Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile
Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile
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DOI：
10.1029/2005wr004241
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发表时间：
2005-11
影响因子：
5.4
通讯作者：
D. Rupp;J. Selker
中科院分区：
文献类型：
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作者：
D. Rupp;J. Selker
Boussinesq方程描述排水到一个完全贯穿的渠道的解决方案已被用于含水层表征。两个解析解存在的早期和晚期排水从饱和，均质，水平含水层瞬时下降。放电Q的解可以表示为dQ/dt = − aQ B，其中a是常数，B在早期和晚期分别取3和3/2的值。虽然许多因素可能导致偏离这两个预测，我们探讨了渗透性随深度下降的影响，因为它是已知的，许多天然土壤表现出这种特性。我们推导出一组新的解析解的Boussinesq方程k zn，其中k是饱和导水率，z是一个不可渗透的基础上的高度，和n是一个常数。结果表明，在早期，B保持为3，而与n的值无关，而在晚期，当n从0变化到∞时，B的范围从3/2到2。与流量相似，后期水位高度h可以表示为dh/dt = −chd，其中d = 2，k为常数，d → ∞，n → ∞。从理论上讲，包含幂律k剖面不会使含水层参数估计复杂化，因为当将B拟合到后期数据时，可以求解n，而之前假定B为3/2。然而，如果早期或晚期数据缺失，则存在额外的未知数。在适当的条件下，地下水位高度的测量可以用来解决一个未知的参数。
Solutions to the Boussinesq equation describing drainage into a fully penetrating channel have been used for aquifer characterization. Two analytical solutions exist for early‐ and late‐time drainage from a saturated, homogeneous, and horizontal aquifer following instantaneous drawdown. The solutions for discharge Q can be expressed as dQ/dt = −aQb, where a is constant and b takes on the value 3 and 3/2 for early and late time, respectively. Though many factors can contribute to departures from the two predictions, we explore the effect of having permeability decrease with depth, as it is known that many natural soils exhibit this characteristic. We derive a new set of analytical solutions to the Boussinesq equation for k ∝ zn, where k is the saturated hydraulic conductivity, z is the height above an impermeable base, and n is a constant. The solutions reveal that in early time, b retains the value of 3 regardless of the value of n, while in late time, b ranges from 3/2 to 2 as n varies from 0 to ∞. Similar to discharge, water table height h in late time can be expressed as dh/dt = −chd, where d = 2 for constant k and d → ∞ as n → ∞. In theory, inclusion of a power law k profile does not complicate aquifer parameter estimation because n can be solved for when fitting b to the late‐time data, whereas previously b was assumed to be 3/2. However, if either early‐ or late‐time data are missing, there is an additional unknown. Under appropriate conditions, water table height measurements can be used to solve for an unknown parameter.