{"title":"时空分布补给矩形域地下水流动解析模型","authors":"Ping-Cheng Hsieh, Po-Wen Yu, Ming-Chang Wu","doi":"10.1002/hyp.70004","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This study introduces a reliable analytical solution to the two-dimensional linearised Boussinesq equation, applicable to groundwater flow in an anisotropic rectangular aquifer over an impervious stratum. Validation is performed using a numerical solution based on the finite difference method for the nonlinear Boussinesq equation. Additionally, the proposed two-dimensional analytical model for finite or semi-infinite domains effectively estimates groundwater level changes due to diffuse recharge, with converging simulation results as the finite domain size increases. By incorporating Horton's equation to represent the spatiotemporally varying diffuse recharge, the study provides a more accurate method for estimating groundwater level fluctuations, allowing the model to simulate real-world recharge patterns more effectively than previous analytical models. The analytical simulations for groundwater level estimations in the Zeng Wen river basin agree well with field data and display that the peak groundwater levels shift in the <span></span><math>\n <semantics>\n <mrow>\n <mi>x</mi>\n </mrow>\n <annotation>$$ x $$</annotation>\n </semantics></math> direction at both observation stations, with a time lag of approximately 2–5 days, demonstrating its applicability in predicting groundwater levels under various hydrological and geological conditions. This suggests that the current model offers advantages over previous analytical methods, such as greater accuracy and efficiency, allowing for quicker assessments and broader applicability to various recharge patterns and aquifer conditions.</p>\n </div>","PeriodicalId":13189,"journal":{"name":"Hydrological Processes","volume":"39 3","pages":""},"PeriodicalIF":3.2000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical Model of Groundwater Flow in a Rectangular Domain for Spatiotemporally Distributed Recharge\",\"authors\":\"Ping-Cheng Hsieh, Po-Wen Yu, Ming-Chang Wu\",\"doi\":\"10.1002/hyp.70004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>This study introduces a reliable analytical solution to the two-dimensional linearised Boussinesq equation, applicable to groundwater flow in an anisotropic rectangular aquifer over an impervious stratum. 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引用次数: 0
摘要
本研究引入了二维线性化Boussinesq方程的可靠解析解,适用于不透水地层上各向异性矩形含水层的地下水流动。利用基于有限差分法的非线性Boussinesq方程的数值解进行验证。此外,所提出的有限域或半无限域二维解析模型能有效地估算地下水弥漫性补给引起的水位变化,且随着有限域尺寸的增大,模拟结果趋于收敛。通过结合Horton方程来表示时空变化的弥漫性补给,该研究提供了一种更准确的估算地下水位波动的方法,使该模型比以往的分析模型更有效地模拟现实世界的补给模式。曾文河流域地下水位估算的分析模拟结果与实测数据吻合较好,两个观测站的地下水位峰值均沿x $$ x $$方向移动,时间滞后约为2 ~ 5天,表明了该方法在各种水文地质条件下的地下水位预测的适用性。这表明,目前的模型比以前的分析方法更有优势,例如更高的准确性和效率,允许更快的评估和更广泛的适用于各种补给模式和含水层条件。
Analytical Model of Groundwater Flow in a Rectangular Domain for Spatiotemporally Distributed Recharge
This study introduces a reliable analytical solution to the two-dimensional linearised Boussinesq equation, applicable to groundwater flow in an anisotropic rectangular aquifer over an impervious stratum. Validation is performed using a numerical solution based on the finite difference method for the nonlinear Boussinesq equation. Additionally, the proposed two-dimensional analytical model for finite or semi-infinite domains effectively estimates groundwater level changes due to diffuse recharge, with converging simulation results as the finite domain size increases. By incorporating Horton's equation to represent the spatiotemporally varying diffuse recharge, the study provides a more accurate method for estimating groundwater level fluctuations, allowing the model to simulate real-world recharge patterns more effectively than previous analytical models. The analytical simulations for groundwater level estimations in the Zeng Wen river basin agree well with field data and display that the peak groundwater levels shift in the direction at both observation stations, with a time lag of approximately 2–5 days, demonstrating its applicability in predicting groundwater levels under various hydrological and geological conditions. This suggests that the current model offers advantages over previous analytical methods, such as greater accuracy and efficiency, allowing for quicker assessments and broader applicability to various recharge patterns and aquifer conditions.
期刊介绍:
Hydrological Processes is an international journal that publishes original scientific papers advancing understanding of the mechanisms underlying the movement and storage of water in the environment, and the interaction of water with geological, biogeochemical, atmospheric and ecological systems. Not all papers related to water resources are appropriate for submission to this journal; rather we seek papers that clearly articulate the role(s) of hydrological processes.