Prediction of spatial distribution of soil organic matter based on improved OK models: A case study of Honghuatao Town in Yidu City
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摘要: 选择合适的土壤有机质（SOM）预测模型是提高区域化空间分布模拟精度的前提，也是监测土壤碳库动态变化和指导农田土壤肥力投入的基础。以湖北宜都红花套镇柑橘区为例，设置普通克里格（OK）插值的SOM结果作对照，分别建立SOM及其最显著相关辅助变量碱解氮间的建模协同克里格（COK1）、全局协同克里格（COK2）和两个融合辅助变量协同相关性的改进OK模型（CCOK1、CCOK2），探讨纳入辅助变量、改变辅助信息插值数量以及结合辅助变量协同相关性对SOM含量预测的影响。结果表明：1）OK、CCOK1和CCOK2的块基比为25%~75%，表现出中等空间自相关性，而COK1和COK2的块基比小于25%，具有强烈的空间自相关，SOM的空间异质性受结构性因素影响的比重更大。2）SOM的预测含量范围为7.38~29.03 g·kg-1，使用COK1和COK2模型插值获得的有机质空间分布较OK更为破碎，CCOK1和CCOK2的插值结果则呈连续片状分布，更符合研究区土地利用类型分布的实际情况。3）SOM的空间分布预测精度由高到低依次为CCOK1 ≈ CCOK2 > COK2 > COK1 ≈ OK，OK和COK1两者精度指标相近，COK2的拟合效果有一定改进，但CCOK1和CCOK2的相关系数（r）分别从0.10升高到0.70和0.69，均方根误差（RMSE）分别降低了15.40%和14.78%，预测精度最高。因此，本研究提出的融合辅助变量协同相关性的改进OK模型的估算效果最优且在最大程度上提高辅助信息的参与度，可为SOM预测提供参考。Abstract: Choosing a suitable prediction model to estimate soil organic matter (SOM) content is not only a prerequisite to improve the accuracy of spatial distribution simulation, but also the basis for monitoring dynamic changes in soil carbon pool and for guiding soil fertility input in farming. In order to achieve this, a research was set up to investigate the advantages of combined traditional Ordinary Kriging (OK) interpolation and Co-Kriging (COK) interpolation in constructing a new model that integrates Cooperative Correlation of auxiliary variables with OK model (CCOK). The following three aspects were thus discussed:1) whether the inclusion of auxiliary variables had an impact on SOM prediction result; 2) what were the differences in SOM prediction results caused by changes in the number of auxiliary information interpolations; and 3) how improved SOM prediction accuracy by cooperative correlation of auxiliary variables. To address these research questions, we collected 329 soil samples from a citrus plantation in Honghuatao Town located in the north Yidu City, Hubei Province. Through physical and chemical analysis, 14 soil properties were extracted. The correlation between SOM and other soil properties were discussed based on Pearson correlation coefficient (r) and available nitrogen was chosen as model auxiliary variable with the most significant correlation with SOM. With reference of OK (the control), we constructed modeling COK (COK1), global COK (COK2) and two improved OK models (CCOK1 and CCOK2). Among the models, COK1 was a COK model which used modeling set auxiliary variables to participate in modeling. Based on COK1, COK2 changed the modeling set auxiliary variables to global auxiliary variables. CCOK1 and CCOK2 represented the OK interpolation models of two forms of functions constructed by the target variables and its auxiliary variables. Some of the results obtained were as follows:1) the range of the nugget/sill proportions of OK, CCOK1 and CCOK2 were 25%-75%, which belonged to medium spatial autocorrelation. However, the nugget/sill proportions of COK1 and COK2 were less than 25%, belonging to strong spatial autocorrelation. It then showed that the spatial variability of SOM as cross-variance function with auxiliary variables was more easily recognized by semi-variogram models. 2) The predicted SOM in the study area was within 7.38-29.03·kg-1. Compared with OK interpolation, the strong spatial autocorrelation of COK1 and COK2 meant that the spatial distribution of SOM was even more fragmented. Furthermore, plots of CCOK1 and CCOK2 predictions were flaky, with digital mapping results of SOM with higher or lower values, which was more consistent with the actual distribution of land use in the study area. 3) The accuracies of COK1 and OK were similar, but that of COK2 was higher than the above two. Nevertheless, the correlation coefficients (r) of CCOK1 and CCOK2 increased from 0.10 to 0.70 and 0.69, with root mean square errors (RMSE) decreasing by 15.40% and 14.78%, respectively. Finally, the overall accuracy of SOM digital soil mapping was CCOK1 ≈ CCOK2 > COK2 > COK1 ≈ OK. This indicated that CCOK model minimized error between measured and predicted values in SOM prediction. Thus, the synergy of combined SOM estimation and auxiliary variables was a better correlation than the addition of only auxiliary variables or changing the amount of auxiliary variables. The improved OK model proposed in this study improved the maximum participation of auxiliary information, thereby providing a reliable reference for SOM prediction.
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图 1 研究区地理位置、土地利用概况及土壤样点分布
Figure 1. Geographical location, land use profile and soil sample distribution in the study area
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图 2 研究区不同克里格插值模型的土壤有机质半方差函数图
Figure 2. Semivariograms of soil organic matter with different Kriging interpolation models in the study area
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图 3 不同克里格插值模型对研究区土壤有机质空间分布预测的异同
Figure 3. Similarities and differences of predicted spatial distribution of soil organic matter (SOM) by different Kriging interpolation models in the study area
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图 4 不同克里格插值模型对研究区土壤有机质预测的精度指标对比
Figure 4. Comparison of accuracy indexes of predicted soil organic matter content by different Kriging interpolation models in the study area
表 1 研究区样点土壤属性数据获取内容及方法
Table 1 Contents and obtaining methods of attribute data of soil samples in the study area
变量名称
Variable name获取方法
Method有机质Soil organic matter (g·kg-1) 重铬酸钾容量法-外加热法Potassium dichromate volumetric method - external heating method 酸碱度pH 水浸提-电位计法Water extraction - potentiometer method 全氮Total nitrogen (g·kg-1) 半微量开氏法Semi-micro Kjeldahl method 全磷Total phosphorus (g·kg-1) 氢氧化钠熔融-钼锑抗比色法Sodium hydroxide melting - molybdenum antimony anti-colorimetric method 全钾Total potassium (g·kg-1) 氢氧化钠熔融-火焰光度法Sodium hydroxide melting - flame photometry 全铜Total bronze (mg·kg-1) 原子吸收光谱法Atomic absorption spectroscopy 碱解氮Available nitrogen (mg·kg-1) 碱解扩散法Alkaline diffusion method 速效磷Available phosphorus (mg·kg-1) 0.5 mol·L-1碳酸氢钠法0.5 mol·L-1 sodium bicarbonate method 速效钾Available potassium (mg·kg-1) 醋酸铵浸提-火焰光度法Ammonium acetate extraction - flame photometry 有效锌Available zinc (mg·kg-1) DTPA-TEA浸提-原子吸收光谱法DTPA-TEA extraction - atomic absorption spectroscopy 有效铁Available iron (mg·kg-1) DTPA溶液浸提-原子吸收光谱法DTPA extraction - atomic absorption spectroscopy 阳离子交换量Cation exchange capacity (cmol·kg-1) 乙酸钠-火焰光度法Sodium acetate - flame photometry 交换性钙Exchangeable calcium (cmol·kg-1) 乙酸铵交换-原子吸收光谱法Ammonium acetate exchange - atomic absorption spectroscopy 交换性镁Exchangeable magnesium (cmol·kg-1) 
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表 2 研究区土壤有机质含量的基本统计特征
Table 2 Basic statistical characteristics of soil organic matter content of the study area
样本量
Simple size平均值
Mean (g·kg-1)最小值
Min (g·kg-1)最大值
Max (g·kg-1)极差
Range (g·kg-1)标准差
SD (g·kg-1)变异系数
CV (%)偏度系数
Skewness峰度系数
Kurtosis正态分布检验
K-S分布类型
Type of distribution全部数据
All dataset329 16.97 6.07 29.18 23.11 4.22 24.87 0.05 0.02 0.800 正态
Normality建模集
Calibration dataset263 17.24 7.18 29.18 22.00 4.09 23.72 0.07 -0.08 0.949 正态
Normality验证集
Validation dataset66 15.91 6.07 28.67 22.60 4.60 28.91 0.14 0.30 0.960 正态
Normality
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表 3 研究区土壤有机质与影响因子的相关性
Table 3 Correlation between soil organic matter and its influencing factors in the study area
土壤有机质
Soil organic matter碱解氮
Available nitrogen有效铁
Available iron交换性镁
Exchangeable magnesium全氮
Total nitrogen阳离子交换量
Cation exchange capacity速效钾
Available potassium全磷
Total phosphorus土壤有机质
Soil organic matter1.000 0.815** 0.483** -0.361** 0.266** -0.232** -0.155* 0.141* **和*分别表示在0.01和0.05水平(双侧)上显著。** and * indicate significant correlation at 0.01 and 0.05 levels (bilateral), respectively.
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表 4 研究区土壤有机质、碱解氮空间自相关与交互相关分析
Table 4 Spatial autocorrelation and cross-correlation analysis of soil organic matter and available nitrogen in the study area
莫兰指数
Moran’s IP值
P-valueZ得分
Z-value土壤有机质(SOM)
Soil organic matter0.11 0.02 2.14 碱解氮(AN)
Available nitrogen0.08 0.07 1.48 SOM/AN 0.19 0.00 3.47 AN/SOM 0.15 0.00 2.68
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表 5 研究区不同克里格插值模型的土壤有机质半方差模型参数
Table 5 Parameters of soil organic matter semi-variance models with different Kriging interpolation models in the study area
插值方法
Kriging interpolation method拟合模型
Model模型参数
Model parameter预测误差
Prediction error块金值
Nugget (C0)拱高
Partial sill (C)基台值
Sill (C0+C)块基比
Proportion [C0/(C0+C), %]变程
Range (m)步长
Lag (m)平均值
Mean (gkg-1)均方根误差
RMSE(gkg-1)OK 高斯模型Gaussian 10.14 6.12 16.26 62.36 194.03 27.13 0.02 4.22 COK1 球状模型Spherical 0.00 16.50 16.50 0.00 194.03 26.72 -0.05 2.40 COK2 指数模型Exponential 4.00 12.74 16.74 23.89 203.51 28.10 -0.01 2.73 CCOK1 指数模型Exponential 0.02 0.01 0.03 66.67 3 627.41 302.28 0.00 0.17 CCOK2 指数模型Exponential 0.21 0.43 0.64 32.81 194.03 31.54 0.01 0.85 OK为普通克里格; COK1和COK2分别为协同克里格和全局协同克里格; CCOK1和CCOK2为两个融合辅助变量协同相关性的改进OK。OK: ordinary Kriging; COK1 and COK2 are modeling Cokriging and global Cokriging; CCOK1 and CCOK2 are two improved OK models with cooperative correlation of auxiliary variables.
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