高斯函数参量法及其在山区降水计算中的应用

Gauss parameter method and its application in calculating the rainfall from the mountainous areas

本文根据乌鲁木齐河流域7个雨量站点多年（17～61年）的月平均降水数据的统计规律，提出一种新的、能够同时满足空间维和时间维插值需求的降水分布及降水量计算模型——高斯函数参量化法。该模型根据高斯函数的几何意义和降水分布规律，给高斯函数的参数赋予了明确的物理意义，从而把对降水量和分布函数规律的计算转化为对高斯函数少量参数（1～3个）的估计。不仅能够实现山区降水在时间上和空间上的插值，而且能够实现降水量和降水分布函数的相互转换。特别是能解决在高山区降水数据稀缺条件下的降水量和降水分布估计的问题。大大提高了降水数据的可用性。

Based on the seven monthly mean precipitation data averaged over years from the Urumqi River basin, the authors put forward the Gauss parameter model which can meet the interpolation demand in time and space dimensions. The fitting goodness of the models is 4%. This model builds the relationship between the Gauss function and precipitation, according to the mathematical meaning of the Gauss function and distributional rule of precipitation, and converts the traditional interpolation into function model, advances the application of the precipitation data, solves the problem of calculating precipitation and precipitation distribution under the conditions of the scarcity of rainfall data, especially in the alpine mountain with sparse meteorological stations. It will significantly improve the availability of precipitation data. This paper presents the principle, derivation process and the typical application methods, integrating with specific data. The precipitation distribution simulated by the Gaussian function is consistent with the actual precipitation amount. Each parameter of Gaussian function has a very clear physical meaning. The method of Gaussian function parameter has a strong practical value, and is widely used. The details are discussed below. As the time function of precipitation distribution, the model can calculate precipitation amount of any time. Through integration of the precipitation distribution function within a certain period, the precipitation amount of any time cycle can be calculated. Through the spatial interpolation of rainfall distribution parameters of different sites, the precipitation distribution function can be achieved in different regions, thereby calculating the precipitation amount of any time periods and at any time. The simplified Gauss model can transform the estimates of three parameters into one parameter, which can meet the needs of application in the high mountains with sparse meteorological stations, but also can calculate precipitation amount in the historical period. The promoted model can be applied to the precipitation distribution of more than one peak, which expands the application of Gaussian parameters. However, we must point out that the method of the Gaussian model is based on the data of meteorological stations in Urumqi River valley. The application of models might have some limitations, especially in this region.