Water levels in aquifers typically vary in response to time‐varying rates of recharge, suggesting the possibility of inferring time‐varying recharge rates on the basis of long‐term water level records. Presumably, in the southwestern United States (Arizona, Nevada, New Mexico, southern California, and southern Utah), rates of mountain front recharge to alluvial aquifers depend on variations in precipitation rates due to known climate cycles such as the El Niño‐Southern Oscillation index and the Pacific Decadal Oscillation. This investigation examined the inverse application of a one‐dimensional analytical model for periodic flow described by Lloyd R. Townley in 1995 to estimate periodic recharge variations on the basis of variations in long‐term water level records using southwest aquifers as the case study. Time‐varying water level records at various locations along the flow line were obtained by simulation of forward models of synthetic basins with applied sinusoidal recharge of either a single period or composite of multiple periods of length similar to known climate cycles. Periodic water level components, reconstructed using singular spectrum analysis (SSA), were used to calibrate the analytical model to estimate each recharge component. The results demonstrated that periodic recharge estimates were most accurate in basins with nearly uniform transmissivity and the accuracy of the recharge estimates depends on monitoring well location. A case study of the San Pedro Basin, Arizona, is presented as an example of calibrating the analytical model to real data.