Results and Discussion

One of the images from the sequence of radar images obtained from the lowest elevation scan of the Fort Worth weather radar is shown in Figure 2. That image, when filtered by the large-scale smoothing technique of Wolfson et al. (1999) is shown in Figure 3. The output of the modified filtering process on the same image is shown in Figure 4. For easier comparison, the absolute difference between the two output images is shown in Figure 5.

Both the effects described in Section 2.6 are observed. The assumption of the periodicity of the image shows up as large errors along the sides of the image. Where radar data are missing (close to the storm envelope and at some places within it), the pixels sport large errors because we need to retain shift-invariance to successfully use the transform method.

The time in seconds taken by the original technique and the modified technique to process each image in the sequence of radar images using different filter sizes is shown in Table 1. The larger the filter size, the greater the relative speed-up. Note that the modified technique takes longer on the first image. This is because of the filter FFTs that need to be computed. As is apparent from Table 1, one can perform the operation in a fraction of the time taken using the original technique. In addition, since the time for the modified technique does not depend on filter sizes, the time advantage increases as the filter size increases. The increase in time of  Wolfson et al. (1999)'s technique as the sequence progresses is an artifact of the storm case chosen: the storms strengthened and there were more valid pixels to process. The transform method, is of course data independent, since we had to assign an ad-hoc value to each pixel in the image. If every pixel in the image had corresponded to valid data, the processing would have taken about 740 seconds using the original technique.

It is seen from Table 1 that the transform-based large-scale filtering method introduced in this paper is significantly faster. In fact, the time requirements are lower than the 30-second update interval of radar elevation scans. Thus, this method can be used for filtering both volume and elevation products. It is also noticed from Figure 4 that the resulting image, though not indentical to that obtained by the technique of Wolfson et al. (1999), works well in extracting the larger scales. Hence, if one is willing to live with the assumption on the data values that the transform method imposes, the modified large scale filter technique can be performed in significantly less time. In environments where real-time performance is very critical, the modified large-scale filter is a good choice.