Calibration of transient groundwater models using time series analysis and moment matching

A comprehensive and efficient approach is presented for the calibration of transient groundwater models. The approach starts with the time series analysis of the measured heads in observation wells using all active stresses as input series, which may include rainfall, evaporation, surface water levels, and pumping. The time series analysis results in the impulse response function of each stress at the observation well. For each impulse response function, the temporal moments M0 and M1 may be computed. Both moments fulfill differential equations that are equivalent to the differential equation for steady groundwater flow, with known values along physical boundaries. The model of M0 may be calibrated for the transmissivity, as it does not depend on the storage coefficient; the computed values of M0 at the observation wells are used for calibration. The model of M1 may be calibrated for the storage coefficient, once the transmissivity is known from the M0 model; the computed values of M1 at the observation wells are used for calibration. The approach is intended for systems that may be approximated as linear. In summary, our proposed calibration process for transient models reduces to the calibration of only two steady models. Several examples are given to demonstrate the accuracy and efficiency of the proposed approach.