Analysis of space-time non-stationary patterns of rainfall-groundwater interactions by integrating empirical orthogonal function and cross wavelet transform methods

Rainfall-groundwater interactions are complex and can depend upon a variety of hydro-geological and geographical conditions and can commonly present high nonlinearity. This study proposed an integration of cross wavelet transform and empirical orthogonal function (EOF) analysis to analyze the space-time nonlinear relationships between the precipitation and groundwater changes. The proposed method was applied to investigating the non-stationary and nonlinear precipitation-groundwater relationships in Pingtung Plain aquifer during 2005-2010. We analyzed daily groundwater and rainfall observations at 47 wells and 27 stations across the study area operated by Taiwan Water Resources Agency and Central Weather Bureau respectively. Results show that EOF method revealed three major space-time patterns of the groundwater levels. The cross wavelet transform further identified the lagged effects between precipitation and groundwater changes. The temporal lags can vary not only with respect to the temporal scales of groundwater processes, but also the different identified groundwater regions, which can associate with distinct physical mechanisms. In general, the lagged periods between high frequency signals of precipitation and groundwater can range from 0 to 18. days, showing how rainfall events perturbed the groundwater levels across space. The long-term lags for the three identified underlying groundwater processes were 3.71, 56.6, and 72.07. days, respectively, showing seasonal recharge patterns can depend upon the geographical and geological conditions. Our results distinguished the space-time recharge processes in different frequencies, which present nonlinear and non-stationary rainfall-recharge interactions of a groundwater system, which can be spatially and frequency dependent.