2-DIMENSIONAL STOCHASTIC-ANALYSIS AND OPTIMAL ESTIMATION IN AQUIFERS - RANDOM RECHARGE

This paper investigates two-dimensional aquifer flow under naturally v ariable recharge and its application to optimal estimation in groundwa ter. The adopted framework is a stochastic one in which the governing stochastic equation is solved quasi-analytically using the Galerkin fi nite element method and matrix exponentials. The continuous-time stoch astic solution relates head perturbations to random initial head and a convolution of the pertinent stochastic recharge process. Based on th e quasi-analytical solution, continuous time autocorrelation matrices for aquifer head are developed conforming to (1) white noise recharge fluctuations in time and (2) fully correlated recharge fluctuations in time. From a stochastic point of view, transient aquifer flow in its conventional meaning is only inferred when recharge fluctuations ai e fully correlated in time, provided that the mean flow approaches stead y state. Application to optimal state feedback estimation is demonstra ted by adopting Kalman filtering and forecasting to a numerical experi ment consisting of two-dimensional aquifer flow instigated by variable leakage. Filtering results demonstrate that under scarce measurements , statistical conditioning on available measurements Can result in an estimated aquifer hydraulic response that captures the actual variabil ity that may exist under natural field conditions. Forecasted aquifer heads, however, are sufficient for a relatively short period; they con verge asymptotically to their respective average values.