Nonparametric Estimation of Raindrop Size Distributions from Dual-Polarization Radar Spectral Observations

2007 ◽  
Vol 24 (6) ◽  
pp. 1008-1018 ◽  
Author(s):  
Dmitri N. Moisseev ◽  
V. Chandrasekar
Keyword(s):  
Elevation Angle ◽  
Power Spectra ◽  
High Elevation ◽  
Size Distributions ◽  
Dual Polarization ◽  
Mean Velocity ◽  
Colorado State University ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Doppler Power

This paper presents a method to retrieve raindrop size distributions (DSD) from slant profile dual-polarization Doppler spectra observations. It is shown that using radar measurements taken at a high elevation angle raindrop size distributions can be retrieved without making an assumption on the form of a DSD. In this paper it is shown that drop size distributions can be retrieved from Doppler power spectra by compensating for the effect of spectrum broadening and mean velocity shift. To accomplish that, spectrum deconvolution is used where the spectral broadening kernel width and wind velocity are estimated from spectral differential reflectivity measurements. Since convolution kernel is estimated from dual-polarization Doppler spectra observations and does not require observation of a clear-air signal, this method can be used by most radars capable of dual-polarization spectra measurements. To validate the technique, sensitivity of this method to the underlying assumptions and calibration errors is evaluated on realistic simulations of radar observations. Furthermore, performance of the method is illustrated on Colorado State University–University of Chicago–Illinois State Water Survey radar (CSU–CHILL) measurements of stratiform precipitation.

scholarly journals On the Shape–Slope Relation of Drop Size Distributions in Convective Rain

2005 ◽  
Vol 44 (7) ◽  
pp. 1146-1151 ◽  
Author(s):  
Axel Seifert
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Drop Size ◽  
Empirical Relation ◽  
Size Distributions ◽  
Shape Parameters ◽  
Raindrop Size Distribution ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Good Agreement

Abstract The relation between the slope and shape parameters of the raindrop size distribution parameterized by a gamma distribution is examined. The comparison of results of a simple rain shaft model with an empirical relation based on disdrometer measurements at the surface shows very good agreement, but a more detailed discussion reveals some difficulties—for example, deviations from the gamma shape and the overestimation of collisional breakup.

Dual-Polarization Spectral Analysis for Retrieval of Effective Raindrop Shapes

2006 ◽  
Vol 23 (12) ◽  
pp. 1682-1695 ◽  
Author(s):  
D. N. Moisseev ◽  
V. Chandrasekar ◽  
C. M. H. Unal ◽  
H. W. J. Russchenberg
Keyword(s):  
Spectral Analysis ◽  
Optimization Problems ◽  
Spatial Scales ◽  
Elevation Angle ◽  
Ambient Air ◽  
Retrieval Algorithm ◽  
Dual Polarization ◽  
Radar Observations ◽  
Raindrop Size ◽  
Parameter Retrieval

Abstract Dual-polarization radar observations of precipitation depend on size–shape relations of raindrops. There are several studies presented in literature dedicated to the investigation of this relation. In this work a new approach of investigating raindrop size–shape relation on short time and spatial scales from radar observations is presented. The presented method is based on the use of dual-polarization Doppler power spectral analysis. By measuring complete Doppler spectra at a sufficiently high elevation angle at two polarization settings, namely, horizontal and vertical, it is possible to retrieve drop size distribution (DSD) parameters, ambient air velocity, spectral broadening, and the slope of the assumed linear dependence of raindrop size–shape relation. This paper is mainly focused on the development of the retrieval algorithm and analysis of its performance. As a part of the proposed method an efficient algorithm for DSD parameter retrieval was developed. It is shown that the DSD parameter retrieval method, which usually requires the solution of five-parameter nonlinear optimization problems, can be simplified to a three-parameter nonlinear least squares problem. Furthermore, the performance of the proposed retrieval technique is illustrated on the dual-polarization measurements collected by the S-band Transportable Atmospheric Radar (TARA) at Cabauw, Netherlands, and by the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar from Greeley, Colorado.

scholarly journals Retrieval of Arbitrarily Shaped Raindrop Size Distributions from Wind Profiler Measurements

2005 ◽  
Vol 22 (4) ◽  
pp. 433-442 ◽  
Author(s):  
Takahisa Kobayashi ◽  
Ahoro Adachi
Keyword(s):  
Drop Size ◽  
Large Data ◽  
Doppler Spectrum ◽  
Wind Profiler ◽  
Size Distributions ◽  
Vertical Profiles ◽  
Large Variability ◽  
Median Volume ◽  
Raindrop Size ◽  
Drop Size Distributions

Abstract An efficient iterative retrieval method for arbitrarily shaped raindrop size distributions (ITRAN) is developed for Doppler spectra measured with a wind profiler. A measured Doppler spectrum is a convolution of the precipitation spectrum and the turbulent spectrum. Deconvolution of the Doppler spectra is achieved through repeated convolutions. The developed method assumes no prior shape of drop size distributions and automatically obtains raindrop size distributions; additionally, it can be applied to large data volumes. Furthermore, it is insensitive to initial values. The method was applied to both simulated and observed spectra. Derived drop size distributions agree with simulated values. Narrower turbulent spectral widths yield better results. Integral values of median volume diameter (D0), liquid water content (LWC), and radar reflectivity factor are estimated with errors of less than 10%. Accurate vertical profiles of raindrop size distributions result when this method is applied to wind profiler data. The technique performed very well with most observed spectra. Some recovered spectra departed from the corresponding measured spectra, for cases in which a clear-air peak could not be accurately reproduced because of uncertainties in the location of the minimum position between the clear-air echo and the precipitation echo. Statistical relationships between LWC and integral rainfall parameters yield interesting features. The median volume diameter is statistically independent of the LWC and is associated with the large variability of the total number of drops, NT, between events. Vertical profiles from one event show a clear inverse relationship between NT and D0

Examination of the μ–Λ Relation Suggested for Drop Size Distribution Parameters

2007 ◽  
Vol 24 (5) ◽  
pp. 847-855 ◽  
Author(s):  
Dmitri N. Moisseev ◽  
V. Chandrasekar
Keyword(s):  
Gamma Distribution ◽  
Method Of Moments ◽  
Drop Size ◽  
Size Distributions ◽  
Data Filtering ◽  
Wide Range ◽  
Distribution Parameters ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Physical Correlations

Abstract Raindrop size distributions are often assumed to follow a three-parameter gamma distribution. Since rain intensity retrieval from radar observations is an underdetermined problem, there is great interest in finding physical correlations between the parameters of the gamma distribution. One of the more common approaches is to measure naturally occurring drop size distributions (DSDs) using a disdrometer and to find DSD parameters by fitting a gamma distribution to these observations. Often the method of moments is used to retrieve the parameters of a gamma distribution from disdrometer observations. In this work the effect of the method of moments and data filtering on the relation between the parameters of the DSD is investigated, namely, the shape μ and the slope Λ parameters. For this study the disdrometer observations were simulated. In these simulations the gamma distribution parameters Nw, D0, and μ were randomly selected from a wide range of values that are found in rainfall. Then, using simulated disdrometer measurements, DSD parameters were estimated using the method of moments. It is shown that the statistical errors associated with data filtering of disdrometer measurements might produce a spurious relation between μ and Λ parameters. It is also shown that three independent disdrometer measurements can be used to verify the existence of such a relation.

scholarly journals Rain Attenuation of Radar Echoes Considering Finite-Range Resolution and Using Drop Size Distributions

2010 ◽  
Vol 27 (5) ◽  
pp. 829-842 ◽  
Author(s):  
Gerhard Peters ◽  
Bernd Fischer ◽  
Marco Clemens
Keyword(s):  
Attenuation Correction ◽  
A Priori ◽  
Real Data ◽  
Rain Attenuation ◽  
Size Distributions ◽  
Finite Range ◽  
Near Surface ◽  
Range Resolution ◽  
Raindrop Size ◽  
Drop Size Distributions

Abstract The classical rain attenuation correction scheme of Hitschfeld and Bordan (HIBO) and the newer iterative approach by Hildebrand (HL) are reconsidered. Although the motivation for the HL algorithm was an extension into ranges, where HIBO tends to be unstable, it is shown here that the contrary is the case. The finite-range resolution causes an intrinsic instability of HL already at moderate attenuation, where HIBO would still deliver stable results. Therefore, the authors concentrate the further analysis on HIBO, and confirm that the usual implementation of HIBO does not account correctly for finite-range resolution. They suggest a modified scheme that produces exact retrievals in the ideal case of perfect measurements. For vertically pointing Doppler radars a new element is explored in the attenuation correction—namely, calculating rain attenuation κ and rainfall R from Doppler spectra via the raindrop size distributions (RSDs). Although this spectral scheme (SIBO) avoids the uncertainty of Z–R and Z–κ relations, the superiority of this approach is not a priori obvious because of its sensitivity to vertical wind. Therefore, radar rain rates, based on a Z–R relation and on RSDs, respectively, are compared with in situ measurements. The results indicate better agreement for RSD-based retrievals. Because κ is closely correlated with R, the authors assert the advantage of RSD-based retrievals of κ. The application of HIBO and SIBO to real data shows that the uncertainty of standard Z–R relations is the main source of deviation between the two versions. In addition, the comparison of profiles suggests that the parameters of Z–R relations aloft can deviate considerably from near-surface values. Although artifacts cannot be excluded with certainty, there is some evidence that this observation actually reflects microphysical processes.

Observed Bulk Hook Echo Drop Size Distribution Evolution in Supercell Tornadogenesis and Tornadogenesis Failure

2021 ◽  
Author(s):  
Kristofer S. Tuftedal ◽  
Michael M. French ◽  
Darrel M. Kingfield ◽  
Jeffrey C. Snyder
Keyword(s):  
Drop Size ◽  
Thermodynamic Characteristics ◽  
Radar Data ◽  
Number Concentration ◽  
Size Distributions ◽  
Polarimetric Radar ◽  
Dual Polarization ◽  
Near Surface ◽  
Microphysical Processes ◽  
Drop Size Distributions

AbstractThe time preceding supercell tornadogenesis and tornadogenesis “failure” has been studied extensively to identify differing attributes related to tornado production or lack thereof. Studies from the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX) found that air in the rear-flank downdraft (RFD) regions of non- and weakly tornadic supercells had different near-surface thermodynamic characteristics than that in strongly tornadic supercells. Subsequently, it was proposed that microphysical processes are likely to have an impact on the resulting thermodynamics of the near-surface RFD region. One way to view proxies to microphysical features, namely drop size distributions (DSDs), is through use of polarimetric radar data. Studies from the second VORTEX used data from dual-polarization radars to provide evidence of different DSDs in the hook echoes of tornadic and non-tornadic supercells. However, radar-based studies during these projects were limited to a small number of cases preventing result generalizations. This study compiles 68 tornadic and 62 non-tornadic supercells using Weather Surveillance Radar–1988 Doppler (WSR-88D) data to analyze changes in polarimetric radar variables leading up to, and at, tornadogenesis and tornadogenesis failure. Case types generally did not show notable hook echo differences in variables between sets, but did show spatial hook echo quadrant DSD differences. Consistent with past studies, differential radar reflectivity factor (ZDR) generally decreased leading up to tornadogenesis and tornadogenesis failure; in both sets, estimated total number concentration increased during the same times. Relationships between DSDs and the near-storm environment, and implications of results for nowcasting tornadogenesis, also are discussed.

scholarly journals Drop Size Distributions Measured by a 2D Video Disdrometer: Comparison with Dual-Polarization Radar Data

2001 ◽  
Vol 40 (6) ◽  
pp. 1019-1034 ◽  
Author(s):  
Terry J. Schuur ◽  
Alexander V. Ryzhkov ◽  
Dusan S. Zrnić ◽  
Michael Schönhuber
Keyword(s):  
Drop Size ◽  
Radar Data ◽  
Size Distributions ◽  
Dual Polarization ◽  
Drop Size Distributions

scholarly journals On the Influence of Raindrop Collision Outcomes on Equilibrium Drop Size Distributions

2012 ◽  
Vol 69 (5) ◽  
pp. 1534-1546 ◽  
Author(s):  
Olivier P. Prat ◽  
Ana P. Barros ◽  
Firat Y. Testik
Keyword(s):  
Drop Size ◽  
Number Concentration ◽  
Drop Diameter ◽  
Size Distributions ◽  
Left Hand ◽  
Dynamical Simulation ◽  
Drop Number ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
The Impact

Abstract The objective of this study is to evaluate the impact of a new parameterization of drop–drop collision outcomes based on the relationship between Weber number and drop diameter ratios on the dynamical simulation of raindrop size distributions. Results of the simulations with the new parameterization are compared with those of the classical parameterizations. Comparison with previous results indicates on average an increase of 70% in the drop number concentration and a 15% decrease in rain intensity for the equilibrium drop size distribution (DSD). Furthermore, the drop bounce process is parameterized as a function of drop size based on laboratory experiments for the first time in a microphysical model. Numerical results indicate that drop bounce has a strong influence on the equilibrium DSD, in particular for very small drops (<0.5 mm), leading to an increase of up to 150% in the small drop number concentration (left-hand side of the DSD) when compared to previous modeling results without accounting for bounce effects.

scholarly journals Wideband Reception and Processing for Dual-Polarization Radars with Dual Transmitters

2007 ◽  
Vol 24 (1) ◽  
pp. 95-101 ◽  
Author(s):  
Sutanay Choudhury ◽  
V. Chandrasekar
Keyword(s):  
Doppler Radar ◽  
Negative Impact ◽  
Spectral Width ◽  
Parameter Estimates ◽  
Dual Polarization ◽  
Mean Velocity ◽  
Colorado State University ◽  
State Water ◽  
Differential Reflectivity ◽  
The Impact

Abstract Oversampling pulsed Doppler radar returns at a rate larger than the pulse bandwidth, whitening the range samples, and subsequent averaging has been pursued as a potential way to decrease the measured standard deviation of signal parameter estimates. It has been shown that the application of oversampling, whitening, and subsequent averaging improves the quality of reflectivity, mean velocity, and spectral width estimates in agreement with theory. Application of this procedure to a dual-polarization radar with dual transmitters is evaluated in this paper. Oversampled data collected from the Colorado State University (CSU)-University of Chicago–Illinois State Water Survey (CHILL) radar using a wideband receiver are analyzed to evaluate the performance of dual-polarization parameter estimators, such as differential reflectivity and differential phase. The negative impact of relative phase characteristics of the transmitted pulses in two polarizations on the copolar correlation, and subsequently on polarimetric parameter estimation, is analyzed. CSU-CHILL radar’s transmitted pulse sampling capability is used to evaluate the impact of the transmitted waveform’s mismatch on whitening and estimation.

Controls on the space-time variability of raindrop size distributions

2021 ◽  
Author(s):  
Remko Uijlenhoet
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Space Time ◽  
Drop Size Distribution ◽  
Time Variability ◽  
Statistical Interpretation ◽  
Size Distributions ◽  
Scaling Exponents ◽  
Raindrop Size ◽  
Drop Size Distributions

<p>It has been stated that "the study of drop-size distributions, with its roots in both land-surface processes [e.g. interception, erosion, infiltration and surface runoff] and atmospheric remote sensing [e.g. radar meteorology], provides an important element to an integrated program of hydrometeorological research" (Smith, 1993). Although raindrop size distributions have been studied from a scientific perspective since the early 20th century, it was not until the mid-1990s that researchers realized that all parameterizations for the drop size distribution published until then could be summarized in the form of a scaling law, which provided "a general phenomenological formulation for drop size distribution" (Sempere Torres et al., 1994). The main implication of the proposed expression is that the integral rainfall variables (such as rain rate and radar reflectivity) are related by power laws, in agreement with experimental evidence. The proposed formulation naturally leads to a general methodology for scaling all raindrop size data in a unique plot, which yields more robust fits of the drop size distribution. Here, we provide a statistical interpretation of the law’s scaling exponents in terms of different modes of control on the space-time variability of drop size distributions, namely size-control vs. number-control, inspired by the work of Smith and De Veaux (1994). Also, an attempt will be made toward interpreting the values of the scaling exponents and the shape of the scaled drop size distribution in terms of the underlying (micro)physical processes.</p><p>REFERENCES</p><p>Smith, J. A., 1993: Precipitation. In Maidment, D. R., editor, Handbook of Hydrology, pages 3.1–3.47. McGraw-Hill, New York.</p><p>Sempere Torres, D., J.M. Porrà, and J.-D. Creutin, 1994: A general formulation for raindrop size distribution. J. Appl. Meteor., 33, 1494–1502.</p><p>Smith, J.A. and R.D. De Veaux, 1994: A stochastic model relating rainfall intensity to raindrop processes. Water Resour. Res., 30, 651–664.</p>

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