INTEGRATION OF MONTE CARLO SIMULATION TECHNIQUE WITH URBS MODEL FOR DESIGN FLOOD ESTIMATION

INTEGRATION OF MONTE CARLO SIMULATION TECHNIQUE WITH URBS MODEL FOR DESIGN FLOOD ESTIMATION Ataur Rahman 1, Don Carroll 2, Erwin Weinmann 3 1 Physical Infrastructure Centre, School of Civil Engineering, Queensland University of Technology; 2 City Design, Brisbane City Council; 3 Department of Civil Engineering, Monash University and CRC for Catchment Hydrology Abstract The Monte Carlo simulation technique, based on the Joint Probability Approach, incorporates the probabilistic nature of key input variables such as rainfall intensity, duration, temporal pattern and initial loss, and their correlations in flood estimation. Previous application of the technique to three small gauged catchments in Victoria had shown promising results. However, the runoff routing was based on a single lumped storage placed at the catchment outlet and accordingly applicable to small catchments only. URBS is a RORB based distributed non-linear runoff routing model and one of several industry models used for design flood estimation for small to very large catchments. This paper shows that Monte Carlo simulation technique can be integrated with industry based models such as URBS. The integrated URBS-Monte Carlo Technique can be used to obtain more precise flood estimates for small to large catchments. The integrated model is now available in the window-based URBS model. It is expected that the integrated approach will have wider applications in flood studies, assessment of the hydrologic impacts of land use changes and hydrologic research. Key Words: flood estimation, Monte Carlo simulation, URBS, Joint Probability Approach Introduction The currently adopted rainfall-based design flood estimation technique in Australia is based on the Design Event Approach (I.E. Aust., 1998). For a selected average recurrence interval (ARI), a number of trial rainfall burst durations and their corresponding average rainfall intensities are used with fixed temporal patterns, initial loss and other inputs to obtain flood estimates. The result for the critical rainfall duration, i.e. the one that produces the highest peak flow, is adopted as the design flood for that ARI. In the Design Event Approach, it is assumed that all other model inputs except the rainfall depth are probabilityneutral ; however, in practice, model inputs such as rainfall temporal patterns and losses show a wide variability. Due to the non-linearity of the rainfall-runoff process, the use of representative values (e.g. mean or median) of model inputs is unlikely to preserve the ARI of the input rainfall intensity in the final design flood estimates. More recently, an improved design flood estimation technique based on the Joint Probability Approach called Monte Carlo Simulation Technique has been developed in Australia that can be implemented easily in practice (Rahman et al., 1998; 2000, 2001a,b; Rahman and Weinmann, 2002; Weinmann et al., 1998, 2000; Hoang et al., 1999; 2001). This new technique treats four inputs (rainfall duration, intensity, temporal pattern and initial losses) as probability-distributed variables. A large number of runoff events (in the order of thousands) are simulated using these probability-distributed and other fixed input variables/model parameters and then routed through a calibrated runoff routing model. The resulting flood peaks are then subjected to a non-parametric frequency analysis to determine a derived flood frequency curve. The previous applications of the Monte Carlo Simulation Technique had been limited to small catchments in the range less than about 200 km 2 because it adopted a simple runoff routing procedure based on a single storage concentrated at the catchment outlet. This paper presents a method of integrating the Monte Carlo Simulation Technique with the distributed nonlinear runoff routing model URBS.

Monte Carlo Simulation Technique for Design Flood Estimation In the Monte Carlo Simulation Technique, to provide the basis for a rigorous assessment of flood probabilities, a new storm event definition is required that produces rainfall events of random durations. Two different storm event definitions have been developed, the first one for a complete storm and the second one for a storm-core within each complete storm (the most intense part of the storm) (Hoang et al., 1999; Rahman et al., 2001a). A complete storm has been defined as a period of significant rain preceded and followed by at least a period of dry hours (e.g. 6 hours). The corresponding storm-core has been selected as the period within a complete storm that has the highest rainfall intensity ratio compared to the 2- year ARI design rainfall The basic idea underlying the Monte Carlo Simulation Technique is that the distribution of the flood outputs can be directly determined by simulating the likely combinations of hydrologic model inputs and parameter values to produce flood output events. In each run of the Monte Carlo Simulation, a set of input/ parameter values is selected by randomly drawing a value from their respective distributions (for probability distributed variables) and by choosing a representative value (for other variables). Any significant correlation between the input variables is allowed for by using conditional probability distributions. For example, the strong correlation between rainfall duration and intensity is 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. flood peaks at the catchment outlet) are stored and the Monte Carlo simulation process is repeated a sufficiently large number of times to fully reflect the range of variation of input/ 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 (Rahman et al., 2001a). The particular advantages of the Monte Carlo Simulation Technique are that: (a) It does not require the concept of critical duration. (b) It does not require to select representative values of model inputs that show a wide variability such as rainfall temporal pattern and initial losses. (c) It does not require the assumption that frequency of output flood peak, for the critical duration, is equal to that of the input design rainfall intensity. (d) It can be applied with commonly used design data and models. Runoff Routing Model URBS The URBS runoff routing model is based on a network of sub-catchments whose centroidal inflows are routed along a prescribed routing path to generate runoff. The catchment discretisation in URBS is similar to the RORB model (Laurenson and Mein, 1997). One important feature of URBS is that it considers the splitting of the routing into catchment and channel components. This can also account for urbanisation/forestation on a sub-catchment basis. More detailed information on the URBS model can be found in Carroll (2001). Integration of Monte Carlo Simulation Technique with URBS The integration method is done in two steps: (a) Generation of runoff events using the Monte Carlo Method and (b) Runoff routing using a calibrated URBS model. The procedures for generating stochastic runoff events are described in detail in Rahman et al. (2001a). The probability distribution of storm-core duration (d c ) has been found to be exponential for Victorian catchments with little variation between sites in the same region. The conditional distribution of average rainfall intensity (I c d c ) is expressed in the form of intensity-frequencyduration (IFD) curves. The observed set of rainfall temporal patterns (TP c ) is converted to a dimensionless form and used directly in the Monte Carlo simulation to randomly select a historical temporal pattern. The distributions of observed initial losses (IL c ) have been approximated by a four-parameter Beta distribution for the Victorian catchments. In the Monte Carlo simulation, a set of values of d c, I c, TP c and IL c are generated which defines a stochastic runoff event; these are written into a runoff event file with other fixed inputs/model parameters for input into the URBS model. A large number (N) of such stochastic runoff events are generated, constituting N runoff event files. In the runoff routing step, the URBS model is formulated and calibrated for the selected catchment as usual. Each of the runoff events generated in the previous step is routed using the calibrated URBS model to obtain a streamflow

hydrograph at the catchment outlet. The time to peak, peak discharge and runoff volume associated with each hydrograph are noted in a file, which can then be used for non-parametric frequency analysis to determine frequency curves of the selected hydrograph characteristic. Study Catchment The procedure of integrating the Monte Carlo Simulation Technique with the URBS model has been applied to the Tarwin River catchment in Victoria. This is one of the three catchments used to test the Monte Carlo Simulation Technique initially by Rahman et at. (2001a,b), adopting the simple concentrated runoff routing model. The Tarwin River catchment has an area of 127 km 2 and 27 years of continuous streamflow data. Pluviograph Station 85106, located near the upstream boundary, is used in the study; it has 22 years of continuous rainfall data. The continuous streamflow and rainfall data are abstracted at hourly intervals using the HYDSYS package (HYDSYS, 1994). These data are used to estimate the probability distributions of d c, I c and IL c and for building the database of the observed temporal patterns (TP c ). Results Rainfall and Loss Analysis To identify the probability distributions of stormcore duration (d c ) and rainfall intensity (I c ) in the form of IFD curves, and to prepare the database of the observed storm-core temporal patterns (TP c ), a FORTRAN program called storma1.for is used. The basic input data for this program are (i) hourly pluviograph data; and (ii) design rainfall intensity data from Australian Rainfall and Runoff (ARR) Volume 2 (I.E. Aust., 1987). The ARR design rainfall intensities are used to select those complete storm and storm core events that have the potential to produce significant runoff. More detailed information on selection of storm events can be found in Hoang et al. (1999, 2001) and Rahman et al. (2001a,b). The catchment area is required to allow the computation of areal reduction factors which convert the point design rainfall intensities to average catchment rainfall intensities. The required input data to the program is provided through a parameter file, as shown in Table 1 for the Tarwin River catchment. The program storma1.for took less than a minute to run the rainfall analysis on a Pentium 3 personal computer. To identify the probability distribution of stormcore initial loss (IL c ), a FORTRAN program called lossa1.for is used. The basic data input to this program are concurrent hourly streamflow and pluviograph data. The program lossa1.for took less than 2 ½ minutes to compute losses for the Tarwin River catchment. Generation of Runoff Events To generate d c, I c and IL c and randomly select a TP c from the observed temporal pattern database, a FORTRAN program called mcsg1.for is used. This program uses output files from the programs (storma1.for and lossa1.for) described in Section 6.1 and, a number of additional inputs, as provided in the parameter file in Table 2. The program mcsg1.for took less than 2 minutes to generate 10,000 stochastic runoff event files for the Tarwin River catchment.

Table 1 Parameter file for rainfall analysis for the Tarwin River catchment using program storma1.for Input 85106 p85106.dat 6 0.4 0.5 18.6 5 1.6 39.5 8.9 3 0.38 127 Table 2 Input TarwinRiver a 10000 12.5 127 tartab.dat lista.tar 1 49 24 11 10 0.90 Description Pluviograph station ID Hourly pluviograph data file, rainfall in mm Dry period between successive complete storm events, hours Reduction factor to identify significant complete storm events Reduction factor to identify significant complete storm events 2 i 1 (log-normal design rainfall intensity, 2 years ARI-1 hour duration), mm 2 i 12 (log-normal design rainfall intensity), mm 2 i 72 (log-normal design rainfall intensity), mm 50 i 1 (log-normal design rainfall intensity), mm 50 i 12 (log-normal design rainfall intensity), mm 50 i 72 (log-normal design rainfall intensity), mm Skewness Catchment area, km 2 Parameter file for generating runoff events for the Tarwin River catchment using program mcsg1.for Description Catchment name Run (To distinguish one run of simulation from the next) Number of runoff events to be generated Mean value of storm-core duration d c (output from storma1.for) Catchment area, km 2 IFD table (output from program storma1.for) Database file of observed dimensionless temporal patterns (output from program storma1.for) Lower limit of complete storm initial losses (IL s ), mm (output from program lossa1.for) Upper limit of IL s, mm (output from program lossa1.for) Mean value of IL s, mm (output from program lossa1.for) Standard deviation of IL s, mm (output from program lossa1.for) Number of intervals in dimensionless temporal pattern mass curve Continuing loss rate, mm/h One of the generated runoff event files for input into the URBS model is presented in Table 3. These 10,000 stochastic runoff events represent 2000 years of runoff data with λ = 5 (number of partial series runoff events per year). The value of λ is similar to the average number of storm-core events being selected per year by the program storma1.for. Table 3 Example of stochastic runoff event file for input to URBS model Sequence Storm No 1 Design Run Time Increment: 0.25 Run Duration: 8.000000 Storm Duration: 2.000000 Pluviograph. Data Interval: 2.000000E-01.06.09.09.11.20.05.11.13.11.06 Rain on Subareas: 22.356440 Loss: Variable Continuing IL: 15.456730 CL: 9.000000E-01 Generation of Streamflow Hydrographs Using URBS The Tarwin River catchment URBS model was subdivided into 11 sub-catchments. The URBS Basic Model was used. The model was calibrated using three observed rainfall and streamflow events for three sets of catchment non-linearity parameter m (0.6, 0.8 and 1) and alpha (URBS model parameter) values. It took 23 minutes to generate 10,000 streamflow hydrographs for the Tarwin River catchment using a Pentium 3. For each hydrograph, the time to peak (hours), peak discharge (m 3 /s) and runoff volume (ML) were noted in an output file. A baseflow of 0.40 m 3 /s was added to the generated peak discharge to represent the total streamflow. The new version of the window-based URBS model has the necessary facility to automate the above Monte Carlo simulation technique.

Construction of Derived Flood Frequency Curves The N (10,000) values of generated peak discharges, obtained previously, are used to construct a derived flood frequency curve for the Tarwin River catchment. 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: (i) Arrange the N simulated peaks in decreasing order of magnitude. (ii) Assign rank (m) 1 to the highest value, 2 to the next and so on. (iii) For each of the ranked floods, compute an ARI from the following equation: N + 0.2 1 ARI = m 0.4 λ where N is the number of simulated peaks, m is the rank, λ is the average number of storm-core events per year for the catchment of interest (here λ = 5). (iv) Prepare a plot of ARI versus flood peaks, i.e. a plot of the empirical flood frequency curve defined by the simulated flood peaks. (v) Compute flood quantiles for selected ARIs by interpolation between neighbouring points. Comparison of Results The resulting derived flood frequency curve for the Tarwin River catchment is compared in Figure 1 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 results show that the derived flood frequency curve compares quite well over a wide range of frequencies with the results of flood frequency analyses of the flood series available at the site. Q (m 3 /s) 350 300 250 200 150 100 50 Observed partial series DFFC (URBS, m=0.8) 0 0.1 1 10 100 1000 ARI (year) Figure 1 Derived flood frequency curves using URBS runoff routing model for Tarwin River catchment To investigate the sensitivity of the derived flood frequency curves to variations in the catchment non-linearity parameter (m), three sets of values of m and alpha were used in simulating the streamflow hydrographs. The results are compared in Figure 2, which shows that the upper part of the simulated flood frequency curves is quite sensitive to the adopted value of m. For higher m values, the flood frequency curve is flatter at higher ARIs. This is because for a higher m, there is a greater increase in storage S with increasing Q, resulting in reduced flood peaks. The result also shows the importance of appropriate calibration of the URBS model to obtain the right set of alpha and m values for the flood range of interest. Q (m 3 /s) 400 350 300 250 200 150 Observed partial series DFFC (URBS, m=0.6) DFFC (URBS, m=0.8) DFFC (URBS, m=1.0) 100 50 0 0.1 1 10 100 1000 ARI (year) Figure 2 Simulated flood frequency curves for various m values

Other Applications and Possible Extensions In addition to deriving frequency curves for peak flows, the generated 10,000 values of time to peak and runoff volumes can be used to determine frequency distributions of these variables. Figure 3 shows the frequency distribution of runoff volumes. The frequency distribution of time to peak may be useful in land use impact studies to examine the effects of urbanisation on catchment response. The frequency distribution of flood runoff volumes can be used in the design of detention basins and in catchment yield analysis. application of the CRC-FORGE methodology (Weinmann et al., 1999), would allow the estimation of rarer design floods, but further research is required before the approach can be confidently applied to the estimation of extreme floods. At this stage, a uniform spatial pattern of rainfall over the catchment has been assumed, but URBS allows the specification of non-uniform spatial rainfall distributions on a sub-catchment basis, if observed storms suggest a systematic pattern. In principle, it would also be possible to introduce stochastic variation into spatial rainfall patterns, if the observed storms suggest a high degree of variability between events. Runoff volume (ML) 16000 14000 12000 10000 8000 6000 4000 2000 0 0.1 1 10 100 1000 ARI (year) The use of a distributed runoff routing modelling package such as URBS also allows ready incorporation of existing or planned special storages, such as reservoirs and detention basins, and the assessment of their impacts on flood hydrographs. With a relatively small modification to the existing modelling package, it would also be possible to allow for the stochastic variation of reservoir storage contents at the start of a runoff event. Conclusions Figure 3 Simulated frequency curve for runoff volume The applications described in this paper were for gauged catchments with good availability of pluviograph data within the catchment. Previous studies have shown that the distributions of storm durations and temporal patterns do not vary greatly within a region (Hoang, 2001; Rahman et al., 2001a). It is thus quite acceptable to use data from an adjacent pluviograph station in the analysis of rainfall event durations and temporal patterns. There are also promising indications that existing IFD data can be used to determine design rainfall intensities for the Monte Carlo simulation approach in ungauged catchments, but additional research is required to develop appropriate procedures. Research towards the regional estimation of loss values for use with this approach is currently underway (Ilahee et al., 2002). It should also be noted that the present applications are based on IFD curves derived from analysis of at-site pluviograph records of limited length. The limit of extrapolation of these results is thus an ARI of 50 to 100 years. The use of regional design rainfall data, e.g. from The paper describes how a Monte Carlo simulation technique can be applied with the industry-based runoff routing model URBS to determine derived flood frequency curves. The following conclusions can be drawn from this study: The routine application of a Monte Carlo simulation technique to derive flood frequency curves using the industry-based runoff routing model URBS has been shown to be quite feasible. Currently, the application of the Monte Carlo simulation technique is restricted to gauged catchments; it requires hourly rainfall and streamflow data of at least 20 years in length to determine derived flood frequency curves in the range of ARIs up to 100 years. It takes less than an hour for data analysis and determination of flood frequency curves. The URBS-Monte Carlo Technique can also be used to determine derived frequency distributions of other streamflow hydrograph characteristics like time to peak and runoff volume. Its scope of application could be readily extended to include the joint probability analysis of reservoir inflows and initial storage contents.

The integrated model is available in the latest window-based URBS model, which is expected to have wider applications in flood studies, assessment of the hydrologic impacts of land use changes and hydrologic research. Acknowledgments The Monte Carlo simulation technique described in this paper originated from the CRC for Catchment Hydrology s project Holistic approach to rainfall-based design flood estimation. Some of the FORTRAN programs used in this study were developed by the first author as part of that CRCCH project. The authors would like to specifically thank Ms Tam Hoang, Bureau of Meteorology, for her inputs to the development of some of the FORTRAN programs. References Carroll, D. G. (2001). URBS A Catchment Runoff Routing and Flood Forecasting Model, Version 3.9 User manual, Oct, 2001. Hoang, T., Rahman, A., Weinmann, P. E., Laurenson, E. M., Nathan, R. J. (1999). Joint probability descriptions of design rainfalls. Intl. Hydrology and Water Resour. Symp of the I.E. Aust. and 2nd Int. Conference on Water Resour. and Env. Research, Brisbane, Australia, 6-8 July, 1999. Hoang, T.M.T. (2001). Joint Probability Approach to Design Flood Estimation. PhD Thesis, Dept. of Civil Eng., Monash University, Australia. HYDSYS (1994). HYDSYS User Manual. Release 5.0, HYDSYS Pty Ltd, ACT, Australia. I. E. Aust. (1987). Australian Rainfall and Runoff A guide to flood estimation. Vol. 2, Institution of Engineers, Australia. I. E. Aust. (1998). Australian Rainfall and Runoff A guide to flood estimation. Institution of Engineers, Australia. Ilahee, M., Rahman, A. and Boughton, W.C. (2002). Derivation of new initial losses for flood estimation in Queensland. (Proceedings of this Symposium) Laurenson, E. M. and Mein, R. G. (1997). RORB Version 4 Runoff Routing Program User Manual, Dep. of Civil Eng., Monash University. pp. 186. Rahman, A., Hoang, T.M.T., Weinmann, P.E. and Laurenson, E.M. (1998). Joint Probability Approaches to Design Flood Estimation: A Review. Report 98/8, CRC for Catchment Hydrology, Monash University. pp. 77. Rahman, A., Weinmann, P. E., Mein, R.G. (2000). Probabilistic nature of initial losses and its impacts on design flood estimates. In Proc. 3rd Intl. Hydrology and Water Resources Symp., Perth, Western Australia, 20-23 Nov., 2000, Vol. 1, pp. 71-75. Rahman, A., Weinmann, P.E., Hoang, T.M.T., Laurenson. E.M. and Nathan, R.J. (2001a). Monte Carlo Simulation of Flood Frequency Curves from Rainfall. Report 01/4. CRC for Catchment Hydrology. pp. 63. Rahman, A., Weinmann, P.E., Hoang, T.M.T., Laurenson. E.M. (2001b). Monte Carlo Simulation of Flood Frequency Curves from Rainfall. Journal of Hydrology (In press). Rahman, A., Weinmann, P.E., (2002). Flood estimation in Northern Australian catchments using Monte Carlo Simulation Technique. (Proceedings of this Symposium) Weinmann, P. E., Rahman, A., Hoang, T., Laurenson, E. M., Nathan, R. J. (1998). A new modelling framework for design flood estimation. International Conference on Hydraulics in Civil Engineering, Adelaide, Australia, 1998: 393-398. Weinmann, P.E., Nandakumar, N., Siriwardena, L., Mein, R.G. and Nathan, R.J. (1999). Estimation of rare design rainfalls for Victoria using the CRC-FORGE methodology. Intl. Hydrology and Water Resour. Symp of the I.E. Aust. and 2nd Int. Conference on Water Resour. and Env. Research, Brisbane, Australia, 6-8 July, 1999, pp 284-289. Weinmann, P. E., Rahman, A, Hoang, T., Laurenson, E. M., Nathan, R. J. (2000). Monte Carlo simulation of flood frequency curves from rainfall the way ahead. In Proc. 3 rd Intl. Hydrology and Water Resources Symp., Perth, Western Australia, 20-23 Nov., 2000. Vol. 1, pp. 564-569.

Authors Biographies Dr Ataur Rahman is a Research Fellow in the Physical Infrastructure Centre, School of Civil Engineering, Queensland University of Technology. He obtained his PhD in Hydrology from Monash University in 1997 and Masters in Hydrology degree from National University of Ireland in 1991. He has worked as a Research Fellow in the CRC for Catchment Hydrology, Statistical Hydrologist in the Water and Catchment Management Group, Sinclair Knight Merz, Melbourne and Senior Water Resources Engineer in Bangladesh Water Development Board. His research interest includes Joint Probability Approach to flood estimation, regionalisation, application of statistical techniques to hydrology, environmental risk assessment and urban hydrology. Postal Address: Dr Ataur Rahman, School of Civil Engineering, Queensland University of Technology, 2 George St, GPO Box 2434, Brisbane, Queensland 4001, Australia E-mail: a.rahman@qut.edu.au Erwin Weinmann is a Senior Lecturer at Monash University s Department of Civil Engineering, and a Project Researcher with the Cooperative Research Centre for Catchment Hydrology. He holds a Diploma in Agricultural Engineering and Surveying from the Swiss Federal Institute of Technology in Zurich, and a MEngSc from Monash. His professional experience includes over 20 years in the Victorian water industry. His main research and consulting interests are in flood estimation, water resource studies and water data collection networks. He has been a member of IEAust s National Committee on Water Engineering, and maintains a continuing involvement in the revision of Australian Rainfall and Runoff. He is the co-author of Book VI of ARR on Estimation of Large to Extreme Floods. Postal Address: Erwin Weinmann, Department of Civil Engineering, PO Box 60, Monash University, VIC 3800. E-mail: erwin.weinmann@eng.monash.edu.au Don Carroll has over 20 years experience in public and private industry both in Australia and overseas. His main interests are flood and damage modelling, stormwater management, water resource estimation, environmental impact assessment and ecological risk assessment. Don has developed hydrological and GIS applications and is the main developer of the URBS model. Postal Address: Don Carroll, Locked Mail Bag 6996, Albion, Qld 4010. E-mail: urbs@iprimus.com.au