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

We investigate the statistical properties of den- dritic drainage areas from diverse geological environments (Deception Canyon, Utah and the Loess Plateau, China) us- ing 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 −� where k is a wave number anda scale invariant exponent. In spite of this good isotropic scal- ing, images with very similar �'s and similar isotropic mul- tifractal exponents have distinct textures; we suggest that the differences are primarily due to anisotropy, which is never- theless scaling. We develop the new "Differential Anisotropy Scaling" technique to characterize this scale-by-scale (dif- ferential) 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 in- variant anisotropy exponents. Viewed as a method of esti- mating these exponents, it has the advantage of relying on two linear regressions rather than on complex higher dimen- sional nonlinear ones. When applied to dendritic drainage basins we find that they have distinct anisotropies character- ized by differential anisotropy stretching and rotation param- eters as well as by a distinct absolute anisotropy at the refer- ence scale of 960 m. Our new method allows us to statisti- cally distinguish, not only between two geologically different drainage basins (the China Loess Plateau and Utah Decep- tion Canyon), but also between different regions of the same China drainage system.