Abstract. The Representative Elementary Watershed (REW) approach proposed by Reggiani et al. (1998Reggiani et al. ( , 1999 represents an attempt to develop a scale adaptable modeling framework for the hydrological research community. 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 widelyused 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 within the Thermodynamic Watershed Hydrological Model (THModel, Tian, 2006) and then applied to the headwaters of the Urumqi River in Western China. The results of the 5-year calibration and 3-year validation analyses show that THModel can indeed simulate runoff processes in this glacier and snow-dominated catchment reasonably well, which shows the prospects of the REW approach and the developed closure schemes for cold regions processes.

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 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 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 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 validity of the developed closure schemes for cold regions processes.

Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement--soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale. scale issue, constitutive relationship, soil water retention curve, Richards equation