A daily runoff simulation in semi-arid watersheds based on soil water deficit calculations

Initial soil water content just before a rainfall event is an input required for the calculation of a basin's water balance including infiltration and runoff. However, for most watersheds such information is not available because its evaluation involves a large amount of labor. The objective of this study is to describe a practical model with which to estimate time-dependent changes of a basins soil water content. It is further used for predicting runoff water yield when rainfall depth is the only known component of the water balance equation (WBE). Two distinct cases of the WBE are discussed: (1) a runoff-producing storm; (2) a storm without runoff. Runoff events from four watersheds in southern Arizona were measured throughout 8 to 17 years and analyzed in this study. Rainfall-runoff relationships are described in this model by an empirical quadratic regression equation which includes four parameters. They were estimated by an optimization subroutine which was used to determine the minimum difference between measured and modeled results. The optimized parameters enable simulations of the continuous dynamic change of an index of the soil water content as well as predictions of runoff depths. It was found that the predicted runoff agrees reasonably well with the observed runoff. The minimum coefficient of determination (r²) between the computed and actual runoff for the multi-annual data sets was 0.62 and the maximum 0.86. Runoff threshold value was found to be a function of the basin average soil texture. The lowest threshold was 4.6 mm for clay soil and the largest was 9.0 mm for sandy soil. Since direct soil water measurements were not taken, we interpreted the acceptable agreement between measured and predicted runoff as an indirect validation of the soil water model. It is concluded that the model could be useful for extending short records of simulated runoff on nearby ungaged watersheds in semi-arid regions.