P20.3

IMPROVED DETECTION CAPABILITY OF SINGLE-DOPPLER VELOCITY SIGNATURES
OF FAR-RANGE MESOCYCLONES

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

1. INTRODUCTION

Doppler radar suffers from a resolution-related problem in observing Doppler velocity signatures of mesocyclones at far ranges. The problem arises from the degradation of Doppler velocities owing to the widening of the radar beam with range relative to the vortex size, as discussed by Donaldson (1970), Burgess et al. (1993), and others. Using simulated WSR-88D data collected at 1^o azimuthal sampling intervals, Wood and Brown (1997) extended the discussion of resolution-related problems to that owing to the random position of the radar beam center with respect to the peak velocities of the mesocyclone. The position can significantly affect the apparent size and strength of far-range mesocyclones. The important implication presented in the Wood and Brown study is that short-term variations in far-range mesocyclone intensity may be due to evolution or due to changes in the position of the radar beam relative to the vortex's maximum tangential velocities or due to some combination of both.

Burgess (1976) and Burgess and Donaldson (1979) presented data that suggest that 0.5^o azithumal sampling improves mesocyclone detection at far ranges. However, it was unclear how much the detection capability was improved when comparing 0.5^o azithumal sampling to the conventional 1.0^o azimuthal sampling.

For the WSR-88D, an azimuthal sampling interval of 0.5^ocould be achieved by decreasing the number of transmitted pulses, decreasing the antenna rotation rate, or some combination of the two. For data collection modes used in thunderstorm situations, decreasing the antenna rotation rate is not feasible because it would then take longer to obtain one full volumetric scan. Therefore, the most viable way to get 0.5^o data collection for the operational WSR-88Ds is to cut the number of pulses in half while maintaining the same antenna rotational rate as for 1.0^o azimuthal sampling.

The purpose of this paper is to investigate a potential procedure for improving the detection capability of long-range mesocyclones by WSR-88Ds. The effects of azimuthal sampling on simulated Doppler velocity signatures of modeled mesocyclones are examined by collecting 0.5^o resolution Doppler velocity data and comparing the results to those produced by the routine 1.0^o azimuthal sampling interval.

2. DOPPLER RADAR SIMULATION

The approach of Wood and Brown (1997) was used to produce simulated WSR-88D data. Radar measurements were derived by scanning a simulated Doppler radar beam through a three-dimensional velocity field characterized by a Rankine (1901) combined vortex. The effective half-power beamwidth (circular beam essentially broadened in the direction of antenna rotation) was calculated from the curve in Fig. 7.25 of Doviak and Zrni (1993) as a function of one-way half-power beamwidth, number of pulses sampled to compute the mean Doppler velocity value, antenna rotation rate and pulse repetition time. For 1.0^o and 0.5^o data collection modes, the mean effective beamwidths calculated by Wood and Brown (1997) were, respectively, 1.29^o and 1.02^o. These values were based on the average characteristics of WSR-88Ds in the nationwide network.

In lieu of calculating the mean Doppler velocity from a number of pulses, the mean Doppler velocity was computed as the two-dimensional weighted mean within the radar beam. The mean Doppler velocity was computed from 21 data points in the azimuthal direction extending over a distance twice the effective half-power beamwidth (using an antenna pattern weighting function), and 5 data points in the elevation angle direction extending over the regular half-power beamwidth.

As the number of pulses decreases, the noisiness of the Doppler velocity estimate increases. To approximate the effect of decreasing the number of pulses by two for 0.5^o sampling, the standard deviation of the Gaussian-distributed noise added to each computed mean Doppler velocity was increased by 2^1/2. Based on typical WSR-88D operating characteristics, the standard deviation of the mean Doppler velocity estimate is approximately 0.7 m s^-1 for 1.0^oazimuthal sampling. To approximate 0.5^o azimuthal sampling, the standard deviation of the Gaussian noise was increased to 1.0 m s^-1.

3. RESULTS

In this section, we examine the effect of sampling on Doppler velocity signatures of mesocyclones at far ranges by collecting velocity data using a 0.5^o azimuthal sampling interval and comparing the results to those produced by the 1.0^o sampling interval. The modeled mesocyclone is axisymmetric with a Rankine combined velocity profile having a typical peak tangential (rotational) velocity of 25 m s^-1 at a core radius of 2.5 km.

Wood and Brown (1997) showed that, with discrete sampling, the random positions of the center of the radar beam relative to the rotational velocity maxima produced variations in mesocyclone signatures at far ranges. This angular separation (denoted by AS in Fig. 1) is the difference between the vortex center and the center of the nearest range bin. AS varies between 0.5AZ, which represents the full discrete azimuthal sampling interval AZ. Extreme AS values are 0.5^o (0.25^o) for AZ = 1^o (AZ = 0.5^o). The azimuthal profiles of Doppler velocity values for AS values of -0.500^o, -0.250^o, and -0.125^o(not shown) are mirror images of AS values of 0.125^o, 0.250^o, and 0.500^o.

When WSR-88D measurements (AZ = 1^o) are made at all ranges from the radar, mean rotational velocities (the average of maximum and minimum Doppler velocity values at the core radius) and core diameters (the distance between the peak rotational velocities) change owing to the random positions of the sampling volume. To understand why the mesocyclone signature fluctuates owing to the random placement of the radar beam relative to the center of the mesocyclone, we refer to Fig. 1, which shows the azimuthal profile (normal to the radar viewing direction) of Doppler velocity values (black dots) through the mesocyclone at a range of 150 km. For the sake of illustration, noise was not added to the data points in the figure. When the radar beam is centered on the mesocyclone (AS = 0.0 in Fig. 1a), data points at B and D essentially coincide with the locations of the negative and positive Doppler velocity peaks, producing a mean rotational velocity of 18.3 m s^-1. Positions B and D are separated by two azimuthal increments. When the center of the radar beam is offset from the mesocyclone center (AS = +0.25), the mean rotational velocity value decreases to 17.2 m s^-1 because positions B and D are no longer at the peaks of the measured curve (Fig. 1b), although the deduced core diameter of 5.2 km remains unchanged. When the mesocyclone is centered midway between two range bins (Fig. 1c), the extreme measured values (A and D) are separated by three azimuthal increments, producing deduced values of mean rotational velocity of 16.4 m s^-1 and core diameter of 7.9 km.

For data collection at a 0.5^o azimuthal sampling interval (i.e., AZ = 0.5^o in Figs. 1d-f), measured mean rotational velocities and core diameters do not vary as much as in Figs. 1a-c. It is apparent that an advantage of 0.5^o sampling over 1.0^osampling is that with a combination of narrower effective beamwidth (1.02^o vs. 1.29^o) and smaller azimuthal sampling interval (0.5^o vs. 1.0^o), there are more data points available to delineate the stronger velocity profiles and therefore the signatures can be detected much more readily.

In the examples shown thus far, mean rotational velocities were computed for AZ = 0.5^o and 1.0^o at a range of 150 km from the radar. Fig. 2 shows the variation of estimated mean rotational velocities as a function of range for the 0.5^o and 1.0^o data collection modes. The shaded band's vertical width represents the full spread of mean rotational velocity values computed for 121 angular separation values between 0.5AZ. The solid curve running down the middle of each band is the average of 121 individual mean rotational velocity values at each range. Close to the radar (Figs. 2a-b), a given mean rotational velocity can lie anywhere over an interval of about 2-3 m s^-1 due to the random position of beam center relative to the peak rotational velocities of the mesocyclone. The interval increases to about 4 m s^-1 in Fig. 2a (3 m s^-1in Fig. 2b) at far ranges of 150 km or more. The reason for the oscillating width of the band in Fig. 2a is explained by Wood and Brown (1997).

It is possible to investigate how much detectability improves with 0.5^o azimuthal sampling by selecting common threshold values and determining how far in range that values greater than or equal to the threshold can be detected. For example, the 17 m s^-1 threshold value, which is detected at 156 km for AZ = 1.0^o, can be detected out to a range of 230 km with 0.5^o azimuthal intervals, as shown by the intersection of the thin solid line with the curves in Fig. 2b. This indicates that sampling at 0.5^o intervals extends the range of mesocyclone detectability by ~50% (Fig. 3). The results of these simulations have important implications for long-range mesocyclone detection because the coverage area for detection is essentially doubled using 0.5^o azimuthal increments. This is reflected in the ratio of coverage area at AZ = 0.5^o to coverage area at AZ = 1.0^o (Fig. 3).

A comparison of the frequency distributions of mean rotational velocity data at 1.0^o and 0.5^o azimuthal sampling intervals is shown in Fig. 4 (corresponding to the data at 150 and 200 km in range in Fig. 2). Here the sampling distribution consists of 1001 rotational velocity values uniformly spaced between 0.5AZ. The distributions reveal that the magnitudes of mean rotational velocities are stronger and closer to their true values of 25 m s^-1 when data are collected using a 0.5^o azimuthal sampling interval versus a 1.0^o azimuthal sampling interval. Also, there is less variation (i.e., a smaller standard deviation) among the various estimates of the mean rotational velocity with 0.5^o azimuthal sampling.

4. CONCLUSIONS

To demonstrate that it is possible to improve WSR-88D detection of far-range mesocyclones, simulations were run using 0.5^o in addition to the conventional 1.0^o azimuthal sampling intervals. The results show that, with 0.5^o azimuthal sampling, resolution was improved not only due to increased azimuthal sampling but also due to the narrowing of the effective beamwidth. The simulations presented in this study reveal that at all ranges, typical sized mesocyclones (peak rotational velocity of 25 m s^-1 at a core radius of 2.5 km) can be detected at least 45% farther in range using 0.5^oazimuthal sampling intervals versus using conventional 1.0^o sampling intervals. This is equivalent to at least a doubling of the detection area.

5. ACKNOWLEDGMENTS

The authors thank Jeff Trapp and Arthur Witt of NSSL for reviewing and providing helpful comments and suggestions on the early version of the manuscript. Appreciation is expressed to Dale Sirmans (NWS Operational Support Facility) for fruitful discussions about WSR-88D operational capabilities.

6. REFERENCES

Burgess, D. W., 1976: Single Doppler radar vortex recognition. Part I: Mesocyclone signatures. Preprints, 17^th Conf. on Radar Meteorology, Seattle, WA. Amer. Meteor. Soc., 97-103.

_________, and R. J. Donaldson, Jr., 1979: Contrasting tornadic storm types. Preprints, 11^th Conf. on Severe Local Storms, Kansas City, MO. Amer. Meteor. Soc., 189-192.

_________, _________, and P. R. Desrochers, 1993: Tornado detection and warning by radar. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., No. 79, Amer. Geophys. Union, 203-221.

Donaldson, R. J., Jr., 1970: Vortex signature recognition by a Doppler radar. J. Appl. Meteor., 9, 661-670.

Doviak, R. J., and D. S. Zrni, 1993: Doppler Radar and Weather Observations. Academic Press, 562 pp.

Rankine, W. J. M., 1901: A Manual of Applied Mechanics. 16^th ed. Charles Griff and Company, 680 pp.

Wood, V. T. and R. A. Brown, 1997: Effects of radar sampling on single-Doppler velocity signatures of mesocyclones and tornadoes. Wea. Forecasting, 12, 928-938.