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

2007 ◽  
Vol 4 (5) ◽  
pp. 3627-3686
Author(s):  
L. Mou ◽  
F. Tian ◽  
H. Hu ◽  
M. Sivapalan
Keyword(s):  
Energy Balance ◽  
Soil Freezing ◽  
Western China ◽  
Unfrozen Water ◽  
Balance Equations ◽  
Freezing And Thawing ◽  
Modeling Framework ◽  
Cold Regions ◽  
Constitutive Relationships ◽  
Unfrozen Water Content

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.

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

2008 ◽  
Vol 12 (2) ◽  
pp. 565-585 ◽  
Author(s):  
L. Mou ◽  
F. Tian ◽  
H. Hu ◽  
M. Sivapalan
Keyword(s):  
Energy Balance ◽  
Soil Freezing ◽  
Western China ◽  
Unfrozen Water ◽  
Balance Equations ◽  
Freezing And Thawing ◽  
Modeling Framework ◽  
Cold Regions ◽  
Constitutive Relationships ◽  
Unfrozen Water Content

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. (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. 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.

scholarly journals Extension of the Representative Elementary Watershed approach for cold regions via explicit treatment of energy related processes

2006 ◽  
Vol 10 (5) ◽  
pp. 619-644 ◽  
Author(s):  
F. Tian ◽  
H. Hu ◽  
Z. Lei ◽  
M. Sivapalan
Keyword(s):  
Energy Balance ◽  
Hydrological Modeling ◽  
Simulation Method ◽  
Subsequent Paper ◽  
Balance Equations ◽  
Freezing And Thawing ◽  
Momentum Exchange ◽  
Stream Network ◽  
Cold Regions ◽  
Constitutive Relationships

Abstract. The paper extends the Representative Elementary Watershed (REW) theory for cold regions through explicit treatment of energy balance equations to include associated processes and process descriptions. A new definition of REW is presented which subdivides the REW into six surface sub-regions and two subsurface sub-regions. Vegetation, snow, soil ice, and glacier ice are included in the system so that such phenomena as evaporation/transpiration, melting, freezing, and thawing can be modeled in a physically reasonable way. The sub-stream-network is separated from other sub-regions so that the sub-REW-scale runoff routing function can be modeled explicitly. The final system of 24 ordinary differential equations (ODEs) can meet the requirements of most hydrological modeling applications, and the formulation procedure is re-arranged so that further inclusion of sub-regions and substances could be done more easily. The number of unknowns is more than the number of equations, which leads to the indeterminate system. Complementary equations are provided based on geometric relationships and constitutive relationships that represent geomorphological and hydrological characteristics of a watershed. Reggiani et al. (1999, 2000, 2001) and Lee et al. (2005b) have previously proposed sets of closure relationships for unknown mass and momentum exchange fluxes. Tian (2006) has applied Lee's procedures and formulas and Monte Carlo simulation method, and has come up with a determinate system based on the equations, though precluding energy balance ones, proposed in this paper. The additional geometric and constitutive relationships required to close the new set of balance equations will be pursued in a subsequent paper.

scholarly journals Extension of the Representative Elementary Watershed approach by incorporating energy balance equations

2006 ◽  
Vol 3 (2) ◽  
pp. 427-498
Author(s):  
F. Tian ◽  
H. Hu ◽  
Z. Lei ◽  
M. Sivapalan
Keyword(s):  
Energy Balance ◽  
Hydrological Modeling ◽  
Subsequent Paper ◽  
Balance Equations ◽  
Freezing And Thawing ◽  
Momentum Exchange ◽  
Constitutive Relationships ◽  
Glacier Ice ◽  
Watershed Approach ◽  
Definition Of

Abstract. The paper extends the Representative Elementary Watershed (REW) theory for cold regions by extending the energy balance equations to include associated processes and descriptions. A new definition of REW is presented which separates the REW into six surface sub-regions and two subsurface sub-regions. Soil ice, vegetation, vapor, snow and glacier ice are included in the system so that such phenomena as evaporation, transpiration, freezing and thawing can be modeled in a physically reasonable way. The final system of 24 ordinary differential equations (ODEs) can meet the requirement for most hydrological modeling applications, and the formulation procedure is re-arranged so that further inclusion of sub-regions and substances could be done more easily. The number of unknowns is more than the number of equations, which leads to the indeterminate system. Complementary equations are provided based on geometric relationships and constitutive relationships that represent geomorphological and hydrological characteristics of a watershed. Reggiani et al. (1999, 2000, 2001) and Lee et al. (2005b) have previously proposed sets of closure relationships for unknown mass and momentum exchange fluxes. The additional geometric and constitutive relationships required to close the new set of balance equations will be pursued in a subsequent paper.

scholarly journals Coupled cellular automata for frozen soil processes

SOIL ◽  
2015 ◽  
Vol 1 (1) ◽  
pp. 103-116 ◽  
Author(s):  
R. M. Nagare ◽  
P. Bhattacharya ◽  
J. Khanna ◽  
R. A. Schincariol
Keyword(s):  
Cellular Automata ◽  
Phase Change ◽  
Water Content ◽  
Soil Water ◽  
Soil Water Potential ◽  
Frozen Soil ◽  
Soil Freezing ◽  
Unfrozen Water ◽  
First Order ◽  
Unfrozen Water Content

Abstract. Heat and water movement in variably saturated freezing soils is a strongly coupled phenomenon. The coupling is a result of the effects of sub-zero temperature on soil water potential, heat carried by water moving under pressure gradients, and dependency of soil thermal and hydraulic properties on soil water content. This study presents a one-dimensional cellular automata (direct solving) model to simulate coupled heat and water transport with phase change in variably saturated soils. The model is based on first-order mass and energy conservation principles. The water and energy fluxes are calculated using first-order empirical forms of Buckingham–Darcy's law and Fourier's heat law respectively. The liquid–ice phase change is handled by integrating along an experimentally determined soil freezing curve (unfrozen water content and temperature relationship) obviating the use of the apparent heat capacity term. This approach highlights a further subtle form of coupling in which heat carried by water perturbs the water content–temperature equilibrium and exchange energy flux is used to maintain the equilibrium rather than affect the temperature change. The model is successfully tested against analytical and experimental solutions. Setting up a highly non-linear coupled soil physics problem with a physically based approach provides intuitive insights into an otherwise complex phenomenon.

scholarly journals Development of WEP-COR model to simulate land surface water and energy budgets in a cold region

2017 ◽  
Vol 50 (1) ◽  
pp. 99-116 ◽  
Author(s):  
Jia Li ◽  
Zuhao Zhou ◽  
Hao Wang ◽  
Jiajia Liu ◽  
Yangwen Jia ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Water Content ◽  
Heat Fluxes ◽  
Frozen Soil ◽  
Unfrozen Water ◽  
Cold Regions ◽  
Transfer Processes ◽  
Unfrozen Water Content ◽  
Freezing Depth ◽  
Daily Discharge

Abstract The Water and Energy transfer Processes in Cold Regions (WEP-COR) model is an improved version of the Water and Energy transfer Processes in Large basins (WEP-L) model that integrates a multi-layer frozen soil model to simulate the hydrological processes in cold regions and the heat fluxes at different depths of frozen soil. The temperature, water content, freezing depth of the soil, and daily discharge were simulated and compared with observations. The simulated and observed data were used to analyze the runoff flow components. The results showed that the WEP-COR model can effectively simulate the distributions of the soil temperature and water content. The average root mean squared errors of the temperature, unfrozen water content, total water content, and freezing depth of the soil were 1.21 °C, 0.035 cm3/cm3, 0.034 cm3/cm3, and 17.6 cm, respectively. The mean Nash–Sutcliffe efficiency and relative error of the daily discharge were 0.64 and 6.58%, respectively. Compared with the WEP-L model, the WEP-COR model simulated the discharge with higher accuracy, especially during the soil thawing period. This improvement was mainly due to the addition of the frozen soil mechanism. The WEP-COR model can provide support for agricultural and water resources management in cold regions.

Effects of Ambipolar Diffusion on Prominence Thread Models

1994 ◽  
Vol 144 ◽  
pp. 315-321 ◽  
Author(s):  
M. G. Rovira ◽  
J. M. Fontenla ◽  
J.-C. Vial ◽  
P. Gouttebroze
Keyword(s):  
Energy Balance ◽  
Transition Region ◽  
Ambipolar Diffusion ◽  
Line Profiles ◽  
Balance Equations ◽  
Model Calculations ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Theoretical Structure

AbstractWe have improved previous model calculations of the prominence-corona transition region including the effect of the ambipolar diffusion in the statistical equilibrium and energy balance equations. We show its influence on the different parameters that characterize the resulting prominence theoretical structure. We take into account the effect of the partial frequency redistribution (PRD) in the line profiles and total intensities calculations.

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