Drawdown due to Temporally Varying Pumping Discharge: Inversely Estimating Aquifer Parameters

A ramp kernel method is proposed for accurately calculating the drawdown due to any temporal variation in pumping discharge. The use of the ramp kernels assumes the linear variation between the two consecutive measured pumping discharges. The prior studies assume a rectangular variation between the two consecutive measured pumping discharges. In the rectangular variation, a uniform pumping rate is assumed during a time span. An analytical equation for calculating the ramp kernel is derived. An optimization method is used with the proposed ramp kernels for inversely estimating the aquifer parameters from drawdown due to an arbitrary unsteady pumping discharge. Unlike the prior methods, the proposed method accurately identifies the parameters even when the sampling interval for the drawdown and pumping discharge is longer than that needed for assuming a linear variation. The proposed method outperforms the prior method. Application of the proposed method is illustrated using examples.