A modified spatial soil moisture storage capacity distribution curve for the Xinanjiang model

The Xinanjiang model provides a statistically integral structure to describe the runoff generation on partial areas over a catchment. In the original version of the model, a single parabolic curve is used to describe the soil moisture variation. In reality however, the spatial and temporal distribution of soil moisture is quite complex because many different states, which change with seasons of the year, co-exist in the catchment. In this study, a more general double parabolic curve is proposed to describe the complex soil moisture variation. It consists of lower and upper branches, with the lower branch for the wet condition, the upper branch for the dry condition, and a smooth transition. Two parameters, c and b represent the relative weight between the lower and the upper branches and their gradients. The single parabolic curve of the original Xinanjiang model can be thought of as a special case of the proposed double parabolic curve. Both the single and double parabolic curves perform similarly when used with storm events isolated from daily data in the wet seasons, but the double parabolic curve improves the predictions significantly when used with data from the dry seasons. When used with hourly event data there is no significant difference between the two curves because of the dominance of the wet soil moisture condition. Even in this case, the double parabolic curve differentiates the parameter values more clearly for different soil moisture states. There is also a slight improvement on the predictions for storms in the dry seasons.