The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect of all individual components acting on a single component, and thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture and parametrize the numerous local interactions related to lateral fluxes of soil water in terms of the average soil moisture.
Porporato, A., M. Bartlett (2016): Mean field approach to watershed hydrology. Calhoun CZO 2016 Summer Science Meeting, Clinton, SC.
This Paper/Book acknowledges NSF CZO grant support.