Comparison Between Two Simple Linear Catchment Models For The Yala River Basin

Abstract

In this study, two simple linear catchment models were used to model the rainfall-runoff characteristics over Yala catchment. The first model was based on the response function. In this model a linear stochastic process for the rainfall runoff system which yields the wiener-Hopf integral equation was assumed. The method of maximum likelihood was then used to compute optimum response functions. The average response function together with the computed areal rainfall were finally used to estimate stream flow during the verification period. In the second method, a multivariate autoregressive model was used in which linear transfer functions of different orders were fitted to the daily areal rainfall and streamflow data. The optimum autoregressive model was again used to estimate discharge during the verification period. The results from the two approaches were lastly compared statistically. Prior to fitting the models, the statistical characteristics of the computed daily areal rainfall and daily discharge series were investigated through time series analysis. The characteristics of the auto-correlation, cross-correlation, spectral and cross-spectral functions were examined. xvii Yala river basin is located in drainage area one in western Kenya. The study was carried out in this drainage basin using daily rainfall and discharge records for nine years (1968 to 1976). The first seven years were used for calibration of the models, while the last two years were used for verification of the skill of the fitted models. The calendar year was divided into two seasons namely the long and short rain seasons • . The models were fitted for both seasons. Results from spectral analysis, indicated periods of 2 - 4 days, 5 - 7 days and 8 - 10 days in both rainfall and discharge records. The results from the cross correlation and coherence analyses showed significant correlations between,time lags of 2 - 6 days with peaks at a lag of 3 days during the first rain season and a lag of 4 days during the-second rain season. " The response functions had peaks at a constant time lag of 3 days during the first rain season and - 4 days during t]1e second rain season. The results from the fitted autoregressive models indicated that the autoregressive models with four rainfall and two discharge lag terms fitted the discharge- data best. It was noted that although both models could not adequately estimate the extreme discharge values, the response function model was better in real time xviii forecasting. This model however, was poor in giving the actual estimates of the observed discharge. On the other hand, the autoregressive models gave good estimates of the magnitudes of the discharges. The peak discharge values were, however, shifted in some cases. It was therefore suggested that the response function models which gave good estimates of the time of occurrence of the discharge peaks would be the best models for the Yala river basin for real time forecasting.