Articles | Volume 20, issue 3
Hydrol. Earth Syst. Sci., 20, 1225–1239, 2016
https://doi.org/10.5194/hess-20-1225-2016

Special issue: HYPER Droughts (HYdrological Precipitation – Evaporation...

Hydrol. Earth Syst. Sci., 20, 1225–1239, 2016
https://doi.org/10.5194/hess-20-1225-2016

Technical note 22 Mar 2016

Technical note | 22 Mar 2016

Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Chia-Hao Chang, Ching-Sheng Huang, and Hund-Der Yeh Chia-Hao Chang et al.
  • Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan

Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table movement. The solution to the model for the head is developed with the methods of Laplace transform and double-integral transform. Based on Duhamel's theorem, the present solution is applicable to flow problems accounting for arbitrary time-dependent recharge rates. The solution to depth-average head can then be obtained by integrating the head solution to elevation and dividing the result by the aquifer thickness. The use of a rectangular aquifer domain has two merits. One is that the integration for estimating the depth-average head can be analytically achieved. The other is that existing solutions based on aquifers of infinite extent can be considered as special cases of the present solution before the time when the aquifer boundary had an effect on head predictions. With the help of the present solution, the assumption of neglecting the vertical flow effect on the temporal head distribution at an observation point outside a recharge region can be assessed by a dimensionless parameter related to the aquifer horizontal and vertical hydraulic conductivities, initial aquifer thickness, and the shortest distance between the observation point and the edge of the recharge region. The validity of assuming aquifer incompressibility is dominated by the ratio of the aquifer specific yield to its storage coefficient. In addition, a sensitivity analysis is performed to investigate the head response to the change in each of the aquifer parameters.

Download
Short summary
Most previous solutions for groundwater flow due to localized recharge assumed either aquifer incompressibility or 2-D flow without vertical flow. This paper develops a 3-D flow model for hydraulic head change induced by the recharge with random transient rates in a compressible unconfined aquifer. The analytical solution of the model for the head is derived. The quantitative criteria for the validity of those two assumptions are presented by the developed solution.