Numerical representation of rainfall field in basins of the Upper Jordan River and of the Yarmouk River

A non-linear complex rain–elevation regression model is proposed for the numerical representation of rainfall field in an area with complex plain/mountainous topography, non-uniform distribution of rain gauge network and scarce data of observations. The model is applied to basins of the Upper Jordan River (of the Lake Kinneret) and of the Yarmouk River in which the major flow of the Jordan River is formed. The model is implemented in two steps: (1) study of the rainfall field, based on the average long-term (climatic) data, its description by the function of elevation and other factors, and optimization of model parameters (normalized coefficients of the Taylor series); and (2) estimation of rainfall in each historical year using the available data (less complete and irregular than climatic data) as well as a priori known parameters. The basic hypothesis is inter-annual stability of the model parameters. As a necessary primary stage, the Upper Jordan River (Lake Kinneret) Basin and the Yarmouk River Basin were divided, respectively, into seven and five regions, considering the specific regional relationships between the mean annual rain depth and elevation. It occurred that both basins are represented by a common system of rain–elevation curves as a single rain field where the mean annual rain increases with altitude and decreases from west to east and from north to south. For each region, the parameters of the model were optimized as a base for estimating the annual (month) rain (mean or yearly volume/depth) in each point of grid, in each basin (sub-basin) or in the whole watershed. The necessary condition is numerical presentation of the topography. Derived rain rates can serve as fundamental input data for numerical modeling of surface- and groundwater flow. This method can be applied to other areas at different temporal and spatial scales.