Derivation of the SCS-CN parameter S from linearized Fokker-Planck equation

Acta Geophysica Polonica

Volumn 51, Issue 2, 2003, Pages 179-202

  Mishra, Surendra Kumar ^a   Singh, Vijay P ^b  

^a NATIONAL INSTITUTE OF HYDROLOGY   (India)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Curve number; Fokker Planck equation; Infiltration; Maximum soil retention; SCS CN method

Indexed keywords

CLAY; DIFFUSION; HYDRAULIC CONDUCTIVITY; INFILTRATION; MOISTURE; PRESSURE EFFECTS; SOIL CONSERVATION;

FOKKER-PLANCK EQUATION;

GEOPHYSICS;

INFILTRATION; RAINFALL-RUNOFF MODELING; SOIL WATER;

EID: 0037590180     PISSN: 00015725     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (57)

1. Black, T.A., W.R. Gardner and G. W. Thurtell, 1969, The prediction of evaporation, drainage, and soil water storage for a bare soil, Soil Sci. Soc. Am. Proc. 33, 655-660.
2. Bonta, J.V., 1997, Determination of watershed curve number using derived distributions, J. Irrig. and Draing. Engrg., ASCE 123, 1, 28-36.
3. Campbell, G.S., 1974, A simple method for determining unsaturated conductivity from moisture retention data, Soil Science 117, 6, 311-314.
4. Chang, K.P., and J.H. Sonu, 1993, Capillary hysteresis model in unsaturated flow: State of the art, Korean J. Hydrosciences 4, 33-49.
5. Chen, C.-L., 1981, An evaluation of the mathematics and physical significance of the soil conservation service curve number procedure for estimating runoff volume. In: V.P. Singh (ed.), "Rainfall-Runoff Relationship", Water Resources Publications, Littleton, Colorado.
6. Collis-George, N., 1977, Infiltration equations for simple soil systems, J. Water Resour. Res. 13, 2, 395-403.
7. Crawford, F.S., 1965, Waves: Berkeley Physics Course, Vol. 3, McGraw-Hill, New York.
8. de Souza, P.A., and R.K. Price, 1980, The Saint Venant Equations: A Linearised Analysis, Report No. IT 203, Institute of Hydrology, Wallingford, Sept.
9. Elrick, D.E., and D.H. Bowman, 1964, Note on an improved apparatus for soil moisture flow measurements, Soil Sci. Soc. Am. Proc. 28, 450-453.
10. Feddes, R.A., P. Kabat, P.J.T. Van Bakel, J.J.B. Bronswijk and J. Halbertsma, 1988, Modelling soil water dynamics in the unsaturated zone - State of the art, J. Hydrology 100, 69-111.
11. Gardener, W.R., D. Hillel and Y. Benzamin, 1970, Post irrigation movement of soil water: I. Redistribution, Water Resour. Res. 6(3), 851-61; II. Simultaneous redistribution and evaporation, Water Resour. Res. 6(4), 1148-53.
12. Green, R.E., 1962, Infiltration of water into soils as influenced by antecedent moisture, Ph. D. Dissertation, Iowa State University, Iowa (unpublished).
13. Hawkins, R.H., 1993, Asymptotic determination of runoff curve numbers from data, J. Irrig. and Draing. Engrg., ASCE 119, 2, 334-345.
14. Hillel, D., 1976, Soil and Water: Physical Properties and Processes, Academic Press, New York.
15. Jarvis, N.J., P.E. Jansson, P.E. Dik and I. Messing, 1991, Modeling water and solute transport in macroporous soil. I. Model description and sensitivity analysis, J. Soil Sci. 42, 59-70.
16. Knisel, W.G., 1980, CREAMS: a field scale model for chemicals, runoff, and erosion from agricultural management systems, Conser. Res. Rep., USDA 26, 643 p.
17. Kundzewicz, Z.W., and J.C.I. Dooge, 1989, Attenuation and phase shift in linear flood routing, J. Hydrol. Sci. 34, 1, 21-40.
18. Laiberte, G.E., A.T. Corey and R.H. Brooks, 1966, Properties of unsaturated porous media, Hydrology 17, Colorado State University, Fort Collins, Colorado.
19. Lee, H.W., 1983, Determination of infiltration characteristics of a frozen palouse silt loam soil under simulated rainfall, Ph. D. Dissertation, University of Idaho Graduate School (unpublished).
20. Mallants, D., Peng-Hsiang Tseng, M. Vanclooster and J. Feyen, 1998, Predicted drainage for a sandy loam soil: sensitivity to hydraulic property description, J. Hydrology 206, 136-148.
21. Marshall, T.J., J.W. Holmes and C.W. Rose, 1996, Soil Physics, Cambridge University Press, New York.
22. McCuen, R.H., 2002, Approach to confidence interval estimation for curve numbers, J. Hydrol. Engrg 7, 1, 43-48.
23. Mein, R.G., and C.L. Larson, 1971, Modelling the infiltration component of the rainfall-runoff process, Bull. 43, Water Resources Res. Centre, University of Minnesota, Minneapolis.
24. Mishra, S.K., and S.M. Seth, 1996, Use of hysteresis for defining the nature of flood wave propagation in natural channels, Hydrologic. Sci. J. 41(2).
25. Mishra, S.K., and V.P. Singh, 1999a, Another look at the SCS-CN method, J. Hydrol. Engrg., ASCE 4, 3, 257-264.
26. a-λ spectrum, Proc. Int. Conf. on Water, Environment, Ecology, Socio-economics, and Health Engineering, Seul Nat. University, Korea, Oct. 18-21.
27. Mishra, S.K., and V.P. Singh, 1999c, Hysteresis-based flood wave analysis, J. Hydrol. Engrg., ASCE 4, 4, 358-365.
28. Mishra, S.K., and V.P. Singh, 2001a, Hysteresis-based flood wave analysis using the concept of strain, J. Hydrological Processes 15, Ref. 176/225.
29. Mishra, S.K., and V.P. Singh, 2001b, On Seddon speed formula, J. Hydrol. Sci. (Journal-des Sciences Hydrologiques) IAHS 46, 3, 333-347.
30. Mishra, S.K., and V.P. Singh, 2002, SCS-CN-based hydrologic simulation package. Ch. 13 in Mathematical Models in Small Watershed Hydrology. In: V.P. Singh, Frevert and Meyer (eds.), "Water Resources Publications", Littleton, Colorado.
31. Mishra, S.K., and V.P. Singh, 2003, SCS-CN method. Part-II: Analytical treatment, Acta Geophys. Pol. 51, 1, 107-123.
32. Mishra, S.K., M.K. Jain and S.M. Seth, 1997, Characterization of flood waves by rating curves, J. Nordic Hydrology 28(1), 51-64.
33. Mishra, S.K., S.R. Kumar and V.P. Singh, 1999, Calibration of a general infiltration model, J. Hydrol. Processes 13, 1691-1718.
34. Mockus, V., 1949, Estimation of total (peak rates of) surface runoff for individual storms, Exhibit A of Appendix B, Interim Survey Report Grand (Neosho) River Watershed, USDA.
35. Mockus, V., 1964, Letter to Orrin Ferris, March 5, In: R.E. Rallison (ed.), "Origin and Evolution of the SCS Runoff Equation", Proc. ACSE Symp. Watershed Management, Boise, Idaho.
36. Moore, R.E., 1939, Water conduction from shallow water tables, Hilgardia 12, 383-426.
37. Pedlosky, J., 1979, Geophysical Fluid Dynamics, Springer Verlag, Berlin.
38. Philip, J.R., 1957, Theory of Infiltration, Chapters 1 and 4, Soil Sci. 83(5), 345-357.
39. Philip, J.R., 1969, Theory of Infiltration. In: V.T. Chow (ed.), "Advances in Hydrosciences", Academic Press, New York.
40. Philip, J.R., 1974, Recent progress in the solution of nonlinear diffusion equations, Soil Sci. 117, 257-264.
41. Ponce, V.M., 1989, Engineering Hydrology: Principles and Practices, Prentice Hall, Englewood Cliffs, New Jersey.
42. Ponce, V.M., and R.H. Hawkins, 1996, Runoff curve number: Has it reached maturity?, J. Hydrol. Engrg., ASCE 1, 1, 11-19.
43. Ponce, V.M., and D.B. Simons, 1977, Shallow wave propagation in open channel flow, J. Hydraul. Div., ASCE 103 (HY12), 1461-1476.
44. Ponce, V.M., R.M. Li and D.B. Simons, 1978, Applicability of kinematic and diffusion models, J. Hydraul. Div., ASCE 104 (HY3), 353-360.
45. Rallison, R.E., 1980, Origin and evolution of the SCS runoff equation, Proc. ASCE Symp. Watershed Management, Boise, Idaho.
46. Rankine, M., 1870, On the thermodynamic theory of waves of finite longitudinal disturbance, Philos. Trans. Royal Society of London 160, 277-288.
47. Singh, V.P., 1997, Kinematic Wave Modeling in Water Resources: Environmental Hydrology, John Wiley and Sons, New York.
48. Singh, V.P., and F.X. Yu, 1990, Derivation of infiltration equation using systems approach, J. Irrig. and Drainage Engrg., ASCE 116, 6, 837-857.
49. Soil Conservation Service, 1956, 1971, Hydrology, National Engineering Handbook, Suppl. A, Sect. 4, Ch. 10, Soil Conserv. Service, USDA, Washington D.C.
50. Todd, D.K., 1980, Groundwater Hydrology, John Wiley and Sons, New York.
51. Vanclooster, M., P. Viane, J. Diels and K. Chrismans, 1994, Water and agrochemicals in the soil and vadose environment, Reference and User's Manual, Release 2.0, Institute for Land and Water Management, Leuven, Belgium.
52. Visser, W.C., 1969, An empirical expression for the desorption curve. In: P.E. Rijtema and H. Wassnik (eds.), "Water in the Unsaturated Zone", UNESCO, Paris/IAHS, Gentbrugge, 329-35.
53. Vreugdenhill, C.B., 1972, Mathematical Methods for Flood Waves, Delft Hydraulics Laboratory, Research Report S89-IV, August.
54. Wagenet, R.J., and J.L. Hutson, 1987, LEACHM: leaching estimation and chemistry model, Continuum Ser. Publ. 2, Water Resource Inst., Cornell Univ., Ithaca, N.Y. 1-80.
55. Young, E.G., 1957, Moisture profiles during vertical infiltration, Soil Sc. 84, 283-290.
56. Young, E.G., 1964, An infiltration method measuring the hydraulic conductivity of unsaturated porous materials, Soil Sci. 97, 307-311.
57. Yu, B., 1998, Theoretical justification of SCS-CN method for runoff estimation, J. Irrig. and Drain. Engrg. 124, 6, 306-310.