Optimization of karst water monitoring network based on information entropy: A case study in typical groundwater source sites in Xuzhou
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摘要: 在各级水利与自然资源部门地下水监测数据共享机制逐步完善背景下，针对日益凸显的原有监测系统中存在的监测井布局不合理问题以及岩溶含水系统具有的非均质性和各向异性特征，选取徐州市丁楼-茅村和七里沟2个典型水源地，分别采用互信息-距离（T-D）和最大信息最小冗余（MIMR）模型对研究区监测网信息冗余性和最优监测井组合进行了研究。结果显示：丁楼-茅村水源地水位监测数据离散程度、信息熵、信息传递量和信息衰减速率均大于七里沟水源地，2个水源地在ε取10-1时的水位信息有效传递距离分别为4.7，4.8 km，指示出两地相似的岩溶发育程度和水力传导性能。通过对比监测井控制范围的实际值和理论值发现2个水源地监测井之间均存在信息冗余。现有监测条件下，丁楼-茅村水源地最优监测井数为6眼，最优监测井组合为D1-D2-D4-D5-D7-D9；七里沟水源地最优监测井数量为5眼，最优组合为Q1-Q3-Q4-Q5-Q7。将优化结果与原监测网相比，2个水源地监测井数量均减少3眼，分别能提供原监测网信息总量的98.5%，94.9%，监测网控制范围分别下降0.4%，1.2%，信息冗余量分别减少49.0%，56.4%。表明优化后的监测网能够提供与原站网相当的信息量和控制范围，同时可以显著降低信息冗余度与监测成本。
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关键词:
- 信息熵 /
- 岩溶水 /
- 监测网优化 /
- 互信息-距离模型 /
- 最大信息最小冗余模型
Abstract: In view of the unreasonable layout of monitoring wells and heterogeneity and anisotropy of the karst aquifer monitoring system, mutual information-distance (T-D) and maximum information minimum redundancy (MIMR) models can be used to study the information redundancy of the monitoring network and the optimal monitoring well combination.Dinglou-Maocun and Qiligou in Xuzhou City were selected to do the research.The results show that: the data dispersion degree, information entropy, information transfer amount and information attenuation rate in Dinglou-Maocun are all greater than those in Qiligou.When ε is set to be 10-1, the effective transmission distance of water level information is 4.7 km and 4.8 km respectively, indicating the similar karst development degree and hydraulic conductivity of the two sites.By comparing the actual value and the theoretical value of the control area of monitoring well, it can be found that information redundancy exists in both two water source sites.The optimized number of monitoring wells in Dinglou-Maocun is 6, and the corresponding combination of monitoring wells is D1-D2-D4-D5-D7-D9, while the optimized number of monitoring wells is 5 and the corresponding combination of monitoring wells is Q1-Q3-Q4-Q5-Q7 in Qiligou.Compared to the original monitoring network, three monitoring wells are reduced in both two water source sites with 98.5% and 94.9% of the total information retention, 0.4% and 1.2% of control range decrease, 49.0% and 56.4% of the information redundancy reduction, respectively.It shows that the optimized monitoring network can provide the same amount of information and control range as the original site network, and significantly reduce information redundancy and monitoring costs. -
图 2 研究区水位信息-距离拟合模型
Figure 2. Fitting model of water level mutual information-distance in the study area
图 3 监测井控制范围分布图
Figure 3. Distribution diagram of the control range of groundwater monitoring wells
图 4 不同λ取值条件下研究区MIMR模型计算结果
a.丁楼-茅村水源地；b.七里沟水源地
Figure 4. Results of MIMR model calculation in the study area corresponding to the λ with different value
表 1 研究区各监测井2014-2020年水位数据特征值
Table 1. Characteristic value of water level for each monitoring well in the study area from 2014-2020
研究区 原始编号 统一编号 最大值 最小值 平均值 中位数 方差 标准差 水位h/m 丁楼-茅村水源地 09133 D1 20.58 13.17 17.03 17.21 3.97 1.99 70002 D2 13.93 -0.56 4.49 3.15 10.73 3.28 70004 D3 29.33 14.79 23.86 24.68 12.35 3.51 09191 D4 20.69 -5.73 10.09 8.95 47.89 6.92 09171 D5 30.81 -2.37 14.22 14.66 98.22 9.91 09048 D6 28.04 -9.56 11.71 16.00 144.73 12.03 70003 D7 29.80 -7.70 13.71 17.35 145.80 12.07 70009 D8 32.31 -9.29 11.06 13.55 154.52 12.43 09175 D9 31.52 -9.47 11.28 14.03 157.18 12.54 七里沟水源地 70011 Q1 36.23 27.46 31.29 31.05 3.50 1.87 09206 Q2 26.73 15.22 21.88 21.79 5.71 2.39 75011 Q3 27.10 16.19 22.20 21.92 5.80 2.41 70010 Q4 28.58 16.50 23.89 23.69 5.93 2.44 70007 Q5 28.93 15.73 22.83 22.83 7.32 2.71 09068 Q6 28.07 14.94 22.29 22.33 7.52 2.74 09064 Q7 28.31 12.74 21.74 22.05 9.58 3.10 75017 Q8 21.67 5.63 13.51 13.80 9.64 3.10 注：原始编号始于7代表水利监测井，始于0代表自然资源监测井 
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表 2 不同ε取值对应的监测井控制范围
Table 2. Monitoring well control range corresponding to the ε with different value
研究区 T0/bits Tmin/bits K/km-1 ε/bits L/km 丁楼- 茅村水源地 3.545 1.636 0.623 10-4 15.82 10-3 12.13 10-2 8.43 10-1 4.73 七里沟水源地 1.368 0.397 0.471 10-4 19.48 10-3 14.60 10-2 9.71 10-1 4.83
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表 3 优化前后监测网信息对照
Table 3. Comparison of monitoring network information before and after optimization
优化对照 监测井/眼 H/bits T/bits C/bits G/bits 丁楼-茅村 优化前 9 6.345 0 24.313 0.213 水源地 优化后 6 6.249 5.7 12.393 7.096 七里沟 优化前 8 6.273 0 12.573 2.504 水源地 优化后 5 5.952 5.3 5.477 7.903
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