A perturbative view on the subsurface water pressure response at hillslope scale

Water Resources Research

Volumn 44, Issue 5, 2008, Pages

  Cordano, E ^a   Rigon, R ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

OFFSHORE OIL WELL PRODUCTION; PERTURBATION TECHNIQUES; POLYNOMIAL APPROXIMATION; WATER TREATMENT;

BASIC IDEA; BOUSSINESQ EQUATIONS; BOUSSINESQ MODELS; FIRST ORDERS; FIRST-ORDER APPROXIMATIONS; HILL SLOPES; PERTURBATION SERIES; PRESSURE FLOW; PRESSURE HEADS; RICHARDS EQUATION; SUB-SURFACE FLOW; SUBSURFACE WATERS; TEMPORAL VARIATIONS; TRANSIENT COMPONENTS; WATER PRESSURES; WATER TABLE LEVEL;

INTEGRATION;

BOUSSINESQ EQUATION; DIMENSIONLESS NUMBER; HILLSLOPE; HYDROSTATIC PRESSURE; PERTURBATION; RICHARDS EQUATION; SUBSURFACE FLOW; TEMPORAL VARIATION; WATER TABLE;

EID: 46049112872     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2006WR005740     Document Type: Article

References (48)

1. Abbott, M., J. C. Bathurst, J. A. Cunge, P. E. O. Connell, and J. Rasmussen (1986), An introduction to the European Hydrological System - Systeme Hydrologique Europeen, SHE. 1: Hystory and philosophy of a physically-based distributed modelling system, J. Hydrol., 87, 45-59.
2. Barry, D. A., and G. C. Sander (1991), Exact solution for water infiltration with an arbitrary surface flux or non linear solute adsorption, Water Resour. Res., 27(10), 2667-2680.
3. Barry, D. A., J. Y. Parlange, G. C. Sander, and M. Sivaplan (1993), A class of exact solutions for Richards' equation, J. Hydrol., 142, 29-46.
4. Basha, H. A. (1999), Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface, Water Resour. Res., 35(1), 75-84, doi:10.1029/1998WR900015.
5. Basha, H. A., and S. F. Maalouf (2005), Theoretical and conceptual models of subsurface hillslope flows, Water Resour. Res., 41, W07018, doi:10.1029/2004WR003769.
6. Bear, J. (1972), Dynamics of Fluids in Porous Media, American Elsevier Publisher, New York.
7. Berne, A., R. Uijlenhoet, and P. A. Troch (2005), Similarity analysis of subsurface flow response of hillslopes with complex geometry, Water Resour. Res., 41, W09410, doi:10.1029/2004WR003629.
8. Bixio, A. C., S. Orlandini, C. Paniconi, and M. Putti (2000), Physically-based distributed model for coupled surface runoff and subsurface flow formulation at the catchment scale, in Surface Water Systems and Hydrology and Water Res. Symp., vol. 2, edited by L. B. Brookfield, et al., Computational Water Resources, pp. 115-122, A. Balkema, Vt.
9. Broadbridge, P., and I. White (1988), Constant rate rainfall infiltration: A versatile nonlinear model, 1. Analytic solution, Water Resour. Res., 24(1), 145-154.
10. Brutsaert, W. (1994), The unit response of groundwater outflow from a hillslope, Water Resour. Res., 30(10), 2759-2764.
11. Brutsaert, W. (2005), Hydrology: An Introduction, Cornell University, New York.
12. Cordano, E., P. Bartolini, R. Rigon, and G. Bertoldi (2004a), A flexible numerical approach to solving a generalized Richards' equation problem and some applications, in Saturated and Unsaturated Zone: Integration of Process Knowledge Into Effective models, Proc. COST 629 Int. Workshop, edited by P. Aagard et al., pp. 107-112, Universitá degli Studi di Roma "La Sapienza", La Gogliardica Pavese, Rome, Italy.
13. Cordano, E., R. Panciera, R. Rigon, and P. Bartolini (2004b), Sulla soluzione diffusiva dell'equazione di Richards, Atti XXIV Conv. Naz. Idraul. Costr. Idraul., 2, 71-78.
14. Croton, J. T., and D. A. Barry (2001), WEC-C: A distributed, deterministic catchment model - Theory, formulation and testing, Env. Mod. Software, 16, 583-599.
15. Daly, E., and A. Porporato (2004), A note on groundwater flow along a hillslope, Water Resour. Res., 40, W01601, doi:10.1029/2003WR002438.
16. Dietrich, W. E., and D. Montgomery (1994), A physically based model for the topographic control on shallow landsliding, Water Resour. Res., 30(4), 1153-1171.
17. D'Odorico, P., S. Fagherazzi, and R. Rigon (2005), Potential for landsliding: Dependence on hyetograph characteristics, J. Geophys. Res., 110(2), F01007, doi:10.1029/2004JF000127.
18. Hewlett, J. D., and A. R. Hibbert (1967), Factors affecting the response of small watersheds to precipitation in humid areas, in Forest Hydrology, edited by W. E. Sopper and H. W. Lull, pp. 275-290, Pergamon Press, New York.
19. Hilberts, A. G., P. A. Troch, and C. Paniconi (2005), Storage-dependent drainable porosity for complex hillslopes, Water Resour. Res., 41, W06001, doi:10.1029/2004WR003725.
20. Hilberts, A. G. J., P. A. Troch, C. Paniconi, and J. Boll (2007), Low-dimensional modeling of hillslope subsurface flow: Relationship between rainfall, recharge, and unsaturated storage dynamics, Water Resour. Res., 43, W03445 doi:10.1029/2006WR004964.
21. Hogarth, W. L., and J. Y. Parlange (2000), Application and improvement of a recent approximate analytical solution of Richards' equation, Water Resour. Res., 36(7), 1965-1968.
22. Holmes, M. H. (1995), Introduction to Perturbation Methods, Springer-Verlag, New York.
23. Iverson, R. M. (2000), Landslide triggering by rain infiltration, Water Resour. Res., 36(7), 1897-1910.
24. Marinelli, F., and D. Dumford (1998), Semianalytical solution to Richards' equation for layered porous media, J. Irrig. Drain. Eng., 124(6), 290-299.
25. Mualem, Y. (1976), A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12(3), 513-522.
26. O'Loughlin, E. (1986), Prediction of surface saturation zones in natural catchments by topographic analysis, Water Resour. Res., 22(5), 794-804.
27. Paniconi, C., and M. Putti (1994), A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems, Water Resour. Res., 30(12), 3357-3374.
28. Paniconi, C., P. A. Troch, E. E. van Loom, and A. Hilberts (2003), Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hill-slopes: 2. Intercomparisons with a three dimensional model, Water Resour. Res., 39(11), 1317, doi:10.1029/2002WR001730.
29. Philip, J. R. (1955), Numerical solution of equations of the diffusion type with diffusivity concentration-dependent, Trans. Faraday Soc., 51(7), 391.
30. Philip, J. (1991a), Hillslope infiltration: Planar slopes, Water Resour. Res., 27(1), 109-117.
31. Philip, J. (1991b), Hillslope infiltration: Divergent and convergent slopes, Water Resour. Res., 27(6), 1035-1040.
32. Philip, J. (1991c), Infiltration and downslope unsaturated flows in concave and convex topographies, Water Resour. Res., 27(6), 1041-1048.
33. Pikul, M., R. Street, and I. Remson (1974), A numerical model based on coupled one-dimensional Richards and Boussinesq Equations, Wat. Resour. Res., 10(2), 295-302.
34. Rasmussen, T. C., R. H. Baldwin Jr., J. F. Dowd, and A. G. Williams (2000), Tracer vs. pressure wave velocities through unsaturated saprolite, Soil Sci. Soc. Am. J., 64(1), 75-85.
35. Richards, L. A. (1931), Capillary conduction of liquids in porous mediums, Physics, 1, 318-333.
36. Rigon, R., G. Bertoldi, and T. Over (2006), A distributed hydrological model with coupled water and energy budgets, J. Hydrometeorol., 7(3), 371-388.
37. Ross, P. J., and J. Y. Parlange (1994), Comparing exact and numerical solutions of Richards' equation for one-dimensional infiltration and drainage, Soil Sci., 157(6), 341-344.
38. Segol, G. (1994), Classic Groundwater Simulations, pp. 316-323, Prentice Hall, Englewood Cliffs, N. J.
39. Simunek, J., M. Sejna, and M. T. V. Genuchten (1998), The HYDRUS 1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media, version 2.0, Tech. Rep., US Salinity Laboratory, ARS/USDA, Riverside, Calif.
40. Tracy, F. T. (2006), Clean two- and three-dimensional analytical solutions of Richards' equation, Water Resour. Res., 42, W08503, doi:10.1029/2005WR004638.
41. Tracy, F. T. (2007), Three-dimensional analytical solutions of Richards' equation for a box-shaped soil sample with piecewise-constant head boundary conditions on the top, J. Hydrol., 336, doi:10.1016/j.jhydrol.2007.01. 011.
42. Troch, P. A., C. Paniconi, and E. E. van Loon (2003), Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 1. Formulation and characteristic response, Water Resour. Res., 39(11), 1316, doi:10.1029/2002WR001728.
43. Troch, P. A., E. E. van Loon, and A. G. J. Hilberts (2004), Analytical solution of the linearized hillslope-storage Boussinesq equation for exponential hillslope width functions, Water Resour. Res., 40, W08601, doi:10.1029/2003WR002850.
44. VanGenuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898.
45. Vogel, T., and J. Disek (2006), Comparison of two different approaches to modeling subsurface runoff at the hillslope scale, in Geophys. Res. Abstract, vol. 8, European Geosciences Union, Vienna, Austria, 03733.
46. Wallach, R., D. Zaslavsky, and M. Israeli (1989), Small perturbations solution for steady but nonuniform infiltration, Water Resour. Res., 25(9), 1989-1997.
47. Wallach, R., M. Israeli, and D. Zaslavsky (1991), Small perturbation solution for steady nonuniform infiltration into soil surface of a general shape, Water Resour. Res., 27(7), 1665-1670.
48. Warrick, A. (2003), Soil Water Dynamics, pp. 247-258, Oxford University Press, New York.