A two-parameter exponential function approach to simply and accurately characterize spatial regime of topographic index for land-surface parameterizations

The concept of topographic index (TI), for characterizing the likely distribution of variable source areas within a watershed, has been successfully incorporated into some land-surface processes parameterizations and climate models. Representing the spatial distribution regime of TI accurately and simply is a crucial issue for those topography-based landatmosphere interactions studies. In this paper, a simple but effective method, named as two-parameter exponential function, was developed to solve such problem. Since the important runoff generation mechanism occurs chiefly in lowland areas of a catchment or a simulating grid unit, it is not necessary to accurately capture the distribution where the TI values are less than the mean TI value (corresponding to upland areas). As a special case of the three-parameter gamma distribution, the twoparameter exponential function is used to fit only the part of the actual discrete CDF where TI is larger than its mean value so that it performs better than the previous gamma distribution does.In this exponential function, two significant parameters, the maximum fractional saturated area (Fmax) and the exponential coefficient (Cs) should be determined by topographic characteristics. So we investigated the relationships of these two important parameters with the mean value of TI, λm. Fortunately, it was found that the value of Fmax (0.35≈0.55) can be derived directly from actual CDF curve, and the exponential coefficient, Cs (0.58≈0.68), can also be obtained from a simple equation of Cs =0.04λm +0.21. Fifty 0.5°×0.5° DEM blocks of 90- m resolution, which were chosen randomly to represent a wide range of terrain complexity, were clipped from STRM DEM3 datasets covering the central part of China to verify the validity of this exponential function approach. The experimental results suggested that the two-parameter exponential function agrees fairy well with the actual cumulative distribution function (CDF) curves in lowland part of those grid cells located at mountainous areas, where the general three-parameter gamma distribution fails to fit the discrete distribution of TI , as well as at flat areas. The two-parameter exponential function approach, which can accurately and simply characterizing spatial regime of TI in lowland areas under different topographic conditions, improves the expression of fractional saturated area and the parameterization of topography-based land-surface processes.