1. Introduction

Cintineo et al. (2012) presented a radar-based hail climatology for the continental United States for 2007–10 that illustrates the advantage of multiradar, grid-based techniques in deriving a high-resolution hail climatology. The Weather Surveillance Radar-1988 Doppler (WSR-88D) “maximum expected size of hail” (MESH) product was used to determine days with any hail and days with severe hail. The size of their dataset, quality control and processing of their dataset, and results are noteworthy. For example, Cintineo et al. illustrated substantial differences between the radar-based hail climatology and the corresponding reports-only climatology, drawing into question the reliability of the reports-based climatology in some cases.

While discussing challenges with using the WSR-88D data, the authors correctly noted that beam widening becomes a problem in regions of single-radar coverage at long ranges from the radar. However, we believe that in doing so they interpreted partial beam-filling artifacts incorrectly. We do not contend this changes their results in any meaningful way, but we would like to take this opportunity to clarify some of the problems associated with partial beam filling at relatively long ranges from the radar.

2. Beam filling at long ranges from the radar

For purposes of this comment an illustrative long range is taken to be 185 km [100 nautical miles (n mi)], which is consistent with other radar-based studies such as Blair et al. (2011). For simplicity a 1.0° beamwidth, which is near the effective one-way beamwidth (1.03°) for fine-resolution WSR-88D measurements (Wood et al. 2001), was assumed. At this distance the WSR-88D beam is approximately 3230 m (10 590 ft) wide, and at 333 km (180 n mi)—the approximate distance between the Big Bend area in southwestern Texas and the nearest WSR-88Ds—the beam is approximately 5810 m (19 070 ft) wide.

We take note of two items from Cintineo et al. (2012). First, on p. 1240 the authors state (italics added):

In regions of single-radar coverage (e.g., Big Bend of southwest Texas), beam widening becomes a problem. The resolution volume of the radar is very large at far ranges. When a precipitation echo is present in this volume, the radar will fill the entire resolution volume with the reflectivity value of that precipitation, even if it is only present in a small fraction of the volume. Thus, strong reflectivity may be spatially overestimated, potentially creating a bias of too much hail fall in MESH.

This topic is revisited later on p. 1245 (italics added):

However, southwest Texas has limited low-level radar coverage, which contributes to an elevated beam height (over 10 000 ft, or 3048 m) and becomes subject to the beam-spreading problem. … Here, overestimates of hail are possible, since the resolution volume at this range is relatively large (several cubic km) and may be entirely assigned with a high reflectivity, even if it is only partially filled with high reflectivity in actuality. Furthermore, if the melting level is below 10 000 ft where reflectivity is present, the MESH algorithm will create an underestimate.

Two conflicting factors are at work here, and the phraseology used by the authors does not describe the issue clearly. If precipitation only partially fills a radar resolution volume (e.g., Fig. 1), the measured radar reflectivity will be lower than the true reflectivity of the precipitation in the limited part of the volume where it is present. The radar equation basically averages the reflectivity over the pulse volume, so partial beam filling can only yield lower reflectivity factor values than those in the part of the beam where the particles are located. At the same time, this underestimated value will be attributed to the entire resolution volume (e.g., Battan 1973, p. 166). This specific impact on MESH would combine a tendency to underestimate the MESH value with a tendency to show it applying to a larger region (i.e., the full resolution volume) than is actually occupied by the precipitation. Thus, the resulting bias would be toward indicating hail not as large as that actually present (or no hail at all), but spread over a wider area. The first effect would produce fewer hail days but the second effect would produce more hail grid boxes (equating to days) when the hail threshold is met.

Fig. 1.

Conceptual model of an idealized radar echo that is intersected by a 1.0° radar beam at a range of 185 km. The echo is offset left of the center of the beam such that it fills one-third of the range bins, which are indicated by the dotted lines.

Fig. 1.

Conceptual model of an idealized radar echo that is intersected by a 1.0° radar beam at a range of 185 km. The echo is offset left of the center of the beam such that it fills one-third of the range bins, which are indicated by the dotted lines.

As an example of the first effect, consider Fig. 1 with an idealized storm echo that is 3 dB above the MESH threshold but covers only one-third of the range bins. Recall that if the returned power changes by a factor of 2 (3) the reflectivity changes by 3 dB (5 dB). Thus, the radar will average this echo over the whole volume to give an indicated reflectivity that is 2 dB below the hail threshold, resulting in a “no hail” indication. Conversely, the second effect would occur if the idealized storm reflectivity is 7 dB above the hail threshold; then, the radar-indicated reflectivity will be 2 dB above the hail threshold and assigned to the entire range-bin area, resulting in an indicated hail area that will be larger than the true storm area. Cintineo et al. (2012) used a horizontal grid spacing of ~1 km × 1 km, which means that in such a case hail could have been assigned to 3 times the true area at this range, resulting in two extra grid boxes containing hail days.

The net effect of the beam broadening and partial beam filling would therefore be convoluted—decreasing the number of hail days because some of the MESH values would drop below the threshold, but increasing hail days when the MESH threshold is exceeded because the hailstorm would be spread over a larger area. As such, it is difficult to determine any overall bias in the hail day statistics at longer ranges. Moreover, the effect of the melting level on the MESH algorithm would create an underestimate as stated by Cintineo et al. (2012), further complicating the bias.

3. Summary

The focus of Cintineo et al. (2012) was on using the gridded multiradar analyses to detect the presence of any hail and severe hail. They used ~30 million volume scans covering 4 years and applied substantial smoothing to their results, so the complicated bias due to partial beam filling is not expected to have a significant impact on their results. However, we believe it is important to clarify that partial beam filling at long ranges from the radar will always reduce the reflectivity, and in the case of strong storms (Battan 1973, p. 166) it will spread the reduced reflectivity over a larger area than what truly exists.

Acknowledgments

We appreciate the reviews provided by Dave Carpenter, Jeff Manion, and Jon Zeitler. The views expressed are those of the authors and do not necessarily represent those of the National Weather Service.

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Footnotes

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/WAF-D-11-00151.1.