Anisotropic scaling of remotely sensed drainage basins: the differential anisotropy scaling technique

Abstract

Abstract.We investigate the statistical properties of dendritic drainage areas from diverse geological environments (Deception Canyon, Utah and the Loess Plateau, China) using narrow band visible ASTER satellite images. We show that from 240 m to 7680 m, the isotropic (angle integrated) energy spectra E(k) of all the fields closely follow a power law form: E(k)∝k −β where k is a wave number and β a scale invariant exponent. In spite of this good isotropic scaling, images with very similar β's and similar isotropic multifractal exponents have distinct textures; we suggest that the differences are primarily due to anisotropy, which is nevertheless scaling. We develop the new "Differential Anisotropy Scaling" technique to characterize this scale-by-scale (differential) anisotropy and we test it on simulated anisotropic scaling fields. The method gives useful characterizations of the scale by scale anisotropy irrespective of whether or not the analyzed field is scaling. When the anisotropy is not too strong, the parameters can be interpreted as scale invariant anisotropy exponents. Viewed as a method of estimating these exponents, it has the advantage of relying on two linear regressions rather than on complex higher dimensional nonlinear ones. When applied to dendritic drainage basins we find that they have distinct anisotropies characterized by differential anisotropy stretching and rotation parameters as well as by a distinct absolute anisotropy at the reference scale of 960 m. Our new method allows us to statistically distinguish, not only between two geologically different drainage basins (the China Loess Plateau and Utah Deception Canyon), but also between different regions of the same China drainage system.

Single‐ and Multiscale Remote Sensing Techniques, Multifractals, and MODIS‐Derived Vegetation and Soil Moisture

“…In the figure, we see that the contours are fairly roundish, indicating that, to some approximation, the second‐order statistics are isotropic. Careful scale‐by‐scale analyses of the anisotropy would be rewarding (see, e.g., Pflug et al, 1993; Lewis et al, 1999; Beaulieu et al, 2007), but is outside our present scope. Analysis of the individual radiance bands revealed a degree of isotropy similar to the indices shown in Fig.…”

A simple and effective method for quantifying spatial anisotropy of time series of precipitation fields

“…Beaulieu et al . [] on the other hand estimate the GSI parameters by visually examining scatterplots describing properties of isolines in , presenting a method that is easy to approach but laborious when estimating parameters of more than a few fields.…”

“…Beaulieu et al . [] reported that while SIG yielded reasonable estimates for theoretical simulations with a diversity of anisotropic and statistical characteristics, it was not able to quantify the true anisotropy of many empirical fields. Consequently, they proposed a new “Differential anisotropy scaling” technique.…”