Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 12 2 2008 10.5194/hess-12-565-2008 http://www.hydrol-earth-syst-sci.net/12/565/2008/ http://www.hydrol-earth-syst-sci.net/12/565/2008/hess-12-565-2008.html http://www.hydrol-earth-syst-sci.net/12/565/2008/hess-12-565-2008.pdf 565 585 2008-03-17 Extension of the Representative Elementary Watershed approach for cold regions: constitutive relationships and an application L. Mou F. Tian tianfq@tsinghua.edu.cn H. Hu M. Sivapalan State Key Laboratory of Hydroscience and Engineering & Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China Departments of Geography & Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 220 Davenport Hall, MC-150, 607 S. Mathews Ave., Urbana, IL 61801, USA 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. (2006) extended the original REW theory for cold regions through explicit treatment of energy balance equations to incorporate associated cold regions processes, such as snow and glacier melting/accumulation, and soil freezing/thawing. 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 schemes for cold regions processes within the extended framework. An 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. 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