A unifying framework for watershed thermodynamics: constitutive relationships

The balance equations for mass and momentum, averaged over the scale of a w atershed entity, need to be supplemented with constitutive equations relati ng flow velocities, pressure potential differences, as well as mass and for ce exchanges within and across the boundaries of a watershed. In this paper , the procedure for the derivation of such constitutive relationships is de scribed in detail. This procedure is based on the method pioneered by Colem an and Noll through exploitation of the second law of thermodynamics acting as a constraint-type relationship. The method is illustrated by its applic ation to some common situations occurring in real world watersheds. Thermod ynamically admissible and physically consistent constitutive relationships for mass exchange terms among the subregions constituting the watershed (su bsurface zones, overland flow regions, channel) are proposed. These constit utive equations are subsequently combined with equations of mass balance fo r the subregions. In addition, constitutive relationships for forces exchan ged amongst the subregions are also derived within the same thermodynamic f ramework. It is shown that, after linearisation of the latter constitutive relations in terms of the velocity, a watershed-scale Darcy's law governing flow in the unsaturated and saturated zones can be obtained. For the overl and flow, a second order constitutive relationship with respect to velocity is proposed for the momentum exchange terms, leading to a watershed-scale Chezy formula. For the channel network REW-scale Saint-Venant equations are derived. Thus, within the framework of this approach new relationships gov erning exchange terms for mass and momentum are obtained and, moreover, som e well-known experimental results are derived in a rigorous manner. (C) 199 9 Elsevier Science Ltd. All rights reserved.