Technical note: Discharge response of a confined aquifer with variable thickness to temporal nonstationary random recharge processes

Abstract. This work develop a transfer function to describe the variation of the integrated specific discharge in response to the temporal variation of the rainfall event in the frequency domain. It is assumed that the rainfall-discharge process takes place in a confined aquifer with variable thickness, and it is treated as nonstationary in time to represent the stochastic nature of the hydrological process. The presented transfer function can be used to quantify the variability of the integrated discharge field induced by the variation of rainfall field or to simulate the discharge response of the system to any varying rainfall input at any time resolution using the convolution model. It is shown that with the Fourier-Stieltjes representation approach a closed-form expression for the transfer function in the frequency domain can be obtained, which provide a basis for the analysis of the influence of controlling parameters occurring in the rainfall rate and integrated discharge models on the transfer function.