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Edward A. Brandes
,
Guifu Zhang
, and
Juanzhen Sun

Abstract

Polarimetric radar measurements are used to retrieve drop size distributions (DSD) in subtropical thunderstorms. Retrievals are made with the single-moment exponential drop size model of Marshall and Palmer driven by radar reflectivity measurements and with a two-parameter constrained-gamma drop size model that utilizes reflectivity and differential reflectivity. Results are compared with disdrometer observations. Retrievals with the constrained-gamma DSD model gave better representation of total drop concentration, liquid water content, and drop median volume diameter and better described their natural variability. The Marshall–Palmer DSD model, with a fixed intercept parameter, tended to underestimate the total drop concentration in storm cores and to overestimate significantly the concentration in stratiform regions. Rainwater contents in strong convection were underestimated by a factor of 2–3, and drop median volume diameters in stratiform rain were underestimated by 0.5 mm. To determine possible DSD model impacts on numerical forecasts, evaporation and accretion rates were computed using Kessler-type parameterizations. Rates based on the Marshall–Palmer DSD model were lower by a factor of 2–3 in strong convection and were higher by about a factor of 2 in stratiform rain than those based on the constrained-gamma model. The study demonstrates the potential of polarimetric radar measurements for improving the understanding of precipitation processes and microphysics parameterization in numerical forecast models.

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Edward A. Brandes
,
Kyoko Ikeda
,
Gregory Thompson
, and
Michael Schönhuber

Abstract

Terminal velocities of snow aggregates in storms along the Front Range in eastern Colorado are examined with a ground-based two-dimensional video disdrometer. Power-law relationships for particles having equivalent volume diameters of 0.5–20 mm are computed for the temperatures −1°, −5°, and −10°C. Fall speeds increase with temperature. Comparison with relationships found in the literature suggests that temperature-dependent relations may be surrogates for relations based on aggregate composition (e.g., plates, columns, or dendrites) and the degree of riming.

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Edward A. Brandes
,
Robert P. Davies-Jones
, and
Brenda C. Johnson

Abstract

The structure and steadiness of radar-observed supercell thunderstorms are examined in terms of their particular distribution of vorticity. The data confirm that the vorticity vector in supercells points in the direction of the storm-relative velocity vector and that supercell updrafts contain large positive helicity (V·ω). The alignment of vorticity and velocity vectors dictates that low pressure associates not only with vorticity but also with helicity. Accelerating pressure gradients and helicity, both thought important for suppressing small-scale features within supercells, may combine with shear-induced vertical pressure gradient forces to organize and maintain the large-scale persistent background updrafts that characterize supercells.

Rear downdrafts possess weak positive or negative helicity. Thus, the decline of storm circulation may be hastened by turbulent dissipation when the downdraft air eventually mixes into supercell updrafts.

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Kyoko Ikeda
,
Edward A. Brandes
, and
Roy M. Rasmussen

Abstract

An unusual multiple freezing-level event observed with polarimetric radar during the second phase of the Improvement of Microphysical Parameterization through Observational Verification Experiments (IMPROVE-2) field program is described. The event occurred on 28 November 2001 when a warm front moved over the Oregon Cascade Mountains. As the front approached, an elevated melting layer formed above a preexisting melting layer near ground. Continued warming of the lower atmosphere eventually dissipated the lower melting layer.

The polarimetric measurements are used to estimate the height of the freezing levels, document their evolution, and deduce hydrometeor habits. The measurements indicate that when the two freezing levels were first observed melting was incomplete in the upper melting layer and characteristics of particles that passed through the two melting layers were similar. As warming progressed, the character of particles entering the lower melting layer changed, possibly becoming ice pellets or frozen drops. Eventually, the refreezing of particles ended and only rain occurred below the elevated melting layer.

The Doppler radial winds showed a well-defined wind maximum apparently associated with a “warm conveyor belt.” The jet intensified and descended through the elevated melting layer with time. However, the increase in wind speed did not appear connected with melting or result in precipitation enhancement.

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Edward A. Brandes
,
J. Vivekanandan
, and
James W. Wilson

Abstract

Radar reflectivity–based rainfall estimates from collocated radars are examined. The usual large storm-to-storm variations in radar bias and high correlation between radar estimates and rain gauge observations are found. For three storms in Colorado, the radar bias factor (the ratio between gauge observations and radar estimates) with the National Center for Atmospheric Research’s S-band, dual-polarization radar (S-Pol) varied from 0.78 (an overestimate with radar) to 1.88. The correlation coefficient between gauge and radar amounts varied from 0.78 to 0.90. For a collocated Weather Surveillance Radar-1988 Doppler (WSR-88D), the bias factor varied from 0.56 to 1.49, and the correlation between gauge and radar amounts ranged from 0.77 to 0.87. In Kansas, bias factors varied from 0.86 to 1.41 for S-Pol (10 storms) and 0.82 to 1.71 for a paired WSR-88D (9 storms). The spread in correlation coefficients was 0.82–0.95 for S-Pol and 0.87–0.95 for the WSR-88D.

Correspondence between the radar-derived rainfall estimates for the paired radars was very high; correlation coefficients were 0.88 to 0.98. Moreover, the ratio between rainfall estimates (S-Pol/paired WSR-88D) varied only from 0.72 to 0.85 in Colorado and 0.82 to 1.05 in Kansas. The total variation in radar-to-radar rainfall estimates, roughly a factor of 1.2, is attributed primarily to nonmeteorological factors relating to radar hardware and processing. The radar-to-radar variation is small compared to the spread in storm-to-storm biases, which varied from a low of 1.64 with the S-Pol radar in Kansas to a high of 2.66 with the WSR-88D in Colorado. For this investigation, the storm-to-storm bias must have a large meteorological component—probably due to temporal and spatial changes in drop size distributions and consequently variations in the relationship between radar reflectivity and rainfall rate.

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Edward A. Brandes
,
Alexander V. Ryzhkov
, and
Dus̆an S. Zrnić

Abstract

Specific differential propagation phase (K DP) is examined for estimating convective rainfall in Colorado and Kansas. Estimates are made at S band with K DP alone and in combination with radar reflectivity (Z H). Results are compared to gauge observations by computing bias factors, defined as the sum of gauge-measured rainfalls divided by the sum of radar estimates at gauges reporting rainfall, and the correlation coefficient between the gauge and radar-estimated amounts. Rainfall accumulations computed from positive-only values of K DP (provided Z H ≥ 25 dBZ) yield bias factors that vary from 0.76 to 2.42 for 3 storms in Colorado and from 0.78 to 1.46 for 10 storms in Kansas. Correlation coefficients between gauge-observed and radar-estimated rainfalls are 0.76 to 0.95. When negative K DP’s are included as negative rainfall rates, bias factors range from 0.81 to 3.00 in Colorado and from 0.84 to 2.31 in Kansas. In most storms, the correlation between gauge and radar rainfalls decreases slightly.

In an experiment with the K DP/Z H combination, rainfall rates are computed from K DP when K DP is ≥0.4° km−1 and from Z H for K DP < 0.4° km−1 and Z H ≥ 25 dBZ. Neglect of the negative K DP’s and substitution of the always positive Z H rainfall rates result in a tendency to overestimate rainfall. Bias factors are 0.63–1.46 for Colorado storms and 0.68–0.97 for Kansas storms, and correlation coefficients between gauge and radar amounts are 0.80–0.95. In yet another test with the K DP/Z H pair, rainfall estimates are computed from K DP when Z H ≥ 40 dBZ and from Z H when 25 ⩽ Z H < 40 dBZ. For this experiment, bias factors range from 0.90 to 1.91 in Colorado and from 0.88 to 1.46 in Kansas. Correlation coefficients are 0.80–0.96.

Since bias factors and correlation coefficients between estimated rainfalls and gauge observations for K DP are similar to those for radar reflectivity, there was no obvious benefit with K DP rainfalls for a well-calibrated radar. Large underestimates with K DP in two storms were attributed to rainfalls dominated by small drops. In one storm, the problem was aggravated by widespread negative K DP’s thought related to vertical gradients of precipitation. An advantage of K DP-derived rainfall estimates confirmed here is an insensitivity to anomalous propagation.

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Qing Cao
,
Guifu Zhang
,
Edward A. Brandes
, and
Terry J. Schuur

Abstract

This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization ZH and differential reflectivity Z DR. With this approach, the authors apply a constrained-gamma model with an updated constraining relation to retrieve DSD parameters. Long-term DSD measurements made in central Oklahoma by the two-dimensional video disdrometer (2DVD) are first used to construct a prior probability density function (PDF) of DSD parameters, which are estimated using truncated gamma fits to the second, fourth, and sixth moments of the distributions. The forward models of ZH and Z DR are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of ZH and Z DR is assumed to be a bivariate normal function with appropriate standard deviations. The Bayesian algorithm has a good performance according to the evaluation with simulated ZH and Z DR. The algorithm is also tested on S-band radar data for a mesoscale convective system that passed over central Oklahoma on 13 May 2005. Retrievals of rainfall rates and 1-h rain accumulations are compared with in situ measurements from one 2DVD and six Oklahoma Mesonet rain gauges, located at distances of 28–54 km from Norman, Oklahoma. Results show that the rain estimates from the retrieval agree well with the in situ measurements, demonstrating the validity of the Bayesian retrieval algorithm.

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J. Vivekanandan
,
David N. Yates
, and
Edward A. Brandes

Abstract

The effect of beam blockage on rainfall estimates derived from radar reflectivity and specific propagation phase was evaluated from measurements of a convective rainfall event from the National Center for Atmospheric Research’s S-band polarized (S-Pol) radar. This storm produced a flash flood in a mountainous watershed to the southwest of Denver, Colorado, and widespread rainfall over the plains. A beam blockage map of the region, based on a digital elevation model and characteristics of the S-Pol radiation pattern, was computed. Rain-rate estimates over both low and high beam-blockage areas were compared. Results supported the hypothesis that specific propagation phase–based quantitative precipitation estimates tend to be less influenced by terrain than reflectivity-based precipitation estimates are.

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Guifu Zhang
,
J. Vivekanandan
,
Edward A. Brandes
,
Robert Meneghini
, and
Toshiaki Kozu

Abstract

The three-parameter gamma distribution n(D) = N 0 D µ exp(–ΛD) is often used to characterize a raindrop size distribution (DSD). The parameters µ and Λ correspond to the shape and slope of the DSD. If µ and Λ are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified, which facilitates retrieval of rain parameters from remote measurements. It is important to determine whether the µ–Λ relation arises from errors in estimated DSD moments, or from natural rain processes, or from a combination of both statistical error and rain physics.

In this paper, the error propagation from moment estimators to rain DSD parameter estimators is studied. The standard errors and correlation coefficient are derived through systematic error analysis. Using numerical simulations, errors in estimated DSD parameters are quantified. The analysis shows that errors in moment estimators do cause correlations among the estimated DSD parameters and cause a linear relation between estimators μ̂ and Λ̂ . However, the slope and intercept of the error-induced relation depend on the expected values µ and Λ, and it differs from the µ–Λ relation derived from disdrometer measurements. Further, the mean values of the DSD parameter estimators are unbiased. Consequently, the derived µ–Λ relation is believed to contain useful information in that it describes the mean behavior of the DSD parameters and reflects a characteristic of actual raindrop size distributions. The µ–Λ relation improves retrievals of rain parameters from a pair of remote measurements such as reflectivity and differential reflectivity or attenuation, and it reduces the bias and standard error in retrieved rain parameters.

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Howard B. Bluestien
,
Stephen D. Hrebenach
,
Chee-Foong Chang
, and
Edward A. Brandes

Abstract

The synthetic dual-Doppler (SDD) analysis technique is applied to the 6–7 May 1985 mesoscale convective system (MCS) that occurred during the Oklahoma-Kansas Preliminary Regional Experiment-STORM Central. This system had a cyclonic mesoscale circulation in its stratiform precipitation region. The SDD analyses are compared to corresponding actual dual-Doppler analyses. The sensitivity of the former to various parameters is discussed.

The SDD analysis technique is also applied to an MCS that passed by the NEXRAD (Next Generation Weather Radar) facility in Norman, Oklahoma, on 13 June 1989. Analyses of both the leading line of convective cells and the trailing stratiform precipitation area we presented; the salient features were similar to those found in dual-Doppler analyses of other systems. There was a mesoscale cyclonic circulation present at low and midlevels in the stratiform precipitation area. Vertical wind profiles obtained from the SDD analysis are compared to those obtained front velocity-azimuth display (VAD) analyses and from a conventional sounding. Vertical profiles of divergence and vertical velocity that were determined from VAD analyses indicated upward motion ahead of the convective line, and sinking motion and rising motion in the lower and upper troposphere, respectively, in the stratiform precipitation area behind the leading line. Rising motion and sinking motion in the lower and upper troposphere, respectively, were indicated in the vicinity of the mesoscale cyclonic circulation.

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