广州市表层土壤磁学性质的空间插值方法比较

本文利用广州市范围内的350个表层土壤样品χ_lf、χ_ARM/SIRM、HIRM等14个磁学参数的测试结果，在对各磁学参数分别进行统计特征分析和正态性检验的基础上，对满足正态或近似正态分布的磁学参数进行趋势分析。利用确定性插值法（包括反距离权重法和径向基函数法）和地统计法（包括普通克里金法和泛克里金法）对14个磁学参数进行空间插值并根据交叉验证法（比较不同插值方法的交叉验证参数）的结果，比较地统计法和确定性插值法的预测误差，从而确定14个磁学参数的最优插值方法。结果表明：1）地统计法中，χ_ARM、χ_lf、χ_hf、S₁₀₀、S₃₀₀、S_-100、SIRM和HIRM的普通克里金法插值效果最好；SIRM/χ的泛克里金法插值效果最好；χ_ARM/SIRM和S_-300的普通克里金法（OK）和泛克里金法（UK）的插值效果接近。OK法作为最常用的地统计空间插值方法，在表土磁学参数上也相较于UK适用范围更广。2）确定性插值法中，χ_ARM、χ_lf、χ_hf、χ_fd（%）、χ_ARM/χ、χ_ARM/SIRM、HIRM的径向基函数法插值效果最优；S₁₀₀、S_-100、S_-300和SIRM的反距离权重法插值效果最优；反距离权重法和径向基函数法均可作为χ_fd、SIRM/χ、S₃₀₀的插值方法。3）综合比较地统计法和确定性插值法，发现χ_ARM、χ_lf、χ_hf、χ_fd、χ_fd（%）、χ_ARM/χ、χ_ARM/SIRM、S₃₀₀、HIRM的空间插值应采用径向基函数法；S₁₀₀、S_-100和S_-300的空间插值应选择反距离权重法；而SIRM/χ和SIRM空间插值建议分别采用泛克里金法和普通克里金法。

Comparative Study on Spatial Interpolation of Surface Soil Magnetic Properties in Guangzhou City

Soil magnetism is an important indicator of soil quality. Spatial distribution and environmental significance of surface soil magnetic properties have been reported from many areas worldwide. Spatial distribution of magnetic parameters was acquired through the spatial interpolation method and data of sampling sites was measured for a specific spatial scale in most of these studies. However, a limited number of studies in this field have appropriately reported on the accuracy of these spatial interpolation methods. Based on statistical characteristics analysis, normality test, and trend analysis, the results of 14 magnetic parameters of 350 surface soil samples collected from Guangzhou city were used to perform several spatial interpolation methods. Geostatistics (including Ordinary Kriging and Universal Kriging) and deterministic interpolation methods (including Inverse Distance Weighting and Radial Basis Function) were employed to conduct the spatial interpolation methods. The accuracy of spatial interpolation methods was measured by cross-validation. Mean Error, Root Mean Square Error, Mean Standardized Error, Root Mean Square Standardized Error and Average Standard Error were used to measure the accuracy of results of geostatistics methods; the optimal spatial interpolation method of each magnetic parameter of Ordinary Kriging and Universal kriging was selected. Next, Mean Error and Root Mean Square Error were used to measure the accuracy of results of deterministic interpolation methods; the optimal spatial interpolation method of each magnetic parameter of Inverse Distance Weighting and Radial Basis Function was selected. Finally, by comparing the Mean Error and Root Mean Square Error of the optimal deterministic interpolation method and geostatistical interpolation method, the optimal interpolation method of each magnetic parameter was determined. The results show that: First, among the geostatistical interpolation methods, the Ordinary Kriging method is effective for spatial interpolation of magnetic parameters χ_ARM, χ_lf, χ_hf, S₁₀₀, S₃₀₀, S_-100, SIRM, and HIRM; spatial interpolation of SIRM/χ should use the Universal Kriging method; Ordinary Kriging and Universal Kriging can be used for spatial interpolation of χ_ARM/SIRM and S_-300. Second, in the deterministic interpolation methods, the Radial Basis Function method is an optimal choice for spatial interpolation of χ_ARM, χ_lf, χ_hf, χ_{fd (%)}, χ_ARM/χ, χ_ARM/SIRM, and HIRM; for spatial interpolation of S₁₀₀, S_-100, and S_-300, SIRM Inverse Distance Weighting method was the best alternative; Inverse Distance Weighting and Radial Basis Function methods could be used for spatial interpolation of χ_fd, SIRM/χ, and S₃₀₀. Third, a comprehensive comparison of geostatistical interpolation methods and deterministic interpolation methods shows that spatial interpolation of χ_ARM, χ_lf, χ_hf, χ_fd, χ_{fd (%)}, χ_ARM/χ, χ_ARM/SIRM, S₃₀₀, and HIRM should use the Radial Basis Function method; the Universal Kriging method is suitable for spatial interpolation of SIRM/χ. The Inverse Distance Weighting method should be chosen for spatial interpolation of S₁₀₀, S_-100, and S_-300, spatial interpolation of SIRM should be measured with the Ordinary Kriging method.