Introduction

Tornadoes and very large hail are commonly observed with supercell severe thunderstorms. One radar feature often associated with supercells is the Bounded Weak Echo Region (BWER). The presence or absence of a BWER within a storm is important information for a weather forecaster. A BWER is a region of relatively low radar reflectivity which extends upward into, and is surrounded by, higher reflectivities aloft (Figure 1 [5,13]). Sometimes called a ``vault,'' this radar signature is usually indicative of a high speed updraft. This is because such a strong updraft (with speeds of around 50 $m.sec^{-1}$) is so fast that the processes forming precipitation cannot operate rapidly enough to develop high radar reflectivities until the air parcels have ascended to relatively great heights. BWERs are representative of local storms that develop in a strongly sheared environment and which tend to a steady state circulation [1].

Figure 1: Vertical cross-section of a well-defined BWER associated with an intense updraft. The contours represent constant radar reflectivity. From Lemon 1980.

Figure 2: Volume coverage of a WSR-88D radar with bandwidth of 0.95 degrees and 9 elevation scans. From Smith 1995.

The weather surveillance radars used by the National Weather Service scan through thunderstorms starting at a low elevation angle ($0.5^o$) and, after completing a full $360^o$ azimuthal sweep, progressively increase the elevation angle until an upper limit is reached ($19.5^o$, see Figure 2) [2,16]. As these constant radar elevation ``sweeps'' step upward to sample through a BWER, the BWER first appears as a region of relatively low reflectivities surrounded by higher reflectivities (see Figure 3 [8]) and then, at higher elevation angles, becomes ``capped'' by a broad region of high reflectivity.

Figure 3: Horizontal cross-section of a strong BWER. The contours represent constant radar reflectivity. From Krauss and Marwitz 1984.

There are several reasons, besides updraft intensity, why the radar signature of a BWER rarely appears as clear cut as would be expected from the idealized structure indicated in Figure 1. Since the area scanned by a radar increases the farther away one gets from the radar (see Figure 4), a higher proportion of the storms analyzed will be located at fairly distant ranges from the radar. As the distance between the radar and the storm increases, the ability of the radar to properly sample small- scale features within the storm, such as the BWER, becomes more difficult, since the radar sampling volume becomes larger. Also, as distance increases, the lowest part of the storm that the radar can scan is at increasingly higher altitudes. Close to the radar, the top of the storm may be missed by the higher elevation scans (see Figure 5). Another problem can occur with rapidly moving storms. In the time it takes for the radar to scan upward through the storm, the higher altitude capping region of the BWER may have moved (with the storm) such that it no longer is located over the relative reflectivity minimum, detected at a lower altitude. There is also an error associated with vertical height as measured by the radar [6] and this error varies with weather conditions.

Figure 4: The area scanned by a radar and the sampling volume increase with distance from the radar. The beamwidth ($0.95^o$) and radial resolution ($1 km$) shown are for a WSR-88D reflectivity scan.

Figure 5: Whether the structure is capped or not can not be deduced from the radar data because the higher elevation scans miss the top of the storm.

Previous attempts (e.g. [15]) at machine perception of weak echo regions got around these uncertainties by finding weak echo region (WER) patterns in two dimensions using information about local minima, reflectivity gradients and the relative organization of high and low reflectivity regions. False alarms were minimized by accepting only those 2D patterns that were associated with 2D patterns in other elevation angle planes.

We consider the three-dimensional profile to be integral to the definition of a BWER. Purely two-dimensional methods have had limited success because they detect all local minima in the reflectivity field of the radar data set. False alarms will be common in schemes where the 3D radar profile is not considered.

Fuzzy logic has been used to improve the performance of meteorological machine vision algorithms in the past, notably in gust front detection [3]. Because of the various uncertainties associated with the appearance of a BWER in radar images, we decided to design a fuzzy logic scheme where the dependency of the detection technique on any particular feature is quite low.