THE UTILITY OF WAVELET ANALYSIS TO INFORM LINEAR MODELS OF HYDROLOGICAL TIME SERIES: APPLICATION TO QUANTIFY THE COMPARATIVE EFFECTS OF CLIMATE AND PUMPING ON SPRING DISCHARGE AT MADISON BLUE SPRINGS, FLORIDA (Invited Presentation)

The use of wavelet analysis is an under-utilized technique to inform and understand causative effects on hydrological time series. Commonly used in geophysics and atmospheric subdisciplines, wavelet analysis has seen a slower acceptance for use in hydrological applications. As a major advantage of wavelet analysis is the time-frequency localization which can be used to characterize temporally variant power of a signal, it is well suited for hydrological time series which commonly exhibit non-stationarity.

The core benefit of wavelet analysis derives from the signal decomposition using wavelets: which are finite oscillations that are modified by coefficients as they are passed over a windowed time series signal. This process effectively filters the signal into high and low frequency components providing multiresolution decomposition of the time series into distinct signals. The decomposed signal can be analyzed for temporally varying periodicities and patterns, correlated to potential impactful exogenous signals and used to inform additional model development to improve accuracy of model predictions.

We illustrate the benefit and utility in wavelet analysis to complement and inform linear models of hydrological time series. The analysis is applied to a karst springshed in northern Florida, where it is unknown whether agricultural pumping transiently impacts spring discharge. The aim of the model environment is to quantify the comparative effects of climate and pumping on Madison Blue Springs (MBS) which discharges from the highly transmissive Floridan Aquifer System (FAS). As the groundwater contributing area to MBS sources municipal pumping wells and irrigation for an agriculturally active region, the effects of pumping may have a significant impact on seasonal and long-term spring discharge. We analyze the strength of the long-term and seasonal relationship between transient pumping and climate with MBS discharge using wavelet analysis and coherence. The energy at each decomposed level is then used to relatively determine the time-variant impacts of climate and pumping on MBS discharge. The decomposed MBS signal is then used to inform and develop hierarchal Autoregressive Moving Average (ARMA) models to quantify the effects of pumping on seasonal and long-term discharge.