基于混合地理加权回归与克里格的区域降水量空间插值方法

doi:10.3969/j.issn.1000-6362.2018.10.006

摘要/Abstract

摘要： 基于四川省区域范围内144个气象站点的实测降水数据，在综合考虑空间位置、地形等影响因素的基础上，采用改进的回归克里格模型，即混合地理加权回归克里格模型（MGWRK）对四川省年降水量的空间分布进行空间插值，并与普通克里格（OK）、全局回归克里格（GRK）和地理加权回归克里格（GWRK）等模型的插值效果进行对比分析。结果表明：（1）应用逐步回归法筛选确定的用于回归分析的影响因子组合为经度、纬度和坡度，可有效消除解释变量间的多重共线性，为后续的空间插值奠定基础；（2）同一回归变量在地理加权回归（GWR）与全局回归（GR）两种回归模型中的AICc（修正的赤池信息量准则，Corrected Akaike Information Criterion）值之差（ΔAICc）可用于定量判定各回归变量的空间非平稳性类型，据此将变量坡度设为全局变量，经度和纬度设为局部变量进行处理。在此基础上，通过MGWRK模型对四川省年降水量进行空间插值；（3）MGWRK插值模型综合考虑了空间位置、地形等多个影响因素及其与降水相互关系的空间非平稳性特征，相对于传统的OK和GRK法具有更高的插值精度。

关键词: 降水量, 混合地理加权回归, 克里格, 空间插值

Abstract: Based on the precipitation data of 1981?2010 from 144 meteorological stations in Sichuan province, using mixed geographical weighted regression Kriging interpolation (MGWRK) model, and considering the impact of topographic factors, the spatial distribution of the average annual precipitation was obtained in this paper. The effect of interpolation value was compared with those values from OK, GRK, and GWRK methods. The result showed that the optimal influencing factors combination was longitude, latitude and slope, determined by using the stepwise regression method, could decrease the multi-collinearity among the explanatory variables significantly. The types of spatial variability of the explanatory variables were analyzed quantitatively based on the index ΔAICc, which was the difference between the value of AICc (Corrected Akaike Information Criterion) of the same variable calculated by GWR model and by GR model. Then set the slope variable as global variable, and the longitude and latitude variables as local variables, the interpolation of the average annual precipitation in Sichuan province was conducted by the MGWRK model. The MGWRK method presented in this paper showed higher accuracy than those of the ordinary Kriging (OK) and global regression Kriging (GRK), because the method has taken into consideration of various influence factors of the spatial position and topography, and the variability of the relationship between these factors and precipitation.

Key words: Precipitation, Mix geographically weighted regression, Kriging interpolation, Spatial Interpolation

李豪，刘涛，徐精文. 基于混合地理加权回归与克里格的区域降水量空间插值方法[J]. 中国农业气象, 2018, 39(10): 674-684.

LI Hao, LIU Tao, XU Jing-wen. Spatial Interpolation of Regional Precipitation Based on Mixed Geographical Weighted Regression Combined with Kriging Interpolation[J]. Chinese Journal of Agrometeorology, 2018, 39(10): 674-684.

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