Introduction

It has been shown (Browning et al., 1982) that large-scale radar signatures (features such as mesoscale precipitation areas) are more predictable than smaller-scale ones (features such as individual convective rain echoes). Therefore, extracting the larger scale features from radar images of storms has been extensively studied. One way of extracting features of arbitrary scales from images is to convolve the images with appropriate filters. Authors (e.g. Bellon and Zawadzki, 1994; Browning, 1979) have traditionally used filters where the region of support is isotropic. However, storms are often organized such that they are several times longer than they are wide. Hence, a filter that accounts for this elongation, having a support area that is elongated along the front direction would be expected to perform better in extracting large-scale signatures.

Wolfson et al. (1999) used a filter where the region of support was an ellipse with the major axis of the ellipse about four times longer than the minor axis. ²Since the direction of the front was not known apriori, several filters with the ellipse at different orientations were used and the filter that yielded the maximum response at a particular location was assumed to be the one aligned with the front direction at that location.

Weather radar commonly used in the United States provide resolution of about 1km per pixel ³ and a range of more than 250km at the lowest elevations. A weather radar makes a new volume scan every 300 seconds on average and a new elevation scan every 30 seconds on average. Thus, filtering commonly needs to be done for volume products in under 300 seconds and for elevation products in under 30 seconds. For any filtering technique to be effectively used in a near-real-time environment, the filtering will have to meet these time criteria.

The filtering of a time sequence by a filter window can be achieved by multiplying the Fourier transform of the time sequence with the the Fourier transform of the filter. Since there are fast algorithms available to compute the Digital Fourier Transform of sequences whose lengths are composites of small prime numbers, significant speedups can be realized by using this approach.