An Analytical Solution of Boussinesq Equation to Predict Water Table Fluctuations Due to Time Varying Recharge and Withdrawal from Multiple Basins, Wells and Leakage Sites

Recharging and pumping are the integral part of any scheme of ground water resources development and both processes significantly affect the dynamic behavior of the aquifer system. Leakage from the aquifer’s base, if present, is other process which affects the water table variation. Therefore, an accurate estimation of water table fluctuation induced by recharging, pumping and leakage is pre-requisite to ensure sustainability of groundwater resources. In the present work an analytical solution of a 2-D linearized Boussinesq equation is developed to predict water table fluctuations in the presence of time varying recharge, pumping and leakage from any number of recharge basins, wells and leakage sites of any dimension for any number of recharge and pumping cycles. The rate of time varying recharge (or pumping) is approximated by using a series of linear elements of different lengths and slopes which are dependent on the nature of variation in the recharge (or pumping) rate. Application of the solution in the prediction of water table fluctuation in the presence of time varying recharge, pumping and leakage is demonstrated with the help of a numerical example. These numerical results indicate significant effect of the time varying recharge/pumping rates and leakage on the water table variation. Such information is useful for the proper management of groundwater.