Fractals and morphometric measures: is there a relationship? (original) (raw)
Related papers
The fractal properties of topography: A comparison of methods
Earth Surface Processes and Landforms, 1992
In this study the fractal characteristics of fifty-five digital elevation models from seven different United States physiographic provinces are determined using seven methods. The self-similar fractal model tested in this analysis is found to provide a very good fit for some landscapes, but an imperfect fit for others. Thus, outright rejection of this model does not appear to be warranted, but neither does a blind application. The three implementations of the dividers methods considered in this study consistently produce lower dimensions than those produced by the other methods, and those dimensions consistently do not vary much between surfaces. Although the dimensions produced by the cell counting method (applied to the digital elevation model itself) display consistent intersurface variation, the dimensions are generally lower than those produced by the variogram-based methods. Among the variogram-based methods, the dimensions of the quarter-sections of the digital elevation models are generally greater than the dimensions obtained from the other variogram-based methods. The dimensions produced by the variogram method which considered the surfaces on a directional basis are very similar, on average, to the dimensions produced by the entire-surface variogram.
Measurement of DEM roughness using the local fractal dimension
Géomorphologie : relief, processus, environnement, 2006
La rugosité ou la texture des Modèles Numériques de Terrain (MNT) est susceptible de fournir des informations relatives à la géologie régionale. En effet, les MNT étant une représentation de la surface, différents attributs peuvent les décrire. Entre autres, la dimension fractale permet de ca-ractériser la texture dans la mesure où la topographie terrestre est sensée présenter un comportement fractal indépendamment de l'échelle d'observation. Cet article concerne l'étude de la rugosité de surface à l'aide de la mesure de la dimension fractale locale dans un espace tridimensionnel, en vue de mettre en évidence ou d'accentuer divers traits géomorphologiques.
Apparent Fractal Dimensions from Continental Scale Digital Elevation Models Using Variogram Methods
Transactions in GIS, 2000
It is often assumed that real land surfaces demonstrate the statistically self-affine scaling behaviour of fractional Brownian surfaces. Tests of this assumption against empirical data, however, show many deviations. Estimates of fractal properties vary between methods and over different scale ranges. So far, this empirical evidence has come from the analysis of variograms for DEMs representing areas up to tens of kilometres in diameter. Here we report results obtained by using variograms to analyse land surface DEMs at the continental scale, with a grid resolution of 30 arc seconds. Results reveal variogram curvature and breaks of slope, but also linear sections over distance lags of hundreds of kilometres. The estimated mean fractal dimension calculated from these sections is 2.66, substantially higher for all continents at these broad scales (around 200 km) than values calculated at the erosional landscape scale (around 200 m). Thus the land surface is not self-affine, and it is not clear that it follows any simple multifractal model. At the longest wavelengths, patterns found in the variograms appear to be related to broad tectonic features of the Earth's surface. For the reader to assess their quality and generality, estimates of fractal dimension should always be accompanied by statements of the scale range covered and the goodness of fit to a log-linear relationship.
Fractal is an applicable implement for evaluation of the complicated patterns of natural features. Geoinformatics allow not only representing data, but also performing geostatistical analysis and building models. This paper investigates the deformation pattern of land surfaces applying Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM) through a combined geo-information and fractal approach. The covering divider method is applied in order to extract fractal dimension of the earth surface (D ) directly for estimating surface roughness of the earth topography surf through geographic information system (GIS) approaches. Specifying the function of the geomorphologic processes on the spatial variability of fractal properties of the earth surface is accessible through this assessment. Fractal dimension mapping us to ascertain geomorphic domains where variability of fractal dimension of the earth surface represents the roughness of the land form topography and is an assessment of texture of topography. Results show that the presented approach in this research using the presented flow chart provides a rapid and facile procedure to evaluate the spatial distribution of the earth surface deformation within geological regions. Relatively higher fractal dimensions are observed where loose alluvial deposits and irregularities exists whilst the lower fractal dimension represents existence of the competent formations. The results showed that the Kharmankuh anticline has formed in a NE-SW direction and shows nearly symmetrical deformation pattern.
International Journal of Geosciences, 2013
Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.
Fractal dimension estimates of a fragmented landscape: sources of variability
Landscape Ecology, 1994
Although often seen as a scale-independent measure, we show that the fractal dimension of the forest cover of the Cazaville Region changes with spatial scale. Sources of variability in the estimation of fractal dimensions are multiple. First, the measured phenomenon does not always show the properties of a pure fractal for all scales, but rather exhibits local self-similarity within certain scale ranges. Moreover, some sampling components such as area of sampling unit, the use of a transect in the estimation of the variability of a plane, the location, and the orientation of a transect all affect, to different degrees, the estimation of the fractal dimension. This paper assesses the relative importance of these components in the estimation of the fractal dimension of the spatial distribution of woodlots in a fragmented landscape. Results show that different sources of variability should be considered when comparing fractal dimensions from different studies or regions.
Statistical properties of ecological and geologic fractals
Ecological Modelling, 1996
To use fractal models for ecological and geologic data, the statistical properties of fractals need to be clarified. No sampling or estimation theory for fractals currently exists. Several concrete steps in this direction are taken here. First, the information fractal dimension is proposed as a new measure that is relatively robust with respect to sampling error and can handle intensive data. The information fractal is tested with field data and is shown to be capable of delineating stratified structures and defining the scale of heterogeneity in the data. Comparison to semivariance analysis reveals the superiority of the fractal model for sample data that are nonisotropic and nonstationary. It is argued that approaches using regression to estimate fractal dimensions of spatial patterns are statistically invalid, and alternatives are proposed. Sampling of natural objects with transects (e.g., wells) is explored. For nonisotropic media (or maps), random placement of transects is shown to give an unreliable estimate of pattern. For transects taken perpendicular to a directional pattern (i.e., strata), it is shown that the mean of multiple estimates of the multiscale fractal dimensional profile does converge to the true value. Other sampling issues are addressed.