A new approximate solution of the one-dimensional Boussinesq equation is presented for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. Estimates for recharge, discharge, and elevation of the water table are given. The simplicity and accuracy of the approximation are compared with exact numerical and analytical solutions. The method of solution is illustrated with several examples including the commonly treated case of a constant boundary head and a nonmonotonically varying boundary head. ¿ 1999 American Geophysical Union