Interpreting Annual Rainfall from the Levels of Lake Victoria

Abstract

This paper presents a water balance model for Lake Victoria that can be inverted to estimate annual rainfall over the lake. The model is calibrated using a fixed value of evaporation and the regression expressions for inflow, discharge, and rainfall. Rainfall totals at stations in the catchment are used to estimate over-lake rainfall, applying a regression between catchment and over-lake rainfall derived from satellite data. The inflow regression is authenticated using a cross-validation technique applied to inflow estimates for the years 1956?78, and the discharge regression is validated using discharge data for the years 1901?55. The model is first written as an autoregression (AR) model form for the lake-level term. Model predictions of lake level are verified by comparing them with measured lake levels for the time period 1931?94. In doing so, the model is initialized using the end-of-year lake level for 1930 and then using only over-lake rainfall as external input. Predicted levels of the lake levels are compared to the measured levels, with a correlation of 0.98. This confirms that fluctuations of Lake Victoria are driven predominantly by rainfall. The model is then ?inverted? so that the current year's over-lake rainfall is expressed as a function of the two lake-level terms. If the beginning and ending lake levels in a year are known, the over-lake rainfall in the same year is easy to obtain. Applying the inverse model to the measured lake levels in 1899?1994, over-lake annual rainfall in 1900?94 is estimated. A comparison with over-lake rainfall for the period 1931?94 gives a root-mean-square error of 98 mm yr?1, corresponding to 6% of the over-lake annual mean rainfall. This model is also compared with the previous water balance model, which can be employed only for multiyear mean rainfall estimates. The two models complement each other, with the current model's advantage being the ability to calculate annual rainfall. However, the previous model still provides better estimates of multiyear means.