Extension of the Representative Elementary Watershed approach for cold regions: constitutive relationships and an application

Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract The representative elementary watershed (REW) approach proposed by Reggiani et al. (1998, 1999) represents an attempt to develop a scale adaptable modeling framework for the hydrological research community. Tian et al. (2006a) extended the original REW theory for cold regions through explicit treatment of energy balance equations to 5 incorporate associated cold regions processes, such as melting and accumulation of glacier and snow, and freezing and thawing of soil ice. However, constitutive relationships for the cold regions processes needed to complete these new balance equations have been left unspecified in this derivation. In this paper we propose a set of closure scheme for cold regions processes within the extended framework provided by Tian 10 et al. (2006a). A rigorous energy balance method is proposed to close the balance equations of melting/accumulation processes as well as the widely-used and conceptual degree-day method, whereas the closure schemes for soil freezing and thawing are based on the " maximum unfrozen-water content " model. The proposed closure schemes are coupled to the previously derived balance equations and implemented 15 within Thermodynamic Watershed Hydrological Model (THModel, Tian, 2006b) and then applied to the headwaters of the Urumqi River in Western China. The results of the 4-year calibration and 1-year validation analyses show that THModel can indeed simulate runoff processes in this snow and glacier-dominated catchment very well, which confirms the applicability of the modeling based on the REW approach and the 20 validity of the developed closure schemes for cold regions processes.