Extension of the Representative Elementary Watershed approach by incorporating energy balance equations

Abstract

The paper extends the Representative Elementary Watershed (REW) theory for cold regions by extending the energy balance equations to include associated processes and descriptions. A new definition of REW is presented which separates the REW into six surface sub-regions and two subsurface sub-regions. Soil ice, vegetation, vapor, snow and glacier ice are included in the system so that such phenomena as evaporation, transpiration, freezing and thawing can be modeled in a physically reasonable way. The final system of 24 ordinary differential equations (ODEs) can meet the requirement for most hydrological modeling applications, and the formulation procedure is re-arranged so that further inclusion of sub-regions and substances could be done more easily. The number of unknowns is more than the number of equations, which leads to the indeterminate system. Complementary equations are provided based on geometric relationships and constitutive relationships that represent geomorphological and hydrological characteristics of a watershed. Reggiani et al. (1999, 2000, 2001) and Lee et al. (2005b) have previously proposed sets of closure relationships for unknown mass and momentum exchange fluxes. The additional geometric and constitutive relationships required to close the new set of balance equations will be pursued in a subsequent paper.