Design flood estimation using a modelling approach: a case study using the ACRU model

Transcription

1 Sustainabilityof Water Resources under Increasing Uncertainty (Proceedings of the Rabat Symposium SI, April 1997). IAHS Publ. no. 240, Design flood estimation using a modelling approach: a case study using the ACRU model JEFF SMITHERS, ROLAND SCHULZE & STEFAN KIENZLE Department of Agricultural Engineering, University of Natal, Pietermaritzburg, Private Bag X01, Scottsville 3209, South Africa Abstract The potential of using streamflow simulated by a continuous model to estimate design floods at ungauged sites in KwaZulu, South Africa is investigated. The ACRU model was selected and simulated daily volume and peak discharge was verified against observed data at two sites. Design floods computed from the simulated output compared well with those computed from the observed data. The model was used to investigate the effect of farm dams and river reaches on the design flood. The advantages of using a continuous simulation model which models the flood attenuating effects of dams and reaches, as compared to single event type models, are highlighted. INTRODUCTION The economic cost, and potential loss of life, resulting from the failure of hydraulic structures can be enormous (e.g. Dawdy & Letttenmaier, 1987; Wallis, 1988) and highlights the importance of obtaining the "best possible" design flood estimate. The best estimate is usually limited by the available reliable data. Furthermore a number of approaches are possible when estimating design floods. In cases where long records of measured streamflow data are available, a direct statistical analysis of the data may be feasible. However, the streamflow data series are often short and assumptions of consistency, homogeneity and stationarity are often not valid. In practice, the most frequently occurring case is that no measured streamflow data are available at or near the site of interest. Under such conditions an estimate of the design flood has to be based on some hydrological model, with the range of possible models extending from the rational method to dynamic, continuous simulation modelling. In South Africa, as is the case in many countries in the world, the density and length of record of rainfall stations far exceeds that of runoff gauging stations. The designer thus frequently has to resort to estimating a design flood from the available rainfall data. An event-based model may be used to estimate the designfloodfrom the design rainfall. Schulze (1989) examines the validity of these types of models which generally assume that the T-year design rainfall event produces the J-year flood event, and which generally do not take cognisance of antecedent soil moisture conditions prior to rainfall events. The merits of using a continuous simulation model to simulate streamflow are listed by Schulze (1989) and include the use of a longer data series for analysis, the ability to simulate streamflow under future land use/climate conditions which may be present during the design life of the structure and the explicit modelling of the effect of soil moisture conditions on streamflow, thus not assuming a direct transformation of a design rainfall to a design flood.

2 366 Jeff Smithers et al. The objective of this paper is to investigate and assess the potential of using streamflow simulated by a continuous simulation model to estimate design floods at ungauged sites. The peak discharge simulated by the ACRU model (Schulze, 1995) is verified at two sites in KwaZulu-Natal, South Africa, and comparisons are made between design floods estimated from observed and simulated data. The combined effect of numerous relatively small farm dams and the attenuation of hydrographs in river reaches is illustrated. During the course of the investigation it became apparent that at some sites where observed streamflow data were available, gauging structure limitations and other problems associated with the data made the use of simulation modelling in the estimation of design floods the preferred approach. THE ACRU AGROHYDROLOGICAL MODEL The model selected for the simulation was the ACRU model (Schulze, 1995), which has been developed in South Africa over the past 15 years and is still undergoing further development and refinement. ACRU is a physical conceptual agrohydrological model which generally operates with a daily time step. The model simulates all major processes of the hydrological cycle which affect the soil water budget and is capable of simulating, inter alia, streamflow volume, peak discharge and hydrograph, reservoir yield, sediment yield, crop yield for selected crops and irrigation supply and demand. ACRU can operate at a point as a lumped catchment model or as a distributed cell-type model in order to account for variability in climate, land use and soils. Where automatically recorded rainfall data are not available, the model is capable of using synthetic rainfall distributions to disaggregate the daily rainfall into shorter time increments which enables the generation of hydrographs displaying intra-daily variations in peak discharge. The lagging and attenuation of the hydrograph as it passes through a river reach or reservoir is also modelled with time increments of less than one day. Simulation of streamflow volume In ACRU the stormflow depth is simulated using a modified SCS approach where the soil moisture deficit, computed from a daily water budget of the soil profile, is used as a surrogate for a curve number. The baseflow is added to the stormflow to compute the volume of streamflow for each day. Simulation of peak discharge The ACRU model simulates peak discharge from the individual sub-catchments using the SCS triangular-shaped unit hydrograph approach. Where automatically recorded rainfall data with time increments of less than one day are not available, synthetic design rainfall distributions, as developed for southern Africa by Weddepohl (1988), may be used to disaggregrate daily rainfall totals into shorter time intervals, thus allowing incremental storm hydrographs to be generated for each time interval. These are then aggregated to form the stormflow hydrograph at the outlet to each sub-catchment. The

3 Design flood estimation using a modelling approach 367 hydrographs are routed from the outlet of a sub-catchment through the next downstream sub-catchment to the outlet of the downstream sub-catchment, and are added to the hydrographs generated for both the downstream sub-catchment and all other upstream sub-catchments which flow directly into the downstream catchment. This procedure is detailed by Smithers & Caldecott (1993, 1995). Flow routing in river reaches The flow routing options in the ACRU model are based on the Muskingum method which is detailed in many standard hydrology texts (e.g. Chow et al., 1988; Fread, 1993). Details on the manner in which is it implemented in ACRU are reported by Smithers & Caldecott (1993, 1995). Flow routing through reservoirs The storage indication method for level pool routing of flows through dams has been implemented in the ACRU model in a manner similar to that explained by Chow et al. (1988). Details on the method and the manner in which is it implemented in ACRU are reported by Smithers & Caldecott (1993, 1995). The ACRU model is structured such that dams may be located at the outlet of a subcatchment, as "external" dams, or as "internal" dams within the sub-catchment, with the latter to enable the modelling of the cumulative effect of many small dams which may be present within a sub-catchment. When modelling external dams, the entire streamflow from the sub-catchment, including all upstream contributions, are assumed to flow into the dam. In the case of internal dams, only the streamflow simulated from that portion of the sub-catchment in which the dam is located is assumed to flow into the dam. For internal dams, the hydrographs generated on a daily basis at the sub-catchment outlet are apportioned such that the ratio of the volume of water flowing into the internal dams to the total volume of the hydrograph for a particular day is the same as the ratio of the catchment area contributing to the internal dam to the total catchment area. The volume of water not flowing into the dam is assumed to flow directly into the downstream sub-catchment. Hence, when the flood routing options are invoked, internal dams which may be off-channel dams are assumed to be in-channel dams, and are assumed to be located at the outlet to the sub-catchment, and only a user specified fraction of the streamflow, simulated only from the sub-catchment in which the dam is located, flows into the dam. METHODOLOGY The model was applied to the Lions and Mfofana catchments which have a combined area of 760 km 2 and which form part of the upper reaches of the Mgeni River catchment (4353 km 2 ) in KwaZulu-Natal, South Africa (Fig. 1). The mean annual precipitation in these two catchments ranges from 870 to 1040 mm. The major land cover classifications

4 368 Jeff Smithers et al. Fig. 1 Location, catchment discretization and schematic flow path. in the catchments are natural grassland, bushveld, dryland and irrigated agriculture (maize and pastures) and commercial afforestation. The Schmidt-Schulze option in ACRU for estimating catchment lag time, which was developed for natural catchments in sub-humid areas, was used in this study (Schmidt & Schulze, 1984; Smithers & Schulze, 1995). Unfortunately, automatically recorded rainfall data with time increments of less than one day were not sufficiently abundant in the study area to warrant their use in this application of the model. Therefore, the synthetic design rainfall distributions developed for southern Africa by Weddepohl (1988) were used to disaggregrate daily rainfall totals into selected shorter time intervals, thus allowing incremental storm hydrographs to be generated for each time interval. The multiple reach routing with varying parameters option was invoked to estimate the Muskingum parameters (Smithers & Schulze, 1995). This option is based on the Muskingum-Cunge method of flow routing, and requires physically-based parameters such as channel dimensions and shape of the cross-sectional area of the river, the slope and length of the reach and Manning's roughness coefficient. These values were derived inter alia from field surveys (Kienzle et al., 1995; Gôrgens et al., 1994). Daily streamflow volume and discharge simulated by ACRU was verified against observed data at two sites in the Mgeni catchment. Gauging station U2H013, with an upstream area of 296 km 2, is located on the Mpofana River and for the purposes of modelling has been delineated into seven sub-catchments with sub-catchment areas ranging from 5.9 to 85.8 km 2. Gauging weir U2H007 is located on the Lions River and

5 Design flood estimation using a modelling approach 369 has an upstream area of 362 km 2 and has been subdivided into 10 sub-catchments which have areas ranging from 2.3 to km 2. With the exception of sub-catchment 15, all sub-catchments have either an internal or external dam with the modelled full supply capacities of the dams ranging from 14.0 X 10 3 to 5.5 x 10 6 m 3. The individual and combined effect of farm dams and river reaches on design floods was assessed by comparing design floods estimated from streamflow simulated with, and without, attenuation of the hydrograph through the dams and reaches. SIMULATION RESULTS A 33-year period ( ) of observed daily rainfall from seven stations was used to simulate streamflow with the model. The land cover information used in the simulations was obtained from satellite imagery flown in 1986, and is therefore not representative of the catchment for the earlier part of the observed data. Tarboton & Schulze (1992) showed that the simulation of streamflows is highly sensitive to changes in land use over time. Thus, for the purposes of verifying the daily volumes and peak discharges simulated by the model, a 7-year period on either side of the date of the land cover survey (i.e. from 1979 to 1993) was used in computing the statistics of performance of the model. Daily totals of streamflow volume The simulated vs observed daily streamflow volume is depicted in Fig. 2 and selected statistics of performance of the model with respect to the simulation of streamflow volume are contained in Table 1. These results are considered to be highly acceptable. Table 1 Observed vs simulated statistics for daily flows (mm) for the period Sample size Conservation statistics: Sum of observed values Sum of simulated values Variance of observed values Variance of simulated values Skewness coefficient of observed values Skewness coefficient of simulated values Regression statistics: Correlation coefficient (Pearson's r) Slope of the regression line 7 intercept of the regression line U2H013 U2H

6 370 Jeff Smithers et al U2H013( ) _J g < STRf /y / SIMULATED, 0- i i i I OBSERVED w /1/79 1/1/81 2/1/83 2/1/85 3/1/87 3/1/89 4/1/91 Fig. 2 Simulated vs observed daily streamflow volume. 4/1/93 DATE 7"" E Ul 400- O <r < O 300- co Q UJ 200- H < Z) co 0- t o ygae o a s ^? " (1.1) S e e U2H013( ) a C SIMULATED DISCHARGE (m 3.s Fig. 3 (1.1) U2H007 ( ) e o o * e» Q «a «a»..itywf.tjijii afjit^m,.f.mfl.ft rf»u r% V * *! «4 l i l t ,3 =-1 1 OBSERVED DISCHARGE (m J.s' 1 ) Simulated vs observed daily peak discharge. o 0 o e o

7 Design flood estimation using a modelling approach 371 Peak discharge The simulation of daily peak discharge at both gauging weirs U2H013 and U2H007 is depicted in Fig. 3. This shows that the observed daily peak discharges at U2H007 do not exceed a threshold of 31.7 m 3 s" 1, presumably because the gauging structure was not designed to measure events exceeding this value. Thus, the data from weir U2H007 had SIMULATED OBSERVED 0-1/9/ VVJL^A A L ^ jjfa_,_.., 1/12/1987 ~~n^ 1/10/ /12/1989 1/4/1990 1/7/ /9/1990 DATE Fig. 4 Examples of simulated and observed daily peak discharge at U2H013.

8 372 Jeff Smithers et al. to be rejected in verifying the simulated peak discharge, and only data from U2H013 could be analysed. Further examples of simulated vs observed discharge at U2H013, using 30 min interval simulation steps, are shown in Fig. 4. A frequency analysis of the simulated and observed daily peak discharge data at TJ2H013 was performed, with the results of the analysis contained in Fig. 5. The analysis was performed on all the data ( ) for all months of the year. As illustrated in Fig. 5, the simulations were very good at both the 50th percentile of nonexceedance (2-year return period) and the 80th percentile (5-year return period), and were still highly acceptable at the 90th percentile (10-year return period) and the 95th percentile (20-year return period). JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC MONTH Fig. 5 Frequency analysis of simulated and observed daily peak discharge: U2H013. Extreme value analysis An extreme value analysis was performed on the annual maximum series (AMS) of simulated and observed daily peak discharge at U2H013, which were extracted from the simulated and observed hydrographs respectively. In this study the lognormal (LN2), 3-parameterlognormal(LN3), log Pearson type3 (LP3), Pearson type 3 (PE3), Gumbel (EV1), log Gumbel (L-EV1), general extreme value (GEV), generalized Pareto (GPA), generalized logistic (GLO) and Wakeby (WAK) probability distributions (PDs) were fitted to the data by the method of L-moments. The characteristics of these PDs are summarized by Stedinger et al. (1993). L-moments, defined by Hosking (1990), are linear combinations of probability weighted moments, and have several important advantages over ordinary product moments (Vogel et al, 1993). In order to estimate the sample variance and sample skew, ordinary product moments require the squaring and cubing of the observations respectively. Sample estimators of L-moments are linear combinations of the ranked observations, and do not require squaring and cubing of the observations. Thus L- moments are subject to less bias than ordinary product moments (Vogel et al., 1993). This characteristic of L-moments was deemed to be important in this study, as in

9 Design flood estimation using a modelling approach 373 September 1987 the simulated daily peak discharge (513 m 3 s" 1 ) exceeds the observed value (405 m 3 s" 1 ), and hence may have unduly influenced the results of the extreme value analysis had the method of moments been used to fit the distributions to the data. In order to select an appropriate PD to use in the analysis, the goodness-of-fit (GOF) tests as described by Smithers (1994, 1996) were used. These include using plotting position formulae and L-moment diagrams (Vogel & Fennessey, 1993; Vogel et al., 1993) to obtain a graphical depiction of the GOF, chi-squared tests (Kite, 1988) and standardized deviations similar to those used by Benson (1968), Bobée & Robitaille (1977) and Kite (1988). The GOF tests indicated that the GEV PD is an appropriate distribution to use. A comparison of design flood estimates computed from both observed and simulated data at gauging weir TJ2H013 is shown in Fig. 6. Included in Fig. 6 are the estimates of the design flood assuming no attenuation of the flood in dams and river reaches. GEVPD RETURN PERIOD Fig. 6 Design flood estimates for simulated and observed data: U2H013 (+reach = attenuation in reaches; +dams = attenuation in dams; reach = no attenuation in reaches; dams = no attenuation in dams). DISCUSSION AND CONCLUSIONS A comparison of the simulated daily volumes and hydrographs with observed data indicates that the model is capable of adequately simulating both the volume and discharge from the catchments. A close correlation is evident between estimates of the design floods computed from the observed and simulated streamflow, with the design floods based on the simulated discharge slightly overestimating those from the observed data for return periods greater than 20 years. It is concluded that the ACRU model is suitable for use in estimating design floods at ungauged sites in KwaZulu-Natal. The effect of farm dams on peak discharge was found to be greater than the influence of river reaches, and the combined effect of disregarding their flood attenuation effect would lead to considerably larger estimates of design floods. Single event type models which do not account explicitly for these attenuating effects could thus lead to

10 374 Jeff Smithers et al. considerable over-design. This study has illustrated the importance of carefully checking and interpreting all observed data. The use of the observed data from U2H007, where gauging limitations resulted in an upper threshold of peak discharge, in a direct statistical analysis would have resulted in highly erroneous design flood estimates. However, the use of a continuous simulation model capable of simulating the hydrology and peak discharge from the catchment reasonably well would have resulted in improved and more realistic design flood estimates. When performing design flood estimation based on simulated streamflow, it is recommended that other deterministic and empirical approaches to design flood estimation should be performed at the site of interest, to confirm the estimates obtained using continuous simulation modelling. These approaches should be modified to include the flood attenuating effects of river reaches and the numerous small dams. The use of a continuous simulation model, such as the ACRU model, which simulates the hydrology and peak discharge from catchments, and models the hydrological effects of climate, soils and land cover, has been shown to be a valuable tool in the estimation of design floods. In particular, where no streamflow data are available, or where observed data are suspect, the modelling of peak discharge in regions where the model has proven to be reliable and enables design floods to be estimated directly from simulated peak discharges. REFERENCES Benson, M. A. (1968) Uniformflood-frequencyestimating methods for federal agencies. Wat. Resour. Res. 4(5), Bobée, B. B. & Robitaille, R. (1977) The use of the Pearson type 3 and log-pearson type 3 distribution revisited. Wat. Resour. Res. 13(2) Chow, V. T., Maidment, D. R. & Mays, L. W. (1988) Applied Hydrology. McGraw-Hill, New York. Dawdy.D.R.&Lettenmaier.D. P. (1987) Initiative for risk-based flood design. J. Hydraul. EngngASCE 113, Fread, D. L. (1993) Flow routing. In: Handbook of Hydrology (ed. by D. R. Maidment). McGraw-Hill, New York. Gôrgens, A., Howard, G., Pegram, G. & Dunn, P. (1994) Mgeni catchment water quality management plan. Hydrology and Hydraulics. DWAF Report No. WQ U200/00/0194, Pretoria, RSA. Hosking.J. R. M. (1990)L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Statist. Soc. B 52(1), Kienzle, S. W., Lorentz, S. A. & Schulze, R. E. (1995) Hydrology and water quality of the Mgeni catchment. Report to the Water Research Commission, Pretoria, RSA. (in press). Kite, G. W. (1988) Frequency and Risk Analysis in Hydrology. Water Resources Publications, Littleton, USA. Schmidt, E. J. & Schulze, R. E. (1984) Improved estimation of peakflowrates using a modified SCS lag equations. Water Research Commission, Pretoria, RSA, Report 63/1/84. Schulze, R. E. (1989) Non-stationary catchment responses and other problems in determining flood series: A case for a simulation modelling approach. In: Proc. Fourth South African National Hydrological Symposium (ed. by S. W. Kienzle & H. Maaren). SANCHIAS, Pretoria, RSA. Schulze, R. E. (1995) Hydrology and agrohydrology: a text to accompany the ACRU 3.00 agrohydrological modelling system. Water Research Commission, Pretoria, RSA, Report TT69/95. Smithers, J. C. (1994) Short duration rainfall frequency model selection in southern Africa. In: 50 Years of Water Engineering in South Africa. Water Engineering Division, SAICE, Johannesburg, RSA. Smithers, J. C. (1996) Short duration rainfall frequency model selection in southern Africa. Water SA 22(3), Smithers, J. C. &Caldecott, R. E. (1993) Development and verificationofhydrograph routing in a daily simulation model. Water SA 19(3), Smithers, J. C. & Caldecott, R. E. (1995) Hydrograph routing. Chapter 13, in: Hydrology and Agrohydrology : A Text to Accompany the ACRU 3.00 AgrohydrologicalModelling System (ed. by R. E. Schulze). Water Research Commission, Pretoria, RSA Report TT69/95. Smithers, J. C. & Schulze, R. E. (1995) ACRU Agrohydrological Modelling System. User Manual: Version 3.0. Water Research Commission, Pretoria, RSA Report TT70/95.

11 Design flood estimation using a modelling approach 375 Stedinger, J. R., Vogel, R. M. & Foufoula-Georgiou, E. (1993) Frequency analysis of extreme events. In: Handbook of Hydrology (ed. by D. R. Maidment). McGraw-Hill, New York. Tarboton, K. C. & Schulze, R. E. (1992) Distributed hydrological modelling system for the Mgeni catchment. Water Research Commission, Pretoria, RSA Report TT234/1/92. Vogel, R. M. &Fennessey,N. M. (1993) L-Moment diagrams should replace product moment diagrams. Wat. Resour.Res. 29(6) Vogel, R. M., McMahon, T. A. & Chiew, F. H. S. (1993) Floodflow frequency model selection in Australia. J. Hydrol. 146, Vogel, R. M., Thomas, W. 0. & McMahon, T. A. (1993) Flood-flow frequency model selection in southwestern United States. J. Wat. Resour. Plan. Manage. 119(3), Wallis, J. R. (1988). Catastrophes, computingand containment: Living with our restless habitat. Research ReportRC IBM Research Division, Yorktown Heights, New York. Weddepohl, J. P. (1988). Design rainfall distributions for southern Africa. Unpublished MSc dissertation. Department of Agricultural Engineering, University of Natal, Pietermaritzburg, RSA.