Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 10 5 2006 10.5194/hess-10-619-2006 http://www.hydrol-earth-syst-sci.net/10/619/2006/ http://www.hydrol-earth-syst-sci.net/10/619/2006/hess-10-619-2006.html http://www.hydrol-earth-syst-sci.net/10/619/2006/hess-10-619-2006.pdf 619 644 2006-09-13 Extension of the Representative Elementary Watershed approach for cold regions via explicit treatment of energy related processes F. Tian tianfq@tsinghua.edu.cn H. Hu Z. Lei M. Sivapalan Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China Department of Geography, University of Illinois at Urbana-Champaign 220 Davenport Hall, MC-150, 607 South Mathews Avenue, Urbana, IL 61801, USA 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. Abbott, M. B., Bathurst, J. C., Cunge, J. A., O'Connell, P. E., and Rasmussen, J.: An introduction to the European Hydrological System – Systeme Hydrologique European, SHE, 1: History and philosophy of a physically based, distributed modeling system, J. Hydrol., 87, 45–59, 1986a. Abbott, M. B., Bathurst, J. C., Cunge, J. A., O'Connell, P. E., and Rasmussen, J.: An introduction to the European Hydrological System – Systeme Hydrologique European, SHE, 2: Structure of a physically based, distributed modeling system, J. Hydrol., 87, 61–77, 1986b. Arnold, J., Srinivasan, G. R., Muttiah, R. S., and Williams, J. R.: Large area hydrologic modeling and assessment, part I: Model development, J. Amer. Water Res. Assoc., 34, 73–89, 1998. Beven, K. J. and Kirkby, M. J.: A physically-based variable contributing area model of basin hydrology, Hydrol. Sci. Bull., 24, 43–69, 1979. Beven, K. J., Calver, A., and Morris, E.: The Institute of Hydrology distributed model, Institute of Hydrology Report No. 98, UK, 1987. Beven, K. J.: Changing ideas in hydrology-the case of physically-based models, J. Hydrol., 105, 157–172, 1989. Beven, K. J.: Prophecy, reality and uncertainty in distributed hydrological modeling, Adv. Water Resour., 16, 41–51, 1993. Beven, K. J.: A discussion of distributed modelling, in: Distributed Hydrological Modelling, edited by: Refsgaard, J. C. and Abbott, M. B., Kluwer, Dordrecht, Netherlands, 255–278, 1996. Beven, K. J.: Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system, Hydrol. Processes, 16, 189–206, 2002. Calver, A. and Wood, W. L.: The Institute of Hydrology distributed model, in: Computer models of watershed hydrology, edited by: Singh, V. P., Water Resources Publications, USA, 595–626, 1995. Cao, Y. and Liu, C.: The development of snow-cover mapping from AVHRR to MODIS, Geography and Geo-Information Science, 21, 15–19, 2005. Chen, X., Li, X., Lu, A., and Li, W.: Progresses on quantitative remote sensing of snowcover, Remote Sensing Technology and Application, 11, 46–52, 1996. Cong, Z.: Study on the coupling between the winter wheat growth and the water-heat transfer in soil-plant-atmosphere continuum (dissertation), Tsinghua University, China, 2003. Duffy, C. J.: A two-state integral-balance model for soil moisture and groundwater dynamics in complex terrain, Water Resour. Res., 32, 2421–2434, 1996. Dunne, T., Moore, T. R., and Taylor, C. H.: Recognition and prediction of runoff-producing zones in humid regions, Hydrol. Sci. J., 20(3), 305–327, 1975. Dunne, T.: Field studies of hillslope flow processes, in: Hillslope Hydrology, edited by: Kirkby, M. J., John Wiley & Sons, Chichester, UK, 227–293, 1978. Ewen, J.: "Blueprint" for the UP Modelling System for Large-scale Hydrology, Hydrol. Earth Syst. Sci., 1, 55–69, 1997. Fassnacht, S. R.: Distributed snowpack simulation using weather radar with an hydrologic-land surface scheme model (dissertation), University of Waterloo, Canada, 2000. Freeze, R. A. and Harlan, R. L.: Blueprint for a physically-based digitally-simulated hydrological response model, J. Hydrol., 9, 237–258, 1969. Grayson, R. B., Moore, I. D., and McMahon, T. A.: Physically-based hydrologic modeling: 2. Is the concept realistic, Water Resour. Res., 28, 2659–2666, 1992. Hassanizadeh, S. M. and Gray, W. G.: General conservation equations for multiphase systems: 1. Averaging procedure, Adv. Water Resour., 2, 131–144, 1979a. Hassanizadeh, S. M. and Gray, W. G.: General conservation equations for multiphase systems: 2. Mass, momenta, energy and entropy equations, Adv. Water Resour., 2, 191–203, 1979b. Hassanizadeh, S. M. and Gray, W. G.: General conservation equations for multiphase systems, 3. Constitutive theory for porous media flow, Adv. Water Resour., 3, 25–40, 1980. Hassanizadeh, S. M.: Derivation of basic equations of mass transport in porous media, part 1: Macroscopic balance laws, Adv. Water Resour., 9, 196–206, 1986a. Hassanizadeh, S. M.: Derivation of basic equations of mass transport in porous media, part 2: Generalized Darcy's law and Fick's law, Adv. Water Resour., 9, 207–222, 1986b. Hu, H., Ye, B., Zhou, Y., and Tian, F.: A Land Surface Model Incorporated with Soil Freeze/Thaw and Its Application in GAME/Tibet, Science in China Ser. D, 36, 755–766, 2006. Jacobs, A. F. G., Bert, G. H., and Simon, M. B.: Dew deposition and drying in a desert system: A simple simulation model, J. Arid Environ., 42, 211–222, 1999. Lee, H., Sivapalan, M., and Zehe, E.: Representative Elementary Watershed (REW) approach, a new blueprint for distributed hydrologic modelling at the catchment scale, in: Predictions in ungauged basins: international perspectives on state-of-the-art and pathways forward, edited by: Franks, S. W., Sivapalan, M., Takeuchi, K., and Tachikawa, Y., IAHS Press, Wallingford, Oxon, UK, 2005a. Lee, H., Sivapalan, M., and Zehe, E.: Representative Elementary Watershed (REW) approach, a new blueprint for distributed hydrologic modelling at the catchment scale: the development of closure relations, in: Predicting Ungauged Streamflows in the Mackenzie River Basin: Today's Techniques and Tomorrow's Solutions, edited by: Spence, C., Pomeroy, J. W., and Pietroniro, A., Canadian Water Resources Association (CWRA), Ottawa, Canada, 165–218, 2005b. Lee, H., Sivapalan, M., and Zehe, E.: Representative Elementary Watershed (REW) approach, 10 a new blueprint for distributed hydrologic modelling at the catchment scale: Numerical implementation, in: Physically based models of river runoff and their application to ungauged basins, Proceedings, NATO Advanced Research Workshop, edited by: O'Connell, P. E. and Kuchment, L., Newcastle-upon-Tyne, UK, in press, 2006. Lei, Z., Hu, H., Yang, S.: A review of soil water research, Adv. Water Sci., 10, 311–318, 1999. Maurer, E. P., Rhoads, J. D., Dubayah, R. O., and Lettenmaier, D. P.: Evaluation of the snow-covered area data product from MODIS, Hydrol. Processes, 17, 59–71, 2003. McManamon, A., Day, G. N., and Carroll, T. R.: Snow estimation – a GIS application for water resources forecasting, in: Proceedings of the Symposium on Engineering Hydrology, ASCE Publ., New York, 1993. Refsgaard, J. C. and Storm, B.: MIKE SHE, in: Computer Models of Watershed Hydrology, edited by: Singh, V. P., Water Resources Publications, USA, 809–846, 1995. Refsgaard, J. C., Storm, B., and Abbott, M. B.: Comment on "A discussion of distributed hydrological modelling" by Beven, K. J., in: Distributed Hydrological Modelling, edited by: Refsgaard, J. C. and Abbott, M. B., Kluwer, Dordrecht, Netherlands, 279–287, 1996. Reggiani, P., Sivapalan, M., and Hassanizadeh, S. M.: A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics, Adv. Water Resour., 22(4), 367–398, 1998. Reggiani, P., Hassanizadeh, S. M., and Sivapalan, M.: A unifying framework for watershed thermodynamics: constitutive relationships, Adv. Water Resour., 23, 15–39, 1999. Reggiani, P. and Sivapalan, M.: Conservation equations governing hillslope responses: Exploring the physical basis of water balance, Water Resour. Res., 36, 1845–1863, 2000. Reggiani, P., Sivapalan, M., Hassanizadeh, S. M., and Gray, W. G.: Coupled equations for mass and momentum balance in a stream network: theoretical derivation and computational experiments, Proc. R. Soc. Lond., Series A, 457, 157–189, 2001. Reggiani, P. and Rientjes, T. H. M.: Flux parameterization in the representative elementary watershed approach: application to a natural basin, Water Resour. Res., 41, 1–18, 2005. Robinson, J. S. and Sivapalan, M.: Catchment-scale runoff generation model by aggregation and similarity analyses, Hydrol. Processes, 9, 555–574, 1995. Rodriguez-Iturbe, I. and Rinaldo, A.: Fractal River Basins: Chance and Self-organization, Cambridge University Press, New York, USA, 1997. Rui, X. F.: Principles of Hydrology, China Water Power Press, Beijing, China, 143–152, 2004. Singh, V. P. and Woolhiser, D. A.: Mathematical modeling of watershed hydrology, J. Hydraul. Eng., 7, 270–292, 2002. Smith, R. E., Goodrich, D. R., Woolhiser, D. A., and Simanton, J. R.: Comments on "Physically-based hydrologic modelling: 2. Is the concept realistic?" by Grayson, R. B., Moore, I. D., and McMahon, T. A., Water Resour. Res., 30, 851–854, 1994. Srinivasan, R., Ramanarayanan, T. S., Arnold, J. G., and Bednarz, S. T.: Large area hydrologic modeling and assessment, part II: Model application, J. Amer. Water Resour. Assoc., 34, 91–101, 1998. Tian, F. Q.: Study on thermodynamic watershed hydrological modeling (THModel) (dissertation), Tsinghua University, China, 2006. Viney, N. R. and Sivapalan, M.: A framework for scaling of hydrologic conceptualisations based on a disaggregation-aggregation approach, Hydrol. Processes, 18, 1395–1408, 2004. Ward, R. C. and Robinson, M.: Principles of Hydrology, McGraw-Hill, London, 1990. Whitaker, S.: Introduction to Fluid Mechanics, Krieger, Malabar, Florida, 1981. Williams, K. S. and Tarboton, D. G.: The ABC's of snowmelt: a topographically factorized energy component snowmelt model, Hydrol. Processes, 13, 1905–1920, 1999. Woolhiser, D. A.: Search for physically-based runoff model – a hydrologic El Dorado, J. Hydraul. Eng., ASCE, 122, 122–129, 1996. Yang, D., Herath, S., and Musiake, K.: Comparison of different distributed hydrological models for characterization of catchment spatial variability, Hydrol. Processes, 14, 403–416, 2000. Yang, D., Herath, S., and Musiake, K.: Hillslope-based hydrological model using catchment area and width functions, Hydrol. Sci. J., 47(1), 49–65, 2002a. Yang, D., Oki, T., Herath, S., and Musiake, S.: A geomorphology-based hydrological model and its applications, in: Mathematical Models of Small Watershed Hydrology and Applications, edited by: Singh, V. P. and Frevert, D. K., Water Resources Publications, Littleton, Colorado, Chapter 9, 259–300, 2002b. Yang, Z., Liu, X. R., Zeng, Q. Z., and Chen, Z. T.: Hydrology in Cold Regions of China, Science Press, Beijing, 2000. Zhang G. P. and Savenije, H. H. G.: Rainfall-runoff modeling in a catchment with a complex groundwater flow system: application of the Representative Elementary Watershed (REW) approach, Hydrol. Earth Syst. Sci., 9, 243–261, 2005.