Multiscale Soil Investigations: Physical Concepts And Mathematical Techniques

Soil variability has often been considered to be composed of “functional” (explained) variations plus random fl uctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise (Burrough, 1983). Soils can be seen as the result of spatial variation operating over several scales, indicating that factors infl uencing spatial variability differ with scale. Th is observation points to variability as a key soil attribute that should be studied

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

A correct statistical model of soil pore structure can be critical for understanding flow and transport processes in soils, and creating synthetic soil pore spaces for hypothetical and model testing, and evaluating similarity of pore spaces of different soils. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. Simple fractal models such as fractional Brownian motion that have been proposed to capture the complex behavior of soil spatial variation at field scale rarely simulate irregularity patterns displayed by spatial series of soil properties. The objective of this work was to use CT data to test the hypothesis that soil pore structure at the horizon scale may be represented by multifractal models. X-ray CT scans of twelve, water-saturated, 20-cm long soil columns with diameters of 7.5 cm were analyzed. A reconstruction algorithm was applied to convert the X-ray CT data into a stack of 1480 grayscale digital images with a voxel resolution of 110 microns and a cross-sectional size of 690 × 690 pixels. The images were binarized and the spatial series of the percentage of void space vs. depth was analyzed to evaluate the applicability of the multifractal model. The series of depth-dependent macroporosity values exhibited a well-defined multifractal structure that was revealed by singularity and Rényi spectra. The long-range dependencies in these series were parameterized by the Hurst exponent. Values of the Hurst exponent close to one were observed indicating the strong persistence in variations of porosity with depth. The multifractal modeling of soil macropore structure can be an efficient method for parameterizing and simulating the vertical spatial heterogeneity of soil pore space

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Differing self-similarity in light scattering spectra: A potential tool for pre-cancer detection

The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. Significant differences in the power law behavior ascertained through the scaling exponent was observed in these tissues. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.Comment: 13 pages, 14 figure

Multiscale Analysis for Characterization of Remotely Sensed Images.

In this study we addressed fundamental characteristics of image analysis in remote sensing, enumerated unavoidable problems in spectral analysis, and highlighted the spatial structure and features that increase information amount and measurement accuracy. We addressed the relationship between scale and spatial structure and the difficulties in characterizing them in complex remotely sensed images. We suggested that it is necessary to employ multiscale analysis techniques for analyzing and extracting information from remotely sensed images. We developed a multiscale characterization software system based on an existing software called ICAMS (Image Characterization And Modeling System), and applied the system to various test data sets including both simulated and real remote sensing data in order to evaluate the performance of these methods. In particular, we analyzed the fractal and wavelet methods. For the fractal methods, the results from using a set of simulated surfaces suggested that the triangular prism surface area method was the best technique for estimating the fractal dimension of remote sensing images. Through examining Landsat TM images of four different land covers, we found that fractal dimension and energy signatures derived from wavelets can measure some interesting aspects of the spatial content of remote sensing data, such as spatial complexity, spatial frequency, and textural orientation. Forest areas displayed the highest fractal dimension values, followed by coastal, urban, and agriculture respectively. However, fractal dimension by itself is insufficient for accurate classification of TM images. Wavelet analysis is more accurate for characterizing spatial structures. A longer wavelet was shown to be more accurate in the representation and discrimination of land-cover classes than a similar function of shorter length, and the combination of energy signatures from multiple decomposition levels and multispectral bands led to better characterization results than a single resolution and single band decomposition. Significant improvements in classification accuracy were achieved by using fractal dimensions in conjunction with the energy signature. This study has shown that multiscale analysis techniques are very useful to complement spectral classification techniques to extract information from remotely sensed images