## THE THREE-PARAMETER GAUSS FORMULA AND ITS APPLICATION IN MOUNTAIN PRECIPITATION VERTICAL DISTRIBUTION STUDIES

**Yu Jie ;Yu Jialong(Uepartment of Mathematics, Wuhu Educational College, Wuhu 241000)Yu Jialong (Institute of Geography, Anhui Normal University, Wuhu 241000)**

Many kinds of formulas about Mountain Precipitation Vertical Distribution are presented these days. Among them, Fu's formula is the one applied very often. Based on the shortcomings of Fu's formula, Four-parameter Gauss Formula and its computing method are proposed by Jiang Zhongxin. The formula is described as follows.Where, Pz means precipitation (mm) at the height of z(m) and a, b, c, H are parameters. The computing method he used is to linearize the above equation. Thus,an equation ln(Pz-c)=lna-b . (Z-H)2 is obtained. Then linear regression method is applied to optimize ln(Pz-c). At last,the computing conclusions are compared with those from Fu's formula.There exist some problems in Jiang's formula and its computing method. Firstly, the optimization is only for ln(Pz-c) with respect to (Z-H)2, not for P.with respect to z. Thus, a large error exists. Secondly, the statistical confidence is not strong for the data set used to fit the formula which has not enough observations to estimate four parameters. Thirdly, it is not reasonable to compare conclusions from the four-parameter formula with those from Fu's three-parameter formula.Due to the above problems, three-parameter Gauss formula and its nonlinear regression method are presented by the authors as follows.Compared to the Jiang's formula, c is omitted for the reason that c means the precipitation at very high spaces and usually it is assumed to be zero. Thus, the statistical confidence is improved due to the fewer parameters when the number of observations is small. And it is acceptable to compare the conclusions from this formula with those from Fu's formula.A nonliear regression method is applied directly to optimize Pz with respect to z. By this way,the precision is improved largely.At last, the three-parameter Gauss formula and its nonlinear regression method have been successfully applied to the analysis of mountain areas'precipitations in China, such as Huangshan Mountain, Emeishan Mountain, Qinglin and Tianshan Mountain. The average relative errors are less than 2. 5% and the maximum relative errors are lower than 5. 1%.

【CateGory Index】：
P426.615

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