A simple non-linear rainfall-runoff model with a variable gain factor

A simple non-linear rainfall-runoff model, incorporating a variable gain factor dependent on the prevailing soil moisture state of the catchment, is developed. The simulation mode output of an auxilliary simple linear model is used as an index of the soil moisture state and simple and realistic functional relationships between the gain factor and the prevailing catchment wetness index are assumed. The resulting model, referred to as the variable gain factor model (VGFM), is tested on the data of five catchments, assuming two different functional forms of gain factor variation with the catchment wetness index. The results indicate significant improvement over the performance of the simple linear model for the test catchments. The operation of the model is shown to be equivalent to a special form of the non-linear Volterra model.