Accuracy of Flood Estimation with the Gama I Unit Hydrograph

Abstract

In this study research is performed into the accuracy of flood estimation. In particular the rivers on the island of Java are considered. For these distinctive rivers, the GAMA I unit hydrograph theory was developed (Sri Harto 1985) for flood estimation. The GAMA theory defines 3 basic characteristics to represent a unit hydrograph; time of rise (time from the beginning of the storm to the time of peak discharge), peak discharge and base time (total time of run off). For these characteristics, relationships were derived by means of regression analysis using measured data of floods and related catch ment characteristics. In this study the GAMA equations are again derived by means of a program (REGRES) including the calculation of the standard deviations and the correlations of the regression coefficients. These indicate the accuracy of the model. To include the inaccuracy of the input data a program (SIMCO) is constructed in which the input data (measurements) are extended with stochastic features. It is assumed that all data are normally distributed. A simulation is performed based on the Monte Carlo simulation technique to derive a set of 150 equations for each GAMA equation. The standard deviations and correlations are calculated and indicate the sensitivity of the GAMA equations due to inaccurate measurements. By means of a fault tree for each GAMA equation the propagation of errors in the derivation is determined in a analytical and numerical way; analytically by means of the mean value approach and numerically by means of Monte Carlo simulation. The influence of the stochastic input data is very large and mainly dued to the variation of the measured unit hydrograph, derived from discharge measurements. The equations for the peak discharge and the base time seem to be very sensitive. Expressed in coefficients of variation the predictions can deviate 200% and 80% respectively (time of rise 25%). For further investigation only the model accuracy is taken into account; the predictions of the time of rise, peak discharge and base time deviate approximately 20% , 28% and 15% respectively. For calculation of the total hydrograph another program (HYDROGRAPH) is constructed. This program calculates the total hydrograph for a certain rainfall depth and rainfall distribution. The basic characteristics of the unit hydrograph are assumed to be normally distributed. The program generates the required input data from its distributions. A set of 75 hydrographs can be simulated. The model is applied to the river Putih in Java. Calculations show that the accuracy of the predicted maximum discharge depends highlyon the rainfall distribution. The rainfall depth has no influence on the accuracy. The model HYDROGRAPH cao be applied to every river for which the GAMA equations are valid and shows the accuracy of prediction.