hitesh Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
For the Corang River catchment the DFFC-d (represented by 40% of observed k values)
as shown in Figure 6.15 gives very close match for ARI greater than 2 years with
absolute median relative error in the range of 1.7% to 17%. For the Moonan Brook
catchment even a 70% decrease in observed k value underestimated the flood peak value
by 40.5% as can be seen in Figure 6.16. It was observed that the calibration of model for
this catchment resulted in very high k value (58.6h) which resulted in high values of all
the four parameter k values resulting in gross underestimation.
The absolute median relative error values for all the study catchments are shown in Table
6.17. As shown in Figure 6.17 as the observed value of k is decreased the absolute
median relative error for Wadbilliga catchment increases sharply whereas the median
error for Moonan Brook catchment decreases. A systematic pattern can be seen for
Horton River, Coopers Creek and Corang River catchment where the median error of
estimation first decreases with reduction in value of observed k and then increases with
further decrease in observed value of k.
Table 6.17 Absolute median relative error for all simulation run for the study catchments
considering ARIs 1, 2, 5, 10, 20, 50 and 100 years.
k values
(obs. k)
(80% of obs. k)
(60% of obs. k)
(40% of obs. k)
(30% of obs. k)
Absolute median relative error, %
Horton Coopers Wadbilliga Corang Moonan
36.4
45
11.5
46.5
82
24.7
35.1
14.3
39.4
77.1
8.1
20.5
28.7
27.6
68.2
25.9
4.1
55.3
7.6
51.9
49.2
24.2
78.1
10.9
40.5
142
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
absolute % median relative error
90
80
70
Horton
60
Coopers
50
Wadbilliga
40
Corang
30
Moonan
20
10
0
(obs k)
(80% of obs k) (60% of obs k) (40% of obs k) (30% of obs k)
Figure 6.17 Comparison of simulation runs for all the study catchments
6.6
COMPARISON
TECHNIQUE
OF
WITH
EXISTING
UPDATED
MONTE
CARLO
SIMULATION
MONTE
CARLO
SIMULATION
TECHNIQUE
To assess the performance of the updated Monte Carlo Simulation Technique used in this
study which considers model storage delay parameter k as a random variable, derived
flood frequency curve is obtained using the old FORTRAN program called ‘mcdffc3.for’
and its result are compared with at-site observed floods. In the existing Monte Carlo
Simulation Technique only single representative value of k is used to obtain derived flood
frequency curve. For both (existing Monte Carlo Simulation Technique and updated
Monte Carlo Simulation Technique) same set of parameters (IL, CL, design baseflow, m
and number of simulation runs) is used to obtain flood frequency curve. The mean value
143
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
of k which showed least median relative error compared to at-site flood frequency analysis
using the updated Monte Carlo Simulation Technique is used in existing Monte Carlo
Simulation Technique to obtain derived flood frequency curve.
The simulation results for 6 ARIs (2, 5, 10, 20, 50 and 100 years) using the old Monte
Carlo Simulation Technique and updated Monte Carlo Simulation Technique for all the
study catchments are shown in Table 6.18. Figure 6.18 shows the comparison of derived
flood frequency curve for Horton River catchment, obtained by old Monte Carlo
Simulation Technique and updated Monte Carlo Simulation Technique. The old technique
provides very good estimates for 20 years ARI, where the difference between observed
peak flow and estimated peak flow is almost zero. However, the updated Monte Carlo
Simulation Technique provides overall better results for 6 ARIs compared to old Monte
Carlo Simulation Technique, where the absolute median relative error is almost 4% lower
than the old Monte Carlo Simulation Technique.
Figure 6.19 shows that the old Monte Carlo Simulation Technique grossly overestimates
the derived flood frequency curve and the updated Monte Carlo Simulation Technique
outperforms the old Monte Carlo Simulation Technique for Coopers Creek catchment
where the updated Monte Carlo Simulation Technique predicts the peak floods with about
10% more accuracy. For Wadbilliga catchment the existing technique estimates peakflow
more accurately for ARI 20 years than the updated Monte Carlo simulation Technique (as
can be seen in Figure 6.20). But for 5, 10 and 50 years ARIs the updated Monte Carlo
Simulation Technique outperforms the old Monte Carlo Simulation Technique. The
144
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
absolute median relative error for 6 ARIs is estimated to be 11% for updated technique
and 17% for old technique compared to the observed flow.
Table 6.18 DFFC for Coopers Creek catchment using old MCST and updated MCST
Catchment
name
Horton
Coopers
Wadbilliga
Corang
Moonan
Obs.
ARI,
flow,
years
m3/s
2
173.6
5
291.1
10
316.2
20
451.7
50
508.2
100
576.2
Median
2
153.8
5
257.1
10
302.9
20
349.1
50
459.6
100
491.9
Median
2
88.9
5
202.4
10
300.0
20
426.2
50
434.9
100
440.3
Median
2
169.6
5
292.8
10
315.5
20
338.8
50
446.8
100
508.2
Median
2
19.9
5
69.1
10
117.1
20
123.6
50
136.9
100
147.0
Median
DFFC-O
(Old MCST)
, m3/s
234.4
318.9
383.4
452.7
559.6
662.5
%
diff.
35.0
9.6
21.3
0.2
10.1
15.0
228.6
294.8
343.6
404.3
483.8
548.5
48.7
14.7
13.5
15.8
5.3
11.5
219.6
287.9
339.7
400.7
484.4
539.5
147.0
42.3
13.2
-6.0
11.4
22.5
186.2
246.7
296.9
349.1
425.6
472.7
9.8
-15.8
-5.9
3.0
-4.7
-7.0
36.9
50.0
59.3
70.7
82.9
95.2
85.5
-27.7
-49.4
-42.8
-39.5
-35.2
145
%
diff
(abs)
35.0
9.6
21.3
0.2
10.1
15.0
12.5
48.7
14.7
13.5
15.8
5.3
11.5
14.1
147.0
42.3
13.2
6.0
11.4
22.5
17.9
9.8
15.8
5.9
3.0
4.7
7.0
6.4
85.5
27.7
49.4
42.8
39.5
35.2
41.1
DFFC-U
(Updated
MCST) , m3/s
196.0
269.1
324.2
385.4
464.3
545.7
207.7
267.2
311.7
363.7
433.0
503.1
178.7
237.5
283.4
337.4
409.9
460.9
183.3
242.2
293.0
344.8
419.7
466.1
37.5
50.8
60.2
69.5
86.0
97.8
%
%
diff
diff. (abs)
12.9 12.9
-7.6
7.6
2.5
2.5
-14.7 14.7
-8.6
8.6
-5.3
5.3
8.1
35.1 35.1
3.9
3.9
2.9
2.9
4.2
4.2
-5.8
5.8
2.3
2.3
4.1
101.0 101.0
17.4 17.4
-5.5
5.5
-20.8 20.8
-5.7
5.7
4.7
4.7
11.5
8.1
8.1
-17.3 17.3
-7.1
7.1
1.7
1.7
-6.1
6.1
-8.3
8.3
7.6
88.8 88.8
-26.5 26.5
-48.6 48.6
-43.7 43.7
-37.2 37.2
-33.5 33.5
40.5
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
DFFC Horton-418027
1000
Observed flow
900
DFFC-U (Updated MCST)
800
DFFC-O (Old MCST)
700
Q, m3/s
600
500
400
300
200
100
0
1
10
ARI, years
100
Figure 6.18 Comparison of old MCST and updated MCST for Horton River catchment
DFFC Coopers creek-203002
700
Observed flow
DFFC-O (Old MCST)
600
DFFC-U (Updated MCST)
3
Q, m /s
500
400
300
200
100
0
1
10
ARI, years
100
Figure 6.19 Comparison of old MCST and updated MCST for Coopers Creek catchment
146
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
DFFC Wadbilliga-218007
1000
Observed flow
900
DFFC-U (Updated MCST)
800
DFFC-O (Old MCST)
700
3
Q, m /s
600
500
400
300
200
100
0
1
10
ARI, years
100
Figure 6.20 Comparison of old MCST and updated MCST for Wadbilliga Catchment
DFFC Corang 215004
500
Observed flow
450
DFFC-U (Updated MCST)
400
DFFC-O (Old MCST)
350
3
Q, m /s
300
250
200
150
100
50
0
10 ARI, years
1
100
Figure 6.21 Comparison of old MCST and updated MCST for Corang River Catchment
147
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
DFFC Moonan 210017
140
Observed flow
120
DFFC-U (Updated MCST)
DFFC-O (Old MCST)
Q, m3/s
100
80
60
40
20
0
1
10
ARI, years
100
Figure 6.22 Comparison of old MCST and updated MCST for Moonan Brook Catchment
For Corang River catchment and Moonan Brook Catchment as shown in Figure 6.21 and
Figure 6.22 respectively, both the updated Monte Carlo Simulation Technique and old
Monte Carlo Simulation Technique provide almost similar peakflow results for 6 ARIs. It
is observed that for Horton River, Cooper’s Creek and Wadbilliga catchment, where the
quality and length of concurrent streamflow and pluviograph data are quite good, the
notable difference between the performance of old Monte Carlo Simulation Technique
and updated Monte Carlo Simulation Technique can be seen. Hence, from the results it is
concluded that the updated Monte Carlo Simulation Technique can provide the better
flood estimates for catchments with long concurrent pluviograph and streamflow data.
148
Hitesh D. Patel
Student ID: 16095380
Chapter 6: Results from Monte-Carlo Simulation Using Stochastic Runoff Routing Model
Parameter
The performance of updated Monte Carlo Simulation Technique is shown in Figure 6.23.
The updated Monte Carlo Simulation Technique outperforms the old Monte Carlo
Simulation Technique for Horton River, Coopers Creek, Wadbilliga and Moonan Brook
catchments where the updated Monte Carlo Simulation Technique predicts the peak floods
with 4%, 10%, 6% and 1% greater accuracy than the old Monte Carlo Simulation
Technique.
45
DFFC-O (Old MCST)
absolute % median relative error
40
DFFC-U (Updated MCST)
35
30
25
20
15
10
5
0
Horton
Coopers
Wadbilliga
Corang
Moonan
Catchment
Figure 6.23 Comparison of absolute median relative errors of old MCST and updated
MCST for all the study catchments considering ARIs of 2 to 100 years
149
Hitesh D. Patel
Student ID: 16095380
References
REFERENCES
Aronica, G. T. and Candela A. (2007): Derivation of flood frequency curves in poorly
gauged Mediterranean catchments using a simple stochastic hydrological rainfall-runoff
model. Journal of Hydrology, 347, 132– 142.
Ahern, P. A. and Weinmann, P. E. (1982): Considerations for design flood estimation
using catchment modelling. Hydrology and Water Resources Symposium, Melbourne,
Australia, pp.44-48.
Bates, B. C. (1994): Regionalisation of Hydrological Data: A Review. Cooperative
Research Centre for Catchment Hydrology (CRCCH) Report 94/5. Department of Civil
Engineering, Monash University, Australia.
Becciu, G., Brath, A. and Rosso, R. (1993): A physically based methodology for regional
flood frequency analysis. Proceedings of Journal of Hydraulic Engineering, American
Society of Civil Engineers. San Francisco, July 1993. pp. 461- 466.
Benjamin, J. R. and Cornell, C. A. (1970): Probability, Statistics, and Decision for Civil
Engineers. McGraw-Hill Book Company.
Beran, M. A. (1973): Estimation of design floods and the problem of equating the
probability of rainfall and runoff. Symposium on the Design of Water Resources Projects
with Inadequate Data, Madrid, Spain, pp. 33-50.
Beven, K. J. (1986): Hillslope Runoff Processes and Flood Frequency Characteristics.
Hillslope Processes. Edited by A. D. Abrahams, Allen and Unwin, 181-202.
Bloschl, G. and Sivapalan, M. (1997): Process Controls on Flood Frequency. 2. Runoff
Generation, Storm Properties and Return Period. Centre for Water Research
155
Hitesh D. Patel
Student ID: 16095380
References
Environmental Dynamics Report, ED 1159 MS, Department of Civil Engineering,
University of Western Australia.
Boughton, W.C. (1987): Hydrograph analysis as a basis of water balance modeling.
Institution of Engineers Australia, Civil Engineering Transactions, 29(1), p.p. 28-33.
Cadavid, L. J., Obeysekera, T. B. and Shen, H. W. (1991): Flood frequency derivation
from kinematic wave, Journal of Hydraulic Engineering, American Society of Civil
Engineers, 117(4), 489-510, 1991.
Carroll, D. G. (2007): URBS - A Catchment Runoff-Routing and Flood Forecasting
Model, User Manual.
Charalambous, J., Rahman, A. and Carroll, D. (2003): Application of Monte Carlo
Simulation Technique with URBS model for design flood estimation of large catchments.
In Proceedings of International Congress on Modelling and Simulation, p. 885-890, 14-17
July, Townsville, Australia
Charalambous, J., Rahman, A. and Carroll, D. (2005): Application of URBS-Monte Carlo
Simulation Technique to large catchments for design flood estimation: a case study for the
Johnstone River catchment in Queensland. In Proceedings of 29th Hydrology and Water
Resources Symposium, I. E. Aust., 20-23 Feb., Canberra, 7 pp.
Chow, V. T., Maidment, D. R. and Mays, L. W. (1988): Applied Hydrology, McGrawHill, New York, NY.
Clark, C. O. (1945): Storage and the Unit Hydrograph. Transaction of American Society
of Civil Engineers. 110, 1419-1488.
156
Hitesh D. Patel
Student ID: 16095380
References
CSIRO Atmospheric research (2001): More droughts, more flooding rains. Press Release,
8 May 2001. http://www.dar.csiro.au/news/2001/mr05.html
Cunnane, C. (1989): Statistical Distributions for Flood Frequency Analysis. World
Meteorological Organization Operational Hydrology, Report No. 33, WMO-No. 718,
Geneva, Switzerland.
Diaz-Granados, M. A., Valdes, J. B. and Bras, R. L. (1984): A physically based flood
frequency distribution. Water Resources Research, 20, 7, pp. 995-1002.
Durrans, S. R. (1995): Total probability methods for problems in flood frequency
estimation, in statistical and Bayesian methods in hydrological sciences, Proceedings of
the International Conference in Honour of Jacques Bernier, Sep. 11-13, Chapter III,
UNESCO, Paris.
Eagleson, P. S. (1972): Dynamics of Flood Frequency, Water Resources Research, 8, 4,
pp.878-898.
Feldman, A. D. (1979): Flood hydrograph and peak flow frequency analysis. (Technical
Paper No. 62). The Hydrologic Engineering Centre.
Fontaine, T. A. and Potter, K. W. (1993): Estimating Exceedance Probabilities of Extreme
Floods. San Francisco, A. H. Division Ed., pp. 635-640.
Goel, N. K., Kurothe, R. S., Mathur, B. S. and Vogel, R. M. (2000): A derived flood
frequency distribution for correlated rainfall intensity and duration. Journal of Hydrology,
228, 56-57.
Gupta, V. K., Waymire, E. and Wang, C. T. (1980): A representation of an instantaneous
unit hydrograph from geomorphology. Water Resources Research, 16(5): 855-862.
157
Hitesh D. Patel
Student ID: 16095380
References
Haan, C. T. and Edwards, D. R. (1988): Joint probability estimates of return period flows.
Transactions of the American Society of Agricultural and Biological Engineers, 31(4):
July-August.
Haan, C. T. and Wilson B. N. (1987): Another Look at the Joint Probability of Rainfall
and Runoff. Hydrologic Frequency Modelling, edited by V. P. Singh, Reidel Publishing
Company, pp. 555-569.
Hebson, C. and Wood, E. F. (1982): A derived flood frequency distribution using horton
order ratios. Water Resources Research, 18, 5, 1509-1518.
Hill, P. I. and Mein, R. G. (1996): Incompatibilities between storm temporal patterns and
losses for design flood estimation. Hydrology and Water Resources Symposium 1996,
Hobart, Tasmania, 2, pp.445-451.
Heneker, T., Lambert, M. and Kuczera, G. (2002): Overcoming the Joint Probability
problem associated with initial loss estimation in design flood estimation. 28th Hydrology
and Water Resources Symposium, Institution of Engineers, Australia, 445-451.
Hoang, T. (2001): Joint Probability Approach to Design Flood Estimation, PhD thesis,
Department of Civil Engineering, Monash University, Australia.
Institution of Engineers Australia (1987): Australian Rainfall and Runoff. Institution of
Engineers, Australia.
Institution of Engineers Australia (1977): Australian Rainfall and Runoff. Institution of
Engineers, Australia.
158
Hitesh D. Patel
Student ID: 16095380
References
Institution of Engineers Australia (1958): Australian Rainfall and Runoff. Institution of
Engineers, Australia.
Iacobellis, V. and Fiorentiono, M. (2000): Derived distribution of floods based on the
concept of partial area coverage with a climate appeal. Water Resources Research, 36(2),
469-482.
James, W. and Robinson, M. (1986): Continuous Deterministic Urban Runoff Modelling.
Comparison of Urban Drainage Models with Real Catchment Data. Dubrovnik,
Yugoslavia, C. Maksimovic & M. Radojkovic Ed.
Kite, G. W. (1977): Frequency and Risk Analysis in Hydrology. Water Resources
Publications, Fort Collins, CO.
Kuczera G., Lambert M., Henker T., Jennings S., Frost A., and Combes P., (2006): Joint
probability and design storms at the crossroads. Australian Journal of Water Resources
Volume 10 (2), 5-21.
Kuczera, G., Lambert, M., Heneker, T., Jennings, S., Frost, A. and Coombes, P. (2003):
Joint probability and design storms at the crossroads. Keynote paper. 28th International
Hydrology and Water Resources Symosium, I. E. Aust, 11-13 Nov, Wollongogng,
Australia.
Kuczera, G., Williams, B., Binning, P. and Lambert, M. (2000): An education website
for free water engineering software. Hydro 2000, 3rd International Hydrology and Water
Resources Symposium of the Institution of Engineers, Perth, Australia.
Kuczera, G. (1994): NLFIT - A Bayesian Nonlinear Regression Program Suite. Research
Report, Department of Civil Engineering & Surveying, University of Newcastle,
Australia.
159
Hitesh D. Patel
Student ID: 16095380
References
Laurenson, E. M., Mein, R. G. and Nathan, R.J. (2007): RORB Version 6 Runoff Routing
Program User Manual, Department of Civil Engineering, Monash University, Australia.
Laurenson, E. M. and Pearse, M. A. (1991): Frequency of extreme rainfall and floods.
International Hydrology & Water Resources Symposium, Perth, pp. 392-399.
Laurenson, E. M. (1974): Modelling of stochastic-deterministic hydrologic systems.
Water Resources Research, 10, 5, 955-961.
Lumb, A. M. and James, L. D. (1976): Runoff files for flood hydrograph simulation.
Journal of the Hydraulics Division, American Society of Civil Engineers, 1515-1531.
Ministry of Regional Services, Territories and Local Govt. (MRSTLG) (1999): Budget
statements, 1999-2000.
http://www.dotars.gov.au/dept/budget/9900/macdon/Mbudget_99.htm
Moughamian, M. S., McLaughlin, D. B. and Bras, R. L. (1987): Estimation of Flood
Frequency: An Evaluation of two derived distribution procedures. Water Resources
Research, 23(7), 1309-1319.
Muncaster S. H. and Bishop W. A. (2009): Flood estimation in urban catchment with
RORB-Monte Carlo Simulation - Use of local and historical pluviograph data. 32nd
Hydrology and Water Resources Symposium, Newcastle, Australia.
Muzik, I. (2002): A first order analysis of the climate change effect on flood frequencies
on subalpine watershed by means of hydrological rainfall runoff model. Journal of
Hydrology, 267, 65-73.
160
Hitesh D. Patel
Student ID: 16095380
References
Muzik, I. (1994): Understanding flood probabilities. Stochastic and Statistical Methods in
Hydrology and Environmental Engineering, Volume 1, 199-207, K. W. Hipel (ed),
Kluwer Academic Publishers, Netherlands.
Muzik, I. (1993): Derived, physically based distribution of flood probabilities. Extreme
Hydrological Events: Precipitation, Floods and Droughts. Proceedings of the Yokohama
Sympposium, July 1993, IAHS Publication No. 213. pp. 183-188.
Muzik, I. and Beersing, A. K. (1989): Stochastic-deterministic nature of an elemental
rainfall runoff process. Water Resources Research. Volume 25, No. 8. pp. 1805-1814.
Nandakumar, N., Weinmann, P. E., Mein, R. G. and Nathan, R. J. (1997): Estimation of
Extreme Rainfalls for Victoria Using the CRC-FORGE Method (for rainfall durations 24
to 72 hours), CRC for Catchment Hydrology Report 97/4, Monash University, 118.
Nathan, R. J. and Weinmann, P. E. (2004): An improved framework for the
characterisation of extreme floods and for the assessment of dam safety. British
Hydrological Society Conference, London, July 2004, 1, 186-193.
Philip, J. R. (1957): The theory of infiltration. The infiltration equation and its solution,
Soil Science., 83, 345-357.
Rahman, A. and Kader, F. (2004): Regionalisation of design rainfalls in Victoria Australia
for design flood estimation by Joint Probability Approach. In Proceeding, Second Asia
Pacific Association of Hydrology and Water Resources Conference, 5-8 July 2004, 2, 310.
Rahman, A. and Carroll, D. (2004): Appropriate spatial variability of flood producing
variables in the Joint Probability Approach to design flood estimation. British
Hydrological Society International Conference, London, 12-16 July, 2004, 1, 335-340.
161
Hitesh D. Patel
Student ID: 16095380
References
Rahman, A. and Weinmann, P. E. (2002): Flood Estimation in Northern Australian Using
Monte Carlo Technique. Proc. 27th National Hydrology and Water symposium, The Water
Challenge, Balancing the Risk, I. E. Aust., 20-23 May, Melbourne. CD-ROM Publication.
Rahman, A., Weinmann, P. E., Hoang, T.M., and Laurenson, E. M. (2002a): Monte Carlo
Simulation of flood frequency curves from rainfall. Journal of Hydrology, 256 (3-4), 196210.
Rahman, A., Weinmann, P. E. and Mein, R. G. (2002b): The use of probability-distributed
initial losses in design flood estimation. Australian Journal of Water Resources. 6(1), 1730.
Rahman, A., Carroll, D and Weinmann, P. E. (2002c): Integration of Monte Carlo
Simulation technique with URBS model for design flood estimation. 27th National
Hydrology and Water Resources Symposium, I. E. Aust., 20-23 May, Melbourne.
Rahman, A., Weinmann, P. E., Hoang, T. M. and Laurenson, E. M. (2001): Monte Carlo
Simulation of Flood Frequency Curves From Rainfall, Technical Report No. 1/4 CRC for
Catchment Hydrology, Monash University, Australia.
Rahman, A., Hoang, T. M., Weinmann, P. E. and Laurenson, E. M. (1998): Joint
Probability Approaches to Design Flood estimation: A Review. CRC for Catchment
Hydrology Report 98/8, Monash University, p. 77.
Raines, T. H. and Valdes, J. B. (1993): Estimation of flood frequencies for ungauged
catchments. Journal of the Hydraulics Division, American Society of Civil Engineers,
119(10), 1138-1154.
162
Hitesh D. Patel
Student ID: 16095380
References
Rauf, A. and Rahman, A. (2004): Study of fixed-duration design rainfalls in Australian
Rainfall and Runoff and Joint Probability based design rainfalls. In Proceeding, Second
Asia Pacific Association of Hydrology and Water Resources Conference, 5-8 July 2004,
2, 60-67.
Russell, S. O., Kenning, B. F. I. and Sunnell, G. J. (1979): Estimating design flows for
urban drainage. Journal of the Hydraulics Division, 105, 43-52.
Rodriguez-Iturbe,
I.,
Gonzales-Sanabria,
M.
and
Bras,
R.
L.
(1982a):
A
geomorphoclimatic theory of the instantaneous unit hydrograph. Water Resources
Research, 18(4):877-886.
Rodriguez-Iturbe,
I.,
Gonzales-Sanabria,
M.
and
Caamano,
G.
(1982b):
A
Geomorphoclimatic Theory of the Instantaneous Unit Hydrograph. Water Resources
Research, 18(4):887-903.
Rodriguez-Iturbe, I. and Valdes, J. B. (1979): The geomorphologic structure of hydrologic
response. Water Resources Research, 15(6), 1409-1420.
Sivapalan, M., Bloschl, G. and Gutknecht, D. (1996): Process Controls on Flood
Frequency - Derived Flood Frequency. Centre for Water Research Environmental
Dynamics Report, ED 1158 MS, Department of Civil Engineering, The University of
Western Australia.
Sivapalan, M., Beven, K. J. and Wood, E. F. (1990): On Hydrologic Similarity - A
dimensionless flood frequency model using a generalised geomorphic unit hydrograph
and partial area runoff generation, Water Resources Research, 26(1), 43-58.
Siriwardena, L. and Weinmann, P. E. (1996): Derivation of Areal Reduction Factors for
Design Rainfalls in Victoria. CRC for Catchment Hydrology Report 96/4, Department of
Civil Engineering, Monash University, pp. 60.
163
Hitesh D. Patel
Student ID: 16095380
References
Schaake, J. C., Geyer, J. C. and Knapp, J. W. (1967): Experimental Examination of the
Rational Method. Proceedings of American Society of Civil Engineers, Volume 93(HY6),
pp. 353-370.
Shen, H. W., Koch, G. J. and Obeysekera, J. T. B. (1990): Physically based flood features
and frequencies. Journal of Hydraulic Engineering, Volume 116, No. 4. pp. 494-514.
Soil Conservation Service (1972): Section 4: Hydrology. National Engineering
Handbook.Washington D.C.: U.S. Department of Agriculture.
Stedinger, J. R., Vogel, R. M. and Foufoula-Georgiou, E. (1993): Frequency Analysis of
Extreme Events In: Maidment, D.R. (Edition). Handbook of Hydrology, McGraw-Hill,
New York, Chapter 18.
Tavakkoli, D. (1985): Simulation von Hochwasserwellen aus Niederschlagen. PhD
Thesis, Inst. f. Hydraulik, Technical University of Vienna.
Thompson, D. K., Stedinger, J. R. and Heath, C. D. (1997): Evaluation and presentation
of dam failure and flood risk. Journal of Water Resources Planning and Management,
Volume 123, No.4.
Troch, P. A., Smith, J. A., Wood, E. F. and Troch, F. De. (1994): Hydrologic controls of
large floods in a small basin: Central Appalachian case study, Journal of Hydrology, 156,
285-309.
Walsh, M. A., Pilgrim, D. H. and Cordery, I. (1991): Initial losses for design flood
estimation in New South Wales. International Hydrology and Water Resources
Symposium, Perth, I. E. Aust. Nat. Conf. Pub. No. 91/19, pp. 283-288.
164
Hitesh D. Patel
Student ID: 16095380
References
Walpole, R. E. and Myers, R. H. (1993): Probability and Statistics for Engineers and
Scientists. Fifth Ed., Prentice-Hall International, Inc.
Weinmann, P. E., Rahman, A., Hoang, T. M., Laurenson, E. M. and Nathan, R. J. (2002):
Monte Carlo simulation of flood frequency curves from rainfall-the way ahead. Australian
Journal of Water Resources. 6(1), 71-80.
Weinmann, P. E., Rahman, A., Hoang, T.M., Laurenson, E. M. and Nathan, R. J. (1998):
A New Modelling Framework for Design Flood Estimation, International Conference on
Hydraulics in Civil Engineering, Adelaide, Australia, pp. 393-398.
Weinmann, P. E. (1994): On the origin and variation of skewness in flood frequency
distributions. Water Down Under '94, Adelaide, Australia, pp. 265-270.
Wood, E. F. and Hebson, C. S. (1986): On hydrologic similarity, 1, Derivation of Flood
Frequency curve. Water Resources Research, 22, 1549-1554.
Wood, E. F. (1976): An analysis of the effects of parameter uncertainty in deterministic
hydrologic models. Water Resources Research,12(5), 925-932.
165
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDICES
APPENDIX A
Output plots for FIT runs (RORB Model)
1) Excellent Fit
Storm 1977-X1
Storm
1977-X4
Gauging station
at: Runoff h/g at 203002
Rainfall (mm)
Gross rainfall
Rainfall excess
Calculated
Actual
110
100
90
80
70
60
50
40
30
20
10
0
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Gauging station at: Runoff h/g at 203002
20
18
16
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
Time (hr)
35
40
45
12
11
109
87
65
43
21
0
Gross rainfall
Rainfall excess
Calculated
Actual
22
20
18
16
14
12
10
8
6
4
2
0
0
50
5
10
20
Time (hr)
25
30
35
40
7
6
5
4
3
2
1
0
22
Rainfall (mm)
Gauging
station1978-X2
at: Runoff h/g at 203002
Storm
Gross rainfall
Rainfall excess
Calculated
Actual
7
6
5
4
3
2
1
0
22
20
20
18
18
16
16
14
14
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Gauging station
at: Runoff1978
h/g at 203002
Storm
15
12
10
8
Gross rainfall
Rainfall excess
Calculated
Actual
12
10
8
6
6
4
4
2
2
0
0
0
5
10
15
20
25
Time (hr)
30
35
40
166
0
5
10
15
20
25
Time (hr)
30
35
Hitesh D. Patel
Student ID: 16095380
40
Appendices
Gross rainfall
Rainfall excess
Rainfall (mm)
11
10
9
8
7
6
5
4
3
2
1
0
10
Calculated
Actual
90
8
80
7
70
6
5
4
40
2
20
1
10
0
0
10
15
20
25 30 35
Time (hr)
40
45
50
Calculated
Actual
50
30
5
Gross rainfall
Rainfall excess
60
3
0
Gauging
station1979-X1
at: Runoff h/g at 203002
Storm
45
40
35
30
25
20
15
10
5
0
100
9
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Storm
Gauging
station1978-X3
at: Runoff h/g at 203002
0
55
5
10
Storm 1979-X2
20
25 30
Time (hr)
35
40
45
50
Storm
1979-X3
Gauging station at: Runoff h/g at 203002
55
50
45
40
35
30
25
20
15
10
5
0
25
Gross rainfall
Rainfall excess
Rainfall (mm)
Gauging station at: Runoff h/g at 203002
Rainfall (mm)
15
Calculated
Actual
12
10
8
6
4
2
0
Gross rainfall
Rainfall excess
Calculated
Actual
40
35
20
Discharge (m³/s)
Discharge (m³/s)
30
15
10
25
20
15
10
5
5
0
0
0
5
10
15
20
25
Time (hr)
167
0
5
10
15
20
25
30 35
Time (hr)
40
45
50
55
Hitesh D. Patel
Student ID: 16095380
60
Appendices
Storm
1979-X5
Gauging station
at: Runoff h/g at 203002
16
14
12
10
8
6
4
2
0
Calculated
Actual
120
30
100
25
80
60
Calculated
Actual
20
15
40
10
20
5
0
0
0
Rainfall (mm)
Gross rainfall
Rainfall excess
35
Discharge (m³/s)
Discharge (m³/s)
140
5
10
15
20
25
Time (hr)
30
35
40
45
0
5
Gauging station
at: Runoff h/g at 203002
Storm
1979-X7
45
40
35
30
25
20
15
10
5
0
100
10
15
20
25
Time (hr)
30
35
40
Storm
1980-X1
Gauging station
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Calculated
Actual
12
11
109
87
65
43
21
0
22
Gross rainfall
Rainfall excess
Calculated
Actual
20
90
18
80
16
Discharge (m³/s)
70
Discharge (m³/s)
40
35
30
25
20
15
10
5
0
Rainfall (mm)
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Gauging station
at: Runoff h/g at 203002
Storm
1979-X4
60
50
40
14
12
10
8
30
6
20
4
10
2
0
0
0
5
10
15
20
25 30
Time (hr)
35
40
45
50
0
168
5
10
15
20
25
30 35
Time (hr)
40
45
50
55
Hitesh D. Patel
Student ID: 16095380
60
Appendices
Storm
Gauging 1981-X2
station at: Runoff h/g at 203002
30
25
20
15
10
5
0
Rainfall (mm)
Gross rainfall
Rainfall excess
Calculated
Actual
11
10
9
8
7
6
5
4
3
2
1
0
10
9
8
7
6
5
4
3
2
1
0
Gross rainfall
Rainfall excess
Calculated
Actual
30
25
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Storm
1980-X3
Gauging station
at: Runoff h/g at 203002
20
15
10
5
0
0
2
4
6
8
10 12 14 16 18 20 22 24
Time (hr)
0
5
10
Gross rainfall
Rainfall excess
Calculated
Actual
70
30
35
16
14
12
10
8
6
4
2
0
60
30
50
25
40
30
Calculated
Actual
20
15
20
10
10
5
0
0
0
5
10
15
20
25 30
Time (hr)
35
40
Gross rainfall
Rainfall excess
35
Discharge (m³/s)
Discharge (m³/s)
20
25
Time (hr)
Storm
Gauging
station1981-X4
at: Runoff h/g at 203002
12
10
8
6
4
2
0
Rainfall (mm)
Rainfall (mm)
Gauging station
at: Runoff h/g at 203002
Storm
1981-X3
15
40
45
50
169
0
5
10
15
20
25
Time (hr)
30
35
40
Hitesh D. Patel
Student ID: 16095380
45
Appendices
Storm
Gauging
station1985-X1
at: Runoff h/g at 203002
8
7
6
5
4
3
2
1
0
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Storm
Gauging
station1983-X1
at: Runoff h/g at 203002
Calculated
Actual
12
8
7
6
5
4
3
2
1
0
Gross rainfall
Rainfall excess
Calculated
Actual
10
9
8
7
8
Discharge (m³/s)
Discharge (m³/s)
10
6
4
6
5
4
3
2
2
1
0
0
0
5
10
15
20
25
30 35
Time (hr)
40
45
50
55
60
0
10
20
40
50
Time (hr)
60
70
80
90
4.5
4
3.5
3
2.5
2
1.5
1
.5
0
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
.5
0
Gross rainfall
Rainfall excess
Rainfall (mm)
Storm
Gauging
station1990
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
25
20
15
10
5
0
Calculated
Actual
Calculated
Actual
60
50
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Storm
1986
Gauging station
at: Runoff h/g at 203002
30
40
30
20
10
0
0
5
10
15
20
25
30 35
Time (hr)
40
45
50
55
170
0
5
10
15
Time (hr)
20
25
Hitesh D. Patel
Student ID: 16095380
30
Appendices
2) Reasonable Fit
Storm
1979
Gauging station
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Gauging 1977-X1
station at: Runoff h/g at 203002
Storm
45
40
35
30
25
20
15
10
5
0
Calculated
Actual
1.6
Gross rainfall
Rainfall excess
Calculated
Actual
140
1.4
120
1.2
1
Discharge (m³/s)
Discharge (m³/s)
16
14
12
10
8
6
4
2
0
.8
.6
100
80
60
.4
40
.2
20
0
0
0
10
20
30
40
Time (hr)
50
60
70
0
10
20
11
10
9
8
7
6
5
4
3
2
1
0
4
Gross rainfall
Rainfall excess
Calculated
Actual
60
70
22
20
18
16
14
12
10
8
6
4
2
0
5.5
80
Calculated
Actual
4.5
4
2.5
3.5
Discharge (m³/s)
3
2
1.5
3
2.5
2
1.5
1
1
.5
.5
0
0
0
10
20
30
40
Time (hr)
50
90
Gross rainfall
Rainfall excess
5
3.5
Discharge (m³/s)
40
50
Time (hr)
Storm
1980-X2
Gauging station
at: Runoff h/g at 203002
Rainfall (mm)
Rainfall (mm)
Storm
Gauging
station1979-X6
at: Runoff h/g at 203002
30
60
0
171
10
20
30
40
Time (hr)
50
60
70
Hitesh D. Patel
Student ID: 16095380
Appendices
Storm
Gauging
station1993-X1
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Storm
Gauging
station1981-X5
at: Runoff h/g at 203002
11
10
9
8
7
6
5
4
3
2
1
0
Calculated
Actual
30
12
10
8
6
4
2
0
55
Gross rainfall
Rainfall excess
Calculated
Actual
50
45
40
20
Discharge (m³/s)
Discharge (m³/s)
25
15
35
30
25
20
10
15
10
5
5
0
0
0
5
10 15 20 25 30 35 40 45 50 55 60
Time (hr)
0
5
10
15
20
25 30 35
Time (hr)
40
45
50
Rainfall (mm)
Storm
1994-X1
Gauging station
at: Runoff h/g at 203002
10
9
8
7
6
5
4
3
2
1
0
Gross rainfall
Rainfall excess
Calculated
Actual
8
7
Discharge (m³/s)
6
5
4
3
2
1
0
0
10
20
30
40
50
Time (hr)
60
70
80
172
Hitesh D. Patel
Student ID: 16095380
55
Appendices
2) Poor Fit
Storm
1979-X8
Gauging station
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Gauging station
at: Runoff h/g at 203002
Storm
1978-X1
11
10
9
8
7
6
5
4
3
2
1
0
2
Calculated
Actual
1.8
Gross rainfall
Rainfall excess
Calculated
Actual
2.5
1.6
1.4
2
1.2
Discharge (m³/s)
Discharge (m³/s)
10
9
8
7
6
5
4
3
2
1
0
1
.8
1.5
1
.6
.4
.5
.2
0
0
0
10
20
30
40
Time (hr)
50
60
70
0
10
Calculated
Actual
40
Time (hr)
50
6
5
4
3
2
1
0
1
.9
.9
.8
.8
.7
.7
Discharge (m³/s)
Discharge (m³/s)
1
30
60
70
Storm
1981-X1
Gauging station
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Gauging
station1981
at: Runoff h/g at 203002
Storm
7
6
5
4
3
2
1
0
20
.6
.5
.4
Calculated
Actual
.6
.5
.4
.3
.3
.2
.2
.1
.1
0
Gross rainfall
Rainfall excess
0
0
10
20
30
40
50
Time (hr)
60
70
80
173
0
10
20
30
40
50
60 70
Time (hr)
80
90 100 110 120
Hitesh D. Patel
Student ID: 16095380
Appendices
Storm
1984
Gauging station
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Calculated
Actual
18
20
18
16
14
12
10
8
6
4
2
0
2.2
Gross rainfall
Rainfall excess
Calculated
Actual
2
16
1.8
14
1.6
12
1.4
Discharge (m³/s)
Discharge (m³/s)
Rainfall (mm)
Rainfall (mm)
Storm
1983
Gauging station
at: Runoff h/g at 203002
12
11
109
87
65
43
21
0
20
10
8
1.2
1
.8
6
.6
4
.4
2
.2
0
0
0
20
40
60
80
Time (hr)
100
120
0
10
20
Gross rainfall
Rainfall excess
Calculated
Actual
60
7
6
5
4
3
2
1
0
.55
Gross rainfall
Rainfall excess
Calculated
Actual
.50
4
.45
3.5
.40
Discharge (m³/s)
3
Discharge (m³/s)
50
Gauging
station1993
at: Runoff h/g at 203002
Storm
5
4.5
4
3.5
3
2.5
2
1.5
1
.5
0
4.5
Rainfall (mm)
Rainfall (mm)
Storm
1985
Gauging station
at: Runoff h/g at 203002
30
40
Time (hr)
2.5
2
.35
.30
.25
.20
1.5
.15
1
.10
.5
.05
0
0
0
10
20
30
40
50 60
Time (hr)
70
80
0
90
174
10
20
30
40
50
Time (hr)
60
70
Hitesh D. Patel
Student ID: 16095380
80
Appendices
Storm
Gauging
station1995
at: Runoff h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Storm
Gauging
station1994
at: Runoff h/g at 203002
18
16
14
12
10
8
6
4
2
0
2.2
Calculated
Actual
Gross rainfall
Rainfall excess
Calculated
Actual
.35
2
1.8
.30
1.6
1.4
Discharge (m³/s)
Discharge (m³/s)
14
12
10
8
6
4
2
0
1.2
1
.25
.20
.8
.15
.6
.10
.4
.05
.2
0
0
0
10
20
30
40
Time (hr)
50
60
70
0
175
10
20
30
40
Time (hr)
50
Hitesh D. Patel
Student ID: 16095380
60
Appendices
APPENDIX B
Flood Frequency Analysis Result for the Coopers Creek
catchment
FLIKE program version 4.50
FLIKE file version 2.70
Title: 203002
Input Data for Flood Frequency Analysis for Model: Log Pearson III
& Measurement Error Data
Group Error coefficient Lower bound
of variation rated flow
-----------------------------------------------1
0.000
0.00
& Gauged Annual Maximum Discharge Data
Obs Discharge Year Incremental Error coefficient Cunnane
error zone
of variation ARI,yrs*
-----------------------------------------------------------1
86.60 1
1
0.000 1.34
2 139.95 2
1
0.000 2.22
3 133.63 3
1
0.000 2.07
4 125.08 4
1
0.000 1.54
5 186.89 5
1
0.000 3.51
6 131.21 6
1
0.000 1.94
7 224.64 7
1
0.000 3.97
8 281.32 8
1
0.000 8.39
9 169.98 9
1
0.000 2.85
10
19.21 10
1
0.000 1.02
11 265.47 11
1
0.000 6.57
12 459.57 12
1
0.000 50.33
13 312.75 13
1
0.000 11.62
14 256.00 14
1
0.000 5.39
15
70.34 15
1
0.000 1.23
16
84.40 16
1
0.000 1.28
17
48.12 17
1
0.000 1.14
18 141.16 18
1
0.000 2.40
19 126.21 19
1
0.000 1.62
20 240.59 20
1
0.000 4.58
21
59.41 21
1
0.000 1.18
176
Hitesh D. Patel
Student ID: 16095380
Appendices
22
44.53 22
1
0.000 1.09
23 340.17 23
1
0.000 18.88
24 119.78 24
1
0.000 1.47
25 176.77 25
1
0.000 3.15
26
21.74 26
1
0.000 1.06
27 130.74 27
1
0.000 1.82
28 106.44 28
1
0.000 1.40
29 127.12 29
1
0.000 1.72
30 153.77 30
1
0.000 2.60
Note: Cunnane plotting position is based on gauged flows only
------------------------------------------------------------------------------& Posterior Parameter Results
Data file: C:\AA sandy\Study\Honors\RORB formulations\Lismore RORB mode
203002
Flood model: Log Pearson III
>>> Fitting algorithm: Global probabilistic search
Parameter Lower bound Upper bound
------------------------------------1
1.10445
8.58795
2 -2.59247
2.01270
3 -5.00000
5.00000
Incremental error model: Log-normal
Solution PROBABLY found in 2296 iterations
Maximized log-posterior density = -177.001
No Parameter
Initial value Most probable value
--------------------------------------------------------------------1 Mean (loge flow)
4.84620
4.84619
2 loge [Std dev (loge flow)]
-0.28988
-0.30794
3 Skew (loge flow)
-0.84071
-0.81145
-------------------------------------------------&Zero flow threshold: 0.0000
Number of gauged flows below flow threshold = 0
-------------------------------------------------& Parameter Moments based on Multi-normal Approximation to Posterior Distribution
177
Hitesh D. Patel
Student ID: 16095380
Appendices
No Most probable
Std dev
Correlation
--------------------------------------------------1
4.84619
0.14211 1.000
2 -0.30794
0.18220 -0.539 1.000
3 -0.81145
0.42367 0.108 -0.662 1.000
--------------------------------------------------Note: Parameters are roughly normally distributed.
This approximation improves with sample size.
& Summary of Posterior Moments from Importance Sampling
No
Mean
Std dev
Correlation
-----------------------------------------------1
4.83823
0.14321 1.000
2 -0.25800
0.14957 -0.401 1.000
3 -0.63476
0.35992 0.044 -0.255 1.000
---------------Note: Posterior expected parameters are the most
accurate in the mean-squared-error sense.
They should be used in preference to the most probable parameters
Upper bound = 1440.13
& Recurrence Exp parameter Monte Carlo 90% quantile
interval quantile
probability limits
yrs
--------------------------------------------------------1.010
14.68
5.68
27.83
1.100
42.86
26.46
61.76
1.250
68.24
47.87
90.64
1.500
97.31
72.56
125.00
1.750
119.16
91.63
151.32
2.000
136.93
107.11
172.95
3.000
186.93
149.47
234.82
5.000
244.82
197.08
310.97
10.000
317.70
254.54
417.21
20.000
385.78
306.46
532.90
50.000
469.67
363.12
718.63
100.000
529.00
397.50
884.41
200.000
585.02
427.40
1060.65
500.000
654.31
456.96
1325.99
& Expected Probability Flood based on
Monte Carlo samples = 10000
178
Hitesh D. Patel
Student ID: 16095380
Appendices
Probability weight = 1.000
Scalng factor
= 2.500
Flood
Expected <----------ARI------------>
magnitude probability
yrs 95% limits
--------------------------------------------------------14.68
0.01315 1.01 1.01 1.01
42.86
0.09345 1.10 1.10 1.10
68.24
0.20076 1.25 1.25 1.25
97.31
0.33245 1.50 1.49 1.50
119.16
0.42665 1.74 1.74 1.75
136.93
0.49736 1.99 1.98 2.00
186.93
0.66274 2.97 2.95 2.98
244.82
0.79583 4.90 4.87 4.93
317.70
0.89642 9.65 9.57 9.74
385.78
0.94678 18.79 18.55 19.03
469.67
0.97651 42.57 41.72 43.45
529.00
0.98612 72.06 70.18 74.04
585.02
0.99101 111.22 107.68 114.99
654.31
0.99434 176.79 169.96 184.19
Coopers creek - 203002
1000
Gauged Flow
Ex p para quantile - L P3 (B ayesian Fi t)
90% li mi ts
Discharge (Cumec)
Ex p prob quanti le - L P3 (B ay esian Fit)
100
10
1
1.01
1.5
2
5
10
20
50
100 200
500
A RI (Y ears)
179
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX C
Design run results (RORB model) for the Coopers Creek catchment
Combination of model parameter
Avg IL from all storm
Avg CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Avg CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Avg CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent fit
Avg CL from all storm
IL, kc, CL
35.90
6.23
15.56
11.20
9.96
9.60
11.43
9.75
30.50
6.23
15.56
11.20
9.96
9.60
11.43
9.75
31.40
6.23
15.56
11.20
9.96
9.60
11.43
9.75
23.00
6.23
ARI
1y
%
Error
ARI
2y
%
Error
59.1
76.2
84.5
87.3
74.9
86.1
302.8
419.1
475.7
494.6
410.0
486.6
97.1 -29.1 153.7 -37.2 190.2 -40.1 245.9 -36.3 308.3 -34.4 365.6 -30.9
129.3 -5.5 204.7 -16.4 252.2 -20.6 323.9 -16.0 401.2 -14.6 472.7 -10.7
143.3 4.7 225.9 -7.7 277.7 -12.6 354.4 -8.1 436.0 -7.2 510.9 -3.4
147.9 8.0 232.8 -4.9 285.7 -10.1 363.8 -5.7 446.3 -5.0 522.4 -1.2
127.0 -7.2 201.1 -17.9 247.9 -22.0 318.6 -17.4 395.1 -15.9 465.8 -11.9
146.0 6.6 229.9 -6.1 282.3 -11.1 359.8 -6.7 441.9 -5.9 517.6 -2.2
63.4
83.4
92.5
95.6
81.9
94.3
331.7
468.1
530.2
550.9
458.0
542.1
99.1
132.0
146.3
150.9
129.7
149.0
-27.6
-3.6
6.8
10.2
-5.3
8.8
160.7
209.1
230.5
237.3
205.5
234.4
-34.4
-14.6
-5.9
-3.1
-16.1
-4.2
197.9
262.0
287.4
295.4
257.6
292.0
-37.7
-17.5
-9.5
-7.0
-18.9
-8.1
249.2 -35.4 313.7 -33.2 367.0 -30.6
327.9 -15.0 407.1 -13.3 474.1 -10.4
358.2 -7.1 441.1 -6.1 512.1 -3.2
367.6 -4.7 451.5 -3.9 523.7 -1.0
322.6 -16.4 401.0 -14.6 467.3 -11.7
363.7 -5.7 447.1 -4.8 518.9 -1.9
62.1
81.7
90.6
93.6
80.2
92.3
322.9
456.6
517.4
537.7
446.6
529.1
99.1
132.0
146.3
150.9
129.7
149.0
-27.6
-3.6
6.8
10.2
-5.3
8.8
159.3
207.4
228.7
235.6
203.8
232.7
-34.9
-15.3
-6.6
-3.8
-16.8
-4.9
196.8
260.6
286.0
294.1
256.3
290.7
-38.0
-18.0
-10.0
-7.4
-19.3
-8.5
247.9 -35.7 313.5 -33.2 367.0 -30.6
326.3 -15.4 406.9 -13.4 474.1 -10.4
356.7 -7.5 440.9 -6.1 512.1 -3.2
366.2 -5.1 451.3 -3.9 523.7 -1.0
321.1 -16.8 400.8 -14.7 467.3 -11.7
362.2 -6.1 446.9 -4.8 518.9 -1.9
180
ARI
5y
%
Error
ARI
10y
%
Error
ARI
20y
%
Error
ARI
50y
%
Error
ARI
100y
%
Error
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent and resonable fit
Avg CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Avg CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from all storm
Median CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Median CL from all storm
Avg kc from all storm
Median kc from all storm
15.56
11.20
9.96
9.60
11.43
9.75
35.07
6.23
15.56
11.20
9.96
9.60
11.43
9.75
27.00
6.23
15.56
11.20
9.96
9.60
11.43
9.75
35.90
2.87
15.56
11.20
9.96
9.60
11.43
9.75
30.50
2.87
15.56
11.20
66.6
85.1
93.8
96.9
83.8
95.6
353.5
479.4
539.2
560.2
470.9
551.3
109.8
140.8
153.8
158.1
138.6
156.3
-19.8
2.8
12.3
15.5
1.2
14.2
163.8
217.0
238.5
245.3
213.3
242.4
-33.1
-11.4
-2.6
0.2
-12.9
-1.0
200.9
264.5
289.9
297.9
260.2
294.5
-36.8
-16.7
-8.8
-6.2
-18.1
-7.3
60.7
77.8
84.6
87.3
76.6
86.1
313.6
429.9
476.6
494.6
422.1
486.6
98.2 -28.3 154.9 -36.7 191.5 -39.7 246.5 -36.1 308.3 -34.4 366.8 -30.7
130.8 -4.5 206.3 -15.7 253.8 -20.1 324.6 -15.8 401.2 -14.6 473.9 -10.4
144.9 5.8 227.6 -7.0 279.3 -12.1 355.1 -7.9 436.0 -7.2 512.0 -3.2
149.6 9.2 234.5 -4.2 287.3 -9.6 364.6 -5.5 446.3 -5.0 523.5 -1.0
128.5 -6.2 202.7 -17.2 249.5 -21.5 319.4 -17.2 395.1 -15.9 467.1 -11.7
147.6 7.8 231.6 -5.4 283.9 -10.6 360.6 -6.5 441.9 -5.9 518.7 -1.9
63.8
84.1
93.3
96.4
82.6
95.1
334.5
473.0
535.7
556.6
462.8
547.7
104.1
134.5
149.0
153.7
132.2
151.7
-24.0
-1.7
8.8
12.2
-3.5
10.8
162.2
215.5
237.0
243.8
211.9
241.0
-33.8
-12.0
-3.2
-0.4
-13.5
-1.6
198.7
262.9
288.3
296.4
258.6
292.9
78.8
103.0
113.6
117.3
101.3
115.7
436.6
601.9
673.7
698.9
590.2
688.2
125.1
164.2
181.4
187.1
161.6
184.7
-8.6
19.9
32.5
36.6
18.0
34.9
189.5
248.2
273.1
281.1
244.0
277.7
-22.6
1.4
11.6
14.8
-0.3
13.4
229.5 -27.7 286.4 -25.8 353.9 -24.7 413.6 -21.8
299.8 -5.6 372.3 -3.5 454.7 -3.2 527.8 -0.2
328.7 3.5 405.8 5.2 491.5 4.7 568.5 7.5
337.8 6.3 416.1 7.9 502.7 7.0 580.4 9.7
294.9 -7.2 366.4 -5.0 448.1 -4.6 520.5 -1.6
334.0 5.1 411.7 6.7 498.0 6.0 575.4 8.8
-37.5
-17.2
-9.2
-6.7
-18.6
-7.8
252.8 -34.5 315.2 -32.9 372.2 -29.6
331.9 -14.0 408.6 -13.0 479.1 -9.4
362.1 -6.1 442.5 -5.8 516.5 -2.4
371.3 -3.8 452.8 -3.6 527.7 -0.2
326.7 -15.3 402.6 -14.3 472.4 -10.7
367.4 -4.8 448.4 -4.5 523.0 -1.1
249.8 -35.2 313.7 -33.2 369.2 -30.2
328.5 -14.8 407.1 -13.3 476.3 -10.0
358.9 -7.0 441.1 -6.1 514.0 -2.8
368.2 -4.5 451.5 -3.9 525.5 -0.7
323.3 -16.2 401.0 -14.6 469.5 -11.2
364.3 -5.6 447.1 -4.8 520.7 -1.6
86.2 487.2 129.6 -5.4 195.4 -20.2 237.4 -25.3 292.3 -24.2 360.5 -23.2 417.1 -21.2
113.2 670.8 170.1 24.2 255.7 4.4 309.4 -2.6 379.0 -1.8 461.2 -1.8 531.3 0.4
181
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Median CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent fit
Median CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent and resonable fit
Median CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Median CL from all storm
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
9.96
9.60
11.43
9.75
31.40
2.87
15.56
11.20
9.96
9.60
11.43
9.75
23.00
2.87
15.56
11.20
9.96
9.60
11.43
9.75
35.07
2.87
15.56
11.20
9.96
9.60
11.43
9.75
27.00
2.87
15.56
11.20
9.96
9.60
125.3
129.3
111.3
127.6
753.4
780.8
658.0
769.2
188.0
193.8
167.2
191.3
37.3
41.5
22.1
39.7
280.7
288.6
251.4
285.3
14.6
17.9
2.7
16.5
338.1 6.4 412.2
347.0 9.2 421.9
304.4 -4.2 373.2
343.2 8.0 417.7
84.9
111.5
123.3
127.3
109.6
125.6
478.7
659.2
740.0
767.1
646.6
755.6
129.6
170.1
188.0
193.8
167.2
191.3
-5.4
24.2
37.3
41.5
22.1
39.7
194.1
254.0
279.0
286.9
249.8
283.6
-20.7
3.8
14.0
17.2
2.0
15.8
236.3 -25.6 291.0 -24.6 360.3 -23.3 415.9 -21.4
308.0 -3.0 377.5 -2.1 461.0 -1.8 530.1 0.2
336.8 6.0 410.8 6.5 497.5 5.9 570.5 7.8
345.7 8.8 420.6 9.0 508.4 8.2 582.3 10.1
303.1 -4.6 371.7 -3.7 454.5 -3.2 522.9 -1.2
342.0 7.6 416.3 7.9 503.9 7.3 577.4 9.1
90.7
119.3
132.1
136.3
117.2
134.5
517.5
712.7
800.0
828.5
698.3
816.4
137.5
180.6
198.9
204.7
177.5
202.3
0.4
31.9
45.2
49.5
29.6
47.7
204.2
266.3
291.2
298.8
262.1
295.6
-16.6
8.8
18.9
22.1
7.0
20.7
244.3
317.3
345.6
354.1
312.4
350.7
79.9
104.6
115.4
119.1
102.9
117.5
444.3
612.4
685.9
711.5
600.6
700.6
126.3
165.8
183.2
188.9
163.1
186.5
-7.7
21.1
33.8
38.0
19.1
36.2
190.8
249.8
274.8
282.7
245.6
279.4
-22.1
2.0
12.2
15.5
0.3
14.1
230.8 -27.4 287.1 -25.6 355.1 -24.4 414.8 -21.6
301.4 -5.1 373.0 -3.3 455.9 -2.9 529.0 0.0
330.3 4.0 406.5 5.4 492.7 4.9 569.5 7.7
339.2 6.8 416.8 8.0 503.8 7.3 581.4 9.9
296.4 -6.7 367.2 -4.8 449.4 -4.3 521.7 -1.4
335.5 5.6 412.5 6.9 499.1 6.3 576.5 9.0
89.1
117.1
129.7
133.8
506.6
697.5
783.4
811.7
133.9
175.9
194.0
199.9
-2.2
28.4
41.7
46.0
200.6
262.0
287.0
294.7
-18.1
7.0
17.2
20.4
240.6 -24.3 295.3 -23.5
313.2 -1.4 382.3 -0.9
341.7 7.6 414.9 7.5
350.5 10.3 424.8 10.1
182
-23.1
-0.1
8.8
11.4
-1.7
10.4
6.8
9.4
-3.3
8.3
497.7 6.0 571.5 8.0
508.6 8.3 583.2 10.3
454.7 -3.2 524.0 -0.9
504.1 7.3 578.3 9.3
298.3 -22.7 365.7 -22.1 424.8 -19.7
385.4 -0.1 466.3 -0.7 538.3 1.8
417.8 8.3 502.1 6.9 577.3 9.1
427.6 10.8 512.6 9.1 588.7 11.3
379.7 -1.6 459.9 -2.1 531.3 0.4
423.5 9.8 508.2 8.2 584.0 10.4
362.4 -22.8 419.8 -20.6
463.1 -1.4 533.9 0.9
499.3 6.3 573.6 8.4
510.1 8.6 585.3 10.6
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from all storm
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent fit
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
11.43
9.75
35.90
7.59
15.56
11.20
9.96
9.60
11.43
9.75
30.50
7.59
15.56
11.20
9.96
9.60
11.43
9.75
31.40
7.59
15.56
11.20
9.96
9.60
11.43
9.75
23.00
7.59
15.56
11.20
9.96
9.60
11.43
9.75
115.1 683.8 172.8 26.2 257.7 5.3 308.2 -3.0 376.5
132.1 799.7 197.4 44.2 291.5 19.1 346.8 9.2 420.7
-2.4
9.0
456.6 -2.8 526.6 -0.4
505.6 7.7 580.4 9.7
53.2
68.3
74.3
76.6
67.3
75.6
262.3
365.1
406.2
422.0
358.2
414.9
87.8
116.9
129.6
133.8
114.8
132.0
-35.9
-14.6
-5.3
-2.3
-16.1
-3.6
141.9
187.3
207.0
213.4
184.0
210.7
-42.1
-23.5
-15.4
-12.8
-24.9
-13.9
179.7
233.4
257.3
265.0
229.4
261.7
-43.5
-26.5
-19.0
-16.6
-27.8
-17.6
229.8
304.4
333.6
342.7
299.4
338.9
-40.4
-21.1
-13.5
-11.2
-22.4
-12.2
380.4
414.1
424.4
374.5
420.1
0.0
-19.0
-11.8
-9.6
-20.3
-10.5
450.6
487.9
499.3
443.9
494.6
0.0
-14.8
-7.8
-5.6
-16.1
-6.5
56.2
72.7
80.6
83.3
71.4
82.2
282.9
394.9
449.3
467.6
386.1
459.8
90.2
118.2
131.1
135.3
116.1
133.5
-34.1
-13.6
-4.3
-1.2
-15.2
-2.5
150.4
192.8
210.6
216.8
189.8
214.1
-38.5
-21.3
-14.0
-11.5
-22.5
-12.6
182.9
243.0
267.1
274.6
238.9
271.5
-42.4
-23.5
-15.9
-13.6
-24.8
-14.6
232.2
307.3
336.3
345.5
302.3
341.7
-39.8
-20.3
-12.8
-10.4
-21.6
-11.4
295.1
385.3
418.7
428.4
379.4
424.5
-37.2
-18.0
-10.9
-8.8
-19.2
-9.6
348.0
452.1
489.3
500.6
445.4
495.9
-34.2
-14.5
-7.5
-5.4
-15.8
-6.3
56.1
71.8
78.8
81.4
70.7
80.3
282.1
389.0
436.8
454.6
381.9
447.0
88.8
118.2
131.1
135.3
116.1
133.5
-35.1
-13.6
-4.3
-1.2
-15.2
-2.5
149.0
190.8
209.3
215.7
187.9
213.0
-39.1
-22.1
-14.5
-11.9
-23.2
-13.0
182.5
241.6
265.6
273.3
237.5
270.1
-42.6
-24.0
-16.4
-14.0
-25.2
-15.0
230.9
305.7
334.8
344.0
300.7
340.2
-40.2
-20.8
-13.2
-10.8
-22.1
-11.8
294.9
385.1
418.5
428.6
379.2
424.4
-37.2
-18.0
-10.9
-8.7
-19.3
-9.6
348.0
452.1
489.3
500.6
445.4
495.9
-34.2
-14.5
-7.5
-5.4
-15.8
-6.3
58.4
74.7
81.2
83.9
73.6
82.8
298.0
408.7
453.5
471.6
401.2
463.7
101.1 -26.1 152.4 -37.7 188.1 -40.8 234.9
129.6 -5.4 197.2 -19.4 241.8 -23.9 310.3
141.5 3.3 217.3 -11.2 268.2 -15.6 339.3
145.5 6.2 223.7 -8.6 275.8 -13.2 348.3
127.6 -6.8 193.9 -20.8 240.1 -24.4 305.3
143.8 5.0 221.0 -9.7 272.6 -14.2 344.5
-39.1
-19.6
-12.1
-9.7
-20.9
-10.7
295.7
385.9
419.2
429.0
380.0
425.1
-37.0
-17.8
-10.7
-8.7
-19.1
-9.5
351.5
455.5
492.2
503.4
448.8
498.8
-33.6
-13.9
-7.0
-4.8
-15.2
-5.7
183
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg IL from excellent and resonable fit
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Avg CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from all storm
Median CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Median CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Median CL from excellent fit
35.07
7.59
15.56
11.20
9.96
9.60
11.43
9.75
27.00
7.59
15.56
11.20
9.96
9.60
11.43
9.75
35.90
2.74
15.56
11.20
9.96
9.60
11.43
9.75
30.50
2.74
15.56
11.20
9.96
9.60
11.43
9.75
31.40
2.74
54.7
70.2
76.3
78.3
69.1
77.5
272.9
377.9
419.9
433.7
370.9
427.8
87.9
117.0
129.8
134.0
115.0
132.2
-35.8
-14.5
-5.2
-2.2
-16.0
-3.5
143.2
188.9
208.8
215.2
185.6
212.5
-41.5
-22.8
-14.7
-12.1
-24.2
-13.2
181.0
234.7
258.7
266.3
230.7
263.1
-43.0
-26.1
-18.6
-16.2
-27.4
-17.2
230.4
305.2
334.3
343.5
300.2
339.7
-40.3
-20.9
-13.3
-10.9
-22.2
-12.0
290.6
380.4
414.1
424.4
374.5
420.1
-38.1
-19.0
-11.8
-9.6
-20.3
-10.5
347.8
451.9
489.1
500.5
445.1
495.7
-34.2
-14.6
-7.5
-5.4
-15.9
-6.3
56.6
73.2
81.2
83.9
71.9
82.8
285.6
398.4
453.2
471.6
389.4
463.7
95.5
122.0
133.1
136.7
120.2
135.2
-30.3
-10.9
-2.8
-0.2
-12.2
-1.3
151.1
197.0
217.0
223.4
193.6
220.7
-38.3
-19.6
-11.4
-8.7
-20.9
-9.8
184.9
243.0
267.1
274.6
238.9
271.5
-41.8
-23.5
-15.9
-13.6
-24.8
-14.6
232.5
307.6
336.7
345.8
302.6
342.0
-39.7
-20.3
-12.7
-10.4
-21.6
-11.3
295.1
385.3
418.7
428.4
379.4
424.5
-37.2
-18.0
-10.9
-8.8
-19.2
-9.6
349.3
453.4
490.4
501.7
446.7
497.0
-34.0
-14.3
-7.3
-5.2
-15.6
-6.1
79.7
104.3
114.9
118.6
102.6
117.0
443.2
610.6
682.4
707.8
598.8
697.0
126.3
165.7
182.9
188.6
163.0
186.2
-7.8
21.0
33.6
37.8
19.1
36.0
190.9
249.9
274.9
282.9
245.7
279.6
-22.0
2.1
12.3
15.6
0.4
14.2
231.1 -27.3 288.0 -25.3 355.8 -24.2 415.6 -21.4
301.7 -5.0 374.1 -3.0 457.0 -2.7 530.1 0.2
330.7 4.1 407.8 5.7 493.9 5.2 570.9 7.9
339.8 6.9 418.1 8.4 505.1 7.5 582.8 10.2
296.7 -6.6 368.3 -4.5 450.4 -4.1 522.8 -1.2
336.0 5.8 413.8 7.3 500.4 6.5 577.9 9.2
87.2
114.5
126.6
130.6
112.6
128.9
493.9
679.6
762.1
789.9
666.7
778.2
130.8
171.6
189.6
195.5
168.8
193.0
-4.5
25.3
38.5
42.8
23.3
40.9
196.9
257.5
282.7
290.5
253.2
287.2
-19.6
5.2
15.5
18.7
3.4
17.3
239.0 -24.8 294.0 -23.8 362.4 -22.8 419.2 -20.8
311.2 -2.0 381.0 -1.2 463.5 -1.3 533.7 0.9
340.1 7.0 414.3 7.4 500.1 6.5 574.0 8.5
349.0 9.8 424.1 9.9 511.0 8.8 585.8 10.7
306.3 -3.6 375.2 -2.8 457.0 -2.7 526.5 -0.5
345.2 8.7 419.8 8.8 506.4 7.8 580.9 9.8
184
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent fit
Median CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent and resonable fit
Median CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Median CL from excellent fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from all storm
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
15.56
11.20
9.96
9.60
11.43
9.75
23.00
2.74
15.56
11.20
9.96
9.60
11.43
9.75
35.07
2.74
15.56
11.20
9.96
9.60
11.43
9.75
27.00
2.74
15.56
11.20
9.96
9.60
11.43
9.75
35.90
7.52
15.56
11.20
85.9
112.7
124.6
128.6
110.9
126.9
485.4
668.0
748.7
776.2
655.3
764.6
130.8
171.6
189.6
195.5
168.8
193.0
-4.5
25.3
38.5
42.8
23.3
40.9
195.6
255.9
280.9
288.9
251.6
285.6
-20.1
4.5
14.8
18.0
2.8
16.7
237.8 -25.1 292.7 -24.1 362.2 -22.9 418.0 -21.0
309.9 -2.5 379.5 -1.6 463.3 -1.4 532.6 0.7
338.8 6.6 412.9 7.0 499.9 6.4 573.0 8.3
347.7 9.4 422.7 9.6 510.8 8.8 584.9 10.6
304.9 -4.0 373.7 -3.1 456.8 -2.7 525.3 -0.7
343.9 8.3 418.4 8.5 506.3 7.8 579.9 9.6
91.9
120.8
133.8
138.0
118.8
136.2
526.0
723.1
811.3
840.2
708.9
828.0
138.9
182.3
200.8
206.7
179.2
204.2
1.5
33.1
46.6
50.9
30.9
49.1
205.8
268.2
293.2
300.9
264.0
297.7
-15.9
9.6
19.8
22.9
7.8
21.6
246.0
319.4
347.9
356.2
314.5
352.9
80.9
105.9
116.6
120.4
104.1
118.8
451.0
621.2
694.6
720.4
609.2
709.5
127.5
167.3
184.7
190.5
164.6
188.1
-6.9
22.2
34.9
39.1
20.2
37.3
192.2
251.5
276.6
284.6
247.3
281.2
-21.5
2.7
13.0
16.2
1.0
14.9
232.3 -26.9 288.6 -25.2 357.0 -24.0 416.7 -21.2
303.2 -4.6 374.9 -2.8 457.9 -2.5 531.3 0.4
332.2 4.6 408.5 5.9 495.1 5.4 571.9 8.1
341.2 7.4 418.5 8.5 506.2 7.8 583.8 10.4
298.3 -6.1 369.0 -4.3 451.6 -3.8 524.0 -0.9
337.5 6.2 414.5 7.5 501.5 6.8 578.9 9.4
90.1
118.4
131.1
135.3
116.5
133.5
514.0
706.7
793.2
821.8
693.4
809.7
135.2
177.5
195.8
201.7
174.4
199.2
-1.3
29.6
43.0
47.3
27.4
45.5
202.1
263.8
288.9
296.7
259.5
293.5
-17.5
7.8
18.0
21.2
6.0
19.9
242.3
315.1
343.8
352.6
310.2
348.9
-22.6
0.5
9.5
12.1
-1.0
11.1
-23.7
-0.8
8.2
11.0
-2.4
9.8
300.0 -22.2 367.9 -21.7 427.0 -19.3
387.5 0.5 468.8 -0.2 540.8 2.2
420.0 8.9 504.7 7.4 579.8 9.6
429.8 11.4 515.2 9.7 591.3 11.8
381.7 -1.1 462.4 -1.6 533.8 0.9
425.7 10.3 510.8 8.8 586.5 10.9
297.1 -23.0 364.5 -22.4 422.0 -20.2
384.3 -0.4 465.6 -0.9 536.4 1.4
417.1 8.1 501.9 6.9 576.2 8.9
427.0 10.7 512.6 9.1 587.9 11.1
378.5 -1.9 459.1 -2.3 529.1 0.0
422.9 9.6 508.2 8.2 583.0 10.2
53.5 264.3 88.3 -35.5 142.4 -41.8 180.2 -43.3 230.5 -40.2 291.5 -37.9 347.6 -34.3
68.7 367.8 117.6 -14.1 188.2 -23.1 234.3 -26.2 305.4 -20.8 381.4 -18.8 451.7 -14.6
185
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent fit
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent and resonable fit
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
9.96
9.60
11.43
9.75
30.50
7.52
15.56
11.20
9.96
9.60
11.43
9.75
31.40
7.52
15.56
11.20
9.96
9.60
11.43
9.75
23.00
7.52
15.56
11.20
9.96
9.60
11.43
9.75
35.07
7.52
15.56
11.20
9.96
9.60
74.7
77.1
67.7
76.1
409.0
425.5
360.9
418.3
130.3
134.5
115.5
132.7
-4.8
-1.8
-15.7
-3.1
208.0
214.4
184.9
211.7
-15.0
-12.4
-24.5
-13.5
258.3
266.0
230.3
262.7
-18.7
-16.3
-27.5
-17.3
334.6
343.8
300.4
340.0
-13.3
-10.9
-22.1
-11.9
415.3
425.6
375.5
421.3
-11.6
-9.4
-20.0
-10.3
489.1
500.5
445.0
495.8
-7.5
-5.4
-15.9
-6.3
56.6
73.2
81.2
83.9
71.9
82.8
285.3
398.4
453.2
471.6
389.5
463.8
90.6
119.0
131.9
136.1
116.8
134.3
-33.8
-13.1
-3.7
-0.6
-14.7
-1.9
151.0
193.4
211.4
217.8
188.1
215.1
-38.3
-21.0
-13.7
-11.0
-23.2
-12.1
183.6
244.0
268.1
275.7
239.9
272.5
-42.2
-23.2
-15.6
-13.2
-24.5
-14.2
233.1
308.3
337.5
346.6
303.3
342.8
-39.6
-20.1
-12.5
-10.1
-21.4
-11.1
296.0
386.4
419.8
429.6
380.5
425.7
-37.0
-17.7
-10.6
-8.5
-19.0
-9.4
349.0
453.2
490.4
501.8
446.5
497.0
-34.0
-14.3
-7.3
-5.1
-15.6
-6.0
56.4
72.2
79.4
82.0
70.2
80.9
284.2
391.7
440.7
458.6
378.5
451.0
89.3
119.0
131.9
136.1
116.8
134.3
-34.8
-13.1
-3.7
-0.6
-14.7
-1.9
149.5
191.5
210.2
216.7
188.6
213.9
-38.9
-21.8
-14.1
-11.5
-23.0
-12.6
183.0
242.6
266.7
274.3
238.5
271.1
-42.4
-23.6
-16.1
-13.7
-24.9
-14.7
231.7
306.8
335.9
345.2
301.7
341.3
-39.9
-20.5
-12.9
-10.5
-21.8
-11.5
295.9
386.2
419.7
429.4
380.3
425.5
-37.0
-17.8
-10.6
-8.6
-19.0
-9.4
349.0
453.2
490.4
501.8
446.5
497.0
-34.0
-14.3
-7.3
-5.1
-15.6
-6.0
58.8
75.2
81.8
84.5
74.1
83.3
300.9
412.3
457.4
475.6
404.8
467.7
101.6 -25.8 153.0 -37.5 188.8 -40.6 237.3
130.1 -5.0 198.2 -19.0 245.2 -22.8 311.4
142.1 3.8 218.4 -10.8 269.3 -15.2 340.5
146.1 6.7 224.8 -8.2 276.9 -12.8 349.5
128.2 -6.4 194.9 -20.4 241.1 -24.1 306.4
144.4 5.5 222.1 -9.3 273.7 -13.8 345.7
-38.5
-19.3
-11.7
-9.4
-20.6
-10.4
296.7
387.1
420.4
430.2
381.2
426.3
-36.8
-17.6
-10.5
-8.4
-18.8
-9.2
352.5
456.7
493.5
504.7
450.0
500.0
-33.4
-13.7
-6.7
-4.6
-14.9
-5.5
55.0
70.6
76.7
78.8
275.0 88.4 -35.4 143.7
380.6 117.7 -14.0 189.8
422.8 130.5 -4.7 209.7
436.7 134.7 -1.6 216.2
-40.1
-20.6
-13.1
-10.7
291.5
381.4
415.3
425.6
-37.9
-18.8
-11.6
-9.4
348.8
453.0
490.3
501.6
-34.1
-14.4
-7.3
-5.2
186
-41.3
-22.5
-14.3
-11.7
181.6
235.7
259.7
267.4
-42.9
-25.8
-18.2
-15.8
231.2
306.2
335.4
344.6
Hitesh D. Patel
Student ID: 16095380
Appendices
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Avg kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from all storm
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from all storm
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent fit
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
11.43
9.75
27.00
7.52
15.56
11.20
9.96
9.60
11.43
9.75
35.90
2.80
15.56
11.20
9.96
9.60
11.43
9.75
30.50
2.80
15.56
11.20
9.96
9.60
11.43
9.75
31.40
2.80
15.56
11.20
9.96
9.60
11.43
9.75
69.5 373.5 115.6 -15.5 186.5 -23.8 231.7 -27.1 301.2 -21.9 375.5 -20.0 446.3 -15.6
77.9 430.8 133.0 -2.9 213.4 -12.8 264.2 -16.8 340.7 -11.7 421.3 -10.3 496.9 -6.1
57.0
73.7
81.8
84.5
72.4
83.3
288.1
401.9
457.1
475.6
392.9
467.7
95.9
122.6
133.7
137.5
120.8
135.8
-30.0
-10.5
-2.4
0.4
-11.8
-0.8
151.6
197.9
218.0
224.5
194.5
221.7
-38.1
-19.2
-10.9
-8.3
-20.5
-9.4
185.5
244.0
268.1
275.7
239.9
272.5
79.3
103.7
114.3
118.0
102.0
116.4
440.2
606.6
678.4
703.7
594.9
692.9
125.7
165.0
182.2
187.9
162.3
185.5
-8.2
20.5
33.1
37.2
18.6
35.5
190.3
249.1
274.1
282.1
244.9
278.7
-22.3
1.8
12.0
15.2
0.0
13.9
230.4 -27.5 287.3 -25.5 354.9 -24.4 414.7 -21.6
300.8 -5.3 373.3 -3.2 455.9 -2.9 529.0 0.0
329.8 3.8 406.9 5.5 492.8 4.9 569.8 7.7
338.8 6.7 417.2 8.1 504.0 7.3 581.7 10.0
295.9 -6.9 367.4 -4.8 449.3 -4.3 521.7 -1.4
335.0 5.5 412.8 7.0 499.3 6.3 576.7 9.0
86.7
113.9
126.0
130.0
112.0
128.3
490.8
675.6
758.1
785.7
662.7
774.0
130.2
170.9
188.9
194.7
168.1
192.2
-4.9
24.8
37.9
42.2
22.8
40.4
196.2
256.7
281.8
289.6
252.4
286.3
-19.8
4.8
15.1
18.3
3.1
17.0
238.2 -25.0 293.2 -24.0 361.5 -23.0 418.2 -20.9
310.4 -2.3 380.1 -1.5 462.4 -1.5 532.6 0.7
339.2 6.8 413.3 7.1 499.0 6.2 572.8 8.3
348.0 9.5 423.1 9.7 509.9 8.6 584.6 10.5
305.4 -3.9 374.2 -3.0 455.9 -2.9 525.4 -0.7
344.3 8.4 418.8 8.6 505.3 7.6 579.7 9.6
85.5
112.1
124.0
128.0
110.3
126.3
482.3
663.9
744.7
772.0
651.3
760.4
130.2
170.9
188.9
194.7
168.1
192.2
-4.9
24.8
37.9
42.2
22.8
40.4
194.9
255.0
280.0
288.0
250.8
284.7
-20.4
4.2
14.4
17.6
2.4
16.3
237.1 -25.4 291.9 -24.3 361.3 -23.1 417.0 -21.2
309.0 -2.7 378.6 -1.9 462.2 -1.6 531.4 0.5
337.9 6.3 411.9 6.8 498.8 6.2 571.8 8.1
346.7 9.1 421.7 9.3 509.7 8.5 583.7 10.3
304.1 -4.3 372.8 -3.4 455.7 -3.0 524.2 -0.9
343.0 8.0 417.5 8.2 505.2 7.6 578.7 9.4
187
-41.6
-23.2
-15.6
-13.2
-24.5
-14.2
233.8
308.7
337.8
346.9
303.6
343.2
-39.4
-20.0
-12.4
-10.1
-21.3
-11.0
296.0
386.4
419.8
429.6
380.5
425.7
-37.0
-17.7
-10.6
-8.5
-19.0
-9.4
350.3
454.6
491.6
502.9
447.9
498.2
-33.8
-14.1
-7.1
-4.9
-15.3
-5.8
Hitesh D. Patel
Student ID: 16095380
Appendices
Median IL from excellent fit
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Avg IL from excellent and resonable fit
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
Median IL from excellent and resonable fit
Median kc from excellent and resonable fit
Avg kc from all storm
Median kc from all storm
Avg kc from excellent fit
Median kc from excellent fit
Avg kc from excellent and resonable fit
Median kc from excellent and resonable fit
23.00
2.80
15.56
11.20
9.96
9.60
11.43
9.75
35.07
2.80
15.56
11.20
9.96
9.60
11.43
9.75
27.00
2.80
15.56
11.20
9.96
9.60
11.43
9.75
91.3
120.1
133.0
137.2
118.0
135.4
521.9
718.0
805.8
834.6
703.7
822.4
138.3
181.5
199.9
205.8
178.4
203.3
1.0
32.6
46.0
50.3
30.3
48.5
205.0
267.4
292.3
299.9
263.1
296.7
-16.2
9.2
19.4
22.5
7.5
21.2
245.2
318.4
346.8
355.2
313.5
351.9
80.4
105.3
116.1
119.8
103.5
118.2
447.9
617.1
690.6
716.3
605.3
705.4
127.0
166.6
184.0
189.8
163.9
187.4
-7.3
21.7
34.4
38.6
19.7
36.8
191.5
250.8
275.7
283.7
246.5
280.4
-21.8
2.4
12.6
15.9
0.7
14.5
231.6 -27.1 287.9 -25.4 356.1 -24.2 415.8 -21.4
302.4 -4.8 374.0 -3.0 457.2 -2.7 530.2 0.2
331.3 4.3 407.6 5.7 494.0 5.2 570.8 7.9
340.3 7.1 417.6 8.2 505.1 7.5 582.7 10.2
297.4 -6.4 368.2 -4.6 450.6 -4.1 522.9 -1.1
336.5 5.9 413.6 7.2 500.4 6.5 577.7 9.2
89.6
117.8
130.5
134.6
115.8
132.9
510.6
702.3
788.7
817.1
689.0
805.1
134.6
176.7
195.0
200.9
173.7
198.4
-1.7
29.1
42.4
46.7
26.8
44.9
201.4
263.0
288.0
295.8
258.7
292.6
-17.7
7.4
17.7
20.8
5.7
19.5
241.5
314.2
342.8
351.6
309.3
347.9
188
-22.8
0.2
9.2
11.8
-1.3
10.8
-24.0
-1.1
7.9
10.7
-2.7
9.5
299.2 -22.4 366.9 -21.9 426.0 -19.5
386.6 0.2 467.6 -0.4 539.7 2.0
419.0 8.6 503.5 7.2 578.6 9.4
428.8 11.2 514.0 9.4 590.1 11.6
380.8 -1.3 461.2 -1.8 532.6 0.7
424.7 10.1 509.6 8.5 585.4 10.7
296.3 -23.2 363.5 -22.6 421.0
383.4 -0.6 464.4 -1.1 535.3
416.1 7.9 500.7 6.6 575.0
426.0 10.4 511.5 8.9 586.7
377.6 -2.1 457.9 -2.5 528.0
421.9 9.4 507.0 7.9 581.8
-20.4
1.2
8.7
10.9
-0.2
10.0
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX D
Distribution of storm-core durations
189
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX E
Intensity-Frequency-Duration (IFD) tables and Plot
1
1.11
1.25
2
5
19.1
14.0
8.1
3.6
2.3
1.8
1.4
21.0
15.2
8.7
3.9
2.6
2.0
1.6
23.1
16.6
9.4
4.3
2.8
2.2
1.8
31.6
22.0
12.2
5.7
3.8
3.0
2.5
48.1
32.5
17.7
8.4
5.8
4.7
4.0
60.6
40.5
21.9
10.5
7.4
6.0
5.1
73.1
48.5
26.0
12.5
8.9
7.3
6.2
89.6
59.0
31.5
15.2
10.9
9.0
7.7
100
500
1000
1000000
102.1
67.0
35.7
17.3
12.4
10.3
8.9
131.2
85.5
45.4
22.0
15.9
13.2
11.5
143.7
93.5
49.5
24.1
17.4
14.5
12.6
268.4
172.9
90.9
44.5
32.4
27.2
23.8
Coopers Creek-58072
1000
100
I c (mm/hr)
Duration, h
1
2
6
24
48
72
100
Coopers Creek ARI, years
10
20
50
10
1
1
10
D c (hours)
190
100
Hitesh D. Patel
Student ID: 16095380
Appendices
1
1.11
1.25
2
5
16.5
9.3
4.1
1.8
1.3
1.1
0.9
17.3
9.7
4.3
1.8
1.3
1.1
1.0
18.2
10.2
4.5
1.9
1.4
1.1
1.0
21.7
12.0
5.2
2.2
1.6
1.3
1.1
28.4
15.5
6.6
2.8
2.0
1.6
1.4
Moonan Brook ARI, years
10
20
50
33.4
18.1
7.7
3.2
2.3
1.9
1.7
38.4
20.6
8.7
3.6
2.6
2.2
1.9
45.0
24.0
10.1
4.2
3.0
2.5
2.2
100
500
1000
1000000
50.0
26.6
11.1
4.6
3.3
2.8
2.5
61.6
32.4
13.5
5.6
4.0
3.4
3.0
66.5
35.0
14.5
6.1
4.3
3.7
3.3
116.1
60.1
24.6
10.3
7.4
6.3
5.7
Moonan-61335
1000
100
I c (mm/hr)
Duration, h
1
2
6
24
48
72
100
10
1
1
10
D c (hours)
191
100
Hitesh D. Patel
Student ID: 16095380
Appendices
1
1.11
1.25
2
5
12.0
8.0
4.1
1.7
1.0
0.8
0.6
12.9
8.5
4.3
1.8
1.1
0.9
0.7
13.9
9.1
4.6
1.9
1.3
1.0
0.8
18.1
11.3
5.6
2.5
1.7
1.4
1.2
26.2
15.8
7.7
3.7
2.7
2.3
2.0
32.3
19.2
9.3
4.5
3.4
2.9
2.7
38.5
22.6
10.9
5.4
4.1
3.6
3.3
46.6
27.0
13.0
6.5
5.0
4.5
4.1
100
500
1000
1000000
52.7
30.4
14.6
7.3
5.8
5.1
4.8
66.9
38.3
18.3
9.3
7.4
6.7
6.3
73.0
41.6
19.9
10.2
8.1
7.4
6.9
134.0
75.3
35.7
18.6
15.2
14.0
13.4
Corang-69049
1000
100
I c (mm/hr)
Duration, h
1
2
6
24
48
72
100
Corang River ARI, years
10
20
50
10
1
1
0.1
10
100
D c (hours)
192
Hitesh D. Patel
Student ID: 16095380
Appendices
1
1.11
1.25
2
5
20.7
11.3
5.2
2.8
2.3
2.2
2.1
21.3
11.8
5.6
3.0
2.5
2.3
2.2
22.1
12.4
5.9
3.2
2.6
2.5
2.4
25.0
14.8
7.5
4.1
3.3
3.1
2.9
30.8
19.4
10.4
5.8
4.7
4.3
4.0
Wadbilliga ARI, years
10
20
50
35.2
22.8
12.7
7.1
5.8
5.2
4.8
39.6
26.2
14.9
8.5
6.8
6.1
5.6
45.5
30.7
17.8
10.2
8.2
7.3
6.7
100
500
1000
1000000
49.9
34.1
20.0
11.5
9.2
8.2
7.5
60.3
42.0
25.1
14.6
11.6
10.3
9.4
64.8
45.3
27.3
15.9
12.7
11.2
10.3
109.3
78.9
49.2
29.1
23.1
20.3
18.4
Wadbilliga-69075
1000
100
Ic (mm/hr)
Duration, h
1
2
6
24
48
72
100
10
1
1
10
D c (hours)
193
100
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX F
Storm-core temporal pattern
Coopers Creek-58072
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
5
Period
6
7
8
7
8
9
10
Moonan-61335
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
194
5
6
Period
9
10
Hitesh D. Patel
Student ID: 16095380
Appendices
Wadbilliga-69075
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
Period
7
8
9
10
7
8
9
10
Corang river-69049
100
90
Cumulative % rain
80
70
60
50
40
30
20
10
0
1
2
3
4
195
5
Period
6
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX G
Distribution of initial loss
196
Hitesh D. Patel
Student ID: 16095380
Appendices
197
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX H
Plot of Fitting Results (One Storage model)
Horton 418027_Ev1
6
Qobs
Qcom
4
3
Discharge, m/s
5
3
2
1
0
1
6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86
Time, hours
40
Horton 418027_Ev3
Qobs
35
Qcom
3
Discharge, m/s
30
25
20
15
10
5
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61
Time, hours
198
Hitesh D. Patel
Student ID: 16095380
Appendices
Horton 418027_Ev4
350
Qobs
300
Qcom
3
Discharge, m/s
250
200
150
100
50
0
1
8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113
Time, hours
Coopers 203002_Ev1
140
Qobs
Qcom
120
Discharge, m3 /s
100
80
60
40
20
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67
Time, hours
199
Hitesh D. Patel
Student ID: 16095380
Appendices
Coopers 203002_Ev2
50
Qobs
45
Qcom
40
3
Discharge, m /s
35
30
25
20
15
10
5
0
1
5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81
Time, hours
Coopers 203002_Ev3
450
Qobs
400
Qcom
300
3
Discharge, m /s
350
250
200
150
100
50
0
1
8
15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120
Time, hours
200
Hitesh D. Patel
Student ID: 16095380
Appendices
Coopers 203002_Ev4
90
Qobs
80
Qcom
60
3
Discharge, m /s
70
50
40
30
20
10
0
1
5
9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
Time, hours
Wadbilliga 218007 _Ev1
14
Qobs
12
Qcom
3
Discharge, m/s
10
8
6
4
2
0
1
11 21 31 41 51 61 71 81 91 101 111 121 131 141
Time, hours
201
Hitesh D. Patel
Student ID: 16095380
Appendices
Wadbilliga 218007_Ev2
35
Qobs
30
Qcom
3
Discharge, m/s
25
20
15
10
5
0
1
8
15 22 29 36 43 50 57 64 71 78 85 92 99 106
Time, hours
Wadbilliga 218007_Ev3
16
Qobs
14
Qcom
3
Discharge, m/s
12
10
8
6
4
2
0
1
14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
Time, hours
202
Hitesh D. Patel
Student ID: 16095380
Appendices
Wadbilliga 218007_Ev4
50
Qobs
45
Qcom
3
Discharge, m/s
40
35
30
25
20
15
10
5
0
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73
Time, hours
Corang 215004_Ev1
120
Qobs
Qcom
80
3
Discharge, m/s
100
60
40
20
0
1
9
17 25 33 41 49 57 65 73 81 89 97 105
Time, hours
203
Hitesh D. Patel
Student ID: 16095380
Appendices
Corang 215004_Ev2
60
Qobs
Qcom
3/
Discharge, m s
50
40
30
20
10
0
1
12 23 34 45 56 67 78 89 100 111 122 133 144
Time, hours
Moonan 210017_Ev1
10
Qobs
9
Qcom
8
Discharge, m3/s
7
6
5
4
3
2
1
0
1
9
17 25 33 41 49 57 65 73 81 89 97 105 113 121 129
Time, hours
204
Hitesh D. Patel
Student ID: 16095380
Appendices
APPENDIX I
List Publications from This Research
Patel, H. and Rahman, A. (2010): Design Flood Estimation Using Monte Carlo
Simulation and RORB Model: Stochastic Nature of RORB Model Parameters. World
Environmental and Water Resources Congress, American Society of Civil Engineers
(ASCE) 16-20 May 2010, providence, Rhode Island, USA.
Patel, H. and Rahman, A. (2010): Enhancement of Monte Carlo Simulation Technique to
design flood estimation by incorporating stochastic runoff routing model parameter.
Stochastic Environmental Research and Risk Assessment (In preparation).
Patel, H. and Rahman, A. (2010): Stochastic RORB model parameter kc: A case study for
Lismore catchment in NSW. Australian Journal of Water Resources (In preparation).
205
Hitesh D. Patel
Student ID: 16095380
World Environmental and Water Resources Congress 2010:
Challenges of Change. © 2010 ASCE
4692
Design Flood Estimation Using Monte Carlo Simulation and RORB
Model: Stochastic Nature of RORB Model Parameters
Hitesh Patel and Ataur Rahman
School of Engineering, University of Western Sydney, Australia
Abstract
Rainfall-based flood estimation method is often adopted when a complete design hydrograph is
required and/or in the situations where the recorded streamflow data are not long enough to
characterize the underlying at-site flood frequency distribution with sufficient accuracy. The Design
Event Approach (DEA) is currently recommended rainfall-based flood estimation method in Australia
according to Australian Rainfall and Runoff – the national guide to flood estimation. However, DEA
does not account for the probabilistic nature of the key flood producing variables except for the
rainfall depth. This arbitrary treatment of key inputs and model parameters in DEA can lead to
inconsistencies and significant bias in flood estimates for a given average recurrence interval (ARI). A
significant improvement in design flood estimates can be achieved through a Joint Probability
Approach (JPA), which is more holistic in nature that uses probability-distributed input
variables/model parameters and their correlations to obtain probability-distributed flood output. More
recently, there have been notable researches in Australia on Monte Carlo simulation technique
(MCST) for flood estimation based on the principles of Joint Probability that can employ many of the
commonly adopted flood estimation models and design data in Australia. Recently, the National
Committee on Water Engineering in Australia has resolved that MCST should replace the DEA as the
preferred method of flood hydrograph modeling in Australia. Based on the previous researches on
MCST in Australia, the industry-based software URBS has integrated MCST within the software,
which however, needs further enhancement for applications under a wide range of hydrologic and
catchment conditions. Application of MCST with RORB model, the most widely used hydrologic
model in Australia, has not been well investigated. At present, the RORB model has a limited
capability in terms of implementation of the MCST in flood modeling.
This paper investigates the applicability of the MCST with RORB model, in particular, this examines
the probabilistic nature of key RORB model parameter kc and its impacts on design flood estimates. A
large number of storm and runoff events were selected from Lismore catchment in New South Wales,
Australia and values of kc, initial loss (IL) and continuing loss (CL) were estimated. Values of kc were
categorized according to their goodness-of-fit in the FIT run and were validated using a number of
independent storm events. Finally, peak flows were estimated for many combinations of kc, IL and CL
values. In the RORB modeling, kc is considered to be a fixed parameter. It has been found that the
value of kc may exhibit a high degree of variability, and they result in quite different flood peak
estimates and hence it should be considered as a random variable in rainfall runoff modelling.
1. Introduction
For design flood estimation, rainfall based methods are often preferred over streamflow-based
methods because rainfall data generally have longer records and have greater spatial and temporal
coverage. In Australia, the rainfall based flood estimation method that is currently adopted is known as
Design Event Approach (DEA) (I.E. Aust., 1987). This method considers the probabilistic behavior of
rainfall depth in rainfall runoff modeling but ignores the probabilistic nature of other input variables
such as losses. As a result of the arbitrary treatment of various input variables, the DEA is likely to
introduce significant probability bias in the final flood estimates and has been widely criticized
1
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(Kuczera et al., 2003; Rahman et al., 2002a). In Australia, the DEA is commonly used with a runoff
routing model such as RORB (Laurenson et al., 2007), WBNM (Boyd et al., 2001) and URBS
(Carroll, 2007). The use of this approach involves formulation of a design rainfall event, characterized
by duration, average rainfall depth (intensity) and temporal pattern. A loss model, such as initial loss
(IL) and continuing loss (CL) is then used to produce net rainfall hyetograph.
Rahman et al. (2002a, b; 2007) developed a Monte Carlo simulation technique (MCST) for flood
estimation based on the principles of joint probability that can employ many of the commonly adopted
flood estimation models and design data in Australia. The Joint Probability Approach has the potential
to overcome the limitations of the DEA by considering the probability-distributed inputs and model
parameters and their correlations to determine probability-distributed outputs. The method of
combining probability distributed inputs to form a probability-distributed output is known as the
derived distribution approach, and was pioneered by Eagleson (1972). The new technique has enough
flexibility for its adoption in practical situations and has the potential to provide more precise design
flood estimates than the currently adopted DEA.
The Joint Probability Approach so far has been developed and applied for small gauged catchments
(Rahman et al., 2002a; Rahman and Carroll, 2004). The Joint Probability Approach has been
incorporated with industry-based flood estimation model URBS (Rahman et al., 2002b). Application
of the approach to ungauged catchments has also been investigated (e.g. Rahman and Kader 2004).
Application of the approach to extreme flood range has been tested by Nathan and Weinmann (2004).
Rahman et al. (2002b) presented a study illustrating how MCST can be integrated with industry-based
model such as URBS. It was found that the integrated URBS-Monte Carlo Technique can be used to
obtain more precise flood estimates for small to large catchments.
Charalambous et al. (2003, 2005) extended the URBS-MCST to two large catchments in Queensland.
They found that the URBS-MCST can easily be applied to large catchments. Although the limited data
availability in their application introduced significant uncertainty in the distributions of the input
variables e.g. IFD curves.
Kuczera et al. (2006) compared the joint probability approach and design storm in the case study
involving detention basin, which showed that unacceptably large bias can arise from misspecification
of initial conditions in volume sensitive systems. Aronica and Candela (2007) derived frequency
distributions of peak flow by Monte Carlo simulation procedure using a simple semi-distributed
stochastic rainfall-runoff model.
More recently, there have been notable researches in Australia on MCST (MCST) for flood estimation
based on the principles of Joint Probability that can employ many of the commonly adopted flood
estimation models and design data in Australia. Recently, the National Committee on Water
Engineering in Australia has resolved that MCST should replace the DEA as the preferred method of
flood modeling in Australia.
Based on the previous researches on MCST in Australia, the industry-based software URBS has
integrated MCST within the software, which however, needs further enhancement for applications
under a wide range of hydrologic and catchment conditions. Application of MCST with RORB model,
the most widely used hydrologic model in Australia, has not been well investigated. At present, the
RORB model has a limited capability in terms of implementation of the MCST in flood modeling.
This paper investigates the applicability of the MCST with RORB model, in particular, this examines
the probabilistic nature of key RORB model parameter kc and its impacts on design flood estimates.
2
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2 RORB Principles
RORB is a runoff and streamflow routing program used to calculate hydrographs from rainfall and
other channel inputs. It subtracts losses from rainfall to produce rainfall excess and routes this through
catchment storage to produce hydrographs (Laurenson et al., 2007).
The way in which RORB develops a stream hydrograph is illustrated in Figure 1. The model of the
catchment consists of two parts, a loss model and a catchment storage model. Inputs to the model can
consist of rainfall on a catchment area or direct inflow to the channel system. In the former case,
rainfall is operated on by a loss model to convert rainfall into rainfall-excess, which is then routed
through the catchment storage model to produce the surface runoff hydrograph. In the latter case,
channel inflow enters the catchment storage model directly.
Rainfall
RUNOFF ROUTING MODEL
Loss Model
Rainfall excess
Channel
inflow
Catchment
storage model
Surface Runoff
Hydrograph
Channel outflow
Figure 1 Overall RORB Runoff Routing Model (Laurenson et al., 2007)
RORB provides for spatial variability of rainfall and losses by subdividing the catchment into a
number of sub-areas, typically five to fifteen. This is also necessary for the modeling of the distributed
nature of catchment storage. The subdivision is drawn along watershed lines so that hydrographs
calculated at the downstream boundaries of sub-areas include all of the contributing area upstream.
The adopted sub-areas are assumed to be homogeneous in hydrologic response, i.e. different response
surfaces (e.g. urban, rural) should normally be assigned to separate sub-areas.
The catchment is divided into subareas and the rainfall on each subarea is adjusted to allow for
infiltration and other losses. Each subarea contains a stream segment called its main stream, which
may be part of the catchment main stream or of a tributary stream. The computed rainfall excess of the
subarea is assumed to enter the channel network at a point on the subarea's main stream near the
centroid of the subarea. There, it is added to any existing flow in the channel, and the combined flow
is routed through a storage element by a linear or nonlinear storage routing procedure based on
continuity and a storage function
S = 3600kQm
(1)
Where, S is storage (m3),
Q is outflow discharge (m3/s),
m is a dimensionless exponent,
k is a dimensional empirical coefficient, and
3600 is the number of seconds in an hour.
3
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Detailed descriptions of k and m can be found in RORB manual. The overall catchment storage is
represented in the model by a network of storages arranged like the actual stream or channel network.
Each model storage between the two nodes of the channel network represents storage effects along
river reaches. The nodes represent subarea inflow points, stream confluences, inflow points to storage
reservoirs and other points of interest on the catchment or channel network.
Storm rainfall is input to each sub-area at a node located at, or near its centroid, but generally on a
major stream. These sub-areas nodes are also the points where rainfall-excess enters the storage. The
depth and temporal pattern of rainfall can be the same on all sub-areas, or individually different,
depending on the data available. Thus, temporal and spatial variation of rainfall over a catchment is
provided for in the model; storm movement can also be simulated. Two alternative loss models, initial
loss-proportional loss and initial loss-continuing loss are provided. Both provide for an initial loss,
which is a threshold value of rainfall that must occur before any rainfall-excess is produced. The
model of losses that occur after the initial loss has been satisfied may be either a constant loss rate or a
loss directly proportional to rainfall intensity. Both loss models, therefore, contain two parameters, one
determining the initial loss and the other the remaining loss.
3 Data and study catchment
The Cooper’s Creek catchment with an area of 65.9 km2 and having streamflow gauging station
positioned at Repentance in Lismore located in the northern NSW was selected in this study. The
name of the area in the topographic map is Lismore, map reference number 9540 and catchment ID
203002. The longitude of the catchment is 1530 27` east and latitude is 280 38` south. Around 63% of
the catchment area is covered with the dense forest. The subject catchment is in temporal pattern Zone
1 (I.E. Aust., 1987).
Data availability
Streamflow data at the Repentance gauging station has been available since 4th November 1976 to 1st
January 2007. The data was obtained from Pinnena 9.2 CD (Department of Climate and Water, NSW).
The hourly rainfall data were obtained from the pluviograph station located in federal post office,
which is 50 km away from the catchment outlet. Pluviograph reference number is 58072, from where
rainfall data from 01st November 1965 to 02nd November 1998 have been available. There are some
daily stations in the area; however, as the network of rainfall stations is not very dense when compared
to the size of the catchment, it might be acceptable to use a uniform rainfall pattern.
The catchment was divided into 9 subareas which centered on streams and bounded by drainage
divides, as shown in Figure 2 and Table 1. The drainage network was also subdivided into reaches,
each of which was associated with model storage. The 9 subareas and 10 model storages are shown in
Figure 2. The catchment drainage data required to run the model is tabulated in Table 1. The
subdivision was done on a map which has a scale of 1:100,000 and the areas and reach lengths were
also obtained from the same map.
Selection of storm events
Storm events of comparatively longer duration and of higher intensity were selected from the rainfall
data. In the absence of any pluviograph station or a single pluviograph in the catchment, it appears to
be reasonable to use uniform rainfall pattern throughout the catchment.
4
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4696
Table 1 Catchment sub-areas and reach lengths
SubArea
A
B
C
D
E
F
G
H
I
Total
Area
( km2)
8.5
8.4
7.9
13.2
3.5
1.8
11.8
7.3
3.5
65.9
Reach
1
2
3
4
5
6
7
8
9
10
Length
(km)
3.7
3.6
4.0
5.8
4.9
1.9
7.8
4.9
2.5
2.5
Figure 2 Catchment boundaries, subareas and channel
network and catchment model reach storage
The streamflow data available at the gauging station includes surface runoff from the catchment and
baseflow. It is necessary to separate the baseflow from the surface runoff volume resulting from a
particular storm. The discharge input in the program is the total discharge recorded by the gauging
station minus the baseflow.
The method proposed by Boughton (1987) was adopted in this study which considers that the rate of
increase in baseflow depends on the fraction of the surface runoff α . That is the rate of baseflow at any
time step i (BFi) may be expressed as equal to the baseflow in the previous time step (BFi-1) plus alpha
times the difference of total streamflow at step i (SFi) and baseflow at step i-1 (BFi-1). That is:
BFi = BFi-1 + α (SFi-BFi-1)
(1)
At the beginning of surface runoff, the baseflow is assumed to be equal to the streamflow. The value of
alpha is estimated from the observed streamflow events; the design α value should provide an acceptable
baseflow separation for all the selected storms in the catchment. The baseflow separation for storm of
1981-X1 is shown in Figure 3.
Baseflow separation strom 1981-X1
1.600
Streamflow (m 3/s)
1.400
1.200
1.000
0.800
streamflow
(m3/s)
0.600
0.400
0.200
baseflow
(m3/s)
0.000
1
15 29 43 57 71 85 99 113 127
Time (Hours)
Figure 3 Baseflow separations for storm 1981-X1
5
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Finally 43 different storm events were selected to check the sensitivity of kc on the design flood
estimation. The data for the 43 storms used in the study consist of hourly rainfall quantities and
corresponding hourly discharge at the catchment outlet. Out of these 43 storm events, 40 are used to
calibrate the model in FIT run and 3 storm events are used to validate the model parameters.
Method
The overall modelling steps were used as suggested by Laurenson, et al. (2007). The three functions of
fitting, testing and design are associated with three different types of runs, whose characteristics are
summarised below:
(i) On gauged catchments, FIT runs would be used first with data for one or more of the available flood
events to evaluate the model’s parameters. From the 40 different storm events used to calibrate the
model, the value kc will be categorised according to the goodness-of-fit.
(ii) TEST runs would be used next with data for the remainder of the recorded flood events to test the
model. Three different storm events would be used to validate the key model parameters.
(iii) If the results of the TEST runs proved to be satisfactory, DESIGN runs would then be used to
predict design flood estimate.
(iv) To check the sensitivity of the key model parameters obtained from FIT run, design run with various
combinations of key model parameters i.e. kc, IL and CL will be used to estimate design floods.
(v) Peak flood estimate (i.e. the hydrograph peak) for various ARIs obtained from DESIGN run will be
compared with the at site flood frequency estimate (i.e. the observed flood quantile).
4 Results
FIT Runs
The model parameters to be obtained through calibration are: (i) loss parameters, which involve
calculating the rainfall excess from the total rainfall; and (ii) the routing parameters, which involve the
routing of the rainfall excess through the model storages of the catchment to the outlet. The objective of
FIT runs was (i) to find a best fit value of the model parameter kc using historical streamflow and
rainfall event data and (ii) to find the best fit value of kc by altering IL and kc to match with the observed
streamflow hydrograph (as close as possible) while keeping the parameter m constant (m = 0.8).
Altogether 40 FIT runs were conducted to calibrate the model and the kc value for each run was
categorised according to their goodness-of-fit. The values of kc were obtained from the FIT run and were
categorised as excellent fit (E), reasonable fit (R) and poor fit (P). The results of FIT runs for some
storms are shown in Table 2 and the fitting hydrographs are shown in Figures 4, 5 and 6.
Table 2 Results of the FIT run for selected events
Storm
kc
1984-X1
1984-X2
1984
9.35
11.1
16.85
IL
(mm)
10
10
40
CL
(mm/h)
6.3
3.6
3.46
Peak flow Qp (m3/s)
Calculated Actual
71.2
71.2
234.9
234.9
2.128
2.132
Time to peak (h)
Calculated Actual
42
42
25
22
15
13
% difference in
peakflow
0.000
0.000
-0.188
Type of
fit
E
R
P
6
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Storm 1984-X2, kc=11.1, IL=10mm, h/g at 203002
Gross rainfall
Rainfall excess
Rainfall (mm)
Rainfall (mm)
Storm 1984-X1, kc=9.35, IL=10mm, h/g at 203002
22
20
18
16
14
12
10
8
6
4
2
0
Calculated
Actual
70
50
Discharge (m³/s)
Discharge (m³/s)
60
40
30
20
10
0
0
10
20
30
40
Time (hr)
50
60
70
35
30
25
20
15
10
5
0
240
220
200
180
160
140
120
100
80
60
40
20
0
Gross rainfall
Rainfall excess
Calculated
Actual
0
Figure 4 Excellent fit result for 1984-X1 storm
5
10
15
20
Time (hr)
25
30
35
40
Figure 5 Reasonable fit result for 1984-X2 storm
Rainfall (mm)
Storm 1984, kc=16.85, IL=40mm, h/g at 203002
20
18
16
14
12
10
8
6
4
2
0
2.2
Gross rainfall
Rainfall excess
Calculated
Actual
2
1.8
Discharge (m³/s)
1.6
1.4
1.2
1
.8
.6
.4
.2
0
0
10
20
30
40
Time (hr)
50
Figure 6 Poor fit result for 1984 storm
60
Figure 7 Frequency distribution of all kc values
The distribution of kc values for all the fit runs is shown in Figure 7, which shows a wide variation in
obtained kc values. Due to the observed degree of high variation, it seems to be unreasonable to adopt a
median or mean kc value in the design run which can maintain the probability neutrality in the rainfall
runoff modelling as assumed with the DEA.
Sensitivity studies of kc showed that as kc was increased, the hydrograph peak decreased and the time to
peak (lag) increased while the volume of runoff remained constant. This is to be expected, since kc is the
indicator of the lag parameter of the storage element as well as the size of storage effects. Also it was
interesting to note that three different fit was obtained for the three different storms in the same year of
1984 and the kc value differed significantly for each FIT run. The variability of kc value in FIT run was
very high with the minimum value being 1.72 hour and the maximum value 59 hours. The distribution
of kc values (Figure 7) shows that nearly 35% of kc values were in the range of 8-12 hours. Almost 40%
of kc values were in the range of 13-30 hours. Only for the two fit runs the kc values were greater than 30
hours and both of these hydrographs were having very poor fit. The mean and median kc for all the
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storm events was 15.56 hours and 11.2 hours respectively. Since the kc values show a very high
variability and to check the probabilistic nature of kc and its impacts on design flood estimates various kc
values were used in TEST run (discussed below). Various summary statistics of the kc values are shown
in Table 3.
Table 3 Various summary statistics of the kc values based on 40 storm events
kc (hour)
15.56
11.2
9.96
9.60
11.43
9.75
1.72 to 59
Average from all the storms
Median from all the storms
Average from excellent fit
Median from excellent fit
Average from excellent and reasonable fit
Median from excellent and reasonable fit
Range
IL (mm)
35.90
30.5
31.40
23.00
35.07
27.00
2 to 90
CL(mm/h)
6.23
2.87
7.59
2.74
7.52
2.80
0.08 to 50.33
TEST run
The principal model parameters determined in the "FIT" run, namely the value of all kc from Table 3 and
m = 0.8, were verified using three other storms, which were of single burst storms. Initial loss as
determined from the FIT runs was used for all the storms. The results of TEST run for various
combinations of model parameters are summarized in Table 4 and the percentage error is plotted in
Figure 8. It is observed that for storm 1984-T2 all the considered kc and IL values provided very bad
predictions where the prediction error was as high as 46% and nearly 70% of predictions were below
actual peak flow. Even no particular set of key model parameters provided consistent result.
When using the value of kc selected from the FIT runs for its use in a design run, a high level of
uncertainty is associated with it. However, when validating the kc and IL values obtained from FIT runs
as recommended by the RORB manual on the three independent storm events, there was as high as 46%
difference in peak flow estimation. The errors for predictions were in the range of 20 to -46 %. Hence no
particular values for the set of parameters can be used for design purpose with confidence, as there is
significant bias in the predicted values of peakflow. So the value of kc to be used for the design purpose
remains highly questionable.
Error (%)
30
20
0
R18
R17
R16
R15
R14
R13
R12
R11
R10
R9
R8
R7
R6
R5
R4
R3
R2
-10
R1
Error (%)
10
Error (%)
-20
-30
-40
-50
Test run
Figure 8 Error (%) in peak flow for the test runs
8
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Table 4 Test results for various combinations of model parameters
Storm
kc (hours)
IL
(mm)
1987-T1
1987-T1
1987-T1
1987-T1
1987-T1
1987-T1
1984-T2
1984-T2
1984-T2
1984-T2
1984-T2
1984-T2
1984-T3
1984-T3
1984-T3
1984-T3
1984-T3
1984-T3
15.56
11.2
9.96
9.6
11.43
9.75
15.56
11.2
9.96
9.6
11.43
9.75
15.56
11.2
9.96
9.6
11.43
9.75
35.9
30.5
31.4
23
35.07
27
35.9
30.5
31.4
23
35.07
27
35.9
30.5
31.4
23
35.07
27
CL
(mm/h)
4.85
4.85
4.85
4.85
4.85
4.85
7.34
7.71
7.34
7.71
7.34
7.71
6.51
6.51
6.51
6.51
6.51
6.51
Peak flow Qp (m3/s)
Calculated Actual
382.1
436.6
476.1
436.6
513.1
436.6
525.1
436.6
469.8
436.6
520
436.6
30.5
56.6
39.6
56.6
43.3
56.6
41.5
56.6
39
56.6
41.1
56.6
46.5
71
60.4
71
66.2
71
68.1
71
59.5
71
67.3
71
Time to peak (h)
Calculated Actual
4.8
7.8
4.8
7.8
4.8
7.8
4.8
7.8
4.8
7.8
4.8
7.8
3.8
3.8
5.1
5.1
3.8
3.8
5.1
5.1
3.8
3.8
5.1
5.1
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
Error
(%)
Test
Run
-12.48
9.05
17.52
20.27
7.6
19.1
-46.11
-30.04
-23.5
-26.68
-31.1
-27.39
-34.51
-14.93
-6.76
-4.08
-16.2
-5.21
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
900.00
800.00
Lower 90% CL
(at-site FFA)
At-site FFA
700.00
Uper 90% CL
(at-site FFA)
Observed flow
500.00
3
Qm /s
600.00
S1
400.00
S2
300.00
S3
S4
200.00
S5
100.00
S6
0.00
1
10
100
ARI (years)
Figure 9 Comparison of at-site flood frequency analysis (FFA), observed annual maximum floods and
simulation runs with various kc in design run
The estimated peak flows for various combinations of kc values with fixed IL and CL values are shown
in Figure 9. The flood frequency curve (S1) obtained using average kc value from all the 40 calibrated
storm events provides notable underestimation at higher ARIs but quite good estimation al smaller ARIs
up to about 3 years. The flood frequency curves S4 (represented by median kc value from all the
excellent fit run storms), S3 (represented by average kc value from all the excellent fit run storms) and
S6 (represented by median kc value from all the excellent and reasonable fit run storms) show notable
overestimation. The flood frequency curve S5 (represented by average kc value from all the excellent
9
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and reasonable fit run storms) shows the best fit at ARIs greater than 3 years). These results show that
choice of kc value can influence the design flood frequency curve significantly and it should be
considered as a stochastic variable in rainfall runoff modelling.
5 Conclusions
From the sensitivity analysis of the principal RORB model parameter kc it is found that kc values show a
wide variability from storm to storm and there is no guarantee that the use of a single representative
value of kc (either mean or median) from selected storm events is justifiable as done in the Design Event
Approach of modeling recommended in the current version of Australian Rainfall and Runoff. The
outcome of this study suggests that kc should be used as a stochastic variable in rainfall runoff modeling
in the framework of MCST. The present study should be extended to a greater number of catchments
selected from various Australian regions to confirm the findings of this study and to regionalize the
probability distribution of kc to be used in routine application of the MCST to design flood estimation.
References
Aronica, G.T. and Candela A. (2007). Derivation of flood frequency curves in poorly gauged Mediterranean
catchments using a simple stochastic hydrological rainfall-runoff model. Journal of Hydrology, 347,132– 142
Boughton, W.C. (1987). Hydrograph analysis as a basis of water balance modeling, I.E.Aust. Civil Engineering
Trans., 29(1), p.p. 28-33.
Boyd, M.J., Bates, B.C., Pilgrim, D.H., and Cordery, I. (1987). WBNM: A General Runoff Routing Model.
Fourth National Local Government Engineering Conference. Institution of Engineers Australia. National
Conference Publication No. 87/9, 137-141.
Carroll, D.G. (2007). URBS - A Catchment Runoff-Routing and Flood Forecasting Model, User Manual.
Charalambous J., Rahman, A. and Carroll, D. (2005). Application of URBS-MCST to large catchments for design
flood estimation: a case study for the Johnstone River catchment in Queensland. In Proc. 29th Hydrology and
Water Resources Symposium, I. E. Aust., 20-23 Feb., Canberra.
Charalambous, J., Rahman, A. and Carroll, D. (2003). Application of MCST with URBS Model for Design Flood
Estimation in Large Catchments. Proc. Intl. Congress on Modeling and Simulation, Townsville, Australia.
Eagleson, P.S. (1972). Dynamics of Flood Frequency, Water Resources Research, 8, 4, pp.878-898.
Institution of Engineers Australia (1987). Australian Rainfall and Runoff. Institution of Engineers, Australia.
Kuczera G., Lambert M., Henker T., Jennings S., Frost A., and Combes P. (2006). Joint probability and design
storms at the crossroads. Australian Journal of Water Resources Vol 10, No 1.
Kuczera, G., Lambert, M., Heneker, T., Jennings, S., Frost, A. and Coombes, P. (2003). Joint Probability and
Design Storms at the Crossroads. Keynote paper. 28th International Hydrology and Water Resources
Symposium. E. Aust, 11-13 Nov, Wollongogng, Australia.
Laurenson, E. M., Mein, R. G. and Nathan, R.J. (2007). RORB Version 6 Runoff Routing Program User Manual,
Dept. of Civil Eng., Monash University.
Nathan, R. J. and Weinmann, P. E. (2004). An improved framework for the characterisation of extreme floods and
for the assessment of dam safety. British Hydrological Society Conference, London, July 2004, 1, 186-193.
Rahman, A., Carroll, D., Mahbub, P., Khan, S. and Rahman, K. (2007). Application of the MCST to Design
Flood Estimation in Urban Catchments: A Case Study for the Coomera River Catchment in Gold Coast
Australia, Water Practice and Technology, Volume 2, Issue 2, IWA Publishing, London.
Rahman, A. and Carroll, D. (2004). Appropriate spatial variability of flood producing variables in the Joint
Probability Approach to design flood estimation. British Hydrological Society International Conference,
London, 12-16 July, 2004, 1, 335-340.
Rahman, A. and Kader, F. (2004). Regionalisation of design rainfalls in Victoria Australia for design flood
estimation by Joint Probability Approach. In Proc. Second APHW Conference, 5-8 July 2004, 2, 3-10.
Rahman, A., Weinmann, P.E., Hoang, T.M.T, and Laurenson, E. M. (2002a). Monte Carlo Simulation of flood
frequency curves from rainfall. Journal of Hydrology, 256 (3-4), 196-210.
Rahman, A., Carroll, D and Weinmann, P.E. (2002b). Integration of MCST with URBS model for design flood
estimation. 27th Nat. Hydrology and Water Resource Symposium, I. E. Aust., 20-23 May, Melbourne.
10
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Chapter 7: Summary and Conclusions
CHAPTER 7
SUMMARY AND CONCLUSION
7.1
SUMMARY
Rainfall-based flood estimation methods are often adopted when a complete design
hydrograph is required and/or in the situations where the recorded streamflow data are not
long enough to characterise the underlying at-site flood frequency distribution with
sufficient accuracy. From the literature review presented in Chapter 2 it has been found
that the Joint Probability Approach can overcome the major limitations with the Design
Event Approach to flood estimation (currently recommended rainfall-based flood
estimation method in Australia according to Australian Rainfall and Runoff). It has also
been found that analytical methods with the Joint Probability Approach has limited
flexibility, which involves complicated mathematical functions, which are difficult to
solve for real catchments. Hence, analytical methods have limited practical applicability
as compared to the approximate forms of the Joint Probability Approach like Monte Carlo
Simulation Technique.
The previous applications of the Monte Carlo Simulation Technique in Australia (e.g.
Rahman et al., 2002a) have considered rainfall duration, rainfall intensity, rainfall
temporal pattern and initial loss as random variables in the simulation but the probabilistic
nature of key runoff routing model storage delay parameter k has been disregarded, which
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Hitesh D. Patel
Student ID: 16095380
Chapter 7: Summary and Conclusions
in many circumstances is likely to cause under- or over-estimation of design flood peaks.
Hence this study aims to investigate the stochastic nature of k and its impacts on design
flood estimates.
The basic statistical concepts and the recent research on the Joint Probability Approach
have been presented in Chapter 2. The methodology adopted in this study has been
presented in Chapter 3. In the updated Monte Carlo Simulation Technique, five input
variables have been treated as random variables: rainfall duration, rainfall intensity,
rainfall temporal pattern, initial loss and k. The adopted modelling framework has been
illustrated in Figure 3.8.
In this study, New South Wales has been selected as the study area and a total of 5
catchments have been selected. The data availability and the catchment descriptions have
been presented in Chapter 4. One catchment has been selected to investigate the stochastic
nature of the RORB runoff routing model parameter kc on design flood estimates. The
steps involved in the development of RORB model has been outlined in Section 5.2. The
RORB model has been calibrated using 40 storm events and the model fittings have been
categorised according to their goodness of fit (Section 5.4). Further, the sensitivity of kc
on flood estimates has been investigated. A total of 288 design runs have been conducted
with combinations of kc, IL and CL and peakflows for selected ARIs obtained from these
design runs have been compared with at-site flood frequency estimates.
151
Hitesh D. Patel
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Chapter 7: Summary and Conclusions
Chapter 6 has outlined the application of enhanced Monte Carlo Simulation Technique
which considers k as a random variable. Here the distributions of storm-core duration,
rainfall intensity in the form of IFD curves, temporal patterns and initial loss for the 5
study catchments have been obtained. The procedure for calibration of the adopted runoff
routing model is similar to calibration of the RORB model, as described in Section 5.4.
The updated Monte Carlo Simulation Technique has been applied to the 5 study
catchments. The derived flood frequency curves for these catchments obtained by the old
Monte Carlo Simulation Technique (with constant k) and the updated Monte Carlo
Simulation Technique (with k as a random variable) have been compared with the results
of the at-site flood frequency analysis.
7.2
CONCLUSIONS
This thesis investigates the probabilistic nature of the storage delay parameter (kc) of the
RORB model and its impacts on design flood estimates. This also focuses on the
enhancement of the previously developed Monte Carlo Simulation Technique in Australia
by incorporating runoff routing model storage delay parameter (k) as a stochastic variable.
The new Monte Carlo Simulation Technique has been applied to 5 catchments in New
South Wales. Following conclusions can be made from this thesis:
 It is found that selection of a representative value of kc for RORB model in a particular
application may be quite difficult. The number of events used in calibration, selection
of a representative value (e.g. median or mean) and types of fit (e.g. excellent, good,
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Chapter 7: Summary and Conclusions
reasonable or poor) of the events used in calibration can affect the magnitude of the
final design flood estimate remarkably.

It is found that kc values in a given catchment can show a wide variability from storm
to storm and the use of a single representative value of kc (either mean or median)
from selected storm events is not justifiable as done in the Design Event Approach of
modeling recommended in the Australian Rainfall and Runoff. It is thus suggested that
kc should be treated as a stochastic variable in rainfall runoff modeling in the
framework of the Monte Carlo Simulation Technique

The previously developed Monte Carlo Simulation Technique in Australia has been
successfully upgraded by incorporating storage delay parameter k as a stochastic
variable. The application of upgraded Monte Carlo Simulation Technique on five
catchments in NSW has shown that the new technique outperforms the existing Monte
Carlo Simulation Technique by providing more accurate design flood estimates.
7.3
RECOMMENDATIONS FOR FURTHER STUDY
Although this thesis has demonstrated that the upgraded Monte Carlo Simulation
Technique with runoff routing model storage delay parameter as a random variable can
provide more accurate design flood estimates as compared to the old technique, there are
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Hitesh D. Patel
Student ID: 16095380
Chapter 7: Summary and Conclusions
still some components which would be worth investigating in future studies. These
include the following:

Investigate the use of continuing loss as a stochastic variable in the Monte Carlo
Simulation Technique.

Investigate the addition of inter-event duration (duration between two successive
storm events) as a stochastic variable in the Mote Carlo Simulation Technique.

Extend the present study to a greater number of catchments selected from NSW and
other Australian states representing a wide range of hydrologic and catchment
conditions to confirm the findings of this study.

Enhance RORB model by incorporating the full Monte Carlo Simulation Technique
with storage delay parameter as a random variable.

Regionalise the probability distributions of storage delay parameter and other model
inputs for various Australian states, which will facilitate the routine application of
the Monte Carlo Simulation Technique in the industry.
.
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Hitesh D. Patel
Student ID: 16095380