Water-table variation in a sloping aquifer due to random recharge

Variation in the level of the water table is closely linked with recharge. Therefore, any uncertainty associated with the recharge rate is bound to affect the nature of the water-table fluctuation. In this note, a ditch-drainage problem of a sloping aquifer is considered to investigate the effect of uncertainty in the recharge rate on water-table fluctuation. The rate of recharge is taken as an exponentially decaying function with its decay constant as a Gaussian random variable. Expressions for the first two moments of the water-table height, i.e. mean and standard deviation, are presented. By using these expressions, the effect of uncertainty in the recharge rate on the water-table fluctuation has been analyzed with the help of a numerical example.