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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

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

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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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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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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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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S. Bolen, V. N. Bringi, and V. Chandrasekar

Abstract

An optimal area method is described that is used as a basis for comparing K DP-, (K DP, Z DR)-, and Z h-based estimates of rain rates with gauge-measured rain rates. The location and dimensions of an elliptically shaped optimal area within the radar scan area surrounding the gauge are determined objectively via an rms error minimization of the difference between the K DP-based radar estimate and gauge data and via use of the spatial structure of the rms difference field itself. Four convective events were analyzed with rain rates in the range of 20–120 mm h−1, with two of the events containing marble-sized hail. The analysis shows that excellent results could be achieved using K DP-based rain-rate estimators.

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V. N. Bringi, Taiwen Tang, and V. Chandrasekar

Abstract

A new polarimetrically based (or, pol-based) ZR relation of the form Z = aR 1.5 is described and evaluated where the multiplicative coefficient a is continuously adjusted as the drop size distribution evolves in space and time. The methodology is based on previous studies involving estimation of the normalized gamma drop size distribution parameters (DSD) using radar measurements of Z h, Z dr, and K dp. In moderate-to-intense rainfall, the retrieval of the DSD parameters are formulated to account for the effects of drop oscillations using the “effective” β concept where the axis ratio (r) versus D relation is assumed to be linear and of the form r = 1 − βD in the underlying raindrop shape model. Rayleigh scattering with analytic approximations are used to show that the β estimator in based on Z h, Z dr, and K dp is of the correct form. The changes in the effective β in a storm cell is studied as the cell evolves from the growth phase to the mature phase (with microburst and rain rates of around 100–120 mm h−1). The systematic shift in β with increasing rain rates in this cell is shown to be consistent with the collisional probability model results of . For evaluation of the pol-based ZR relation, six storm events from the Tropical Rainfall Measuring Mission– Large-Scale Biosphere–Atmosphere (TRMM–LBA) experiment and Texas and Florida Underflights Experiment- B (TEFLUN-B) are analyzed using radar data from the NCAR–S-band Polarimetric (SPOL) radar and a network of gauges specially deployed for these two campaigns. For storm total accumulation, the new pol-based ZR algorithm gives a normalized bias of 6% (radar overestimate) and normalized standard error of 20%. The corresponding values for a conventional ZR relation (after stratiform/convective separation) are −18% and 24%. The pol-based ZR method continuously “tracks” the drop size distribution and so no classification of rain types is necessary.

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Yanting Wang, V. Chandrasekar, and V. N. Bringi

Abstract

Transmitting an arbitrary state of polarization while receiving horizontal–vertical polarization states is termed the hybrid polarization mode of operation. A theoretical model is developed for hybrid mode dual-polarization measurements in terms of the covariance matrix under linear horizontal–vertical polarization basis. The cross polarization encountered introduces biases in the copolar parameters estimated in the hybrid mode. Such biases are investigated for different precipitation types and propagation effects resulting from hydrometeor orientation and antenna properties. Polarimetric data measured by the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar transmitting horizontal–vertical polarization states is alternately used to demonstrate the measurement accuracy that would be expected in different storm scenarios observed in the hybrid mode.

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V. N. Bringi, V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić

Abstract

Propagation effects in rainfall are examined at three microwave frequencies corresponding to S (3.0 GHz), C (5.5 GHz), and X (10.0 GHz) bands. Attenuation at horizontal polarization, as well as differential attenuation and differential propagation phase between horizontal (H) and vertical (V) polarizations are considered. It is shown that at the three frequencies both attenuation and differential attenuation are nearly linearly related to differential propagation phase (ϕDP). This is shown through simulation using (a) gamma raindrop size distributions (RSD) with three parameters (N 0, D 0, m) that are varied over a very wide range representing a variety of rainfall types, and (b) measured raindrop size distributions at a single location using a disdrometer. Measurements of X-band specific attenuation and S-band specific differential phase in convective rainshafts using the National Center for Atmospheric Research CP-2 radar are presented in order to experimentally demonstrate the linear relationship between attenuation and differential propagation phase. Correction procedures for reflectivity and differential reflectivity (Z DR) are developed assuming that differential propagation phase is measured using a radar that alternately transmits H and V polarized waves with copolar reception through the same receiver and processor system. The correction procedures are not dependent on the actual rainrate profile between the radar and the range location of interest. The accuracy of the procedure depends on, (a) RSD fluctuations, (b) variability in the estimate of differential propagation phase due to measurement fluctuations, and (c) nonzero values of the backscatter differential phase (δ) between H and V polarizations. Simulations are used to gauge the accuracy of correction procedures at S- and C-bands assuming δ is negligible. The correction accuracy for attentuation at S-band is estimated to be ∼0.05 dB while at C-band it is estimated to be within 1 dB if ϕDP≲60°. Simulations further indicate that C-band differential attenuations effects can be corrected to within ∼35% of the mean value.

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