Pedo-Transfer Function and Regression Kriging Estimation of Saturated Hydraulic Conductivity of Different Soil Layers in Vadose Zone Based on PCA-GWR
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摘要: 饱和导水率是重要的土壤水力学参数，对渗流和溶质运移研究起着至关重要的作用.土壤传递函数可以代替大规模采样和室内外试验间接预测该参数，但由于土壤的空间变异性以及方法的局限性等原因，以往的传递函数往往精度有限.本文以黄河下游沿岸兰考县闫楼乡包气带不同土层为研究对象，基于64个钻孔数据，将土壤粒径分布（黏粒、粉粒和砂粒含量）、土壤结构分形维数、干容重、总孔隙度、pH值、有机质和电导率等9个基本理化特性参数作为影响因素，基于逐步回归、主成分回归和主成分‒地理加权回归（PCA-GWR）三种方法，分别对研究区包气带不同土层的饱和导水率进行回归分析，比较精度后基于PCA-GWR对饱和导水率进行地理加权回归克里金插值.结果显示，除表层粉土以外，PCA-GWR法的预测精度有显著优势.不同土层传递函数和饱和导水率分布的差异性表明，由于黄河下游地区快速多变的沉积过程、黄河的决口改道以及人类活动等因素，包气带土层相变剧烈，土壤饱和导水率在平面上亦具有明显的非平稳特征.而局部地质作用和人类活动是第二层粉土层回归克里金估计结果欠佳的深层原因.Abstract: Saturated hydraulic conductivity is a significant soil hydraulic parameter, which plays an important role in the research of seepage and solute transport. Pdeo-Transfer Functions (PTFs) can indirectly predict this parameter instead of large-scale sampling and indoor and outdoor tests. However, due to the spatial variability of soils and the limitations of methods, previous predictions of PTFs are not accurate enough. This study takes different soil layers in the vadose zone of Yanlou Township, Lankao County, the lower reaches of the Yellow River as the research object. Based on 64 borehole data, nine basic physicochemical properties such as soil particle size distribution (clay, silt and sand content), soil structure fractal dimension, dry bulk density, total porosity, pH value, organic matter and electrical conductivity are considered as the influencing factors of the PTFs. Based on Stepwise Regression, Principal Component Regression and Principal Component Analysis-Geographically Weighted Regression (PCA-GWR), the saturated hydraulic conductivity of different soil layers is regressed separately. After comparison of precision, Geographically Weighted Regression Kriging is carried out for saturated hydraulic conductivity based on PCA-GWR. The results reveal that the prediction accuracy of PCA-GWR method has significant advantages except for the surface silt. The difference of the distribution of saturated hydraulic conductivity and PTFs in different soil layers shows that, due to the rapid and changeable sedimentation process in the lower reaches of the Yellow River, the breach and diversion of the Yellow River and human activities, the phase change of soil layer in the vadose zone is intense, and the saturated hydraulic conductivity also has obvious non-stationary characteristics in the plane. The local geological process and human activities are the deep reasons for the poor regression Kriging estimation results of the second layer of silt.
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图 2 研究区包气带底板等值线图、三维示意图与剖面图
Fig. 2. Contour map, three-dimensional diagram and profile of vadose zone floor in the study area
图 3 研究区采样点分布和代表钻孔剖面柱状图
Fig. 3. Histogram of sampling point distribution and representative borehole profile in the study area
图 4 PCA-GWR的预测值与实测值的关系
Fig. 4. Relationship between predicted value and measured value of PCA-GWR
图 5 不同土层饱和导水率的GWR-EBK插值
Fig. 5. GWR-EBK interpolation of saturated hydraulic conductivity in different soil layers
表 1 土层岩性、厚度和取样情况
Table 1. Lithology, thickness and sampling of soil layers
土层 岩性 样品数 土层平均厚度（m） 取样深度（m） 平均取样深度（m） 表层 粉土 45 0.30 0.15 0.15 表层 粉质黏土 19 0.30 0.15 0.15 第二层 粉土 41 2.25 1.27~1.60 1.42 第三层 粉质黏土 64 0.59 0.51~2.90 1.84 第四层 粉砂 64 1.79 1.24~4.04 2.78 
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表 2 测试项目与方法
Table 2. Test items and methods
测定项目 测试方法 试验设备或参考标准 土壤饱和导水率（cm/s） 变水头渗透仪法 南京宁曦土壤变水头渗透仪BST-1型 土壤结构组成（%） 激光粒度仪法 北京渠道科技QT-2012型 土壤干容重（%） 烘干法 《土工试验方法标准》（GB/T 50123-2019） 土壤总孔隙度（%） 烘干法 《土工试验方法标准》（GB/T 50123-2019） 土壤有机质（g/kg） 重铬酸钾滴定法 《农业行业标准》（NY/T1121.6-2006） 土壤pH值（-） pH酸度计 《农业行业标准》（NY/T1121.6-2006） 土壤电导率（μm/s） 电导率仪法 《农业行业标准》（NY/T1121.6-2006）
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表 3 不同土层土壤饱和导水率和理化特性的经典统计学特征
Table 3. Classical statistical characteristics of saturated hydraulic conductivity and physicochemical properties of soils in different topsoil layers
指标 饱和导水率Ks（m/d） 黏粒（%） 粉粒（%） 砂粒（%） 分形维数 干容重（kN/m3） 孔隙度（%） pH值 有机质(g/kg) 电导率(μs/m) 表层
（粉土）最小值 0.016 2 0.00 16.34 0.03 1.436 12.06 34.47 7.84 1.09 19.37 最大值 1.930 8 4.58 98.65 83.66 2.246 16.44 50.12 9.51 31.20 1 141.20 均值 0.458 9 0.59 76.40 22.99 1.923 13.85 42.02 8.65 8.96 432.06 变异系数 1.024 4 2.110 7 0.283 3 0.961 1 0.109 2 0.067 9 0.093 9 0.041 8 0.620 0 0.615 1 表层
（粉质黏土）最小值 0.001 1 0.00 1.33 0.00 1.229 12.80 38.16 8.01 2.16 102.25 最大值 0.587 2 91.28 93.22 0.60 2.470 16.06 53.24 9.20 27.80 824.85 均值 0.129 5 39.80 54.98 0.0337 2.328 14.57 45.53 8.48 14.14 495.41 变异系数 1.273 0 0.653 3 0.492 8 4.080 4 0.116 4 0.062 1 0.744 8 0.035 1 0.483 9 0.417 2 第二层
（粉土）最小值 0.007 2 0.00 18.80 0.00 1.500 12.01 39.01 8.10 1.02 8.67 最大值 1.575 1 27.03 99.81 81.20 2.258 15.55 67.00 9.70 6.86 242.03 均值 0.432 5 1.17 69.85 28.99 1.802 13.71 46.39 8.74 3.05 137.17 变异系数 0.915 3 3.820 5 0.359 3 0.896 2 0.112 0.064 2 0.106 7 0.036 6 0.498 4 0.507 7 第三层
（粉质黏土）最小值 0.005 8 0.00 17.54 0.00 1.513 12.06 36.09 7.90 1.21 32.76 最大值 0.930 8 82.46 99.95 79.61 2.458 15.84 64.58 9.70 23.30 179.25 均值 0.210 5 19.71 74.14 6.83 2.210 13.69 48.18 8.58 6.51 104.74 变异系数 0.887 8 1.081 2 0.292 0 2.472 9 0.117 0.062 0 0.104 2 0.038 5 0.672 8 0.415 8 第四层
（粉砂）最小值 0.123 7 0.08 0.05 21.51 1.046 13.26 32.30 8.40 0.57 78.77 最大值 1.989 5 3.44 77.32 99.95 1.608 15.36 50.06 9.40 13.50 477.41 均值 0.952 8 1.40 16.01 16.16 0.145 0.54 2.59 0.24 1.98 117.92 变异系数 0.473 0 0.897 4 1.493 5 0.180 9 0.105 0.037 1 0.058 7 0.027 0 1.010 2 0.462 1 注：变异系数和分形维数均为无量纲.
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表 4 逐步回归方程及其精度评价
Table 4. Stepwise regression equation and accuracy evaluation
土层 逐步回归方程 RMSE R2 表层
（粉土）Ks=6.759‒0.162silt+2.06×10‒3silt2‒1.199×10‒5silt3‒0.371pH+3.664×10‒4EC‒4.673EC2+9.760×10‒10EC3 0.320 7 0.524 表层
（粉质黏土）Ks=‒0.586+3.186/OM+3.210×10‒3EC‒6.182×10‒6 EC+3.193×10‒9 EC3 0.115 9 0.880 第二层
（粉土）Ks=1.12‒6.93×10‒3sand+5.48×10‒4sand2‒5.01×10‒6sand3‒3.89×10‒1OM+5.70×10‒2OM2‒2.39×10‒3OM3 0.278 5 0.604 第三层
（粉质黏土）Ks=3.40+9.75×10‒4sand+4.15×10‒4sand2‒4.06×10‒6sand3+1.25×10‒3e(5.594+29.155/silt)+
9.52×10‒1pH+5.93×10‒2pH20.098 8 0.721 第四层
（粉砂）Ks=1.29+6.67e(‒1.489D)‒2.28×10‒1BD+1.60×10‒2BD2 0.312 9 0.511 注：clay（%），silt（%），sand（%），D（‒），BD（kN/m3），n（%），pH值（‒），OM（g/kg），EC（μs/m），Ks（m/d）.
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表 5 不同土层主成分表达式
Table 5. Principal component expression of different soil layers
土层 主成分向量表达式 表层
（粉土）F1=0.260x1+0.413x2‒0.420x3+0.453x4+0.268x5‒0.220x6‒0.286x7+0.362x8‒0.217x9 F2=0.006x1+0.324x2‒0.317x3+0.162x4‒0.550x5+0.600x6‒0.049x7‒0.020x8+0.321x9 F3=0.538x1+0.117x2‒0.147x3+0.138x4+0.136x5‒0.025x6+0.652x7‒0.460x8+0.009x9 F4=0.319x1‒0.126x2+0.104x3+0.004x4+0.110x5‒0.238x6‒0.086x7+0.249x8+0.856x9 F5=0.668x1‒0.365x2+0.318x3+0.098x4‒0.257x5+0.237x6‒0.294x7+0.105x8‒0.302x9 表层
（粉质黏土）F1=0.090x1+0.355x2‒0.533x3+0.503x4+0.046x5+0.056x6‒0.041x7+0.345x8+0.102x9 F2=0.620x1‒0.462x2‒0.152x3+0.234x4+0.476x5‒0.125x6+0.171x7‒0.020x8‒0.229x9 F3=0.294x1‒0.177x2‒0.124x3+0.189x4‒0.464x5+0.676x6+0.147x7‒0.290x8+0.230x9 F4=0.157x1‒0.254x2+0.127x3‒0.089x4‒0.016x5‒0.231x6+0.017x7+0.360x8+0.838x9 第二层
（粉土）F1=0.190x1+0.490x2‒0.506x3+0.479x4‒0.062x5+0.080x6‒0.234x7+0.415x8+0.023x9 F2=0.358x1‒0.031x2‒0.032x3+0.216x4+0.598x5‒0.588x6+0.280x7‒0.044x8‒0.196x9 F3=0.561x1‒0.189x2+0.087x3+0.172x4‒0.155x5+0.165x6+0.290x7‒0.056x8+0.689x9 F4=‒0.231x1‒0.187x2+0.219x3+0.021x4+0.276x5‒0.319x6‒0.568x7+0.324x8+0.508x9 F5=‒0.568x1+0.281x2‒0.175x3‒0.052x4+0.228x5+0.005x6+0.592x7+0.122x8+0.385x9 第三层
（粉质黏土）F1=0.517x1‒0.121x2‒0.492x3+0.591x4‒0.023x5+0.255x6‒0.030x7+0.141x8+0.203x9 F2=‒0.256x1+0.413x2‒0.212x3+0.040x4‒0.322x5+0.434x6+0.379x7‒0.520x8+0.100x9 F3=‒0.261x1+0.556x2‒0.387x3+0.204x4+0.467x5‒0.415x6+0.097x7+0.166x8‒0.063x9 F4=0.244x1‒0.330x2+0.119x3+0.036x4+0.457x5‒0.151x6+0.676x7‒0.353x8‒0.048x9 F5=‒0.103x1+0.003x2+0.125x3‒0.094x4+0.231x5‒0.032x6‒0.114x7‒0.076x8+0.944x9 第四层
（粉砂）F1=0.335x1+0.495x2‒0.499x3+0.464x4‒0.264x5‒0.163x6‒0.045x7+0.271x8‒0.082x9 F2=0.148x1+0.167x2‒0.169x3‒0.082x4‒0.243x5+0.472x6+0.628x7‒0.444x8+0.204x9 F3=0.058x1+0.297x2‒0.296x3‒0.148x4+0.630x5‒0.227x6‒0.153x7‒0.311x8+0.480x9 F4=0.111x1‒0.237x2+0.232x3+0.267x4‒0.104x5‒0.052x6+0.162x7+0.398x8+0.780x9 F5=‒0.647x1+0.257x2‒0.236x3‒0.073x4‒0.019x5+0.520x6‒0.209x7+0.332x8+0.172x9 F6=0.555x1‒0.107x2+0.091x3+0.063x4+0.090x5+0.605x6‒0.540x7‒0.057x8+0.034x9 注：表中x1, x2, …, x9为标准化后的自变量值，依次代表黏粒含量、粉粒含量、砂粒含量、分形维数、容重、总孔隙度、pH值、有机质和电导率.
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表 6 主成分回归方程及其精度评价
Table 6. Principal component regression equation and its accuracy evaluation
土层 主成分回归方程 RMSE R2 表层
（粉土）Ks=‒7.40×10‒2F1‒8.04×10‒3F2‒1.30×10‒1F3+1.79×10‒1F4+6.7×10‒2F5+0.459 0.385 0 0.319 0 表层
（粉质黏土）Ks=‒1.67×10‒1F1‒6.40×10‒2F2+1.01×10‒2F3‒2.12×10‒2F4+2.02×10‒2 0.145 2 0.812 3 第二层
（粉土）Ks=‒1.59×10‒1F1‒4.12×10‒3F2‒6.66×10‒3F3+1.99×10‒2F4‒3.41×10‒2F5+4.33×10‒1 0.268 2 0.541 2 第三层
（粉质黏土）Ks=‒8.09×10‒2F1‒1.62×10‒2F2‒5.56×10‒2F3‒3.66×10‒3F4+2.29×10‒2F5+2.10×10‒1 0.111 2 0.645 8 第四层
（粉砂）Ks=‒1.60×10‒1F1+1.07×10‒2F2+5.23×10‒2F3‒7.28×10‒2F4‒1.15×10‒2F5+5.96×10‒2F6+9.53×10‒1 0.336 6 0.433 2 注：Ks（m/d）.
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表 7 三种回归方法的精度比较
Table 7. Accuracy comparison of three regression methods
指标 逐步回归 主成分回归 PCA-GWR 表层
（粉土）RMSE 0.320 7 0.385 0 0.384 9 R2 0.523 9 0.313 9 0.314 3 表层
（粉质黏土）RMSE 0.113 2 0.145 2 0.063 6 R2 0.752 9 0.583 8 0.852 7 第二层
（粉土）RMSE 0.278 5 0.268 2 0.110 0 R2 0.604 3 0.541 2 0.925 5 第三层
（粉质黏土）RMSE 0.098 8 0.111 2 0.092 0 R2 0.720 6 0.645 8 0.758 7 第四层
（粉砂）RMSE 0.312 9 0.336 6 0.283 5 R2 0.510 5 0.433 2 0.607 6
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表 8 不同土层Ks的PCA-GWR方程的残差的最优变异函数模型
Table 8. Optimal variogram model for PCA-GWR equation of Ks in different soil layers
土层 模型 块金值 基台值 块金系数 变程（m） R2 RMSE 表层 指数 0.001 0.102 0.212 166 0.001 0.009 第二层 球状 0.009 18.000 0.999 678 0.001 1.538 第三层 球状 0.009 9.840 0.001 915 0.659 0.131 第四层 高斯 0.086 45.070 0.002 568 0.444 0.781
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表 9 GWR-EBK法的交叉验证
Table 9. Cross validation of GWR-EBK method
土层 RMSE r 表层 0.320 1 0.697 1 第二层 0.391 8 0.183 0 第三层 0.173 8 0.373 1 第四层 0.385 9 0.506 1
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