A unifying framework for watershed thermodynamics: Balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics

Advances in Water Resources

Volumn 22, Issue 4, 1998, Pages 367-398

  Reggiani, Paolo ^a   Sivapalan, Murugesu ^a   Majid Hassanizadeh, S ^b  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Balance equations; Representative elementary watersheds; Subregions

Indexed keywords

CONSTRAINT THEORY; ENTROPY; HYDROLOGY; THERMODYNAMICS;

BALANCE EQUATIONS; MASS; MOMENTUM; WATERSHED THERMODYNAMICS;

WATERSHEDS;

MATHEMATICAL METHOD; THERMODYNAMICS; WATERSHED;

EID: 0344334033     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(98)00012-8     Document Type: Article

References (36)

1. Abbott M. B., Bathurst J. C., Cunge J. A., O'Connell P. E., Rasmussen J. SHE, 1: History and philosophy of a physically-based, distributed modelling system. J. Hydrol. 87:1986;45-59.
2. Abbott M. B., Bathurst J. C., Cunge J. A., O'Connell P. E., Rasmussen J. SHE, 2: Structure of a physically-based, distributed modelling system. J. Hydrol. 87:1986;61-77.
3. Achanta S., Cushman J. H., Okos M. R. On multicomponent, multiphase thermomechanics with interfaces. Int. J. Engng Sci. 32(11):1994;1717-1738.
4. Bathurst J. C. Future of distributed modelling: the Système Hydrologique Européen. J. Hydrol. 6:1992;265-277.
5. Beven K. J. Changing ideas in hydrology - the case of physically based models. J. Hydrol. 105:1989;157-172.
6. Beven K. J. Prophesy, reality and uncertainty in distributed hydrological modelling. Adv. Water Resour. 15:1993;41-51.
7. Beven K. J., Kirkby M. J. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24(1):1979;43-69.
8. Binley A., Elgy J., Beven K. A physically based model of heterogeneous hillslopes; 1. Runoff production. Water Resour. Res. 25(6):1989;1227-1233.
9. Chorley, R. J., The hillslope hydrological cycle. In Hillslope Hydrology, chap. 1, Kirkby, M. J., ed. Wiley, Chichester, 1978 pp. 1-42.
10. Duffy C. J. A two-state integral-balance model for soil moisture and groundwater dynamics in complex terrain. Water Resour. Res. 32(8):1996;2421-2434.
11. Dunne, T., Field studies of hillslope flow processes. In Hillslope Hydrology, chap. 7, Kirkby, M. J., ed. Wiley, Chichester, 1978, pp. 227-293.
12. Eringen, A. C., Mechanics of Continua, vol. 2, R.E. Krieger, ed. Huntington, New York, 1980.
13. Freeze, R. A., Mathematical models of hillslope hydrology. In Hillslope Hydrology, chap. 6, Kirkby, M. J., ed. Wiley, Chichester, 1978, pp. 177-225.
14. Gray W. G., Lee P. C. Y. On the theorems for local volume averaging of multiphase systems. Int. J. Multiphase Flow. 3:1977;333-340.
15. Gray, W. G., Leijnse, A., Kolar, R. L. & Blain, C. A., Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems. CRC Press, Boca Raton, Florida, 1993.
16. Gupta, V. K. & Waymire, E., Spatial variability and scale invariance in hydrological regionalization. In Scale Invariance And Scale Dependence In Hydrology, Sposito, G., ed. Cambridge University Press, Cambridge, 1998.
17. Hassanizadeh M., Gray W.G. General conservation equations for multiphase systems: 1. Averaging procedure. Adv. Water Resour. 2:1979;131-144.
18. Hassanizadeh M., Gray W. G. General conservation equations for multiphase systems: 2. Mass, momenta, energy and entropy equations. Adv. Water Resour. 2:1979;191-203.
19. Hassanizadeh M., Gray W. G. General conservation equations for multiphase systems, 3. Constitutive theory for porous media flow. Adv. Water Resour. 3:1980;25-40.
20. Hassanizadeh S. M. Derivation of basic equations of mass transport in porous media; Part 2: Generalized Darey's law and Fick's law. Adv. in Water Resour. 9:1986;207-222.
21. Hassanizadeh S. M. Derivation of basic equations of mass transport in porous media; part 1: Macroscopic balance laws. Adv. Water Resour. 9:1986;196-206.
22. Hassanizadeh S. M., Gray W. G. Mechanic's and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour. 13(4):1990;169-186.
23. Hewlett, J. D. & Hibbert, A. R., Factors affecting the response of small watersheds to precipitation in humid areas. In Forest Hydrology, Sopper, W. E. & Lull, H. W., eds. Pergamon Press, Oxford, 1967, pp. 275-290.
24. Horton R. E. Drainage-basin characteristics. EOS Trans. AGU. 13:1932;350-361.
25. Horton R. E. The role of infiltration in the hydrological cycle. Trans. Am. Geophys. Union. 14:1933;446-460.
26. Horton R. E. Hydrologic interrelation of water and soils. Proc. Soil. Sci. Soc. Am. 1:1937;401-429.
27. Horton R. E. Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology. Bull. Geol. Soc. Am. 56:1945;275-370.
28. Horton, R. E., Liech, H. R. & Van Vliet, R., Laminar sheet flow. Trans. Am. Geophys. Union, 15th Annual Meeting, Washington D.C., pp. 393-404, 1934.
29. Crawford, N. H. & Linsley, R. K., Digital simulation in hydrology: Stanford Watershed Model IV. Stanford University, California, Technical Report 39, Department of Civil Engineering, 1966.
30. Nash, J. E., The form of the instantaneous unit hydrograph. In General Assembly of Toronto, vol. 3. International Association for Scientific Hydrology, Wallingford, UK, 1957, pp. 114-121.
31. O'Connell P. E., Todini E. Modelling of rainfall, flow and mass transport in hydrological systems: an overview. J. Hydrol. 175:1996;3-16.
32. Rodriguez-Iturbe, I. & Rinaldo, A., Fractal River Basins. Cambridge University Press, Cambridge, 1997.
33. Strahler, A. N., Quantitative geomorphology of drainage basins and channel networks. In Handbook of Hydrology, chap. 4-11, Chow, V. T., ed. McGraw-Hill, New York, 1964, pp. 4:39-4:76.
34. Whitaker, S., Introduction to Fluid Mechanics. Krieger, Malabar, Florida, 1981.
35. Woolhiser, D. A., Smith, R. E. & Goodrich, D. C., KINEROS, a kinematic runoff and erosion model: documentation and user manual. U.S. Dept. of Agriculture, Agricultural Research Service, ARS-77, 130 pp., 1990.
36. Beven, K. & Kirkby, M. J., Channel Network Hydrology. Wiley, New York, 1993.