Generating Candidate Regions

In the first stage, the radar polar data are pre-processed and mapped into a 256$\times$256 Cartesian grid. Candidate regions are formed by selecting the 0.15-set of applying a fuzzy relation to the grid values and combining the resulting pixels into candidate regions based on four-neighbor contiguity. The volumes formed by stacking the candidate regions (see Figure 7) and Cartesian images corresponding to each elevation scan within a volume scan are used for further processing (see Figure 8).

Figure 7: Candidate regions found at different elevation scans of the radar are stacked spatially to form a volume. Areas with reflectivity greater than 45dBZ are shown shaded. The dotted lines show all the possible mechanisms through which a region can inherit 3D attributes.

Figure 8: Flowchart of the BWER detection scheme.

In the preprocessing stage, all unknown reflectivity values are set to an effective value of -7 dBZ. The search volume is then limited to the areas on each elevation scan where a circulation was detected in the previous volume scan. Circulations are detected using the Mesocyclone Detection Algorithm [17] whose objective is to find all storm-scale circulations within the radar's range. Then, the image corresponding to each elevation scan is convolved with the two-dimensional kernel whose cross-sectional profile is shown in Figure 9.

Figure 9: Cross-section of kernel used to find local minima.

In the absence of noise, the resulting image has a positive value at a location if any of these conditions exist:

1. There is a local minimum in the reflectivity field at that location.
2. The reflectivity field exhibits an inflection at that point.
3. The location is part of the storm base boundary. (A pixel in the Cartesian grid is said to be part of the storm base if it has a positive reflectivity value associated with it.)
4. The location is a background point close to the storm base. (A pixel in the Cartesian grid is said to be part of the background if the reflectivity value associated with it is lesser than or equal to -7 dBZ.)

We eliminate the effect of the fourth condition and minimize that of the third by convolving only at points within the storm base. We assume that all resulting positive values are local minima and use the decision tree later in the process to weed out inflections in the reflectivity field.

Each pixel that has a reflectivity value associated with it in the 256$\times$256 Cartesian grid is assigned a score based on its reflectivity value (favoring lower reflectivity) and proximity to the ``high'' reflectivity values of 35 dBZ and 45 dBZ. The lower of this score and the convolution result is deemed the score of that grid location.

The pixels whose scores fall in the top 15% of the grid are determined. Candidate regions are built recursively based on four-neighbor contiguity from the top pixels. These regions are then labeled.

Labeled regions from successive elevations scans of the radar are stacked vertically together to form a three-dimensional (3D) set of regions. This 3D set along with the 3D set of original Cartesian grids similarly stacked is used for further processing.