CoKriging Method Based on Principal Components to Predict Spatial Distribution of Arsenic in Groundwater
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摘要: 针对目前地下水砷含量的空间模拟考虑的影响因素较少，导致预测精度较低的问题.以江汉平原东部地区为例，利用地下水水化学组分对砷的影响，采用普通克里金(OK)、传统协克里金(COK)和基于主成分的协克里金(COK-Y，Y为经主成分分析得到的综合因子)对地下水体砷含量的空间分布进行模拟.结果表明：COK-Y模型的半变异函数拟合最佳，其预测结果的均方误差和平均绝对误差较OK分别降低21.7%、21.3%；较COK相差不大，分别降低3.5%、3.4%.COK-Y模型预测精度有所提升，绘制的地下水砷空间分布图更能反映砷的高度异质性，最大程度改善了克里金法的削弱效应，更符合实际.综合因子Y指示了地下水中各组分对地下水砷含量分布模拟的贡献，铁的氧化物及氢氧化物还原性溶解是高砷地下水的形成分布的主要因素，多金属矿物如重晶石、磁铁矿和钛铁矿等的风化溶蚀、解析吸附作用也对其有一定的贡献.Abstract: Few factors are considered in the current spatial simulation of arsenic content in groundwater, resulting in low prediction accuracy. To the east of Jianghan Plain as an example, considering the effects of all groundwater chemical components on arsenic, ordinary kriging (OK), traditional CoKriging (COK) and CoKriging based on principal component (COK-Y, where Y is a comprehensive factor obtained by principal component analysis) were used to simulate the spatial distribution of arsenic in groundwater. The results show that the semi-variogram fitting of COK-Y is the best, and the mean square error and mean absolute error for arsenic prediction in groundwater are 21.7% and 21.3% lower than OK, respectively. Compared with COK, the evaluation indexes decrease by 3.5% and 3.4%, severally. The accuracy of COK-Y is improved slightly, and the spatiacl distribution map of arsenic in groundwater can better reflect the high heterogeneity of arsenic, which is more realistic. COK-Y improve the dampening effect of kriging method to the grestest extent. The comprehensive factor Y indicates the contribution of each component on the simulation of arsenic. The reductive dissolution of iron oxide and hydroxide was the main factor for the formation and distribution of high arsenic in groundwater. The weathering, dissolution and analytical adsorption of polymetallic minerals, such as barite, magnetite and ilmenite also contributed part of it.
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图 1 研究区地理位置(a)、取样点分布(b)及A-A'地质剖面图(c)(沈帅等，2018)
Fig. 1. Geographical location of the study area (a), distribution of sampling points (b) and A-A' geological profile (c) (Shen et al., 2018)
图 2 研究区地下水体砷空间分布趋势
Fig. 2. Spatial distribution trend of As in underground water in the study area
图 3 3种模型生成的地下水As含量空间分布
Fig. 3. Spatial distribution of As content in groundwater generated by three models
图 4 Box-Cox转换后砷浓度的预测值与实测值关系
Fig. 4. Relation between predicted and measured arsenic concentrations after Box-Cox conversion
图 5 Fe2+、NH4-N与As，NH4-N与Cl-的相关关系
Fig. 5. Correlation of Fe2+, NH4-N and As, NH4-N and Cl-
表 1 地下水砷含量的基本统计学特征
Table 1. Basic hydrochemical characteristics of groundwater
单位 极小值 极大值 均值 标准差 变异系数 As μg/L 0.06 1 015.14 46.11 89.61 1.94 
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表 2 相关性分析结果
Table 2. The results of correlation analysis
DOC NH4-N Fe2+ Fe Mn Ba As Pearson相关性 0.15* 0.24** 0.42** 0.40** 0.25** 0.39** HCO3- Ca2+ Se V Zn As Pearson相关性 0.26** 0.20** 0.34** 0.21** -0.23** 注：**在置信度(双测)为0.01时，相关性是显著的；* 在置信度(双测)为0.05时，相关性是显著的.
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表 3 正态性转换及检验结果
Table 3. The results of normal conversion and test
As Fe2+ Y 原始数据P值 0 0 0 Box-Cox转换后P值 0.36 0.52 0.55
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表 4 半变异函数模型
Table 4. Cross function of variation model
变量 模型 块金值 基台值 变程(km) 残差平方和RSS 决定系数R2 块金系数 空间
依赖性OK S 2.35 5.72 502 0.46 0.97 0.59 中等 COK-Fe2+ G 1.00 3.29 618.34 0.10 0.99 0.70 中等 COK-Y S 0.41 2.51 1185 0.03 0.99 0.84 较弱 注：球状模型(Spherical model, S)，高斯模型(Gaussian model, G).
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表 5 模型精度评价
Table 5. Comparison of precision of cross vari89+ogram models
空间估计模型 RMSE MAE RI(%) OK 1.82 1.37 COK-Fe2+ 1.47 1.12 18.8 COK-Y 1.42 1.08 21.7
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