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V. Chandrasekar
and
V. N. Bringi

Abstract

Fluctuations in the radar measurements of Z DR are due to both signal power fluctuations and the cross-correlation between the horizontal and vertical polarized signals. In Part I of this study, these signals are simulated for an S-band radar for backscatter from rain media, which is characterized by a gamma model of the raindrop size distribution (RSD). The parameters N 0, D 0, m of the gamma RSD are then varied over the entire range found in natural rainfall. Thus, the radar simulations contain the effects of both statistical fluctuations and physical variations. We also simulate sampling of raindrops by disdrometer. The sampling errors are related to the Poisson statistics of the total number of drops in the fixed sample volume and to the statistics that govern the gamma distribution of drops as a function of size. We simulate disdrometer RSD samples over the entire range of N 0, D 0, m values found in rainfall, so that the effects of statistical fluctuations and physical variations are introduced.

It is shown that Z DR, computed from disdrometer RSD samples, is correlated with Z and with other moments of the RSD when the same disdrometer data is used. This correlation is purely statistical and is independent of the physical correlation. We use the radar and disdrometer simulations to intercompare the rain rate as derived by the radar Z DR-method with the rain rate estimated by the disdrometer. Our simulation results are used to explain the correlation and error structure of radar/disdrometer-derived rain rate intercomparison data reported in the literature.

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V. Chandrasekar
and
V. N. Bringi

Abstract

In Part II of this study, simulations of multiparameter radar observables to include X-band specific attenuation (A) are performed in order to study the relationship between A, Z, and Z DR. We also compute the triplet (A, Z, Z DR) from simulations of disdrometer raindrop spectra. As in Part I, our simulations include the fluctuations due to both measurement errors and physical variations of the gamma raindrop spectra parameters (N 0, D 0, m). We examine the correlation between (A/Z) and Z DR derived from both disdrometer and radar simulations, and show that the disdrometer-based data yields a negative collation (∼ −0.9) between (A/Z) and Z DR, whereas for radar data the correlation ≈ 0. We emphasize that these correlations are due only to measurement fluctuations, and not to physical variations. The large magnitude for the negative correlation compresses the scatter in plots of (A/Z) versus Z DR based on disdrometer RSD samples whereas the same scatter plots using multiparameter radar data show very large scatter. We also simulate A, Z and Z DR from three separate disdrometers (all sampling the same gamma RSD) and show that the scatter is more realistic and much larger than when using a single disdrometer.

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V. Chandrasekar
and
V. N. Bringi

Abstract

Raindrop size distributions (RSDs) are often estimated using surface raindrop sampling devices (e.g., disdrometers) or optical array (2D-PMS) probes. A number of authors have used these measured distributions to compute certain higher-order RSD moments that correspond to radar reflectivity, attenuation, optical extinction, etc. Scatter plots of these RSD moments versus disdrometer-measured rainrates are then used to deduce physical relationships between radar reflectivity, attenuation, etc., which are measured by independent instruments (e.g., radar), and rainrate. In this paper we simulate RSDs of the gamma form as well as radar reflectivity (via time series simulation) to study the correlation structure of radar estimates versus rainrate as opposed to RSD moment estimates versus rainrate. Simulations offer a powerful method of studying the statistics of radar and surface RSD measurements since the “natural” RSD fluctuations can be introduced separately. In our simulations we vary the parameter N o, D o and m of a gamma distribution over the range normally found in rainfall, as well as varying the device sampling volume. We apply our simulations to explain some possible features related to discrepancies which can arise when radar rainfall measurements are compared with surface or aircraft-based sampling devices.

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Roger M. Wakimoto
and
V. N. Bringi

Abstract

A detailed case study of the microbrust-producing storm on 20 July 1986 during the MIST Project is presented, together with visual (based on cloud photogrammetry) and radar observations during the life cycle of the storm. In particular, multiparameter radar information is seen to have important implications for operational detection of this wind shear event. Noteworthy is the observation of a small shaft (less than 1 km in horizontal dimensions) of near zero differential reflectivity (ZDR ) surrounded by large positive ZDR values in the main precipitation core within a microburst-producing downdraft. This “ZDR Zm-Hole-Hole” implies a strong localized downdraft composed of melting hail.

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T. A. Seliga
and
V. N. Bringi

Abstract

The potential use of differential reflectivity measurements at orthogonal polarizations to determine rain-fall rate is examined. The method involves measurements of ZH and ZV , the radar reflectivity factors due to horizontally and vertically polarized incident waves respectively. The differential reflectivity, ZDR = 10 log (ZH /ZV ), which should be precisely determinate, occurs as a result of the distortion of raindrops as they fall at terminal velocity. The approximate theory of Gans for electromagnetic scattering by spheroids is applied to the distorted raindrops. Assuming a general exponential form for the raindrop size distribution, equations are derived relating the distribution parameters to the measurements. The determination of rainfall rate follows directly. Finally, the sensitivity of the distribution parameters to radar inaccuracies is examined, and several methods of implementing the measurements are suggested. It is concluded that good estimates of rainfall rate using a single non-attenuating wavelength radar are possible under ideal conditions.

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J. C. Hubbert
and
V. N. Bringi

Abstract

Effects of three-body scattering on reflectivity signatures at S and C bands can be seen on the back side of large reflectivity storm cores that contain hail. The fingerlike protrusions of elevated reflectivity have been termed flare echoes or “hail spikes.” Three-body scattering occurs when radiation from the radar scattered toward the ground is scattered back to hydrometeors, which then scatter some of the radiation back to the radar. Three-body scatter typically causes differential reflectivity to be very high at high elevations and to be negative at lower elevations at the rear of the storm core. This paper describes a model that can simulate the essential features of the three-body scattering that has been observed in hailstorms. The model also shows that three-body scatter can significantly affect the polarimetric Z DR (differential reflectivity) radar signatures in hailshafts at very low elevation and thus is a possible explanation of the frequently reported negative Z DR signatures in hailshafts near ground.

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Merhala Thurai
and
V. N. Bringi

Abstract

We report on measurements of drop size distributions (DSD) using collocated instruments (a Droplet Measurement Technologies, Inc., Meteorological Particle Spectrometer and a 2D-video disdrometer) from two locations with different rainfall climates (Greeley, Colorado, and Huntsville, Alabama, with measurements from the latter that include the outer rainbands of Hurricane Irma). The combination of the two instruments gives what we term as the “full” DSD spectra, the shape of which generally cannot be represented by the standard gamma model, but instead requires the additional flexibility of the generalized gamma model, which includes two shape parameters (μ and c). The double-moment normalization of DSDs using the third and fourth moments is used to arrive at the intrinsic shapes of the DSD with two shape parameters that are shown to capture simultaneously the drizzle mode as well as the precipitation mode, together with a “plateau” region between the two. The estimation of μ and c is done with a global search using nonlinear least squares, and the error residuals are examined to check the sensitivity of the parameters to a preselected, allowed tolerance around the minimum error in the μ, c plane. This leads to a range of plausible fits for a given normalized DSD mainly governed by the c parameter. The stability or invariance of the shape of the normalized DSDs from the two sites is examined, and on average the shapes are similar with some variability at the large normalized diameter end that is explained by the aforementioned range of plausible fits. Heuristic goodness-of-fit methods are described that demonstrate that the generalized gamma model outperforms the standard gamma model with only one shape parameter (μ).

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J. Hubbert
and
V. N. Bringi

Abstract

Copolar differential phase is composed of two components, namely, differential propagation phase and differential backscatter phase. To estimate specific differential phase K DP, these two phase components must first be separated when significant differential backscatter phase is present. This paper presents an iterative range filtering technique that can separate these phase components under a wider variety of conditions than is possible with a simple range filter. This technique may also be used when estimating hail signals from range profiles of dual-frequency reflectivity ratios.

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J. C. Hubbert
and
V. N. Bringi

Abstract

A polarimetric radar covariance matrix model is described to study the behavior of the co-to-cross covariances in precipitation. The 2 × 2 propagation matrix with attenuation, differential attenuation, and differential phase is coupled to the backscatter matrix leading to a propagation-modified covariance matrix model. System polarization errors are included in this model as well. This model is used to study the behavior of the magnitude and phase of the co-to-cross covariances and the linear depolarization ratio (LDR) in rainfall. It is shown that the model predictions are consistent with data collected with the Colorado State University (CSU)–University of Chicago–Illinois State Water Survey (CHILL) radar in intense rainfall. A method is also given for estimating the system polarization errors from covariance matrix data collected in intense rainfall.

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Merhala Thurai
and
V. N. Bringi

Abstract

Results from an experiment to measure the drop shapes using a 2D video disdrometer (2DVD) are reported. Under calm conditions, drops were generated from a hose located on a bridge 80 m above ground, this height being sufficient to allow drop oscillations to reach a steady state. The disdrometer data had to be carefully processed so as to eliminate the drops mismatched by the instrument and to remove the system spreading function. The total number of drops analyzed was around 115 000. Their axis ratio distributions were obtained for diameters ranging from 1.5 to 9 mm. The mean axis ratio decreases with increasing drop diameter, in agreement with the upper bound of the Beard and Chuang equilibrium shape model. The inferred mode of oscillation appears to be dominated by the oblate–prolate axisymmetric mode for the diameter range of 1.5 to 9 mm.

The mean axis ratio agrees well with two empirically fitted formulas reported in earlier studies. In addition, a linear fit was applied to the data for radar applications relating to rain retrievals from dual-polarization measurements. The 2DVD data taken in moderate stratiform rain were also analyzed in a similar way and the results agree with the artificially generated drop experiment, at least up to 4 mm. No data for larger diameters were available for stratiform precipitation. Finally, the fall velocity was examined in terms of drop diameter. The results closely follow an empirical formula fitted to the Gunn and Kinzer data as well as the Beard and Pruppacher data including a slight decrease in the terminal velocity with a diameter beyond 7 mm.

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