The use of a rainfall-runoff model in the forecasting of Discharge from rainfall in the upper Athi river Catchment

Abstract

For engineering design and planning purposes, forecasts and synthesis of hydrological information is often very necessary. These are usually obtained through the use of hydrological models. This study aims at developing and evaluating the skill of a rainfall-runoff model over the upper Athi river catchment. The model is based on catchment subareas centred about lines of constant time of travel for water to the outlet (isochrones). The study was subdivided into several parts. The first part of the study concentrated on the estimation of missing rainfall and discharge records using arithmetic mean method and the isopleth method. This was followed by testing the quality of both the estimated and observed records using mass curve analysis. Only single straight lines could be fitted to all mass curves at all locations. The homogeneous records were subjected to Principal Component Analysis (PCA) inorder to determine spatial similarities in the characteristics of rainfall within the catchment. The Principal Component Analysis (PCA) results, based on Kaiser's criterion (Kaiser, 1959), indicated that only one Principal Component was dominant over the catchment. The magnitude of the loading of this component was greater than 0.85 at all locations. The point rainfall records were then areally averaged using arithmetic mean method. The second part of the study investigated the statistical characteristics in the discharge and rainfall records through time series analysis. The statistical parameters which were computed included the autocorrelation, auto-spectra, cross-correlation, cospectra, quadrature spectra, coherence and phase. The spectral analysis results indicated the dominance of quasi-periodic fluctuations during the major rainfall seasons and dry months. These were centred around 2-2.5 and 2.8-3.5 days. The 5-6 days cycle was also observed during the dry seasons. Cross-spectral analysis indicated that rainfall was leading discharge. The lead time ranges from 1 to 7 days. The quasi-periodic fluctuation were still evident from cross-spectral analysis. Finally the model was developed through plotting of the isochrones using the cross-correlation and coherence functions. The Kernel functions for the model were then computed through matrix solution using coincident rainfall and discharge records. The longest rainfalldischarge response was also centred within 1 to 7 days. Peak response values were however centred within 1 to 5 days. Tests of skill based on residual error test, using the data which were not used during the model development, indicated that the model gave reliable forecasts of discharge during most of the cases a part from few extreme cases.