Evaluation of correlations between precipitation, groundwater fluctuations, and lake level fluctuations using spectral methods (Wisconsin, USA)

Spectral methods and 2 years of daily data were used to estimate the phase lag between precipitation and groundwater-level response, and two decades of quarterly data were used to analyze the interaction between precipitation, lake levels and groundwater in the Trout Lake watershed located in Vilas County, Wisconsin, USA. The phase-lag function between precipitation and groundwater response is used to estimate recharge travel time. The recharge travel time and precipitation–groundwater–lake interactions have been traditionally studied using time-domain methods such as physically-based modeling. In this article, the innovative and efficient use of spectral methods is demonstrated to uncover the time scales that are significant in those interactions and estimate the recharge travel time, which is extracted from the underlying daily time series data. The results consistently show that precipitation leads groundwater-level response by up to 5 days in all cases. The effects of precipitation on lake and groundwater levels display strong similarities. Both the precipitation–lake level and the precipitation–groundwater level coherency functions show significant peaks at interannual and seasonal frequencies. The groundwater level–lake level coherency function shows a significant, broad peak at interannual frequencies, and no significant peak at seasonal frequencies, demonstrating the predominance of annual and lower frequencies in groundwater–lake interaction.