Modification of Multiresolution Feature Analysis for Application to Three-Dimensional Atmospheric Wind Fields

Abstract

Multiresolution feature analysis (MFA), as originally proposed for estimating the fractal dimension of two-dimensional scalar fields, is described. MFA applies specified correlation filters to a data field (such as a gray-scale image) at different resolutions and examines the scaling of the intensities of the spatial peaks in the filter outputs at the different scales. These scaling properties can be related to different types of fractal dimension. One attractive aspect of MFA is that it gives the analyst flexibility to choose physically significant features for filtering. This paper describes the original MFA technique and then extends the technique from two-dimensional scalar fields to two-dimensional vector fields. In principle, the three-dimensional vector applications allow the estimation of the fractal dimension of the support for turbulent fluctuations but there are limitations on the applicability of the methodology, which are discussed. MFA requires definition of physically significant features, which take the form of small-scale patterns of motion when the technique is applied to three-dimensional flows. The authors describe statistical techniques (similar to principal component analysis) that can be applied to small subvolumes of data to identify those motion patterns that explain the most variance. These small-scale patterns of spatial variability then serve as the features in the version of MFA described here. Possible applications, modifications, and extensions of the methodology that has been developed are given.