Stochastic description of infiltration between aquifers

Aim of this work is to propose a stochastic description of the leakage between two aquifers separated by a semi-permeable layer with low hydraulic conductivity. The source of uncertainty here considered is the random fluctuation of the phreatic surface of surficial aquifer, originated from random rainfall events. The study focuses on an area surrounding a pumping well penetrating the deep aquifer and impacting its piezometric level, where infiltration from the surficial aquifer can be more harmful. Closed form expressions for the leakage between the surficial and the deep aquifer are used to obtain the long-term probability distribution of leakage flow rate, assuming the shallow phreatic surface dynamics modeled with a Poisson-driven stochastic process. A sensitivity analysis is performed to verify the variability of the probability distribution of leakage within the range of feasible parameter values, then the stochastic model is applied to three field cases where time series of the piezometric levels of the phreatic aquifer are available. Results show that the induced variability of the discharge flowing between aquifers is remarkable and that in general it cannot be neglected despite the low hydraulic conductivity of the semi-permeable layer. The proposed probabilistic model is a useful tool for evaluating the risk associated to contaminant transport into deep aquifers and its fate in relation to groundwater withdrawals.