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

Abstract

Scaling processes are increasingly understood to be the result of nonlinear dynamic mechanisms repeating scale after scale from large to small scales leading to nonclassical resolution dependencies. This means that the statistical properties systematically vary in strong, power‐law ways with the resolution. When present in geophysical and remotely sensed fields, it implies that when classical (single‐scale) remote sensing algorithms are used to determine surrogates of various geophysical fields, they can at most be correct at the unique (and subjective) calibration resolution. Scaling analysis and modeling techniques were applied to MODIS TERRA Bands 1 through 7 and to the standard derived vegetation and soil moisture indices in order to quantitatively characterize the wide range of scaling of these fields. The scaling exponents we found are not so large; however, they act across wide scale ranges and imply large effects. For example, for the statistics near the mean, the MODIS (500‐m) resolution would be biased by a factor of ∼1.52 when compared with similar results from an “ideal” sensor at 1‐mm resolution. Applying the standard index algorithms on lower and lower resolution satellite data, we obtained indices with significantly different statistical properties than if the same algorithm was used at the finest resolution and then degraded to an intermediate value (a difference of a factor ∼1.54). This shows that the algorithms can, at best, be accurate at the unique calibration scale and this points to the need to develop resolution‐independent algorithms based on the scaling exponents.