Keywords
Geostatistics
Fractal Dimension
Scaling Analysis
How to Cite
Abstract
The study of spatial variability of specific quantities characterizing the unsaturated soil is very important for the evaluation of polluting phenomena. Geostatistics is a useful tool for estimating the spatial variability of the considered parameters. The aim of this study is to improve the understanding of the spatial variability of the fractal dimension of water retention curves, showing the behaviour of this parameter in the site examined and particularly at the points where measures were not performed. The assessment of the fractal dimension was calculated by the analysis of scaling obtained from some fractal models and a comparison among the correspondent results was performed.
References
Anderson, A. N.; McBratney, A. B. 1995. "Soil aggregates as mass fractals". Australian Journal of Soil Research, 33 (5): 757-772.
Tyler, S. W.; Wheatcraft, S. W. 1989. "Application of fractal mathematics to soil water retention estimation". Soil Society of American Journal, 53 (4): 987-996.
Perfect, E.; Kay, B. D. 1991. "Fractal theory applied to soil aggregation". Soil Science Society of American Journal, 55 (6): 1552-1558.
Crawford, J. W.; Sleeman, B. D.; Young, I. M. 1993. "On the relation between number-size distribution and the fractal dimension of aggregates". Journal of Soil Science, 44 (4): 555-565.
Toledo, G.; Novy, R. A.; Davis, H. T.; Scriven, L. E. 1990. "Hydraulic conductivity of porous media at low water content". Soil Science Society of American Journal, 54 (3): 673-679.
Katz, A. J.; Thompson, A. H. 1985. "Fractal sandstone pores: implications for conductivity and pore formation". Physical Review Letters, 54 (12): 1325-1327.
Bird, N.; Bartoli, F.; Dexter, A. R. 1996. "Water retention models for fractal soil structure". European Journal ofSoil Science, 47 (1): 1-6.
Rieu, M.; Sposito, G. 1991a. "Fractal fragmentation, soil porosity and soil water properties: I. Theory". Soil Science Society of American Journal, 55 (5): 1231-1238.
Rieu, M.; Sposito, G. 1991b. "Fractal fragmentation, soil porosity and soil water properties: II. Applications". Soil Science Society of America Journal, 55 (5): 1239-1244.
Crawford, J. W.; Ritz, K.; Young, I. M. 1995. "The relation between the moisture-release curve and the structure of soil". European Journal ofSoil Science, 46 (3): 369-375.
Perrier, E.; Rieu, M.; Sposito, G.; Marsily, G. 1996. "Models of the water retention curve for soils with a fractal pore size distribution". Water Resources Research, 32 (10): 3025-3031.
Bird, N.; Perrier, E.; Rieu, M. 2000. "The water retention function for a model of soil structure with pore and solid fractal distributions". European Journal of Soil Science, 51 (1): 55-63.
Matheron, G. 1971. "The theory of regionalized variables and its applications". Les Cahiers du Centre de Morphologie Mathématique, Fascicule 5. Centre de Géostatistique, Fontainableau, France, 212.
Journel, A. G.; Huijbregts, C. J. 1978. "Mining Geostatistics". London, ENGLAND: Academic Press.
Deutsch, C. V; Jounel, A. G. 1998. "GSLIB Geostatistical Software Library and User"™s Guide". New York, USA: Oxford University Press.
Isaaks, E. H.; Srivastava, M. 1989. "An Introduction to Applied Geostatistics". New York, USA: Oxford University Press.
Hunt, A. G. 2004. "Continuum percolation theory for pressure-saturation characteristics of fractal soils: extension to non-equilibrium". Advances in Water Resources, 27 (3): 245-257.
Perfect, E. 2005. "Modeling the primary drainage curve of prefractal porous media". Vadose Zone Journal, 4 (4): 959-966.
Perfect, E.; Kenst, A. B.; Diaz-Zorita, M.; Grove, J. H. 2004. "Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters". Soil Science Society of America Journal, 68 (4): 1177-1184.
Tyler, S. W.; Wheatcraft, S. W. 1990. "Fractal processes in soil water retention". Water Resources Research, 26 (5): 1047-1054.
Danielson, R. E.; Sutherland, P. L. 1986. "Porosity. In: Methods of Soil Analysis, Part 1, Physical and Mineralogical Methods". American Society of Agronomy: 443-461.
Perrier, E.; Bird, N.; Rieu, M. 1999. "Generalizing the fractal model of soil structure: the PSF approach". Geoderma, 88 (3-4): 137-164.
Wang, K.; Zhang, R.; Wang, F. 2005. "Testing the poresolid fractal model for the soil water retention function". Soil Science Society of America Journal, 69 (3): 776-782.
Millán, H.; Gonzáles-Posada, M. 2005. "Modelling soil water retention scaling. Comparison of a classical fractal model with a piecewise approach". Geoderma, 125 (1-2): 25-38.
Fallico, C.; Tarquis, A. M.; De Bartolo, S.; Veltri, M. 2010. "Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry". European Journal ofSoil Science, 61 (3): 425-436.
Meakin, P. 1998. "Fractals, Scaling and Growth Far From Equilibrium". Cambridge, ENGLAND: Cambridge University Press.
Matheron, G. 1963. "Principles of geostatistics". Economic Geology, 58 (8): 1246-1266.
Tobler, W. 1970. "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46 (2): 234-240.
Barnett, V; Lewis, T. 1978. "Outliers in Statistical Data". New York, USA: John Wiley and Sons.
Dixon, W. J. 1953. "Processing Data for Outliers". Biometrics, 9 (1): 74-89.
Davis, C. J. 1973. "Statistics and Data Analysis in Geology". New York, USA: John Wiley & Sons.
Kolmogorov, A. N. 1933. "Foundations ofthe Theory of Probability". New York, USA: Chelsea Publishing Company.
Anderson, T. W.; Darling, D. A. 1952. "Asymptotic theory of certain goodness of fit criteria based on stochastic processes". Annals of Mathematical Statistics, 23 (2): 193-212.
Kitanidis, P.; Vomvoris, E. 1983. "A geostatistical approach to the inverse problem in ground water modeling (steady state) and one dimensional simulations". Water Resource Research, 19 (3): 677-690.
Armstrong, M. 1998. "Basic Linear Geostatistics". Berlin, GERMANY: Springer Verlag.
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