A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics

The basic aim of this paper is to formulate rigorous conservation equations for mass, momentum, energy and entropy for a watershed organized around th e channel network. The approach adopted is based on the subdivision of the whole watershed into smaller discrete units, called representative elementa ry watersheds (REW), and the formulation of conservation equations for thes e REWs. The REW as a spatial domain is divided into five different subregio ns: (1) unsaturated zone; (2) saturated zone; (3) concentrated overland how ; (4) saturated overland flow; and (5) channel reach. These subregions all occupy separate volumina. Within the REW, the subregions interact with each other, with the atmosphere on top and with the groundwater or impermeable strata at the bottom, and are characterized by typical flow time scales. The balance equations are derived for water, solid and air phases in the un saturated zone, water and solid phases in the saturated zone and only the w aterphase in the two overland flow zones and the channel. In this way REW-s cale balance equations, and respective exchange terms for mass, momentum, e nergy and entropy between neighbouring subregions and phases, are obtained Averaging of the balance equations over time allows to keep the theory gene ral such that the hydrologic system can be studied over a range of time sca les. Finally, the entropy inequality for the entire watershed as an ensembl e of subregions is derived as constraint-type relationship for the developm ent of constitutive relationships, which are necessary for the closure of t he problem. The exploitation of the second law and the derivation of consti tutive equations for specific types of watersheds will be the subject of a subsequent paper. (C) 1998 Elsevier Science Limited. All rights reserved.