Multiscaling analysis in a structured clay soil using 2D images

Abstract The spatial variability of preferential pathways for water and chemical transport in a field soil, as visualized through dye infiltration experiments, was studied by applying configuration entropy and multifractal analysis. After dye infiltration into a 4 m plot located on a Vertisol soil near College Station, TX, horizontal planes in the subsoil were exposed at 5-cm intervals, and dye stain patterns were photographed. Each of the digitized high-resolution dye images obtained were analysed calculating the maximum configuration entropy ( H ( L )), the characteristic length ( L ), and the generalized dimensions ( D q ). The results indicate that H ( L ) and L are two useful descriptors that give an optimal scale of discrimination in the spatial arrangement of the dye tracer at each horizontal section. In addition, L can be used to choose the scale range at which the multifractal analysis should be applied. It has been showed that D q , being q >0, depend much more on the percentage of black pixels than on the image structure when a box-counting method is used. Finally, a multifractal analysis was applied to maximum dye infiltration depth and amount of dye pixels bellow the area studied, obtained by merging images from the 16 exposed planes. The results show a multiscaling structure and a consistent D q for both measures. This could be useful for statistically describing preferential flow path geometry and flow processes under field conditions.

[1]  H.W.G. Booltink,et al.  Measurement and simulation of bypass flow in a structured clay soil: a physico-morphological approach. , 1993 .

[2]  Antonio Saa,et al.  Scaling and Multiscaling of Soil Pore Systems Determined by Image Analysis , 2003 .

[3]  K. McInnes,et al.  Spatial variability of water fluxes in soil: a field study , 1997 .

[4]  Hannes Flühler,et al.  Tracer Characteristics of Brilliant Blue FCF , 1995 .

[5]  Hannes Flühler,et al.  SUSCEPTIBILITY OF SOILS TO PREFERENTIAL FLOW OF WATER : A FIELD STUDY , 1994 .

[6]  Antoine Saucier,et al.  Influence of multifractal scaling of pore geometry on permeabilities of sedimentary rocks , 1995 .

[7]  John Bennet Lawes,et al.  On the amount and composition of the rain and drainage-waters collected at Rothamsted , 1881 .

[8]  Shaun Lovejoy,et al.  Non-Linear Variability in Geophysics , 1991 .

[9]  Azeddine Beghdadi,et al.  Entropic analysis of random morphologies , 1994 .

[10]  R. E. Phillips,et al.  Consequences of Water Movement in Macropores 1 , 1979 .

[11]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[12]  Jensen,et al.  Direct determination of the f( alpha ) singularity spectrum and its application to fully developed turbulence. , 1989, Physical review. A, General physics.

[13]  Fred J. Molz,et al.  Multifractal analyses of hydraulic conductivity distributions , 1997 .

[14]  Satish C. Gupta,et al.  Prevalence and initiation of preferential flow paths in a sandy loam with argillic horizon , 1999 .

[15]  Antoine Saucier,et al.  Effective permeability of multifractal porous media , 1992 .

[16]  Jiri Muller,et al.  Characterization of pore space in chalk by multifractal analysis , 1996 .

[17]  J. C. Losada,et al.  Multifractal analysis of tori destruction in a molecular Hamiltonian system. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  A. Rinaldo,et al.  Configuration entropy of fractal landscapes , 1998 .

[19]  H.W.G. Booltink,et al.  Using fractal dimensions of stained flow patterns in a clay soil to predict bypass flow. , 1992 .

[20]  Y. Pachepsky,et al.  Scaling Methods in Soil Physics , 2007 .

[21]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[22]  R. Schwartz,et al.  The Vertical Distribution of a Dye Tracer in a Layered Soil , 1999 .

[23]  Antonio Saa,et al.  Fractal and multifractal analysis of pore-scale images of soil , 2006 .

[24]  Toshio Sakuma,et al.  Evaluation of the effect of morphological features of flow paths on solute transport by using fractal dimensions of methylene blue staining pattern , 1992 .

[25]  Magnus Persson,et al.  Modeling plot scale dye penetration by a diffusion limited aggregation (DLA) model , 2001 .

[26]  J. Olsson,et al.  Field-scale variation of preferential flow as indicated from dye coverage , 2002 .

[27]  J. Olsson,et al.  Multiscaling analysis and random cascade modeling of dye infiltration , 2002 .

[28]  Yakov A. Pachepsky,et al.  Conventional and fractal geometry in soil science , 2000 .

[29]  A. Tarquis,et al.  Multifractal analysis of particle size distributions in soil , 1998 .

[30]  Henry Lin,et al.  Effective Porosity and Flow Rate with Infiltration at Low Tensions into a Well-structured Subsoil , 1996 .

[31]  Local entropy characterization of correlated random microstructures , 1996, cond-mat/9611015.

[32]  C. T. Hallmark,et al.  MACROPOROSITY AND INITIAL MOISTURE EFFECTS ON INFILTRATION RATES IN VERTISOLS AND VERTIC INTERGRADES , 1998 .

[33]  F. Molz,et al.  Multifractal scaling of the intrinsic permeability , 2000 .

[34]  Philippe Baveye,et al.  Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils , 1998 .

[35]  Y. Pachepsky,et al.  Fractals in soil science , 2000 .

[36]  J.-Y. Parlange,et al.  Fractals in soil science , 1998 .

[37]  Edward C. Waymire,et al.  Multifractal Dimensions and Scaling Exponents for Strongly Bounded Random Cascades , 1992 .

[38]  J. Bouma,et al.  The Function of Different Types of Macropores During Saturated Flow through Four Swelling Soil Horizons1 , 1977 .

[39]  Philippe C. Baveye,et al.  Surface fractal characteristics of preferential flow patterns in field soils: evaluation and effect of image processing , 1999 .

[40]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[41]  J. Feder,et al.  Microstructural sensitivity of local porosity distributions , 1992 .

[42]  Azeddine Beghdadi,et al.  ENTROPIC AND MULTIFRACTAL ANALYSIS OF DISORDERED MORPHOLOGIES , 1993 .

[43]  Hannes Flühler,et al.  Brilliant Blue FCF as a Dye Tracer for Solute Transport Studies-A Toxicological Overview. , 1994, Journal of environmental quality.