Seawater intrusion characterization and dynamics prediction based on WA-NARX hybrid model in the south of Laizhou Bay
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摘要: 随着我国海岸带经济的快速发展与人类活动的加剧，地下水超采现象十分严峻，由此引发的海水入侵已成为滨海地区普遍存在的地质问题。本研究以莱州湾南岸海水入侵区为研究对象，根据地下水连续监测数据分析了地下水位和电导率的动态变化特征。在此基础上，基于降雨、蒸发、潮汐及农业排灌用电量等影响地下水动态变化的因素，建立了小波分析（WA）与具有外部输入的非线性自回归神经网络（NARX）的混合模型，对地下水水位和电导率进行动态预测，并采用均方根误差和拟合度对预测结果进行评价。研究结果表明，莱州湾南岸地下水年内动态变化特征为降雨入渗–开采型，地下水位和潮汐之间在0.5 d频率上呈现较高相关性，潮汐对地下水电导率的影响要弱于对地下水位的影响；WA-NARX混合模型在训练和测试阶段的均方根误差均小于0.03且拟合度大于0.98，可有效预测研究区海水入侵的变化程度。同时，为验证模型适用性，对比了不同影响因素作为模型输入参数对预测结果的影响。结果表明，降雨和潮汐参数是影响海岸带地下水位和电导率的主要变量，蒸发以及农业排灌用电量反映的部分抽水信息对地下水位和电导率也有影响，其影响程度与观测频率相关。本文研究结果可为海岸带海水入侵的实时监测、预测、预警提供理论与技术支撑。Abstract: With the rapid economic development and increasing anthropogenic activities, the groundwater in the coastal area has been excessively exploited. The resulting seawater intrusion has become a widely distributed environmental geological problem. Taken the coastal area of Laizhou Bay as a research area, the dynamics of groundwater level (GWL) and electrical conductivity (EC) were analyzed with the continuous monitoring data. Based on the rainfall, evaporation, tide and agricultural irrigation and drainage electricity consumption that affect the groundwater variation, the hybrid model of wavelet analysis (WA) and NARX neural network was introduced to predict the dynamics of GWL and EC. The root mean square error (RMSE) and goodness of fit (R2) were used to measure the prediction accuracy. The results showed that the annual variation of GWL was characterized by a type of rainfall infiltration-exploitation. A significant correlation at the frequency of 0.5 d was observed between groundwater level and tide, and the influence of tide on EC was weaker than that on GWL. For the dynamics prediction with WA-NARX method, the RMSE was less than 0.03 and R2 was greater than 0.98 in both the training and testing stages. The results indicated the hybrid model had a good performance and could effectively predict the dynamics of GWL and EC. The effects of different influencing factors as model input parameters on the prediction results were further compared. The results showed that rainfall and tide parameters were the main variables affecting the GWL and EC variations in the coastal zone. The pumping information reflected by the evaporation and agricultural drainage and irrigation power consumption also affected the groundwater dynamics. The degree of influence was related to the observation frequency. The research results can provide theoretical and technical support for real-time monitoring, prediction and early warning of seawater intrusion in coastal zone.
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Key words:
- seawater intrusion /
- groundwater level /
- electrical conductivity /
- wavelet analysis /
- NARX neural network /
- prediction
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图 2 各影响因素时间序列
a. 降雨量；b. 潮汐；c. 蒸发量；d. 农业排灌用电量
Fig. 2 Time series of influencing factors
a. Precipitation; b. tide; c. evaporation; d. electricity consumption of agricultural irrigation and drainage
图 3 研究区剖面图（修改自文献[26]）
1. 粉质黏土；2. 中砂及砾石；3. 黏土；4. 砂质黏土；5. 基岩；6 、1992年（虚线）和2013年（实线）地下水等势面
Fig. 3 Hydrogeology of the cross section from south to north in the study area (modified from reference [26])
1. Clay sand; 2. medium sand and gravel; 3. clay; 4. sandy clay; 5. bedrock; 6. groundwater level surface in 1992 (dash line) and 2013 (solid line)
图 4 WA-NARX模型建模流程
g(n)为低通滤波器；h(n)为高通滤波器；Ci为近似分量；Wi为细节分量
Fig. 4 Flow chart of WA-NARX neural network hybrid model
g(n) is low-pass filters; h(n) is high-pass filters; Ci is low-frequency approximations; Wi is high-frequency details
图 6 监测井2011–2012年间地下水位变化曲线
Fig. 6 Groundwater level variation in monitoring wells from 2011 to 2012
图 7 监测井BH4水位与电导率变化
Fig. 7 Groundwater level and electrical conductivity variation in BH4 monitoring well
图 8 小波相干性分析
a, b. 地下水位与潮汐的相干性；c, d. 地下水电导率与潮汐的相干性
Fig. 8 Wavelet coherence analysis
a, b. Wavelet coherence between groundwater levels and tidal; c, d. wavelet coherence between electrical conductivity values and tidal
图 9 WA-NARX模型地下水位预测与观测对比
Fig. 9 Comparison of groundwater level prediction based on WA-NARX and observation
图 10 WA-NARX模型电导率预测的性能图
Fig. 10 Performance of WA-NARX model for electrical conductivity prediction
图 11 新增蒸发参数的预测和实测地下水位散点图
Fig. 11 Scatter diagrams of predicted and observed groundwater level with newly added evaporation parameters
图 12 新增用电量参数的预测和实测地下水位散点图
Fig. 12 Scatter diagrams of predicted and observed groundwater level with newly added power consumption parameters
图 13 新增蒸发参数的预测和实测电导率曲线图
Fig. 13 Curve diagrams of predicted and observed electrical conductivity with newly added evaporation parameters
图 14 新增用电量参数的预测和实测电导率曲线图
Fig. 14 Curve diagrams of predicted and observed electrical conductivity with newly added power consumption parameters
表 1 监测井地下水位统计特征分析（单位：m）
Tab. 1 Analysis on statistical characteristics of groundwater level in monitoring wells (unit: m)
监测井 最大值 最小值 平均值 标准差 BH1 1.451 –0.854 0.270 0.422 BH2 2.681 –0.230 1.504 0.633 BH3 4.092 –0.266 2.865 0.516 BH4 6.378 3.230 5.033 0.689 BH5 4.014 2.124 3.259 0.403 BH6 4.371 3.196 3.750 0.246 
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表 2 监测井电导率统计特征分析（单位：mS/cm）
Tab. 2 Analysis on statistical characteristics of electrical conductivity in monitoring wells (unit: mS/cm)
监测井 最大值 最小值 平均值 标准差 标准离散率 BH1 2.08 0.63 1.22 0.505 41.39% BH2 1.69 1.53 1.65 0.021 1.27% BH3 1.62 1.01 1.20 0.121 10.08% BH4 13.17 2.39 4.70 2.252 47.91% BH5 16.95 3.68 8.95 3.196 35.71% BH6 15.32 4.12 6.61 3.143 47.55%
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表 3 地下水位预测时WA-NARX模型的均方根误差（RMSE）和拟合度（R2）统计表
Tab. 3 The WA-NARX model performance metrics of RMSE and R2 for groundwater level prediction
监测井 训练数据 测试数据 RMSE R2 RMSE R2 BH1 0.004 1 0.999 9 0.003 9 0.999 8 BH2 0.004 2 1.000 0 0.004 3 0.999 9 BH3 0.028 1 0.997 1 0.014 7 0.998 3 BH4 0.004 9 0.999 9 0.005 4 0.999 9 BH5 0.003 0 0.999 9 0.006 0 0.999 6 BH6 0.003 4 0.999 8 0.003 9 0.998 7
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表 4 电导率预测时WA-NARX模型的均方根误差（RMSE）和拟合度（
$ {{R}}^{2} $ ）统计Tab. 4 The WA-NARX model performance metrics of RMSE and R2 for electrical conductivity prediction
监测井 训练数据 测试数据 RMSE R2 RMSE R2 BH1 0.001 3 1.000 0 0.001 5 0.999 4 BH2 0.000 78 0.998 5 0.000 89 0.989 7 BH3 0.005 1 0.998 4 0.005 0 0.993 6 BH4 0.007 4 1.000 0 0.005 3 0.999 5 BH5 0.003 9 1.000 0 0.002 6 0.990 5 BH6 0.008 5 1.000 0 0.004 4 0.997 8
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表 5 新增蒸发参数的地下水位预测误差及网络性能统计表
Tab. 5 The prediction error of groundwater level and network performance with newly added evaporation parameters
监测井 输入降雨、潮汐参数 输入降雨、潮汐、蒸发参数 网络性能 RMSE R2 网络性能 RMSE R2 BH1 1.619 3×10–5 0.004 0 0.957 1 1.526 1×10–5 0.004 4 0.948 4 BH2 2.569 7×10–5 0.005 1 0.961 9 3.006 6×10–5 0.005 5 0.955 4 BH3 8.991 8×10–5 0.009 5 0.935 7 7.640 4×10–5 0.008 7 0.945 4 BH4 2.476 8×10–5 0.009 8 0.880 7 9.752 6×10–5 0.009 9 0.878 5 BH5 2.381 2×10–4 0.015 4 0.643 7 5.149 2×10–4 0.022 7 0.229 5 BH6 1.392 0×10–5 0.003 7 0.983 9 1.249 7×10–5 0.003 5 0.985 5
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表 6 新增用电量参数的地下水位预测误差及网络性能统计
Tab. 6 The prediction error of groundwater level and network performance with newly added power consumption parameters
监测井 输入降雨、潮汐参数 输入降雨、潮汐、用电量参数 网络性能 RMSE R2 网络性能 RMSE R2 BH1 1.619 3×10–5 0.004 0 0.957 1 2.216 3×10–5 0.004 7 0.941 3 BH2 2.569 7×10–5 0.005 1 0.961 9 7.072 1×10–5 0.008 4 0.895 0 BH3 8.991 8×10–5 0.009 5 0.935 7 2.027 0×10–4 0.014 2 0.855 1 BH4 2.476 8×10–5 0.009 8 0.880 7 2.743 9×10–4 0.016 6 0.658 0 BH5 2.381 2×10–4 0.015 4 0.643 7 1.064 5×10–4 0.010 3 0.840 7 BH6 1.392 0×10–5 0.003 7 0.983 9 1.236 6×10–5 0.003 5 0.985 7
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表 7 不同输入参数电导率预测误差及网络性能评价统计
Tab. 7 The prediction error of electrical conductivity and network performance with different input parameters
监测井 输入降雨、潮汐参数 输入降雨、潮汐、蒸发参数 输入降雨、潮汐、用电量参数 网络性能 RMSE 网络性能 RMSE 网络性能 RMSE BH1 2.005 4×10–5 0.004 5 7.984 9×10–6 0.002 8 1.383 1×10–5 0.003 7 BH2 1.086 4×10–7 0.000 33 1.086 0×10–7 0.000 30 4.927 2×10–8 0.000 31 BH3 1.409 1×10–6 0.001 2 4.998 2×10–7 0.000 71 1.637 8×10–6 0.001 3 BH4 1.072 6×10–5 0.003 3 1.946 0×10–5 0.004 4 1.368 7×10–5 0.003 7 BH5 1.100 0×10–3 0.033 9 3.371 9×10–4 0.005 8 5.466 2×10–4 0.023 4 BH6 1.136 3×10–5 0.003 4 1.161 5×10–5 0.003 4 1.007 5×10–5 0.003 2
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