Spatial variation analysis of soil organic matter in karst area
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摘要:
采用GIS和地统计学研究土壤有机质（SOM）的空间分布、影响因素和预测是指导农业生产、环境治理和土壤碳储计量的重要手段。基于广西马山县北部岩溶区表层土壤 (0~20 cm)的441个SOM数据，建立普通克里格(OK)、回归克里格（RK），以及结合辅助变量的地理加权回归克里格(GWRK)、残差均值（MM_OK）和中值（MC_OK）均一化克里格的5种模型，并比较其预测精度，旨在探讨岩溶区SOM制图中地统计学方法的适用性。结果表明：（1）SOM的变异系数为37.30%，属于中等空间变异；（2）岩溶区SOM空间变异受土地利用方式、土壤类型和地形因子等因素共同影响，SOM高值区分布在西北部、西部和东部等石灰土分布的岩溶区和水田，低值区位于北部红水河沿岸的冲积土地带；（3）RK、GWRK、MM_OK和 MC_OK对SOM解释能力均较优，可用于岩溶区SOM预测制图。结合辅助变量因子的GWRK预测模型能有效消除空间变异因素的影响，克服岩溶区SOM含量的空间非平稳性，从而提高SOM含量模型的稳定性和精度，同时MC_OK模型能提高预测的准确度。
Abstract:As an important parameter for soil quality assessment, soil organic matter (SOM) can provide nutrients for crops, strengthen soil fertility, and improve soil physicochemical properties. Besides, SOM also plays an important role in restricting the activity of heavy metal elements and pesticide residues, and in regulating CO2 in soil. Therefore, the study on spatial distribution of SOM, its influence factors and prediction by GIS and geostatistical analysis is important in agricultural practice, environmental management and the measurement of soil carbon storage.The content of SOM is easily affected by the factors such as geological background, climate change, agricultural activities and land use change. Hence the complexity and non-stationarity of the spatial variability of SOM will make it difficult for the quantitative prediction. The high heterogeneity of SOM and insufficient sampling data in the karst area also leads to low accuracy of spatial prediction. Guangxi is one of the areas with the most widely distributed karst areas in China. Typical karst landforms are developed in the northern part of Mashan county, with a range of land use and parent materials. Different patterns of land use include paddy field, dry land, shrub land, forest land, orchard and grassland, accounting for 10.55%, 29.39%, 29.49%, 12.86%, 0.70% and 0.66% respectively. Paddy fields, consisting of paddy soil, are located in karst valleys; dry lands, consisting of red soil, brown lime soil, and alluvial soil, are distributed at the bottom of slopes and karst depressions on both sides of the valley; shrubland and forest land, mainly consisting of brown lime soil and red soil, spread over mountains. A total of 441 SOM data, with 8 high-density topsoil (0-20 cm) samples per km2 on average, were obtained in the geochemical survey of land quality in the northern karst area of Mashan county, Guangxi in 2017. The data facilitates the spatial prediction of highly heterogeneous SOM in karst areas.In this paper, qualitative variables such as land uses and soil types were converted into quantitative variables through the assignment method of dummy variables, and terrain factors were used as auxiliary variables to meet the requirement of geostatistical regression analysis. With the purpose of exploring the applicability of geostatistical SOM mapping in karst areas, this study respectively established five method models—ordinary Kriging (OK), regression Kriging (RK), Geographically Weighted Regression Kriging (GWRK), Ordinary Kriging of Median Centralization (MC_OK) and Mean Modified Ordinary Kriging (MM_OK)—to compare the prediction results, and select the most suitable prediction model for the karst area.. Results show that the SOM content in the study area ranges from 0.81% to 5.03%, with an average of 2.36%, and the coefficient of variation is 37.3%. The spatial distribution is moderate spatial variation. Results of geostatistical analysis by GS+9.0 show that the fitted theoretical variogram models are all exponential ones. Both nugget value and abutment value are less than 25%, which indicates that there is a certain spatial autocorrelation, and the SOM content is mainly affected by structural factors; hence correlation interpolation analysis can be carried out.In addition, the spatial variation of SOM in the karst area is jointly affected by land use, soil types and topographical factors. The areas with high content of SOM are located respectively in the karst areas and paddy fields where lime soil is distributed in the northwest, west and east of the study area, and the areas with low content are located in the alluvial land along the Hongshui river in the north of the study area. The SOM content shows significantly positive correlation with paddy fields because the reducing environment of paddy fields is conducive to the preservation and accumulation of SOM. But SOM content shows significantly negative correlation with dry land due to the oxidative environment of this land type where frequent disturbance and rapid degradation of SOM will occur.Finally, RK, GWRK, MM_OK and MC_OK can be used for SOM prediction and mapping in karst areas because of their good interpretability. The results of internal verification show that the root-mean-square of GWRK is the smallest, and the average standard error is close to root-mean-square, indicating the better fitness of GWRK model. The results of external verification demonstrate that the mean absolute error and root mean squares error of GWRK are the smallest, suggesting the highest precision and the best stability of GWRK model. Meanwhile, MC_OK shows its best accuracy. Combined with auxiliary variable factors such as land use, soil types, and topography, GWRK model can effectively eliminate the influence of spatial variation factors and overcome the spatial non-stationarity of SOM content in karst areas, thereby improving the stability and precision of the SOM prediction model, while MC_OK model can improve the prediction accuracy.
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表 1 SOM描述性统计
Table 1. Descriptive statistics of SOM
指标 样本数 最大值/
%最小值/
%平均值/
%标准差
（SD）变异系数
（CV）/%峰度 偏度 K-S检验 土地利用方式 水田 83 5.03 1.66 3.56a 0.69 19.90 − − − 旱地 259 4.45 0.81 1.92c 0.58 30.20 − − − 林地 99 3.93 1.02 2.51b 0.64 25.50 − − − 土壤类型 水稻土 98 5.03 0.91 3.19a 0.93 29.10 − − − 红壤 66 4.48 0.93 2.12b 0.77 36.10 − − − 赤红壤 122 4.45 1.02 2.18b 0.66 30.20 − − − 石灰土 95 4.06 1.03 2.28b 0.65 28.30 − − − 冲积土 60 4.30 0.81 1.78c 0.72 40.40 − − − 总样本 441 5.03 0.81 2.36 0.88 37.30 2.83 0.76 0.00 对数转换 − − − − − − 5.52 0.03 0.15 注：平均值列的不同小写字母对应显著性表现。 
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表 2 研究区SOM含量与土地利用方式和土壤类型Pearson相关系数
Table 2. Pearson correlation coefficient of SOM and types of land use and soil
水田 旱地 林地 水稻土 冲积土 赤红壤 红壤 石灰土 相关系数 0.676** −0.622** 0.090 0.526** −0.269** −0.153** −0.131** −0.047 注：**在0.01水平（双侧）上显著相关。
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表 3 OLS模型诊断结果
Table 3. Diagnostic results of OLS model
AICc R2 F-Stat F-Prob Wald-Prob K(BP) K(BP)_Prob JB-Prob 787 0.56 63.9 0.00* 0.00* 25.6 0.002* 0.00* 注：**在0.01水平（双侧）上显著相关。
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表 4 OLS模型诊断系数结果
Table 4. Results of diagnostic coefficient of OLS model
变量 系数 P Robust_SE Robust_t Robust_Pr StdCoef VIF 截距 2.18 0.00 0.26 8.33 0.00 0.00 − 土地
利用水田 0.91** 0.00 0.15 6.13 0.00 0.41 3.06 旱地 −0.56** 0.00 0.08 −6.71 0.00 −0.31 2.02 土壤
类型水稻土 0.28** 0.01 0.13 2.16 0.03 0.13 2.99 赤红壤 0.01 0.95 0.09 0.06 0.95 0.00 2.02 石灰土 0.21* 0.03 0.09 2.33 0.02 0.10 1.98 冲积土 −0.24* 0.02 0.09 −2.84 0.00 −0.10 1.58 地形
因子高程 0.00 0.17 0.00 1.17 0.24 0.06 2.17 坡度 0.00 0.61 0.00 −0.52 0.60 −0.02 1.89 坡向 0.00 0.58 0.00 −0.52 0.60 −0.02 1.09 注：**和*分别在0.01和0.05水平（双侧）上显著相关；土壤类型、土地利用类型使用哑变量处理；P为Probability 概率；Robust_SE为标准差健壮度；Robust_t为T统计量健壮度；Robust_Pr为概率健壮度；StdCoef为回归系数的标准差；VIF为方差膨胀因子。
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表 5 地理加权回归模型拟合参数
Table 5. Fitting parameters of geographically weighted regression model
平滑程度 残差平方和 标准化剩余平方和 AICc R2 校正R2 GWR 3343.22 123.74 0.56 774 0.64 0.59
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表 6 不同插值处理的SOM半方差函数模型与参数
Table 6. Semi-variogram function model for SOM and its corresponding parameters with different methods
方法 理论模型 预测
系数R2变程（A0）
/m块金值
（C0）基台值
（C0+C）结构方差
（C）块金值/基台值
（C0/C0+C）/%OK 指数模型 0.692 1050 0.0155 0.139 0.1235 11.2 RK 指数模型 0.192 480 0.0565 0.371 0.3145 15.2 GWRK 指数模型 0.188 450 0.0525 0.320 0.2675 16.4 MC_OK 指数模型 0.186 450 0.0556 0.320 0.2644 17.4 MM_OK 指数模型 0.187 450 0.0522 0.320 0.2678 16.3
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表 7 不同模型预测精度评价
Table 7. Precision assessment of SOM content prediction with different methods
方法 内部验证 外部验证 MSE RMSS RMS ASE MAE RMSE AC/% r R2 OK −0.0167 1.0028 0.8166 0.8536 0.6822 0.8724 30.8 0.23 0.14 RK 0.0087 0.9836 0.5983 0.5983 0.4626 0.5844 71.9 0.71 0.48 GWRK −0.0218 0.9797 0.5464 0.5546 0.3912 0.4960 79.4 0.79 0.63 MC_OK 0.0075 1.0764 0.5605 0.5211 0.4202 0.5215 89.3 0.77 0.58 MM_OK 0.0071 0.9890 0.5637 0.5703 0.4632 0.5775 87.0 0.72 0.49
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