Informational equivalence between synthetic aperture radar imagery and thethickness of Arctic pack ice

The negative exponential form of the conditional probability of both differ ences in synthetic aperture radar (SAR) intensity and differences in thickn ess between neighbors is used as the basis of a representation of structura l information in terms of textural information for sea ice. The analysis is based on a unique data set involving airborne SAR flights over the track o f a submarine that simultaneously profiled ice thickness by means of an upw ardly directed sonar. It is shown that both sets of data, namely, imagery a nd thickness, possess an identical conditional probability relationship. Th is probability is composed of both a fractal property for spatial separatio ns and a simple negative exponential distribution for intensity or thicknes s differences for fixed separations. These properties allow for the derivat ion of two forms of information: textural and structural. An intercompariso n of the structural information in terms of the textural information is off ered for the same ice field as imaged by a SAR and measured from a submarin e for its thickness. It is shown that the information curves for both the i magery and thickness have a similar geometrical form. It is demonstrated th at three subranges within the information curves correspond to three visibl y identifiable ice types and three thickness ranges associated previously w ith these ice types. It is suggested that an understanding of the transform ation between the two sets of information states might provide estimated st atistics of Arctic ice thickness from SAR imagery.