Nonlinear hydrologic processes: Conservation equations for determining their means and probability distributions

Journal of Hydrologic Engineering

Volumn 8, Issue 2, 2003, Pages 44-53

  Kavvas, M Levent ^a  

^a University of California   (United States)

Author keywords

Equation of motion; Hydrologic aspects; Probability distribution

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; NONLINEAR SYSTEMS; PROBABILITY;

HYDROLOGIC PROCESSES;

HYDROLOGY;

FLUID DYNAMICS; HYDROLOGY; NUMERICAL METHOD;

EID: 0037340744     PISSN: 10840699     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)1084-0699(2003)8:2(44)     Document Type: Article

References (47)

1. Adomian, G. (1986). Nonlinear stochastic operator equations, Academic, New York.
2. Amorocho, J. (1973). "Nonlinear hydrologic analysis." Adv. Hydrosci., 9, 203-251.
3. Bear, J., and Verruijt, A. (1987). Modeling groundwater flow and pollution, Reidel, Boston.
4. Bidwell, V. J. (1971). "Regression analysis of nonlinear catchment systems." Water Resour. Res., 7, 1118-1126.
5. Boyd, M. J., Pilgrim, D. H., and Cordery, I. (1979). "A storage routing model based on catchment geomorphology." J. Hydrol., 42, 209-230.
6. Chen, Z.-Q., Govindaraju, R. S., and Kavvas, M. L. (1994a). "Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Development of models." Water Resour. Res., 30, 523-533.
7. Chen, Z.-Q., Govindaraju, R. S., and Kavvas, M. L. (1994b). "Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Numerical simulations." Water Resour. Res., 30, 535-548.
8. Diskin, M. H., and Boneh, A. (1972). "Properties of the kernels for time-invariant, initially relaxed, second order surface runoff systems." J. Hydrol., 17, 115-141.
9. Dogrul, E. C., Kavvas, M. L., and Chen, Z. Q. (1998). "Prediction of subsurface stormflow in heterogeneous sloping aquifers." J. Hydrologic. Eng., 3(4), 258-267.
10. Duffy, C. J. (1996). "A two-state integral-balance model for soil moisture and groundwater dynamics in complex terrain." Water Resour. Res., 32, 2421-2434.
11. Duffy, C. J., and Cusumano, J. (1998). "A low-dimensional model for concentration-discharge dynamics in groundwater systems." Water Resour. Res., 34, 2235-2247.
12. Gardiner, C. W. (1985). Handbook of stochastic methods, Springer, New York.
13. Gelhar, L. W., and Axness, C. L. (1983). "Three-dimensional stochastic analysis of macrodispersion in aquifers." Water Resour. Res., 19, 161-180.
14. Govindaraju, R. S., Jones, S. E., and Kavvas, M. L. (1990). "Approximate analytical solutions for overland flows." Water Resour. Res., 26(12), 2903-2912.
15. Govindaraju, R. S., and Kavvas, M. L. (1991). "Stochastic overland flows, Part 2: Numerical solutions of evolutionary probability density functions." Stochastic Hydrol. Hydr., 5, 105-124.
16. Hino, M. (1972). "Stochastic approach to linear and nonlinear runoff analysis." Tech. Rep. No. 12, Dept. of Civil Engineering, Tokyo Institute of Technology, Tokyo.
17. Horne, F. E., and Kavvas, M. L. (1997). "Physics of the spatially averaged snowmelt process." J. Hydrol., 191, 179-207.
18. Kapoor, V., and Gelhar, L. W. (1994). "Transport in three-dimensionally heterogeneous aquifers, 1. Dynamics of concentration fluctuations." Water Resour. Res., 30, 1775-1788.
19. Kavvas, M. L. (2001). "General conservation equation for solute transport in heterogeneous porous media." J. Hydrologic Eng., 6(4), 341-350.
20. Kavvas, M. L., and Govindaraju, R. S. (1991). "Stochastic overland flows, Part I: Physics-based evolutionary probability distributions." Stochastic Hydrol. Hydr., 5, 89-104.
21. Kavvas, M. L., and Karakas, A. (1996). "On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers." J. Hydrol., 179, 321-351.
22. Kitanidis, P. K. (1988). "Prediction by the method of moments of transport in a heterogenous formation." J. Hydrol., 102, 453-473.
23. Kubo, R. (1963). "Stochastic Liouville equations." J. Math. Phys., 4(2), 174-183.
24. Laurensen, E. M. (1964). "A catchment storage model for runoff routing." J. Hydrol., 2, 141-163.
25. Mantoglou, A., and Gelhar, L. W. (1987). "Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils." Water Resour. Res., 23, 47-56.
26. Olver, P. J. (1993). Applications of Lie groups to differential equations, Springer, New York.
27. Pilgrim, D. H. (1966). "Radioactive tracing of storm runoff on a small catchment: 2. Discussion of results." J. Hydrol., 4, 306-326.
28. Pilgrim, D. H. (1980). "Characteristics of flood nonlinearity from two tracing studies." Proc., Hydrol. and Water Resour. Symp., Institute of Engineers, Australia, 17-22.
29. Puente, C. E. (1996). "A new approach to hydrologic modeling: derived distributions revisited." J. Hydrol., 187, 65-80.
30. Rao, A. R., and Rao, R. G. S. (1974). "Comparative analysis of estimation; methods in nonlinear function models of the rainfall-runoff process." Tech. Rep. No. 56, Water Resource Center, Purdue Univ., W. Lafayette, Ind.
31. Rehlfeldt, K. R., and Gelhar, L. W. (1992). "Stochastic analysis of dispersion in unsteady flow in heterogeneous aquifers." Water Resour. Res., 28, 2085-2100.
32. Rubin, Y., and Dagan, G. (1988). "Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, I. Constant head boundary." Water Resour. Res., 24, 1689-1710.
33. Serrano, S. (1988a). "General solution to random advective-dispersive transport equation in porous media, I. Stochasticity in the sources and in the boundaries." Stochastic Hydrol. Hydr., 2, 79-98.
34. Serrano, S. (1988b). "General solution to random advective-dispersive transport equation in porous media, 2. Stochasticity in the parameters." Stochastic Hydrol. Hydr., 2, 99-112.
35. Serrano, S. (1995). "Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity." Water Resour. Res., 31, 2733-2742.
36. Serre, J.-P. (1965). Lie algebras and Lie groups, Benjamin Inc., London.
37. Singh, V. P. (1979). "A uniformly nonlinear hydrologic cascade model." Irrigation Power, 36(3), 301-317.
38. Singh, V. P. (1988). Hydrologic systems: rainfall-runoff modelling, Vol. 1, Prentice Hall, Englewood Cliffs. N.J.
39. Tayfur, G., and Kavvas, M. L. (1994). "Spatially averaged conservation equations for interacting rill-interrill area overland flows." J. Hydraul. Eng., 120(12), 1426-1448.
40. Tayfur, G., and Kavvas, M. L. (1998). "Areally-averaged overland flow equations at hillslope scale." Hydro. Sci. J., 43(3), 361-378.
41. Van Kampen, N. G. (1974). "A cumulant expansion for stochastic linear differential equations II. Physica (Amsterdam). 74, 239-247.
42. Van Kampen, N. G. (1976). "Stochastic differential equations." Phys. Rep., 24, 171-228.
43. Wood, B. D., and Kavvas, M. L. (1999a). "Ensemble-averaged equations for reactive transport in porous media under unsteady flow conditions." Water Resour. Res., 35, 2053-2068.
44. Wood, B. D., and Kavvas, M. L. (1999b). "Stochastic solute transport under unsteady flow conditions comparison of theory. Monte Carlo simulations and field data" Water Resour. Res., 35, 2069-2084.
45. Woothiser, D. A. (1974). "Simulation of unsteady flow." Unsteady flow in open channels. Water Resource Publishers, Ft. Collins, Co.
46. Yoon, J. Y., and Kavvas, M. L. (2002). "Probabilistic solution to stochastic overland flow equation." J. Hydrologic Eng., 8(2), 54-63.
47. Zhu, J. (1998). "Specific discharge covariance in a heterogeneous semi-confined aquifer." Water Resour. Res., 34,