Comparative case study of rainfall - runoff models over the Nyando river basin

Abstract

The main objective of this study was to assess the performance of some existing rainfall-runoff linear systems models and a conceptual model using data from the Nyando catchment. In order to estimate the optimum parameters for the various models, split samples of data were used; one sample for calibration and the other for verification. The data used comprised daily areal average rainfall, daily average runoff and daily average evaporation. Regression analysis method was used to estimate missing rainfall and runoff data while seasonal mean 'method was used to estimate missing evaporation records. Homogeneity of the data was tested using the mass curve method. Results of homogeneity test indicated that data from the catchment are generally homogeneous as shown by the high R£ efficiency values. The performance of each of three rainfall-runoff linear systems models, the Simple Linear Model (SLM), the Linear Perturbation Model (LPM) and the Linearly Varying Gain Factor Model (LVGFM), and a conceptual model called the Soil Moisture Accounting and Routing (SMAR) model, was assessed using data from the Nyando catchment. The linear systems models were applied in both non-parametric and also under the constraint of the gamma function impulse responses. Optimum parameters were obtained by the method of Ordinary Least Squares (OLS) and by Rosenbrock's search technique for non-parametric and parametric modes respectively. Results obtained in the simulation mode indicate that there is a good agreement between the actual and estimated stream flow when the conceptual SMAR model is used. For the SLM there is a marked difference between actual and estimated stream flow especially in the case of low and high flow seasons, respectively. The performance .of the other models falls somewhere in between the performance of these two models. The conceptual SMAR model appears to be more superior to the linear systems models with a higher R£ efficiency (71 %) than those of the linear systems models. Among the linear systems models, the LVGFM performs best on the Nyando catchment at R'" efficiency of about 69 %, followed by the LPM at R'" efficiency of 55 % and the SLM at R'" efficiency of 47 % in this order. From these results, the SMAR model may be considered the best model for the Nyando catchment among all the models that were considered in this study. Among the linear systems models considered, the LVGFM is the best model for the catchment followed by the LPM and the SLM in this order.