Abstract
The use of stochastic models in subsurface hydrology is growing at a logistic pace. To tie together a number of different stochastic methodologies for deriving subsurface transport equations, we have put together a brief review of some of the more common techniques. Our attention is confined to a few select methodologies so that we might delve in detail into assumptions required by the various approaches and their strengths and weaknesses. The methods reviewed include: Martingale, stochastic-convective, stochastic-relativist, spectral-integral, perturbative, statistical-mechanical, and generalized hydrodynamics. Within this list, we also have included a few stochastic methodologies which have been used solely to develop expressions for the dispersion tensor.
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Cushman, J.H. Development of stochastic partial differential equations for subsurface hydrology. Stochastic Hydrol Hydraul 1, 241–262 (1987). https://doi.org/10.1007/BF01543097
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DOI: https://doi.org/10.1007/BF01543097