Atmospheric
Turbulence
|
|||||||||||||||
[Background] [Retrieval
of DSD information] For the past several years, RAP has been involved in the development of techniques to retrieve drop-size distribution (DSD) information from remote measurements made with polarimetric radars. Recent activities of E. Brandes, G. Zhang, and J. Vivekanandan have focused on rainfall estimation and the development of procedures for retrieving the DSD with the "constrained-gamma" model using measurements of radar reflectivity and differential reflectivity and an empirical relation between the shape and slope parameters of the gamma DSD. G. Zhang and colleagues continued their work whereby the radial and transverse components are retrieved with single-antenna radars using interferometry techniques. The method determines the transverse wind component from the cross-correlation ratio (CCR) determined at positive and negative lags. In addition, error propagation in the performance of Spaced Antenna systems has been investigated. J. Williams, J. Vivekanandan, and G. Zhang have been developing a dual-wavelength method for retrieving liquid water content (LWC) in clouds. The goal is to provide warnings of potential icing conditions. Recent efforts have documented potential error sources associated with mismatched radar beams and have improved processing procedures for retrieving detailed LWC information.
During PRECIP98, NCAR's S-Pol radar was deployed for evaluating
the potential of polarimetric radar for estimating rain in a subtropical
environment. Rain gauge and raindrop disdrometer observations were also
collected. The data have been used to develop a methodology for retrieving
the governing parameters of gamma raindrop size-distributions from polarimetric
radar measurements. The distribution is assumed given by N(D)=NoDµexp- a. Spatial description of DSD An example of application of DSD parameters derived from radar data is shown in Figure 2.1, with a vertical cross section showing two well-developed storms centered at 26 and 45 km. Positive ZDR (top right panel) suggests that most of the precipitation below 5 km AGL is rain. For a specified ZDR, the drop median diameter, the gamma DSD shape and slope parameters, and total drop concentration NT can be estimated from other radar observables from empirical fits to the data. Applied to this example, maximum raindrop concentrations exceed 1000 per m-3 in some regions of the storms, and values of µ were < 2 in these regions. Drop median volume diameters are large in regions of heavy precipitation and small (<1.5 mm) near the cell boundaries. Rain cell boundaries are characterized by large µ, i.e., narrow DSDs with smaller drop concentrations. Thus, high reflectivity regions in this example corresponded to large number concentrations and broad raindrop spectra. The rain rate is derived from the estimated DSD parameters instead of a fixed power-law relation as is commonly used. Peak rain rates are ~100 mm h-1.
To test the validity of constrined-gamma based polarization
radar estimators, self-consistency in polarization observations is used.
Estimated differential phase and specific differential phase were compared
with measured values. The estimated spedific propagation phase (KeDP)
and propagation phase (
Fig. 2.1. Spatial distribution of polarization radar measurements, retrieved DSD parameters, and rain rate. (a) Reflectivity, (b) differential reflectivity, (c) number concentration, m-3, (d), (e) DSD-based log10 of rain rate in mm h-1, and (f) median volume diameter in mm. Note log10 of number concentration and rain rate are shown. Standard deviation of canting angle is assumed to be 10o. The data were collected by S-Pol at 1901 UTC, 17 September 1998.
Fig. 2.2. Indirect verification of
the
Radial wind is routinely measured by radars using the Doppler method. Winds transverse to the radar beam can be measured using an interferometric technique in which three or more spaced antennas are used (i.e., the Spaced Antenna, SA, technique). In cooperation with R. J. Doviak of the National Severe Storms Laboratory, G. Zhang developed an interferometric technique whereby a single antenna is used to measure both radial and transverse winds. Angular Interferometry (AI) determines the transverse wind component, and Range Interferometry (RI) determines radial wind component (Figure 3.1). The technique is based on the fact that signal correlation is high when the sample volume follows the scatterers' motion, and is low when the resolution volume is sampled in the opposite direction. Therefore, the ratio of cross-correlation function at positive and that at negative lags is directly related to wind velocity. The cross-correlation of signals, received from different angles and from different ranges by a single antenna, is derived based on scattering from random fluctuations of refraction index. The performance of the technique has been studied through error analysis and its dependence on spatial resolution, observation time, and turbulence. These theoretical studies show that AI requires a small beam size to measure transverse wind accurately (contrary to the SA technique), whereas RI requires fine range resolution to perform well.
Figure 3.1: Conceptualizations of Angular Interferometry, (a) and Range Interferometry, (b).
A method for characterizing the accuracy of baseline winds, estimated using spaced antennas (SA) and a full correlation analysis (FCA) method to process signals in the presence of noise, has been developed by G. Zhang. Performance of the FCA method was compared with the theoretical performance of another correlation-based approach (i.e., the cross correlation ratio method, CCR). The theoretical results of the error analysis are supported with numerical simulations and experimental data. It was shown that the theoretical analysis is valid and the results can be applied to improve wind estimates obtained from SA signals contaminated with additive white noise. The theory shows that the noise effect on SA wind estimates depends on system configuration and the lag, and cannot be fully accounted for by a reduced correlation coefficient due to noise as previously hypothesized.
Reliable remote detection of cloud liquid water content and droplet sizes is important both for understanding cloud microphysics and meteorological processes and for providing improved diagnostics of icing potential to the aviation community. One particularly promising technique makes use of the ratio of reflectivities measured by two co-located radars operating at different wavelengths and observing the same region of the atmosphere. The dual-wavelength ratio (DWR) or differential attenuation is obtained as a function of range. The attenuation difference is due to the absorption of the two signals by atmospheric gasses, particularly water vapor, and by cloud droplets, ice crystals, or hydrometeors. In the case where only small water droplets are present, theoretical calculations may be used to remove gaseous absorption and relate the remaining attenuation difference to the liquid water content along the radar beams. Unfortunately, previous attempts to apply this theory as a method for detecting cloud liquid water content (LWC) have been hindered by the contamination of the radar reflectivity by measurement noise, Mie (large droplet or ice) scattering, and mismatched radar beam sizes and locations. These contaminants may cause unrealistic (including negative) LWC retrievals, while averaging the radar data to diminish the contamination produces low-resolution results. RAP scientists J. Williams, J. Vivekanandan and G. Zhang have been working to quantify these undesired effects, develop ways to mitigate them, and design a robust method to obtain accurate, high-resolution liquid water content measurements from dual-wavelength radar data. This research is sponsored by the FAA's Aviation Weather Research Program. There have been two primary achievements this past year. First, a more complete understanding of the mechanisms responsible for contaminating the measured DWR has been obtained through both theoretical analyses and simulation of radar measurements. Most notably, it was discovered that small differences in the radar beam widths, location, or measurement spacing could generate significant artifacts in the DWR and hence in the retrieved LWC (see Figure 5.1). This information may help in designing improved dual-wavelength radar systems. Second, a fuzzy logic algorithm was developed to combine censoring of the raw radar data, a novel smoothing technique, and a "resolution boosting" method to obtain LWC retrievals at the same resolution as the raw radar data. The censoring method considers a number of features of the radar data to derive a "confidence" value for each pixel. These confidence values are used as weights during the smoothing process, so that suspect data regions are effectively interpolated over. Several smoothing methods were developed and applied to the DWR data. The most effective was a "regularization" method that computes a confidence-weighted best fit while penalizing large or negative derivatives. Finally, the LWC computed from the smoothed DWR is used to derive local ratios between the square of the LWC and the reflectivity. This ratio may then be multiplied by a radar's raw reflectivity values to produce a final LWC retrieval having the same high resolution as the radar measurements. The LWC and measured reflectivity may also be used to obtain an estimate of droplet sizes. The new fuzzy-logic algorithm was applied to data from the University of Massachusetts CPRS Ka- and W-band radar collected as part of Mount Washington Icing Sensor Project (MWISP). A sample result, along with a comparison to sounding and radiometer data, is displayed in Figure 5.2.
Figure 5.1. Time series of LWC profiles obtained from the DWR produced via simulation of CPRS Ka and W-band radar measurement of an artificial liquid water field. The liquid water field was constructed from concentrations having Gaussian density with maximum value 1 g m-3 and various shape parameters and lying either in the plane of the radar beams (columns 1, 3, 5 and 6) or 200 m behind the plane (columns 2 and 4); it was advected past the radar beams at 20 m s-1. The radar beams were perfectly aligned, but had different widths (0.5 degrees at Ka-band and 0.18 degrees at W-band). Retrieved LWC values range from -1.2 g m-3 (blue) to +1.2 g m-3 (red) as indicated by the color bar to the right of the plot. Erroneous negative values and paired negative and positive artifacts like those seen here occur frequently in real data and had previously been poorly understood.
Figure 5.2.. (Lower right) Time series
of LWC profiles obtained from CPRS kA and W-band radar data using the
new fuzzy logic retrieval technique described in the text. The data
were collected between 1620 and 1640
[Top]
|
|||||||||||||||
where N0 is a concentration factor, µ is a shape parameter,
DP)
were obtained from power measurements, i.e., Z and ZDR, using
empirical relations. As expected, estimated 
DP
monotonically increases with range and agrees well in the mean with
the measurement (see 
(a) 
