P2.21

THE OPTIMIZATION OF WSR-88D SCANNING STRATEGIES FOR CONVECTIVE STORMS

Vincent T. Wood and Rodger A. Brown
NOAA/ERL/National Severe Storms Laboratory
Norman, Oklahoma 73069

1.   INTRODUCTION

The operational meteorological community generally recognizes that WSR-88D (Weather Surveillance Radar-1988 Doppler) measurement uncertainties of storm top and other height-related parameters are caused by both the volume coverage pattern (VCP) and the range of the storm from the radar (Howard et al. 1997, Maddox et al. 1999). Coarse vertical spacing at low elevation angles makes WSR-88D detections difficult at far ranges.

The purpose of this study is to develop an optimization technique that is designed to produce more uniform vertical resolution at all ranges. That is, we create a set of elevation angles that produces maximum height uncertainties that are comparable at all ranges from a radar. Due to limited space in this paper, we deal only with VCP 11. The results of optimized VCP 11 are presented and compared with original VCP 11.

2.   CHARACTERISTICS OF VCP 11

VCP 11 consists of 14 scans in 5 minutes (FMH-11 Part A 1991). Plotted in Fig. 1 are the elevation angles of VCP 11 and corresponding height underestimates associated with them. The figure is analogous to figures used by Howard et al. (1997). As an example of how to interpret the greyscale bands (Fig. 1), we assume that VCP 11 is used to detect the top of a 16-km-tall storm at a range of 230 km. The storm top (indicated by the dotted horizontal line) is above 2.4o but below 3.35o elevation. The highest elevation angle displaying radar return is 2.4o, which represents an apparent storm top of 13 km at 230-km range. The radar return underestimates storm top by 3 km, as indicated by the dark shading at the 16-km height (Fig. 1).

The jagged curve (Fig. 1) represents the variations that would occur in the measured top of a 16-km-tall storm as it moved toward or away from the radar. There is almost random variation and increasing underestimation with range owing to the irregular and coarse spacing between elevation angles. The jagged curve is analogous to those in the figures of Maddox et al. (1999).

Fig. 1. Height of VCP 11's elevation angles a function of slant range. Each elevation angle curve (zero height underestimate) is labeled. Height of a storm feature that lies between two elevation angles is determined by the lower elevation angle and therefore is underestimated by the amount indicated by the color bands. The dotted horizontal line at 16-km height represents the true height of the storm feature; the jagged line represents the apparent height of the feature measured by the radar.

In addition to 16 km, height variations at 4-, 8-, and 12-km heights are illustrated in Fig. 2. The amount of variation increases nearly linearly with height. It appears that height variation expressed as a fraction of the true height (the dotted lines) is essentially independent of height. To verify this idea, the curves in Fig. 2 were replotted in Fig. 3 as a percentage of the true height. Except for variations attributable to the lowest elevation angles, the maximum height underestimation, expressed in percentage, is about the same at a given range.

Fig. 2. Variation of the apparent height of a storm feature as a function of slant range for VCP 11. The dotted horizontal lines represent the true storm features at 4-, 8-, 12- and 16-km heights. The jagged lines represents the apparent heights of the features measured by the radar. The elevation tilts are indicated by numbers 1-14 and are identified on the right side of the figure.

Fig. 3. The jagged curves from Fig. 2 are replotted as normalized curves for VCP 11. The height of each jagged curve is expressed as a percent uncertainty relative to the true height indicated by the respective dotted line in Fig. 2.

3.   TECHNIQUE FOR OPTIMIZING VCP 11

The relative consistency of the curves in Fig. 3 motivated us to develop a new technique for designing VCPs. The approach is to develop an optimization technique by specifying the maximum height uncertainty desired (expressed as a percentage) and calculating the set of elevation angles that satisfy the constraint. As depicted schematically in Fig. 4, we specify a true height (Zt), height underestimate (Z), and maximum height underestimate (H%). Zt is chosen to be 10 km. H% is specified as a percentage of Zt.

As an example of how to optimize a set of elevation angles (Fig. 4), the procedure is to start at the farthest slant range (450 km in this study). The height of the radar beam is initially given by

where re/ is 6/5 earth radius, the value used with WSR-88D. We specify the minimum elevation angle k to be 0.5o. With decreasing range at that elevation angle, we calculate the height underestimate (Z = Zt - h, where h is the height of slant range rs as a function of elevation angle). The procedure is repeated until Z = H% x Zt. Then, we jump back up to Zt (Fig. 4) and compute a new elevation angle (k+1). That is, we replace h in Eq. (1) by Zt and solve for the new k+1,

We repeat the process until again Z = H% x Zt. New elevation angles are computed until a specified maximum elevation is reached. In this way, we develop a new VCP that has a consistent maximum height underestimate at all ranges.

Fig. 4. Schematic of the process used to compute optimized VCPs. See discussion in the text for details.

As an example of the advantages of the optimization technique, we produced an optimized version of VCP 11. H% was calculated using the same lowest and highest elevation angles and number of elevation angles as in the original VCP 11. The optimized version of VCP 11 has a maximum height underestimate of 19.38%. Compared with Fig. 3, Fig. 5 shows more uniform height underestimates at all ranges. An optimized version of Fig. 1 is shown in Fig. 6. For elevation angles < 5o, there are more elevation angles in the optimized VCP than in the original VCP 11. The optimized VCP provides better coverage at far ranges. Also, the more uniform variation between elevation angles is quite evident.

Fig. 5. Same as Fig. 3, except for optimized VCP 11.

Fig. 6. Same as Fig. 1, except for optimized VCP 11.

4.   CONCLUSIONS

An optimization technique was developed to produce VCPs with more uniform vertical resolution at all ranges. Using the technique, optimized VCP 11 was produced and compared with the original VCP 11. With optimized VCP 11, fine vertical spacing at low elevation angles improves WSR-88D detections at far ranges. The findings suggest that the optimization approach produces VCPs that do a better job in resolving mid- and upper-altitude features at far ranges.

5.   ACKNOWLEDGMENTS

The authors thank Terry Schuur of NSSL for reviewing and providing helpful comments and suggestions on the early version of the manuscript. This study was funded through a Memorandum of Understanding between WSR-88D Operational Support Facility and NSSL.

6.   REFERENCES

Federal Meteorological Handbook (FMH) No. 11, 1991: Doppler Radar Meteorological Observations, Part A: System concepts, responsibilities and procedures. Office of the Federal Coordinator for Meteorological Services and Supporting Research (FCC-H11A-1991).

Howard, K. W., J. J. Gourley, and R. A. Maddox, 1997: Uncertainties in WSR-88D measurements and their impacts on monitoring life cycles. Wea. Forecasting, 12, 166-174.

Maddox, R. A., D. S. Zaras, P. L. MacKeen, J. J. Gourley, R. Rabin, and K. W. Howard, 1999: Echo height measurements with the WSR-88D: Use of data from single versus two radars. Wea Forecasting. (Accepted)