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Analytical Solutions for Fresh Groundwater Lenses in Small Strip Islands With Spatially Variable Recharge
Water Resources Research ( IF 4.6 ) Pub Date : 2021-07-16 , DOI: 10.1029/2020wr029497
Yuening Tang 1 , Min Yan 2 , Xiaoxiong Wang 3 , Chunhui Lu 2 , Jian Luo 1
Affiliation  

Groundwater lens may provide the primary freshwater supply for the inhabitants of small islands. The lens profile and volume are sensitive to spatially variable recharge caused by topography, soil type, land cover, evapotranspiration and human activities. We derive analytical solutions based on the sharp-interface approximation to describe transient and steady-state lens profiles for spatially variable recharge rates in small strip islands. The derived solutions are validated by a steady-state solution for simple spatial recharge patterns and numerical simulations. Numerical investigations show that the spatial recharge pattern has a significant impact on the lens profile. For a given constant total recharge, smaller recharge areas or a more concentrated recharge rate can result in a larger lens volume. The volume increase can be over 20% compared with the lens volume of a uniform recharge. For the steady-state lens profile corresponding to a point recharge, the squared lens thickness peaks at the recharge location and linearly decreases to the boundary, resulting in a triangle shape for the profile of squared lens thickness. Moreover, compared with recharges in other locations, recharge in a small area at the domain center has the greatest impact. Uncertainty analysis can be conveniently implemented based on the derived analytical solution to investigate the lens behavior under spatially variable recharge with uncertainties. Results show that the lens volume tends to have a larger variance for a recharge rate with a higher variance and longer correlation length.

中文翻译:

空间可变补给小带状岛屿淡水透镜体的分析解决方案

地下水透镜体可为小岛居民提供主要的淡水供应。透镜剖面和体积对由地形、土壤类型、土地覆盖、蒸散和人类活动引起的空间可变补给敏感。我们基于锐界面近似推导出解析解,以描述小带状岛中空间可变充电率的瞬态和稳态透镜轮廓。导出的解决方案通过简单空间补给模式和数值模拟的稳态解决方案进行验证。数值研究表明,空间补给模式对透镜轮廓有显着影响。对于给定的恒定总充电量,较小的充电区域或更集中的充电率可导致更大的镜头体积。与均匀充电的镜头体积相比,体积增加可超过20%。对于对应于点再充电的稳态透镜轮廓,平方透镜厚度在再充电位置达到峰值并线性减小到边界,从而导致透镜厚度平方的轮廓为三角形。而且,相对于其他地点的充值,在域中心的小区域充值影响最大。基于导出的解析解,可以方便地进行不确定性分析,以研究具有不确定性的空间可变补给下的透镜行为。结果表明,对于具有较高方差和较长相关长度的再充电率,透镜体积趋于具有较大方差。对于对应于点再充电的稳态透镜轮廓,平方透镜厚度在再充电位置达到峰值并线性减小到边界,从而导致透镜厚度平方的轮廓为三角形。而且,相对于其他地点的充值,在域中心的小区域充值影响最大。基于导出的解析解,可以方便地进行不确定性分析,以研究具有不确定性的空间可变补给下的透镜行为。结果表明,对于具有较高方差和较长相关长度的再充电率,透镜体积趋于具有较大方差。对于对应于点再充电的稳态透镜轮廓,平方透镜厚度在再充电位置达到峰值并线性减小到边界,从而导致透镜厚度平方的轮廓为三角形。而且,相对于其他地点的充值,在域中心的小区域充值影响最大。基于导出的解析解,可以方便地进行不确定性分析,以研究具有不确定性的空间可变补给下的透镜行为。结果表明,对于具有较高方差和较长相关长度的再充电率,透镜体积趋于具有较大方差。导致方形透镜厚度轮廓的三角形形状。而且,相对于其他地点的充值,在域中心的小区域充值影响最大。基于导出的解析解,可以方便地进行不确定性分析,以研究具有不确定性的空间可变补给下的透镜行为。结果表明,对于具有较高方差和较长相关长度的再充电率,透镜体积趋于具有较大方差。导致方形透镜厚度轮廓的三角形形状。而且,相对于其他地点的充值,在域中心的小区域充值影响最大。基于导出的解析解,可以方便地进行不确定性分析,以研究具有不确定性的空间可变补给下的透镜行为。结果表明,对于具有较高方差和较长相关长度的再充电率,透镜体积趋于具有较大方差。
更新日期:2021-07-30
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