Modelling correlations between meteoric forcing and groundwater level in a karst aquifer well

This study uses two complementary stochastic approaches to obtain information about the time response of the groundwater level (output) from a well in the Salento Miocene karst aquifer (southern Italy), subjected to the meteoric forcing of both precipitation and atmospheric pressure (inputs). First, a Langevin equation is used to study the shape of the output correlation functions when forced by two correlated random inputs (a delta-correlated process as precipitation and an exponentially correlated process as atmospheric pressure). The presence of a delayed maximum as consequence of the non-vanishing covariance of the inputs is found. Then, a least square deconvolution is applied as a discrete transfer function model to obtain the response function coefficients for the cross-correlograms of the measured groundwater levels with the precipitation or net infiltration and the atmospheric pressure. Atmospheric pressure has a relevant effect on the groundwater level and is cross correlated to the precipitation in the observed time series. The cross correlograms between output and inputs have been reconstructed with the aim to disentangle the effects of the observed meteoric inputs on the groundwater levels. Thus, the effect of correlations in the deconvolution coefficients is discussed and the inferred results for the groundwater level dynamics in the well are outlined in both the time and the frequency domain. Both approaches suggest the attribution of the short-term maximum in the precipitation-groundwater level cross-correlograms to the correlations between the input forcings, and not specifically to the precipitation recharge. Consequently, as result of the least square deconvolution for the response function, only a delayed medium-term response of about 80 days duration in the groundwater level is attributed to the net infiltration,