H. Remote Sensing [Background] [Raindrop
Distribution Retrieval] 1. Background RAP has been actively involved in the development of techniques for monitoring precipitation with polarimetric radar measurements. Recent activities E. Brandes, J. Vivekanandan, and G. Zhang focused on the refinement and verification of the constrained-gamma method for retrieving drop-size distribution (DSD) information. The retrievals are being used to improve quantitative estimates of rainfall and to study the evolution of drop-size distributions within storms. Motivation for this work comes in part by National Weather Service plans to modify the Weather Surveillance Radar-1988 Doppler Radars (WSR-88Ds) for polarimetric measurements. A method for estimating drop sizes and liquid water contents with dual-wavelength radar was proposed by Vivekanandan. The technique is based on differential attenuation at short radar wavelengths and has promise for the detection of icing conditions. Also discussed in this section are methods for improving the accuracy of wind estimates with profilers. Zhang and colleagues proposed the Cross-Correlation Ratio method for improving wind estimates allowing the transverse wind to be determined with a single radar antenna. Praskovsky has been developing a procedure (UCAR STructure function Analysis of Received Signals) for improved data processing. An advantage over current auto and cross- correlation techniques is a relative insensitivity to ground and point targets. 2. Raindrop distribution retrieval from polarimetric radar measurements a. Verification of the
Rain rate estimation from radar
measurements typically depends on empirical power-law relations such
as R–Z relations. E. Brandes, G. Zhang and J. Vivekanandan developed
an algorithm for retrieving the governing parameters of the Gamma
rain drop-size distribution, Recently, we studied the error
propagation from drop-size distribution (DSD) moment estimates to
DSD parameter retrievals (Zhang et al. 2002a). Standard error and
correlation coefficient were calculated using theoretical analyses
and numerical simulations. The study shows that the errors in moment
estimates can cause correlations among the estimated DSD parameters
and can create a linear relation between estimates of
b. Retrieval verification The constrained-gamma method for retrieving DSD parameters
was applied to polarimetric radar measurements obtained in Florida
during the PRECIP98 field program and has been verified with disdrometer
observations. Figure 2 shows retrieved
total drop concentrations (NT) and drop median volume diameters
(D0) for a long-lived storm observed on 17 September 1998.
Although the disdrometer was 38 km from the radar site and the sampling
volumes for the two instruments differ by many orders of magnitude,
the comparison is excellent. Tests show that the retrievals are more
robust than those based on the assumption of a fixed Rainfall rates determined by the DSD retrieval method
were compared to rain gauge measurements. Results show a mean bias
factor of 0.93 (a small radar overestimate), a bias factor variation
from storm-to-storm of 1.81, and a correlation coefficient between
radar-estimated and gauge-observed rainfall accumulations of 0.91. These
results are equivalent to those obtained with power-law estimators
using the radar reflectivity and differential reflectivity measurements.
This was expected since that methodology incorporates these two measurements.
Rainfall estimates with the DSD retrieval technique are superior to
single parameter estimators that use radar reflectivity or specific
differential phase. The
Figure 2: A comparison of radar-retrieved and disdrometer-observed total drop concentration (NT) and drop median volume diameter (D0). 3. Wind Field Retrieval a. Cross-Correlation Ratio (CCR) method to estimate transverse wind components Spaced-antenna (SA) radars have been widely used for wind profiling. The SA technique is based on the drifting interference patterns corresponding to the medium's motion. Previously, wind estimates from SA measurements were obtained with the Full Correlation Analysis (FCA) method, which makes use of both cross-correlation and auto-correlation functions. G. Zhange has explored an alternative explanation of the SA technique as correlation changes depending on radar orientation and the wind velocity. This technique can be applied to single-antenna radars. When the radar sample volume follows the motion of randomly-distributed scatterers, the correlation is maximumized. For other wind directions, the correlation of the scattered wave signal decreases, becoming minimal when the movement of sample volume and scatterers are in the opposite direction. For SA receivers, the correlation is a maximum when the propagation path is the same for the paired receivers. Based on the above interpretation, a cross-correlation ratio (CCR) method was developed (Zhang et al. 2002b) to estimate the wind, i.e., the CCR at positive lag and at negative lag, which is directly related to mean transverse velocity. Compared to the FCA method, the CCR method is more direct, simpler to implement, and potentially more accurate. A
detailed error analysis procedure for evaluating wind estimators using
interferometry techniques has been lacking. Consequently, we developed
a rigorous error theory and verified it using numerical simulations
as shown in Figure 3 where Mi
is the number of independent samples,
Figure 3.Theoretical and numerical errors for the time delay to correlation peak as a function of peak cross-correlation.
Figure 4. Comparison of the standard error of the transverse wind estimates obtained with the CCR and FCA methods. (v0x = 10 m s–1, turbulence parameter 1 m s–1 ). 4.
UCAR-STARS
UCAR-STARS (UCAR STructure function Analysis of Received Signals) is an alternative method for remotely measuring characteristics of scatterers by spaced antenna (SA) radars. The procedure, developed by A. Praskovsky and E. Praskovskaya of RAP, is based on calculation and analysis of the different order auto and cross-structure functions of the received signals power. The method has been under development for almost five years. During this time, it has been intensively tested with simulated signals over a wide range of the radar parameters and atmospheric conditions and with experimental data from the NCAR multiple antenna profiler (MAPR). Good performance was found in all tests. Efforts this past year focused on potential STARS application to Mesosphere, Stratosphere, and Troposphere (MST) profiling radars. Tests were performed on the Middle and Upper atmosphere Radar (MUR) operated by the Radio Science Center for Space and Atmosphere, Kyoto University, Kyoto, Japan and the Chung-Li radar (CLR) operated by the Center for Space and Remote Sensing Research, National Central University, Chung-Li, Taiwan. A similar data collection strategy was used in both tests. The radars operated in SA mode for approximately 8.2 min and then switched to the Doppler beam swinging (DBS) mode for approximately 1 min. This sequence was repeated for several hours. An example of measured mean horizontal wind speed components with MUR is shown in Fig. 6 (Ux towards east, and Uy towards north). Results with the Halloway - Doviak method (HAD), which is the most advanced correlation function-based SA measurement technique, are also shown. One can see that STARS performance is much better than that of HAD, and even that of DBS. Note that the averaging time (Tav) with STARS is more than a factor of two less than that with HAD. Relatively poor DBS performance results from two factors: 1) relatively low signal-to-noise-ratio (SNR) after 38 coherent integrations, as shown in Fig. 6, and 2) intensive radio interference during data collection. A wind retrieval comparison with CLR is shown in Fig. 7 (upper two panels). Quite poor DBS performance seems surprising given the relatively high SNR (approximately 5 dB after 400 coherent integrations) at this height. DBS failure could result from airplane interference, since CLR is located very close to Chiang Kai-shek International Airport. The radar's return power during data collection is presented in Fig. 7 (lower panel). Dark strikes correspond to airplanes either inside the beam or side lobes. Airplane returns could strongly affect DBS while it does not affect STARS. The latter is not surprising because the structure function-based approach is not very sensitive to ground clutter and point targets. UCAR-STARS tests on MST profiling radars have shown good performance. The tests also demonstrate that STARS is not sensitive to noise that is correlated between receivers, e.g., radio interference, ground clutter, and hard targets such as airplanes
Figure 5. The mean horizontal wind velocity components (Ux towards east, Uy towards north) retrieved by DBS, HAD, and STARS at 8 km above MUR on 21 February 2002. Figure 6. The mean horizontal wind velocity components retrieved with DBS and STARS (upper two panels) at 7.35 km above CLR and the radar's return power during the data collection (lower panel, courtesy Dr. J.-S. Chen) on 19 June 2002.
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relation 
,
from the polarimetric radar measurements of radar reflectivity and
differential reflectivity along with a constraining condition between
the distribution shape 
parameters.
The enabling relation is shown in Figure 1a.
Since the algorithm was reported, there has been concern as whether
is
the time delay to the correlation peak. The error analysis
was then used to evaluate the CCR and FCA methods. The standard errors
of wind estimates using the CCR and FCA methods are calculated and
compared in Figure 4 where v0x
is the wind velocity and 
