广州市表层土壤磁学性质的空间插值方法比较

doi:10.13284/j.cnki.rddl.003279

摘要/Abstract

摘要：

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。

关键词: 磁学参数, 确定性插值法, 地统计法, 表层土壤, 广州市

Abstract:

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.

Key words: magnetic parameters, deterministic interpolation methods, geostatistics, surface soil, Guangzhou city

中图分类号:

P934

贺辰戋, 欧阳婷萍, 彭莎莎. 广州市表层土壤磁学性质的空间插值方法比较[J]. 热带地理, 2020, 40(5): 903-918.

Chenjian He, Tingping Ouyang, Shasha Peng. Comparative Study on Spatial Interpolation of Surface Soil Magnetic Properties in Guangzhou City[J]. Tropical Geography, 2020, 40(5): 903-918.

图/表 11

图1

表1

表2

图2

图3

表3

磁学参数普通克里金（OK）插值的交叉验证结果"

磁学参数	变换	趋势	模型	ME	RMSE	MSE	RMSSE	ASE	ASE-RMSE
χ_ARM(10^-8m³/kg)	Log	二阶	环状	7.211 7	132.911 9	-0.101 2	1.255 2	213.705 3	80.793 4
			球状	7.157 4	132.995 8	-0.105 1	1.268 2	211.871 0	78.875 3
			指数	6.475 2	139.563 4	-0.120 5	1.174 9	237.331 0	97.767 6
			高斯	8.155 9	133.752 1	-0.091 3	1.166 4	227.996 2	94.244 2
χ_lf(10^-8m³/kg)	Log	二阶	环状	-3.793 1	73.770 1	-0.284 2	2.636 5	54.248 3	-19.521 8
			球状	-3.264 0	73.684 0	-0.280 4	2.512 9	56.802 0	-16.882 1
			指数	-3.739 7	73.876 3	-0.308 4	2.562 4	52.737 4	-21.138 9
			高斯	-3.233 4	74.073 8	-0.282 2	2.567 2	56.929 1	-17.144 8
χ_hf(10^-8m³/kg)	Log	二阶	环状	-3.995 6	72.633 8	-0.295 4	2.756 8	50.377 2	-22.256 6
			球状	-3.460 6	72.585 2	-0.289 7	2.624 8	53.005 2	-19.580 0
			指数	-3.911 6	72.767 2	-0.319 1	2.683 0	49.155 7	-23.611 5
			高斯	-3.470 1	72.904 8	-0.290 8	2.683 7	53.002 4	-19.902 4
χ_ARM/SIRM (10^-5m/A)	Log	一阶	环状	-0.946 0	33.543 3	-0.051 0	1.532 2	19.325 9	-14.217 4
			球状	-0.979 4	33.510 5	-0.054 5	1.534 0	19.143 1	-14.367 4
			指数	-0.469 9	33.512 7	-0.029 1	1.388 7	20.859 4	-12.653 4
			高斯	-0.927 7	33.592 0	-0.054 3	1.572 5	19.293 7	-14.298 3
SIRM/χ (kA/m)	Log	一阶	环状	-0.080 3	4.102 5	-0.066 6	1.332 4	3.315 3	-0.787 2
			球状	-0.075 4	4.099 4	-0.062 8	1.321 3	3.338 4	-0.761 0
			指数	-0.097 6	4.108 9	-0.068 5	1.378 5	3.234 7	-0.874 2
			高斯	-0.079 7	4.091 1	-0.064 7	1.323 3	3.325 3	-0.765 8
S₁₀₀	Box-Cox	二阶	环状	-0.000 5	0.117 8	0.013 5	1.020 2	0.117 4	-0.000 4
			球状	-0.000 5	0.117 5	0.007 5	1.003 7	0.118 4	0.000 9
			指数	0.000 4	0.118 3	0.015 8	1.028 0	0.116 0	-0.002 3
			高斯	-0.000 7	0.117 6	0.007 3	1.000 6	0.118 8	0.001 2
S₃₀₀	Box-Cox	二阶	环状	0.001 0	0.091 7	0.021 1	1.154 4	0.080 3	-0.011 4
			球状	0.000 9	0.091 9	0.022 5	1.168 9	0.079 8	-0.012 1
			指数	0.001 9	0.092 1	0.031 0	1.215 7	0.076 3	-0.015 8
			高斯	0.001 0	0.091 4	0.020 0	1.148 4	0.080 5	-0.010 9
S_-100	Box-Cox	二阶	环状	0.001 2	0.119 0	0.023 6	1.084 7	0.110 8	-0.008 3
			球状	0.000 8	0.119 2	0.017 7	1.047 7	0.114 5	-0.004 7
			指数	0.000 6	0.118 8	0.014 5	1.051 5	0.114 2	-0.004 7
			高斯	0.000 6	0.118 8	0.015 7	1.043 3	0.114 8	-0.004 0
S_-300	Box-Cox	二阶	环状	0.001 7	0.089 3	0.029 8	1.195 5	0.075 4	-0.013 9
			球状	0.001 9	0.089 5	0.029 6	1.189 9	0.075 6	-0.013 9
			指数	0.002 0	0.090 1	0.026 1	1.172 6	0.076 4	-0.013 7
			高斯	0.001 8	0.089 2	0.029 7	1.190 0	0.075 5	-0.013 7
SIRM (10^-6Am²/kg)	Log	二阶	环状	-1.160 4	6 506.389 8	-0.205 3	1.734 7	7 132.710 1	626.320 3
			球状	4.830 5	6 509.011 3	-0.202 1	1.686 5	7182.3925	673.3813
			指数	-37.189 2	6 566.430 2	-0.222 7	1.782 4	6763.5871	197.1569
			高斯	7.831 1	6 503.241 7	-0.196 1	1.695 3	7222.9150	719.6732
HIRM (10^-5Am²/kg)	Log	二阶	环状	-0.821 3	58.852 4	-0.205 7	1.883 4	51.5473	-7.3051
			球状	-0.217 1	59.095 7	-0.164 9	-0.164 9	53.4453	-5.6504
			指数	-1.081 7	61.324 1	-0.201 9	1.715 8	56.8566	-4.4675
			高斯	-0.219 4	58.860 0	-0.186 0	1.765 1	53.7368	-5.1232

表3

表4

磁学参数泛克里金（UK）插值的交叉验证结果"

磁学参数	变换	趋势	模型	ME	RMSE	MSE	RMSSE	ASE	ASE-RMSE
χ_ARM (10^-8m³/kg)	Log	二阶	环状	7.323 1	139.703 4	-0.079 2	0.836 1	369.379 7	229.676 4
			球状	7.055 1	140.346 8	-0.084 7	0.858 7	366.770 2	226.423 3
			指数	4.334 1	138.481 2	-0.092 5	0.880 4	355.265 6	216.784 4
			高斯	7.861 1	139.982 0	-0.082 8	0.843 6	371.516 1	231.534 1
χ_lf (10^-8m³/kg)	Log	二阶	环状	-4.101 8	72.385 0	-0.134 7	1.017 5	122.783 4	50.398 4
			球状	-4.437 5	70.425 3	-0.132 5	1.037 2	128.798 0	58.372 7
			指数	-4.565 5	71.929 4	-0.138 3	1.053 5	115.914 3	43.984 9
			高斯	-3.625 3	72.716 4	-0.133 3	1.005 8	128.918 2	56.201 8
χ_hf (10^-8m³/kg)	Log	二阶	环状	-4.361 2	70.977 5	-0.138 2	1.044 9	114.797 1	43.819 6
			球状	-4.462 3	68.937 9	-0.134 7	1.066 2	121.824 2	52.886 3
			指数	-4.297 9	68.478 7	-0.137 9	1.139 8	116.456 6	47.977 9
			高斯	-2.598 2	70.079 9	-0.114 9	1.051 2	127.981 0	57.901 1
χ_ARM/SIRM (10^-5m/A)	Log	一阶	环状	-0.901 0	33.471 0	-0.060 1	1.637 2	21.231 8	-12.239 2
			球状	-0.894 2	33.415 6	-0.055 8	1.691 3	20.791 4	-12.624 2
			指数	-0.478 3	33.382 7	-0.031 7	1.510 3	21.856 1	-11.526 5
			高斯	0.934 1	33.661 2	-0.064 0	1.645 0	21.448 2	-12.213 0
SIRM/χ (kA/m)	Log	一阶	环状	-0.111 0	4.115 2	-0.063 2	1.296 1	3.459 1	-0.656 1
			球状	-0.107 2	4.114 4	-0.064 2	1.301 4	3.443 5	-0.670 9
			指数	-0.113 8	4.105 3	-0.066 8	1.279 2	3.502 7	-0.602 6
			高斯	-0.076 8	4.129 1	-0.061 0	1.319 4	3.504 1	-0.625 0
S₁₀₀	Box-Cox	二阶	环状	-0.004 3	0.163 7	0.027 6	1.000 7	0.143 2	-0.020 5
			球状	-0.009 0	0.229 5	0.019 7	1.005 6	0.148 7	-0.080 8
			指数	0.001 3	0.122 5	0.036 3	1.049 5	0.118 0	-0.004 4
			高斯	-0.003 7	0.161 0	0.027 5	0.996 9	0.142 8	-0.018 2
S₃₀₀	Box-Cox	二阶	环状	0.002 3	0.094 2	0.053 5	1.149 6	0.085 6	-0.008 6
			球状	0.003 0	0.094 2	0.058 9	1.155 4	0.088 0	-0.006 3
			指数	0.007 2	0.123 1	0.066 6	1.191 6	0.096 4	-0.026 7
			高斯	0.002 0	0.095 0	0.052 3	1.155 4	0.086 8	-0.008 1
S_-100	Box-Cox	二阶	环状	0.003 3	0.122 6	0.051 1	1.046 0	0.120 9	-0.001 7
			球状	0.004 2	0.122 4	0.054 1	1.052 3	0.117 5	-0.004 9
			指数	0.001 3	0.123 1	0.037 3	1.065 5	0.119 0	-0.004 1
			高斯	0.003 3	0.123 7	0.052 4	1.053 6	0.121 2	-0.002 5
S_-300	Box-Cox	二阶	环状	0.004 6	0.090 9	0.077 0	1.177 0	0.078 8	-0.012 1
			球状	0.004 5	0.091 0	0.080 5	1.190 8	0.078 5	-0.012 5
			指数	0.003 6	0.091 1	0.067 6	1.165 1	0.080 2	-0.010 9
			高斯	0.004 0	0.092 1	0.078 0	1.174 2	0.081 6	-0.010 5
SIRM (10^-6Am²/kg)	Log	二阶	环状	-122.876 0	6 449.196 5	-0.121 2	0.926 3	17 379.145 8	10 929.949 3
			球状	-128.563 4	6 461.123 0	-0.127 5	0.986 4	16 582.582 7	10 121.459 6
			指数	-98.082 1	6 475.628 5	-0.106 3	0.899 9	17 889.512 7	11 413.884 3
			高斯	-40.977 3	6 410.017 2	-0.112 6	0.896 6	18 731.884 0	12 321.866 7
HIRM (10^-5Am²/kg)	Log	二阶	环状	-0.237 4	64.429 3	-0.115 4	1.001 1	171.694 8	107.265 5
			球状	-0.344 1	64.758 5	-0.108 9	1.016 1	165.732 7	100.974 2
			指数	-0.744 2	65.471 6	-0.118 6	1.083 2	169.993 3	104.521 7
			高斯	0.449 9	67.668 4	-0.104 1	0.944 0	228.899 1	161.230 7

表4

表5

表6

表7

表8

参考文献 0

	Barima Y S, Angaman D M, N'Gouran K P, N'KoffiN' A, Kardel F,Cannière C D and Samson R. 2014. Assessing Atmospheric Particulate Matter Distribution Based on Saturation Isothermal Remanent Magnetization of Herbaceous and Tree Leaves in a Tropical Urban Environment.Science of the Total Environment, 470/471: 975-982.
	Canbay M, Aydin A and Kurtulus C.2010.Magnetic Susceptibility and Heavy-Metal Contamination in Topsoils along the Izmit Gulf Coastal Area and IZAYTAS (Turkey). Journal of Applied Geophysics, 70(1): 46-57.
	董志南，郑拴宁，赵会兵，董仁才．2015．基于空间插值的风场模拟方法比较分析.地球信息科学学报，17（1）：37-44.[Dong Zhinan, Zheng Shuanning, Zhao Huibing and Dong Rencai. 2015. Comparative Analysis of Methods of Wind Field Simulation Based on Spatial Interpolation. Journal of Geo-Information Science, 17(1): 37-44. ]
	Eldeiry A A and Garcial A. 2010. Comparison of Ordinary Kriging, Regression Kriging, and Cokriging Techniques to Estimate Soil Salinity Using LANDSAT Images. Journal of Irrigation and Drainage Engineering, 136(6): 355-364.
	Gotway C A, Ferguson R B, Hergert G W and Peterson T A. 1996. Comparison of Kriging and Inverse-Distance Methods for Mapping Soil Parameters.Soil Science Society of America Journal, 60(4): 1237-1247.
	广州市统计局. 2019. 广州统计年鉴.（2019-11-14）[2020-05-10]. http://112.94.72.17/portal/queryInfo/statistics Yearbook/index. [Guangzhou Statistics Bureau. 2019. Guangzhou Statistical Yearbook 2019.(2019-11-14) [2020-05-10]. http://112.94.72.17/portal/queryInfo/statisticsYearbook/index. ]
	Hay K L, Dearing J A, Baban S M J and Loveland P. 1997. A Preliminary Attempt to Identify Atmospherically Derived Pollution Particles in English Topsoils from Magnetic Susceptibility Measurements. Physics and Chemistry of the Earth, 22(1/2): 207-210.
	胡克林，李保国，吕贻忠，张凤荣. 2004. 非平稳型区域土壤汞含量的各种估值方法比较. 环境科学，25（3）：132-137. [Hu Kelin, Li Baoguo, Lv Yizhong and Zhang Fengrong.2004. Comparison of Various Spatial Interpolation Methods for Non-Stationary RegionalSoil Mercury Content. Environmental Science, 25(3): 132-137. ]
	Hanesch M and Scholger R. 2002. Mapping of Heavy Metal Loadings in Soils by Means of Magnetic Susceptibility Measurements. Environmental Geology, 42(8): 857-870.
	Hutchinson M F. 1998. Interpolation of Rainfall Data with Thin Plate Smoothing Splines- Part I: Two Dimensional Smoothing of Data with Short Range Correlation. Journal of Geographic Information and Decision Analysis, 2(2): 139-151.
	虎雄岗，谈树成，金艳珠，蒋顺德. 2012. 基于地形高程的云南省降雨量空间插值方法研究. 热带地理，32（4）：370-377. [Hu Xionggang, Tan Shucheng, Jin Yanzhu and Jiang Shunde. 2012. Rainfall Spatial Interpolation Methods Based on Terrain Elevation Model for Yunnan Province. Tropical Geography, 32(4): 370-377. ]
	Kamaci Z and Uysal G. 2017. Pollution Determined by Using Magnetic Susceptibility Measurements: A Case Study from İzmir-Aliağa. Acta Physica Polonica, 132(3): 487-489.
	刘爱利，王培法，丁园圆. 2011. 地统计学概论. 北京：科学出版社. [Liu Aili, Wang Peifa and Ding Yuanyuan. 2011. Introduction to Geostatistics. Beijing: Science Press. ]
	Laslett G M, Mcbratney A B, Pahl P J and Hutchinson H F. 2010.Comparison of Several Spatial Prediction Methods for Soil PH.European Journal of Soil Science, 38(2): 325-341.
	龙军，张黎明，沈金泉，周碧青，毛艳玲，邱龙霞，邢世和. 2014. 复杂地貌类型区耕地土壤有机质空间插值方法研究.土壤学报，51（6）：1270-1281. [Long Jun, Zhang Liming, Shen Jinquan, Zhou Biqing, Mao Yanling, Qiu Longxia and Xing Shihe. 2014. Spatial Interpolation of Soil Organic Matter in Farmlands in Areas Complex in Landform. Acta Pedologica Sinica, 51(6): 1270-1281. ]
	刘劲松，陈辉，杨彬云，王卫，相云，赵超. 2009. 河北省年均降水量插值方法比较. 生态学报，29（7）：3493-3500. [Liu Jinsong, Chen Hui, Yang Bingyun, Wang Wei, Xiang Yun and Zhao Chao. 2009. Comparison of Interpolation Methods on Annual Mean Precipitation in Hebei Province. Acta Ecologica Sinica, 29(7): 3493-3500. ]
	李俊晓，李朝奎，殷智慧. 2013. 基于ArcGIS的克里金插值方法及其应用. 测绘通报，（9）：87-90，97. [Li Junxiao, Li Zhaokui and Yin Zhihui. 2013. ArcGIS Based Kriging Interpolation Method and Its Application. Bulletin of Surveying and Mapping, (9): 87-90, 97. ]
	李璐，姜小三，孙永远. 2011. 基于地统计学的降雨侵蚀力插值方法研究——以江苏省为例.生态与农村环境学报，27（1）：88-92. [Li Lu, Jiang Xiaosan and Sun Yongyuan. 2011. Geostatistics-Based Spatial Interpolation Method for Study of Rainfall Erosivity—A Case Study of Jiangsu. Journal of Ecology and Rural Environment, 27(1): 88-92. ]
	雷凌明，喻大松，陈玉鹏，宋卫卫，梁东立. 2014. 陕西泾惠渠灌区土壤重金属空间分布特征及来源. 农业工程学报，30（6）：88-96. [Lei Liming, Yu Dasong, Chen Yupeng, Song Weiwei and Liang Dongli. 2014. Spatial Distribution and Sources of Heavy Metals in Soils of Jinghui Irrigated Area of Shaanxi, China.Transactions of the Chinese Society of Agricultural Engineering, 30(6): 88-96. ]
	李鹏，强小科，唐艳荣，符超峰，徐新文，李续彬. 2010. 西安市街道灰尘磁化率特征及其污染指示意义.中国环境科学，30（3）：309-314.[Li Peng, Qiang Xiaoke, Tang Yanrong, Fu Chaofeng, Xu Xinwei and Li Xuibin. 2010. Magnetic Susceptibility of the Dust of Street in Xi'an and the Implication on Pollution. China Environmental Science, 30(3): 309-314. ]
	刘青松，邓成龙. 2009. 磁化率及其环境意义. 地球物理学报，52（4）：1041-1048. [Liu Qingsong and Deng Chenglong. 2009. Magnetic Susceptibility and Its Environmental Significances. Chinese Journal of Geophysics, 52(4): 1041-1048. ]
	卢升高，白世强. 2008. 杭州城区土壤的磁性与磁性矿物学及其环境意义. 地球物理学报，51（3）：762-769. [Lu Shenggao and Bai Shiqiang. 2008. Magnetic Characterization and Magnetic Mineralogy of the Hangzhou Urban Soils and Its Environmental Implications. Chinese Journal of Geophysics, 51(3): 762-769. ]
	刘玮，辛美丽，吕芳，刘梦侠，丁刚，吴海一. 2018. 关于鼠尾藻群体数量分布的三种统计模型比较. 生态学报，38（6）：2031-2040. [Liu Wei, Xin Meili, Lv Fang, Liu Mengxia, Ding Gang and Wu Haiyi. 2018. Comparison of Three Statistical Models for the Quantitative Distribution of Sargassum Thunbergii Populations. Acta Ecologica Sinica, 38(6): 2031-2040. ]
	李新，程国栋，卢玲. 2000. 空间内插方法比较. 地球科学进展，15（3）：260-265. [Li Xin, Cheng Guodong and Lu Ling. 2000. Comparison of Spatial Interpolation Methods. Advances in Earth Science, 15(3): 260-265. ]
	林忠辉，莫兴国，李宏轩，李海滨. 2002. 中国陆地区域气象要素的空间插值. 地理学报，57（1）：47-56. [Lin Zhonghui, Mo Xingguo, Li Hongxuan and Li Haibin. 2002. Comparison of Three Spatial Interpolation Methods for Climate Variables in China. Acta Geographica Sinica, 57(1): 47-56. ]
	孟庆香，刘国彬，杨勤科.2010.基于GIS的黄土高原气象要素空间插值方法.水土保持研究，17（1）：10-14. [Meng Qingxiang, Liu Guobin and Yang Qinke. 2010. Spatial Interpolation Methods of Weather Data on Loess Plateau Based on GIS. Research of Soil and Water Conservation, 17(1): 10-14. ]
	聂燕，王新，王博，许淑婧，高福元，余晔，夏敦胜，夏昕鸣. 2015. 西北典型工矿型城市街道尘埃重金属污染的环境磁学响应. 环境科学，36（9）：3438-3446. [Nie Yan, Wang Xin, Wang Bo, Xu Shujing, Gao Fuyuan, Yu Ye, Xia Dunsheng and Xia Xinming. 2015. Magnetic Responses of Heavy Metals in Street Dust of Typical Mine-Based City, Northwest China. Envrionmental Science, 36(9): 3438-3446. ]
	Penizek V and Borůvka L. 2006. Soil Depth Prediction Supported by Primary Terrain Attributes: A Comparison of Methods. Plant Soil & Environment, 52(9): 424-430.
	秦俊桃，冯绍元，霍再林，康绍忠，王凤新. 2010. 几种地下水位空间插值方法在干旱内陆区的应用比较. 中国农业大学学报，15（5）：124-129. [Qin Juntao, Feng Shaoyuan, Huo Zailin, Kang Zhaozhong and Wang Fengxin. 2010. Applications of Spatial Interpolation Methods for Groundwater Levels in Arid Inland Area. Journal of China Agricultural University, 15(5): 124-129. ]
	Rossi R E, Mulla D J, Journel A G and Franz E H. 1992. Geostatistical Tools for Modeling and Interpreting Ecological Spatial Dependence. Ecological Monographs, 62(2): 277-314.
	Seyedmohammadi J, Esmaeelnjad L and Shabanpour M. 2016. Spatial Variation Modelling of Groundwater Electrical Conductivity Using Geostatistics and GIS. Modeling Earth Systems and Environment, 2(4): 169.
	孙然好，刘清丽，陈利顶. 2010. 基于地统计学方法的降水空间插值研究. 水文，30（1）：14-17，58. [Sun Ranhao, Liu Qingli and Chen Liding. 2010. Study on Precipitation Interpolation Based on the Geostatistical Analyst Method. Journal of China Hydrology, 30(1): 14-17, 58. ]
	孙智妍，周秋文，张思琪，韦小茶，马龙生. 2019. 喀斯特地区春季土壤水分空间插值方法对比. 热带地理，39（5）：770-779. [Sun Zhiyan, Zhou Qiuwen, Zhang Siqi, Wei Xiaocha and Ma Longsheng. 2019. Comparison and Analysis of Different Spatial Interpolation Methods of Soil Moisture Applied in Karst Area. Tropical Geography, 39(5): 770-779. ]
	汤国安，杨昕. 2006. ArcGIS地理信息系统空间分析实验教程. 北京：科学出版社. [Tang Guoan and Yang Xin. 2006. ArcGIS Geographic Information System Spatial Analysis Experiment Tutorial. Beijing: Science Press. ]
	Thompson R and Oldfield F. 1986. Environmental Magnetism. London: Allen and Unwin.
	谭万能，李志安，邹碧，丁永祯. 2005. 地统计学方法在土壤学中的应用. 热带地理，25（4）：307-311. [Tan Wanneng, Li Zhian, Zou Bi and Ding Yongzhen. 2005. The Application of Geostatistics to Soil Science. Tropical Geography, 25(4): 307-311. ]
	王博，夏敦胜，余晔，贾佳，许淑婧. 2012. 兰州城市表层土壤重金属污染的环境磁学记录. 科学通报，57（32）：3078-3089. [Wang Bo, Xia Dunsheng, Yu Ye, Jia Jia and Xu Shujing. 2012. Magnetic Records of Heavy Metal Pollution in Urban Topsoil in Lanzhou, China. Chinese Science Bulletin, 57(32): 3078-3089. ]
	王冠，陈裕颖，夏敦胜，任非凡，方爱冬，马丽娟. 2018. 上海城市表土磁性特征对重金属污染的指示作用.环境科学学报，38（8）：3302-3312. [Wang Guan, Chen Yuying, Xia Dunsheng, Ren Feifan, Fang Aidong and Ma Lijuan. 2018. Magnetic Property of Urban Topsoil and Its Implication of Heavymetal Pollution in Shanghai. Acta Scientiae Circumstantiae, 38(8): 3302-3312. ]
	王红，宫鹏，刘高焕. 2006. 黄河三角洲多尺度土壤盐分的空间分异. 地理研究，25（4）：649-658. [Wang Hong, Gong Peng and Liu Gaohuan. 2006. Multi-Scale Spatial Variations in Soil Salt in the Yellow River Delta. Geographical Research, 25(4): 649-658. ]
	汪明冲，张新长，王兮之，魏兴琥，李辉霞. 2016. 粤北岩溶区连江流域降雨侵蚀力. 热带地理，36（3）：495-502. [Wang Mingchong, Zhang Xinchang, Wang Xizhi, Wei Xinghu and Li Huixia. 2016. Rainfall Erosivity in the Lianjiang Watershed in Karst Areas of Northern Guangdong, China. Tropical Geography, 36(3): 495-502. ]
	王新，夏敦胜，王博，陈红，刘浩. 2017. 西北干旱区农田土壤磁性特征及其环境意义. 环境科学，38（8）：3507-3518. [Wang Xin, Xia Dunsheng, Wang Bo, Chen Hong and Liu Hao. 2017. Magnetic Properties of Farmland Soils in Arid Regions in Northwest China and Their Environmental Implications. Environmental Science, 38(8): 3507-3518. ]
	吴翼，朱照宇，邱世藩，饶志国. 2013. 1.95~0.40Ma黄土高原东南部风成沉积记录的亚洲冷干化进程.科学通报，58（27）：2823-2831. [Wu Yi, Zhu Zhaoyu, Qiu Shifan and Rao Zhiguo. 2013. A Rock Magnetic Record of Asian Cooling and Aridification Processes During 1.95~0.40 Ma in the Southeastern Chinese Loess Plateau. Chinese Science Bulletin, 58(27): 2823-2831. ]
	王志刚，赵永存，黄标，Darilek Jeremy Landon，孙维侠. 2010. 采样点数量对长三角典型地区土壤肥力指标空间变异解析的影响. 土壤，42（3）：421-428. [Wang Zhigang, Zhao Yongcun, Huang Biao, Darilek Jeremy Landon and Sun Weixia. 2010. Effects of Sample Size on Spatial Characterization of Soil Fertility Properties in an Agricultural Area of the Yangtze River Delta Region, China. Soils, 42(3): 421-428. ]
	徐建华. 2014. 计量地理学. 北京：高等教育出版社. [Xu Jianhua. 2014. Quantitative Geography. Beijing: Higher Education Press. ]
	易湘生，李国胜，尹衍雨，彭景涛. 2012. 土壤厚度的空间插值方法比较——以青海三江源地区为例.地理研究，31（10）：1793-1805. [Yi Xiangsheng, Li Guosheng, Yin Yanyu and Peng Jingtao. 2012. Comparison on Soil Depth Prediction among Different Spatial Interpolation Methods: A Case Study in Three-River Headwaters Region of Qinghai Province. Geographical Research, 31(10): 1793-1805. ]
	于洋，卫伟，陈利顶，杨磊，张涵丹. 2015. 黄土高原年均降水量空间插值及其方法比较. 应用生态学报，26（4）：999-1006. [Yu Yang, Wei Wei, Chen Liding, Yang Lei and Zhang Handan. 2015. Comparison on the Methods for Spatial Interpolation of the Annual Average Precipitation in the Loess Plateau Region. Chinese Journal of Applied Ecology, 26(4): 999-1006. ]
	赵冰雪，王雷，程东亚. 2017. 安徽省气象数据空间插值方法比较与分布特征.水土保持研究，24（3）：141-145. [Zhao Bingxue, Wang Lei and Cheng Dongya. 2017. Comparison of Spatial Interpolation Method for Meteorological Data and Distribution Characteristic in Anhui Province. Research of Soil and Water Conservation, 24(3): 141-145. ]
	张甘霖，赵玉国，杨金玲，赵文君，龚子同. 2007. 城市土壤环境问题及其研究进展. 土壤学报，44（5）：925-933. [Zhang Ganlin, Zhao Yuguo, Yang Jinling, Zhao Wenjun and Gong Zitong. 2007. Urban Soil Environment Issues and Research Progresses. Acta Pedologica Sinica, 44(5): 925-933. ]
	庄国泰. 2015.我国土壤污染现状与防控策略.中国科学院院刊，30（4）：477-483. [Zhuang Guotai. 2015. Current Situation of National Soil Pollution and Strategies on Prevention and Control. Bulletin of Chinese Academy of Sciences, 30(4): 477-483. ]
	卓静，朱延年. 2017. 秦岭主脊区年降水量空间插值最优方法研究.干旱区地理，40（3）：555-563. [Zhuo Jing and Zhu Yannian. 2017. Spatial Interpolation Methods of Annual Average Precipitation on Qinling Mountains. Arid Land Geography, 40(3): 555-563. ]
	朱蕾，黄敬峰. 2007. 山区县域尺度降水量空间插值方法比较. 农业工程学报，23（7）：80-85. [Zhu Lei and Huang Jingfeng. 2007. Comparison of Spatial Interpolation Method for Precipitation of Mountain Areas in County Scale.Transactions of the Chinese Society of Agricultural Engineering, 23(7): 80-85. ]
	张仁平，张云玲，郭靖，冯琦胜，梁天刚. 2018. 新疆地区降水分布的空间插值方法比较. 草业科学，35（3）：521-529. [Zhang Renping, Zhang Yunling, Guo Jing, Feng Qisheng and Liang Tiangang. 2018. Comparison of Spatial Interpolation Methods for Precipitation Distribution in Xinjiang Region. Pratacultural Science, 35(3): 521-529. ]
	Zhang X Y, Sui Y Y, Zhang X D, Meng K and Herbert S J. 2007. Spatial Variability of Nutrient Properties in Black Soil of Northeast China. Pedosphere, 17(1): 19-29.

磁学参数代码	名称	物理意义	测量仪器/计算方法
χ_lf	低频磁化率	反映样品中磁性颗粒的总含量	卡帕桥多频各向异性磁化率仪（MFK1），频率1
χ_hf	高频磁化率	反映样品中除超顺磁颗粒以外的磁性颗粒含量	卡帕桥多频各向异性磁化率仪（MFK1），频率3
χ_ARM	非磁滞剩磁磁化率	反映样品中磁性颗粒的含量，对单畴颗粒敏感	交变退磁仪（D2000）100 mT峰值场叠加0.05 mT直流场下获得、双速旋转磁力仪（JR-6）测试ARM，然后利用χ_ARM=ARM/DC计算得到χ_ARM，其中DC为0.05 mT的弱直流磁场
χ_fd	频率磁化率	反映样品中超顺磁颗粒的含量	χ_fd= χ_lf?χ_hf（刘青松等，2009）
χ_fd(%)	频率磁化率系数	反映样品中超顺磁颗粒对磁化率的贡献	χ_fd(%)=χ_fd /χ_lf×100%（刘青松等，2009）
SIRM	饱和等温剩磁	反映样品中磁性颗粒的含量	脉冲磁化仪（IM-10-30）2T下获得，双速旋转磁力仪（JR-6）测试
HIRM	硬剩磁	反映样品中硬磁性颗粒的含量	HIRM = (SIRM+IRM_-300mT)/2（吴翼等，2013）
χ_ARM/χ	非磁滞剩磁磁化率与磁化率的比值	反映样品中磁性颗粒的粗细，值越大颗粒越细	如指标所示计算
SIRM/χ	饱和等温剩磁与磁化率的比值		如指标所示计算
χ_ARM/SIRM	非磁滞剩磁磁化率与饱和等温剩磁的比值		如指标所示计算
S₁₀₀	S-比值	反映样品中软磁性矿物与硬磁性矿物的相对含量	100 mT磁场下的等温剩磁（IRM_100mT）与SIRM的比值
S₃₀₀	S-比值		300 mT磁场下的等温剩磁（IRM_300mT）与SIRM的比值
S_-100	S-比值		反向100 mT磁场下的等温剩磁（IRM_-100mT）与SIRM的比值
S_-300	S-比值		反向300 mT磁场下的等温剩磁（IRM_-300m）与SIRM的比值

磁学参数	最小值	最大值	平均值	标准差	变异系数/%	K-S
χ_ARM(10^-8m³/kg)	3.617	1 182.120	147.417	193.943	131.561	0.00
χ_lf (10^-8m³/kg)	0.801	990.109	46.549	82.795	177.868	0.00
χ_hf (10^-8m³/kg)	0.759	988.641	44.506	81.262	182.586	0.00
χ_fd (10^-8m³/kg)	0.001	23.664	2.043	3.003	147.029	0.00
χ_fd(%)	0.014	17.790	4.989	3.630	72.749	0.00
χ_ARM/χ	0.291	34.630	3.842	2.182	56.798	0.00
χ_ARM/SIRM(10^-5m/A)	1.010	560.100	41.670	35.002	83.998	0.00
SIRM/χ (kA/m)	2.133	49.257	10.536	4.549	43.174	0.00
S₁₀₀	0.010	0.939	0.636	0.126	19.831	0.06
S₃₀₀	0.076	0.976	0.833	0.103	12.381	0.00
S_-100	0.039	0.920	0.697	0.130	18.723	0.00
S_-300	0.113	1.001	0.845	0.101	11.995	0.00
SIRM(10^-6Am²/kg)	92.800	98 064.500	5 060.193	8 469.926	167.383	0.00
HIRM(10^-5Am²/kg)	1.254	784.516	53.510	71.880	134.330	0.00

磁学参数	权重=1		权重=2		权重=3		权重=4		权重=5
磁学参数	ME	RMSE	ME	RMSE	ME	RMSE	ME	RMSE	ME	RMSE
χ_ARM(10^-8m³/kg)	1.047 1	128.208 8	1.405 2	132.789 5	1.685 4	140.695 8	2.115 4	148.418 3	2.667 2	154.623 4
χ_lf(10^-8m³/kg)	-0.641 7	74.794 8	-1.647 4	75.131 0	-1.881 0	76.636 8	-1.820 4	78.176 8	-1.675 9	79.468 9
χ_hf(10^-8m³/kg)	-0.644 8	73.706 1	-1.665 1	73.996 7	-1.901 5	75.405 7	-1.842 2	76.847 9	-1.701 5	78.060 6
χ_fd(10^-8m³/kg)	0.003 0	2.690 4	0.017 7	2.766 2	0.020 5	2.905 5	0.021 8	3.043 4	0.025 6	3.153 8
χ_fd(%)	0.023 6	3.419 3	0.067 1	3.439 3	0.075 0	3.572 4	0.073 7	3.737 7	0.071 0	3.880 4
χ_ARM/χ	0.018 4	2.177 7	0.022 6	2.223 7	0.020 4	2.318 2	0.017 3	2.402 6	0.012 4	2.454 6
χ_ARM/SIRM(10^-5m/A)	0.300 6	33.874 1	0.173 4	34.294 6	0.028 8	35.504 3	-0.035 4	36.660 3	-0.081 4	37.382 7
SIRM/χ(kA/m)	0.011 1	4.112 9	0.074 4	4.172 6	0.100 3	4.377 9	0.110 9	4.615 6	0.119 6	4.824 4
S₁₀₀	0.000 2	0.119 6	-0.001 5	0.120 8	-0.003 0	0.126 6	-0.004 2	0.133 4	-0.005 2	0.138 9
S₃₀₀	-0.000 3	0.095 2	-0.001 6	0.095 6	-0.002 4	0.100 2	-0.003 0	0.105 9	-0.003 5	0.110 7
S_-₁₀₀	0.000 1	0.120 9	-0.001 6	0.121 8	-0.002 9	0.127 3	-0.003 8	0.133 9	-0.004 4	0.139 3
S-₃₀₀	0.000 1	0.092 5	-0.001 1	0.092 9	-0.001 8	0.097 2	-0.002 3	0.102 6	-0.002 7	0.107 1
SIRM(10^-6Am²/kg)	44.596 8	6 456.401 1	26.827 9	6 679.320 9	8.487 0	6 996.133 9	8.402 7	7 298.996 9	23.292 1	7 563.901 4
HIRM(10^-5Am²/kg)	0.204 9	59.099 8	0.408 9	61.473 1	0.127 5	64.220 4	-0.073 0	66.750 8	-0.085 8	68.977 1

磁学参数	规则样条函数		张力样条函数		高次曲面函数		反高次曲面函数		薄板样条函数
磁学参数	ME	RMSE	ME	RMSE	ME	RMSE	ME	RMSE	ME	RMSE
χ_ARM(10^-8m³/kg)	0.493 7	133.385 3	0.400 5	131.791 0	0.789 0	144.762 0	0.032 3	130.309 2	1.281 8	164.688 1
χ_lf (10^-8m³/kg)	-0.327 0	76.625 3	-0.247 3	76.366 8	-0.914 0	79.272 0	0.397 0	76.625 8	-0.979 2	81.363 1
χ_hf (10^-8m³/kg)	-0.331 5	75.508 2	-0.249 9	75.265 0	-0.926 0	78.018 4	0.406 2	75.530 5	-0.993 2	79.806 5
χ_fd(10^-8m³/kg)	0.004 5	2.785 1	0.002 6	2.756 7	0.012 1	3.040 2	-0.018 2	2.699 9	0.014 0	3.468 9
χ_fd(%)	0.006 6	3.447 9	0.003 8	3.423 2	0.000 7	3.714 0	-0.028 2	3.433 1	-0.024 6	4.236 7
χ_ARM/χ	0.002 1	2.259 2	0.002 0	2.236 9	-0.005 2	2.479 7	-0.004 2	2.176 3	-0.010 9	2.788 9
χ_ARM/SIRM(10^-5m/A)	-0.031 2	34.872 0	-0.009 8	34.591 7	-0.279 9	37.723 5	0.010 4	33.900 0	-0.570 6	41.884 6
SIRM/χ(kA/m)	0.023 8	4.185 6	0.017 6	4.152 8	0.063 0	4.589 9	-0.009 1	4.115 1	0.104 9	5.362 7
S₁₀₀	-0.000 7	0.120 2	-0.000 5	0.119 5	-0.001 5	0.128 3	0.000 5	0.119 3	-0.001 9	0.142 8
S₃₀₀	-0.000 5	0.095 6	-0.000 4	0.095 0	-0.000 7	0.102 4	0.000 5	0.095 2	-0.000 4	0.113 6
S_-100	-0.000 6	0.121 2	-0.000 5	0.120 6	-0.001 0	0.128 3	0.000 6	0.120 8	-0.000 7	0.141 1
S_-300	-0.000 4	0.092 7	-0.000 3	0.092 2	-0.000 5	0.098 9	0.000 6	0.092 5	-0.000 1	0.109 4
SIRM(10^-6Am²/kg)	16.980 9	6 705.550 6	16.986 7	6 650.202 8	12.207 4	7 069.443 1	24.409 1	6 602.762 7	51.871 6	7 784.194 4
HIRM(10^-5Am²/kg)	0.059 6	61.434 1	0.050 5	60.960 6	0.030 5	65.412 3	-0.622 5	59.609 2	0.180 7	74.296 1

磁学参数	IDW（权重）	RBF（函数）	最优确定性法
χ_ARM	1	反高次曲面	RBF反高次曲面
χ_lf	1	张力	RBF反高曲面次
χ_hf	1	张力	RBF反高次曲面
χ_fd	1	张力	IDW权重为1或RBF张力
χ_fd(%)	1	张力	RBF张力
χ_ARM/χ	1	张力	RBF张力
χ_ARM/SIRM	3	反高次曲面	RBF反高次曲面
SIRM/χ	1	反高次曲面	IDW权重为1或RBF反高次曲面
S₁₀₀	1	反高次曲面	IDW权重为1
S₃₀₀	1	张力	IDW权重为1或RBF张力
S_-100	1	张力	IDW权重为1
S_-300	1	薄板	IDW权重为1
SIRM	3	高次曲面	IDW权重为3
HIRM	4	高次曲面	RBF高次曲面