Stochastic representation of aquifer parameters is adopted to incorpor
ate their macroscopic variability (e.g. the horizontal variability at
the scale of the order 1-10 m) into modeling the megascopic flow of gr
ound water (i.e. the scale of the order of 1 km). The mathematical exp
ression of the dynamics of megascopic ground water flow led to two det
erministic coupled partial differential equations that must be solved
simultaneously for the hydraulic head. The hydraulic head and the tran
smissivity 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 negl
ect high-order moments of transmissivity and hydraulic head. The utili
ty 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 transmissi
vity influences the megascopic behavior of the flow in the aquifer in
both space and time. We propose to use the discrete kernels approach t
o reduce the amount of computations in stochastic ground water models.