A comparative study of Kriging and deep learning methods for shallow groundwater level estimation: A case study of the Shenzhen-Shanwei Special Cooperation Zone
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摘要:
掌握区域地下水位分布是地下水资源评价与环境保护的重要基础。由于区域尺度观测的地下水位数据有限, 克里金插值与深度学习方法逐渐被用于区域地下水位预测, 但两者的适用性及鲁棒性缺乏对比分析。针对这个问题, 基于239口监测井水位, 采用普通克里金方法、融合地表高程的协同克里金方法、深度学习方法估计深汕特别合作区地下水位空间分布, 调查3种方法在区域地下水位预测中的应用潜力。为了研究训练集样本量对3种方法预测效果的影响, 将239口监测井分为2组(76口和163口)用于3种模型的训练。结果显示, 使用76眼井的训练数据拟合验证集样本时
RMSE 分别为6.09, 4.04, 7.11, 考虑了地表高程信息的协同克里金法明显优于普通克里金法与深度学习法。而当训练样本量增加到163口水位数据时, 普通克里金、协同克里金及深度学习法的预测精度都明显提升, 3种方法拟合验证数据集的RMSE 相差很小, 分别为1.33, 1.36, 1.54。另外, 使用较大数据样本量进行全区域的地下水位预测时不同方法得到的预测水位分布均有所提高, 但空间分布特征依旧存在明显差异。结果表明, 当观测数据稀疏时, 融合高程信息的协同克里金方法的预测效果显著高于普通克里金方法和深度学习方法, 而当观测数据量增加到达一定数量时, 3种方法预测得到的RMSE 较接近。Abstract:Objective Knowledge of the regional groundwater level is an important foundation for groundwater resource evaluation and protection. Due to the limited amount of groundwater level data available at the regional scale, Kriging interpolation and deep learning methods are gradually being used for regional groundwater level prediction, but their applicability and robustness lack comparative analysis.
Methods In this paper, spatial interpolation of groundwater levels in the Shenzhen-Shanwei Special Cooperation Zone was carried out using ordinary Kriging, coKriging and deep learning methods to explore the potential of these three methods for practical application to regional groundwater level prediction. To investigate the effect of the training set sample size on the prediction effect of the three methods, 239 monitoring wells were divided into two groups of 76 and 163 wells for the training of the three models.
Results The results showed that the RMSEs were 6.09, 4.04, and 7.11 when the training data of 76 wells were used to fit the validation set, and the Kriging method, which accounts for surface elevation information, was significantly better than the ordinary Kriging method and the deep learning method. In addition, the predicted water level distribution improved when a larger number of samples was used to predict the water level in the region. However, the spatial distribution characteristics still differed significantly.
Conclusion The results show that when the observation data are sparse, the prediction effect of coKriging with elevation information is significantly greater than that of ordinary Kriging and deep learning methods, while the RMSEs obtained by the three methods are similar when the amount of observation data increases to a certain amount.
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图 1 研究区地表高程图及地下水位监测井分布图
a.深汕合作区地形高程图；b.76眼监测井位置分布；c.163眼监测井位置分布
Figure 1. Ground surface elevations and the distribution of the groundwater level observation wells in the study area
图 3 不同方向地下水位样本变异函数及变异函数模型分析
Figure 3. Sample variogram of groundwater level and variogram model analysis in different directions
图 4 深汕合作区不同方向DEM样本变异函数及变异函数模型分析
Figure 4. Sample variogram of the Shenshan special cooperation zone DEM and variogram model analysis in different directions
图 5 不同方向地下水位同DEM的样本协同变异函数及变异函数模型分析
Figure 5. Sample cross variograms of the groundwater level and DEM(Δh=100 m) and variogram model analysis in different directions
图 6 3种插值方法训练集为76口井的地下水位预测值与实测值对比及相关性分析
Figure 6. Comparison of the predicted and observed groundwater levels by the three methods with a training sample size of 76
图 7 3种插值方法训练集为163口井的地下水位预测值与实测值对比及相关性分析
Figure 7. Comparison of the predicted and observed groundwater levels by the three methods with a training sample size of 163
图 8 3种插值方法训练集为76口井的地下水位空间分布预测结果对比图
Figure 8. Comparison of the distributions of predicted groundwater levels predicted by the three methods with a training sample set of 76
图 9 3种插值方法训练集为163口井的地下水位空间分布预测结果对比图
Figure 9. Comparison of the distributions of predicted groundwater levels predicted by the three methods with a training sample set of 163
表 1 地下水位样本数据的统计分析结果
Table 1. Statistical results of the observed groundwater level data
地下水位样本测井/口 最大值/m 最小值/m 均值/m 标准差σ 变差系数Cv 偏度系数 峰度系数 239 59.50 0.83 9.80 8.94 0.91 2.32 6.51 
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表 2 log变换后地下水位样本数据的统计分析结果
Table 2. Statistical results of the observed groundwater level data after log transformation
地下水位样本测井/口 最大值 最小值 均值 标准差σ 变差系数Cv 偏度系数 峰度系数 239 1.77 -0.08 0.85 0.34 0.40 0.05 -0.05
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