SCALING THE GROUND-WATER FLOW EQUATION

Stochastic representation of aquifer parameters is adopted to incorporate their macroscopic variability (e.g. the horizontal variability at the scale of the order 1-10 m) into modeling the megascopic flow of ground water (i.e. the scale of the order of 1 km). The mathematical expression of the dynamics of megascopic ground water flow led to two deterministic coupled partial differential equations that must be solved simultaneously for the hydraulic head. The hydraulic head and the transmissivity are assumed to come from a joint Gaussian distribution, and the moment generating function is used to solve the closure problem. The assumption of a Gaussian distribution is more realistic for field applications than the commonly used perturbation techniques which neglect high-order moments of transmissivity and hydraulic head. The utility of the megascopic formulation of the ground water flow equation is demonstrated for the case of an aquifer in hydraulic connection with a stream. The small-scale macroscopic variability of aquifer transmissivity influences the megascopic behavior of the flow in the aquifer in both space and time. We propose to use the discrete kernels approach to reduce the amount of computations in stochastic ground water models.