ONE-DIMENSIONAL STOCHASTIC-ANALYSIS IN LEAKY AQUIFERS SUBJECT TO RANDOM LEAKAGE

The problem of one-dimensional groundwater flow in a homogeneous leaky aquifer is analyzed within a stochastic framework. The stochastic ana lysis is straightforward and exact; it is based on a closed-form solut ion obtained using the Laplace transform method. The solution relates linearly a stochastic perturbation of the aquifer head to uncertainty in the initial aquifer head and stochastic fluctuations of the water t able in an overlying phreatic aquifer. Autocorrelation functions for t he aquifer head, the leakage flow, and the base flow are developed for two cases of the water table fluctuations, namely, delta-correlation fluctuations (i.e., white noise) and fully correlated fluctuations. Th e analysis clearly demonstrates that the stochasticity of the aquifer hydraulic response is highly controlled by the geohydrology of the pro blem: the geometry given by aquifer length and the hydraulic propertie s given by the leakage factor, aquifer diffusivity, and aquitard leaka nce. The results show that the temporal variance of aquifer head induc ed by a random initial head persists longer for larger values of the d imensionless leakage factor. The smaller the dimensionless leakage fac tor, the greater the variance of aquifer head, leakage, and base flow. Asymptotic results obtained for large times reveal that (1) watertabl e fluctuations that are white noise induce a cumulative leakage whose variance is asymptotically linear in time, and quadratic in time if th e fluctuations are fully correlated: (2) the variance of the aquitard leakage flux is asymptotically equal to the variance of its time avera ge if the fluctuations of the water table are fully correlated in time ; (3) cumulative base flow and cumulative leakage have identical autoc orrelation function when water table fluctuations are fully correlated in time; and (4) the attenuating characteristic of aquifer flow syste ms, often observed in the spectral domain, is evident in the case of h ighly variable water table fluctuations (white noise); the base flow h as a finite variance when the leakage flux has an infinite variance.