Multiscaling analysis and random cascade modeling of dye infiltration

Water Resources Research

Volumn 38, Issue 11, 2002, Pages 45-1-45-11

  Olsson, Jonas ^a,b   Persson, Magnus ^b   Albergel, Jean ^c,e   Berndtsson, Ronny ^b   Zante, Patrick ^c,e   Öhrström, Pernilla ^b   Nasri, Slah ^d  

^a SWEDISH METEOROLOGICAL AND HYDROLOGICAL INSTITUTE   (Sweden)

^b LUND UNIVERSITY   (Sweden)

^c ENSAM UR 96 AMBRE Lab: Sol E   (France)

^d UNIVERSITY OF CARTHAGE   (Tunisia)

^e ENSAM UR 096 AMBRE Lab: Sol E   (France)

Author keywords

Cascade; Dye infiltration; Multiscaling; Solute transport

Indexed keywords

CATCHMENTS; DYES; METHOD OF MOMENTS; PROBABILITY DISTRIBUTIONS;

FIELD SOILS;

INFILTRATION;

DYE TRACER; INFILTRATION; SOIL WATER; SOLUTE TRANSPORT; SPATIAL VARIATION;

EID: 0036879794     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2001wr000880     Document Type: Article

References (56)

1. Aeby, P., J. Forrer, C. Steinmeier, and H. Flühler, Image analysis for determination of dye tracer concentration in sand columns, Soil Sci. Soc. Am.J., 61, 33-35, 1997.
2. Baveye, P., C. W. Boast, S. Ogawa, J.-Y. Parlange, and T. Steenhuis, Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils, Water Resour. Res., 34, 2783-2796, 1998.
3. Belfield, W. C., Multifractal characteristics of natural fracture apertures, Geophys. Res. Lett., 21, 2641-2644, 1994.
4. Berntson, G. M., and P. Stoll, Correcting for finite spatial scales of self-similarity when calculating the fractal dimensions of real-world structures, Proc.R. Soc. London, Ser. B, 264, 1531-1537, 1997.
5. Beven, K., and P. Germann, Macropores and water flow in soils, Water Resour. Res., 18, 1311-1325, 1982.
6. Beven, K., and E. Wood, Catchment geomorphology and the dynamics of runoff contributing areas, J. Hydrol., 65, 139-158, 1983.
7. Biggar, J. W., and D. R. Nielsen, Miscible displacement and leaching phenomenon, Agronomy, 12, 254-274, 1967.
8. Block, A., W. vonBloh, T. Klenke, and H. J. Schellnhuber, Multifractal analysis of the microdistribution of elements in sedimentary structures using images from scanning electron microscopy and energy dispersive X ray spectrometry, J. Geophys. Res., 96, 16,223-16,230, 1991.
9. Boufadel, M. C., S. Lu, F. J. Molz, and D. Lavallée, Multifractal scaling of the intrinsic permeability, Water Resour. Res., 36, 3211-3222, 2000.
10. Bouma, J., and L. W. Decker, A case study on infiltration into dry clay soil I, Morphological observations, Geoderma, 20, 27-40, 1978.
11. Davis, A., A. Marshak, W. Wiscombe, and R. Cahalan, Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated, J. Geophys. Res., 99, 8055-8072, 1994.
12. De Smedt, F., and P. J. Wierenga, Solute transfer through columns of glass beads, Water Resour. Res., 20, 225-232, 1984.
13. Durbin, J., and G. S. Watson, Testing for serial correlation in least squares regression I, Biometrika, 37, 409-428, 1950.
14. Feder, J., Fractals, 283 pp., Plenum, New York, 1988.
15. Feller, W., An Introduction to Probability Theory and Its Applications, vol. 2, John Wiley, New York, 1971.
16. Flury, M., and H. Flühler, Brilliant blue FCF as a dye tracer for solute transport studies - A toxicological overview, J. Environ. Qual., 23, 1108-1112, 1994.
17. Flury, M., and H. Flühler, Tracer characteristics of brilliant blue FCF, Soil Sci. Soc. Am. J., 59, 22-27, 1995.
18. Flury, M., H. Flühler, W. A. Jury, and J. Leuenberger, Susceptibility of soils to preferential flow: A field study, Water Resour. Res., 30, 1945-1954, 1994.
19. Folorunso, O. A., C. E. Puente, D. E. Rolston, and J. E. Pinzón, Statistical and fractal evaluation of the spatial characteristics of soil surface strength, Soil Sci. Soc. Am. J., 58, 284-294, 1994.
20. Frisch, U., and G. Parisi, On the singularity structure of fully developed turbulence, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics: Proceedings of the International School of Physics "Enrico Fermi," edited by M. Ghil, R. Benzi, and G. Parisi, pp. 84-88, North-Holland, New York, 1985.
21. Giménez, D., W. J. Rawls, and J. G. Lauren, Scaling properties of saturated hydraulic conductivity in soil, Geoderma, 88, 205-220, 1999.
22. Gupta, V. K., and E. Waymire, Multiscaling properties of spatial rainfall and river flow distributions, J. Geophys. Res., 95, 1999-2009, 1990.
23. Harris, D., M. Menabde, A. Seed, and G. Austin, Multifractal characterization of rain fields with a strong orographic influence, J. Geophys. Res., 101, 26,405-26,414, 1996.
24. Hatano, R., and H. W. G. Booltink, Using fractal dimensions of stained flow patterns in a clay soil to predict bypass flow, J. Hydrol., 135, 121-131, 1992.
25. Jury, W. A., Simulation of solute transport using a transfer function model, Water Resour Res., 18, 363-368, 1982.
26. Katz, A. J., and A. H. Thompson, Fractal sandstone pores: Implications for conductivity and pore formation, Phys. Rev. Lett., 54, 1325-1328, 1985.
27. Kosmas, C., N. Moustakas, C. Kallianou, and N. Yassoglou, Cracking patterns, bypass flow and nitrate leaching in Greek irrigated soils, Geoderma, 49, 139-152, 1991.
28. Lavallée, D., Multifractal analysis and simulation technique and turbulent fields, Ph.D. thesis, McGill Univ., Montreal, Canada, 1991.
29. Lévy, P., Théorie de l'Addition des Variables Aléatoires, Gauthiers-Villars, Paris, 1937.
30. Liu, H. H., and F. J. Molz, Comment on "Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations" by Scott Painter, Water Resour Res., 33, 907-908, 1997a.
31. Liu, H. H., and F. J. Molz, Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res., 33, 2483-2488, 1997b.
32. Lovejoy, S., and D. Schertzer, Fractals, raindrops and resolution dependence of rain measurements, J. Appl. Meteorol., 29, 1167-1170, 1990.
33. Lovejoy, S., and D. Schertzer, Multifractals and rain, in New Uncertainty Concepts in Hydrology and Water Resources, edited by Z. W. Kundzewicz, pp. 61-103, Cambridge Univ. Press, New York, 1995.
34. Lu, S., and F. J. Molz, How well are hydraulic conductivity variations approximated by additive stable processes?, Adv. Environ. Res, 5, 39-45, 2001.
35. Luxmoore, R. J., Micro-, meso- and macroporosity of soil, Soil Sci. Soc. Am. J., 45, 671, 1981.
36. Mandelbrot, B. B., Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier, J. Fluid Mech., 62, 331-358, 1974.
37. Menabde, M, A. Seed, D. Harris, and G. Austin, Self-similar random fields and rainfall simulation, J. Geophys. Res., 102, 13,509-13,515, 1997.
38. Öhrström, P., M. Persson, R. Berndtsson, S. Nasri, P. Zante, and J. Albergel, Field scale variability of preferential flow as indicated from dye coverage, J. Hydrol., 257, 164-173, 2002.
39. Olsson, J., R. Berndtsson, A. Bahri, M. Persson, and K. Jinno, Nonlinear and scaling spatial properties of soil geochemical element contents, Water Resour. Res., 37, 1031-1042, 2001.
40. Pachepsky, Y., and D. Timlin, Water transport in soils as in fractal media, J. Hydrol., 204, 98-107, 1998.
41. Painter, S., Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations, Water Resour. Res., 32, 1183-1195, 1996.
42. Parker, J. C., and M. T. van Genuchten, Flux-averaged and volume averaged concentrations in continuous approach to solute transport, Water Resour. Res., 20, 866-872, 1984.
43. Perillo, C. A., S. C. Gupta, E. A. Nater, and J. F. Moncrief, Prevalence and initiation of preferential flow paths in a sandy loam with argillic horizon, Geoderma, 89, 307-331, 1999.
44. Persson, M., H. Yasuda, J. Albergel, R. Berndtsson, P. Öhrström, S. Nasri, and P. Zante, Modeling plot scale dye penetration by a diffusion limited aggregation (DLA) model, J. Hydrol., 250, 98-105, 2001.
45. Sakiss, N., N. Ennabli, and M. Slimani, La pluviométrie en Tunisie, technical report, Natl. Inst. for Res. on Rural Eng., Water, and For., Tunis, Tunisia, 1991.
46. Savin, N. E., and K. J. White, The Durbin-Watson test for serial correlation with extreme sample sizes or many regressors, Econometrica, 45, 1989-1996, 1977.
47. Schertzer, D., and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res., 92, 9693-9714, 1987.
48. Schertzer, D., and S. Lovejoy, (Eds.), Non-linear Variability in Geophysics, 318 pp., Kluwer Acad., Norwell, Mass., 1991.
49. Schwartz, R. C., K. J. McInnes, A. S. R. Juo, and C. E. Cervantes, The vertical distribution of a dye tracer in a layered soil, Soil Sci., 164, 561-573, 1999.
50. Smettem, K. R. J., and S. T. Trudgill, An evaluation of some fluorescent and non-fluorescent dyes in the identification of water transmission routes in soils, J. Soil Sci., 34, 45-56, 1983.
51. Soil Survey Staff, Keys to Soil Taxonomy, U.S. Dep. of Agric., Washington, D.C., 1996.
52. Tessier, Y., S. Lovejoy, and D. Schertzer, Universal multifractals: Theory and observations for rain and clouds, J. Appl. Meteorol., 32, 223-250, 1993.
53. Tyler, S. W., and S. W. Wheatcraft, Application of fractal mathematics to soil water retention estimation, Soil Sci. Soc. Am. J., 53, 987-996, 1989.
54. Wright, R. R., and M. R. Collings, Application of fluorescent tracings techniques to hydrological studies, J. Am. Water Works Assoc., 56, 748-754, 1964.
55. Yaglom, Y., The influence of fluctuations in energy dissipation on the shape of turbulence characteristics in the inertial interval, Sov. Phys. Dokl., Engl. Transl., 11, 26-29, 1966.
56. Young, I. M., and J. W. Crawford, The fractal structure of soil aggregates: Its measurement and interpretation, J. Soil Sci., 42, 187-192, 1991.