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