Coupled equations for mass and momentum balance in a stream network: Theoretical derivation and computational experiments

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 457, Issue 2005, 2001, Pages 157-189

  Reggiani, Paolo ^a   Sivapalan, Murugesu ^a   Hassanizadeh, S M ^b   Gray, William G ^c  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c University of Notre Dame   (United States)

Author keywords

Balance equations; Channel network; Constitutive relationships; Instantaneous unit response functions; Network routing

Indexed keywords

EID: 57249083916     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0661     Document Type: Article

References (37)

1. Band, L. E. 1986 Topographic partition of watersheds with digital elevation models. Water Resources Res. 22, 15-24.
2. Batchelor, G. K. 1988 An introduction to fluid mechanics. Cambridge University Press.
3. Bates, B. C&; Pilgrim, D. H. 1983 Investigation of storage-discharge relations for river reaches and runoff routing models. Civil Engng Trans. Inst. Engng Aust. 25, 153-161.
4. Beven, K. 1979 On the generalized kinematic routing method. Water Resources Res. 15, 1238-1242.
5. Bray, D. I. 1979 Estimating average velocity in gravel-bed rivers. J. Hydr. Div. ASCE 105, 1103-1122.
6. Cash, J. R&; Karp, A. H. 1990 ACM transactions on mathematical software, vol. 16, pp. 201-222. New York: Association for Computing Machinery.
7. Chow, V. T., Maidment, D. R&; Mays, L. W. 1988 Applied hydrology. McGraw-Hill. Coleman, B. D&; Noll, W. 1963 The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Analysis 13, 168-178.
8. Gunge, J. A., Holly Jr, F. M&; Verwey, A. 1980 Practical aspects of computational river hydraulics. Boston, MA: Pitman.
9. Eagleson, P. S. 1970 Dynamic hydrology. McGraw-Hill.
10. Bringen, A. C. 1980 Mechanics of continua, 2nd edn. Huntington, NY: Krieger.
11. Gray, W. G&; Hassanizadeh, S. M. 1991 Unsaturated flow theory including interfacial phenomena. Water Resources Res. 27, 1855-1863.
12. Gray, W. G., Leijnse, A., Kolar, R. L&; Blain, C. A. 1993 Mathematical tools for changing spatial scales in the analysis of physical systems. Boca Raton, FL: Chemical Rubber Company.
13. Gupta, V. K&; Waymire, E. 1998 Spatial variability and scale invariance in hydrological region-alization. In Scale invariance and scale dependence in hydrology (ed. G. Sposito). Cambridge University Press.
14. Hack, J. T. 1957 Studies of longitudinal stream profiles in Virginia and Maryland. US Geological Survey Professional Paper, no. 294B, pp. 45-81.
15. Hassanizadeh, S. M&; Gray, W. G. 1990 Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resources 13, 169-186.
16. Henderson, F. M. 1966 Open channel flow. New York: Macmillan.
17. Keulegan, G. H. 1938 Laws of turbulent flow in open channels. J. Res. National Bureau Standards 21, 707-741.
18. Lee, K. T. & Yen, B. C. 1997 Geomorphology and kinematic-wave-based hydrograph derivation. J. Hydraulic Engng 123, 73-80.
19. Leopold, L. B&; Maddock, T. 1953 The hydraulic geometry of stream channels and somec physiographic implications. US Geological Survey Professional Paper, no. 252, pp. 9-16.
20. Mesa, O. J&; Mifflin, E. R. 1986 On the relative role of hillslope and network geometry in hydrologie response. In Scale problems in hydrology (ed. V. K. Gupta, I. Rodriguez-Iturbe &;: E. F. Wood), ch. 1, pp. 1-17. Dordrecht: Reidel.
21. Minshall, N. E. 1960 Predicting storm runoff on small experimental watersheds. J. Hydraul. Div. Am. Soc. Civ. Engng 86, 28-33.
22. Mosley, M. P. 1992 River morphology. In Waters of New Zealand (ed. M. P. Mosley), ch. 16, pp. 285-304. Wellington: New Zealand Hydrological Society.
23. Naden, P., Broadhurst, P., Tauveron, N&; Walker, A. 1999 River routing at the continental scale: use of globally available data and an a priori method of parameter estimation. Hydrology Earth System Sci. 3, 109-124.
24. O'Callaghan, J. F&; Mark, D. M. 1984 The extraction of drainage networks from digital elevation data. Computer Vision Graphics Image Processing 28, 323-344.
25. Press, W. H., Teukolsky, S. A., Vetterling, W. T&; Flannery, B. P. 1992 Numerical recipes in C. Cambridge University Press.
26. Prigogine, I. 1967 Introduction to thermodynamics of irreversible processes, 3rd edn. Wiley.
27. Reggiani, P., Sivapalan, M&; Hassanizadeh, S. M. 1998 A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics. Adv. Water Resources 22, 367-398.
28. Reggiani, P., Hassanizadeh, S. M., Sivapalan, M&; Gray, W. G. 1999 A unifying framework for watershed thermodynamics: constitutive relationships. Adv. Water Resources 23, 15-39.
29. Reggiani, P., Sivapalan, M&; Hassanizadeh, S. M. 2000 Conservation equations governing hillslope responses: exploring the physical basis of water balance. Water Resources Res. 36, 1845-1864.
30. Rigon, R., Rinaldo, A., Rodrigucz-Iturbe, I., Bras, R. L&; Ijjasz-Vasquez, E. 1993 Optimal channel networks: a framework for the study of river basin morphology. Water Resources Res. 29, 1635-1646.
31. Rinaldo, A., Marani, A&; Rigon, R. 1991 Geomorphological dispersion. Water Resources Res. 27, 513-525.
32. Rinaldo, A., Vogel, G. K., Rigon, R&; Rodriguez-Iturbe, I. 1995 Can one gauge the shape of a basin? Water Resources Res. 31, 1119-1127.
33. Robinson, J. S&; Sivapalan, M. 1997 An investigation into the physical causes of scaling and heterogenity of regional flood frequency. Water Resources Res. 33, 1045-1059.
34. Robinson, J. S., Sivapalan, M&; Snell, J. D. 1995 On the relative roles of hillslope processes, channel routing and network geomorphology in the hydrologie response of natural catchments. Water Resources Res. 31, 3089-3101.
35. Snell, J. D. 1996 A physically based representation of channel network response, pp. 1-247. PhD thesis, Centre for Water Research, University of Western Australia.
36. Snell, J. D&; Sivapalan, M. 1995 Application of the meta-channel concept: construction of the meta-channel hydraulic geometry for a natural catchment. In Scale issues in hydrological modelling (ed. J. D. Kalma &; M. Sivapalan), pp. 241-261. Wiley.
37. Strahler, A. N. 1964 Quantitative geomorphology of drainage basins and channel networks. In Handbook of hydrology (ed. V. T. Chow), ch. 4-II, pp. 39-76. McGraw-Hill.