Spatial variability of free porosity in the groundwater level fluctuation zone in the Baoding Plain area
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摘要:
科学确定地下水水位变幅带的地学参数是水资源评价与管理中的重要环节。保定平原近40年来强烈开采地下水，水位持续下降形成规模巨大的厚包气带层，南水北调工程通水后，随着河湖生态补水与地下水压采工作的推进，保定平原局部地区地下水水位止跌回升。回补水量与水位变化的定量关系成为超采治理的一个重要科学问题，但水位回升条件下的计算中仍用表示释水过程的给水度参数将造成结果偏差，因此表述水位恢复过程的自由孔隙率参数研究是解决这一问题的重点所在。文章基于保定平原区67个工程地质钻孔采样数据，确定水位变幅带的综合自由孔隙率，通过趋势分析和结果交叉验证方法遴选半变异函数模型，结合普通克里金插值方法对未知点进行无偏最优估计。结果显示：（1）保定平原区水位变幅带综合自由孔隙率的最优半变异函数模型为一阶趋势效应指数模型。数据具有强空间自相关性，主要受变幅带空间位置、地层类型等结构性因素影响。（2）综合自由孔隙率分布表现为西南、西北为高值区，极值可达0.25，数值向中部及东部逐步降低，最小降至0.02。（3）与惯用给水度值进行对比，自由孔隙率值在南北部地区整体升高约0.03，约为惯用给水度的1.2倍。在中部地区降低了约0.06，变为惯用给水度值的一半左右。研究成果对南水北调受水区生态补水与水资源调控具有重要研究价值和借鉴意义。
Abstract:Scientific determination of geological parameters of the groundwater level fluctuation zone is an important step for water resources evaluation and management. In the past 40 years, over-exploitation of groundwater in the Baoding Plain led to a serious deficit of aquifers, thus forming a huge deep vadose zone. After the South-to-North Water Diversion Project was put into operation, with the progress of ecological water supplement of rivers and lakes and groundwater limited-over-exploitation, the groundwater levels in some areas of the Baoding Plain stopped falling and rose. The quantitative relationship between the amount of water supplement and the change of groundwater levels has become an important scientific issue in the management of over-exploitation of groundwater. However, under the condition of groundwater level recovery, the calculation results will be deviated if the specific yield parameter of water release process is still used. Therefore, the free porosity parameter study of groundwater level recovery process is the key to solve this problem. Based on 67 engineering geological boreholes in the Baoding Plain, the comprehensive free porosity during groundwater level recovery is determined according to the lithologic characteristic parameters of the groundwater level fluctuation zone. The semi-variogram model is selected by the trend analysis and cross validation, and the spatial unknown points are interpolated by the Ordinary Kriging interpolation. The results show that (1) the best semi-variogram model of the comprehensive free porosity in the groundwater level fluctuation zone of the Baoding Plain is the 1 order index model. The spatial autocorrelation of the data is obvious, which is mainly affected by structural factors such as spatial location of the groundwater level fluctuation zone and stratigraphic type. (2) The comprehensive free porosity distribution shows that the southwest and northwest are the high value areas, and the extreme value can reach 0.25. The parameter gradually decreases to the central and eastern regions, and the minimum value is 0.02. (3) Compared with the value of the conventional specific yield, the value of the free porosity increases by about 0.03 in the north and south regions, which is about 1.2 times that of the conventional specific yield. In the central region, it is reduced by about 0.06, which is about half that of the conventional specific yield value. The research results are of important research value and great significance for ecological water supplement and water resources regulation in the benefited regions of the South-to-North Water Diversion Project.
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Key words:
- free porosity /
- specific yield /
- unsaturated zone /
- geostatistics /
- spatial variability /
- Baoding Plain area
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表 1 地下水水位恢复阈值指标体系
Table 1. Groundwater level recovery threshold index system
地下水层位 考虑要素 目标水位埋深 浅层 大规模开采对地下水水位影响 20世纪80年代水位埋深 地下水水位降落漏斗区水位恢复 20世纪80年代水位埋深 大中型城市地下空间利用安全性 20～30 m 有利于降水入渗补给、地下水调蓄 10～15 m 地裂缝防控 7～10 m 盐渍化防控 3～4 m 
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表 2 变异函数理论模型
Table 2. Theoretical models of the variation function
模型 公式 变程 块金值 基台值 球状模型 
指数模型 
高斯模型 
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表 3 综合自由孔隙率统计特征表
Table 3. Statistical characteristics of the comprehensive free porosity
数据 中值 平均值 标准差 变异系数 偏度 峰度 偏度标准误差 峰度标准误差 偏度Z评分 峰度Z评分 µ 0.090 0.101 0.054 53.7 0.6066 −0.1638 0.293 0.578 2.071 −0.283 lnµ −2.408 −2.456 0.628 −25.6 −0.7103 0.1331 0.293 0.578 −2.426 0.230 Box-Cox −1.400 −1.387 0.175 −12.6 0.0025 −0.5078 0.293 0.578 −0.008 −0.879 注：Box-Cox变换中λ=0.50。
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表 4 综合自由孔隙率正态性检验结果
Table 4. Normality test results of the comprehensive free porosity
数据 K-S检验 S-W检验 统计 样本 Sig 统计 样本 Sig µ 0.110 67 0.043 0.956 67 0.018 lnµ 0.081 67 0.200 0.949 67 0.008 Box-Cox 0.060 67 0.200 0.981 67 0.418
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表 5 不同趋势阶数插值误差比较
Table 5. Comparison of interpolation errors of different trend orders
趋势 模型 预测误差 阶数 类型 平均误差 均方根误差 平均标准误差 标准化均方根误差 平均标准误差 0 球状 −0.00045 0.0345 −0.0231 1.0753 0.0333 指数 −0.00164 0.0348 −0.0497 0.9871 0.0368 高斯 −0.00031 0.0351 −0.0254 1.1676 0.0309 1 球状 −0.00113 0.0349 −0.0479 1.1160 0.0322 指数 −0.00112 0.0345 −0.0425 1.0093 0.0355 高斯 −0.00126 0.0352 −0.0481 1.1152 0.0320 2 球状 0.00063 0.0349 −0.0106 1.0842 0.0332 指数 0.00050 0.0354 −0.0175 1.0402 0.0347 高斯 0.00040 0.0347 −0.0169 1.0874 0.0328
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表 6 半变异函数类型及模型参数
Table 6. Types of the semi-variation function and model parameters
模型类型 趋势效应 变程/m 各向异性系数 块金值 基台值 块金效应/% 长轴 短轴 指数模型 一阶 24936.15 21944.23 1.14 0.0001 0.0166 0.60
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