基于k-means聚类与泰森去丛聚的代表性地下水位计算方法

Calculation method of representative groundwater level based on k-means cluster analysis and Thiessen de-clustering

在总结前人常用的区域水位变化值计算方法的基础上,结合k-means聚类分析、泰森多边形去丛聚和水均衡法等方法,提出一种基于群井多年连续观测水位数据和储变量数据求解代表性地下水位的新方法,并在数值模拟算例与实例研究区分别进行了计算和验证。结果表明:在算例中使用本方法得到的代表性地下水位结果与传统水均衡法计算结果相比准确度可达90.5%;在实例计算中使用定兴县8口井连续5年水位数据和储变量数据计算得到定兴县2019年代表性地下水位变化值为0.16 m,相较水均衡法计算结果新方法的准确度达到93.3%,算例与实例结果均较为准确,计算结果可用于代表性地下水位变化值快速、科学表征,在实际工作中能够有效简化代表性地下水位变化的计算工作并为结果提供科学依据。

The dynamic change of groundwater level is an intuitive reflection of groundwater reserve change and basic information for studying the characteristics of groundwater occurrence and evolution.The variation characteristics of water level in a single well are affected by supplementary drainage characteristics and hydrogeological conditions.The water level of distributed wells at different points may have different trends with total groundwater reserve changes in a region.How to obtain representative values which can describe the overall regional water level changes becomes a key problem to be solved urgently.A correlation between the observed water level of multiple wells and the water level calculated by regional groundwater reservoir variables was constructed based on water balance method.The k-means clustering analysis method and Thiessen polygon were used to solve the multi-solution problem caused by the gap between the number of wells and the length of continuous water level observations of a single well.By solving the linear equation,a set of weighting coefficients that can describe the relationship between a single well water level change and the whole area water level change was obtained.These weighting coefficients and water level changes of corresponding wells were used to quickly calculate regional representative groundwater level changes.A new method was calculated and validated by numerical simulation and regional example.The results show that in an ideal example,using the water level variation data of five selected observation points and corresponding weight values,the annual variation of overall water level was 0.23 m.The calculated result was 0.02 m,different from the verified annual water level variation of 0.21 m calculated by the water balance method.In an ideal situation,the new method showed good accuracy and it reached 90.5%.In a typical area,a set of coefficients were obtained by water level data of 8 wells in Dingxing County for 5 consecutive years and groundwater storage variable data.The representative groundwater level change in Dingxing County in 2019 was calculated as 0.16 m by an obtained coefficient.This result was 0.01 m in difference from that of the water balance method,with an accuracy of 93.3%.Based on actual water level monitoring data,a systematic method for calculating representative groundwater level changes was proposed in the new method by combining various methods.The accuracy and practicability of the method were verified by ideal examples and in Dingxing County.In the ideal example,the error of this method was 9.5%compared with that of the water balance method.This error was 6.7%in the calculation result taking Dingxing County as an example.New method can be used to calculate regional representative groundwater level changes.During the experiment,it was found that the new method need to add observation wells to ensure the accuracy of results according to the actual situation in areas with less monitoring data but more observation wells or less well distribution density or uneven distribution.After obtaining a set of weighting coefficients of a single well,the observed water level change values and corresponding coefficients of each well can be directly used to calculate the groundwater level change values of the whole representative groundwater level in the study area.The overall change in regional water level can be evaluated,which greatly reduces the workload of statistics and evaluation.