Performance of a Theoretical Model for the Description of Water Balance and Runoff Dynamics in Southern Italy

In the present paper, an analytical work for the description of the soil water balance and runoff production was adopted over a significant number of river basins belonging to a humid region of Southern Italy. The model is based on a stochastic differential equation, where the spatial heterogeneity of a basin is incorporated by a parabolic function describing the distribution of soil water storage capacity at the basin scale. The model provides an analytical description of the probability density function (PDF) of relative saturation of a basin as well as the PDF of daily runoff production. The proposed model includes five parameters that depend on climatic and soil characteristics. In particular, two parameters describe the rainfall process ($\alpha$ and $\lambda$), two characterize the distribution of soil water storage capacity ($w_{\max }$ and $b$), and the last is the soil water loss coefficient ($V$). Application of the model allowed the regionalization of model parameters based on physically consistent characteristics of the river basins. In particular, it was found that the soil water loss coefficient is strongly controlled by the fraction of forest cover of the river basin, while the parameter $b$, controlling the shape of the distribution of soil water storage capacity, is influenced by the basin topography.