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 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.

Shipborne Polarimetric Weather Radar: Impact of Ship Movement on Polarimetric Variables at C Band

2014 ◽  
Vol 31 (7) ◽  
pp. 1557-1563 ◽  
Author(s):  
M. Thurai ◽  
P. T. May ◽  
A. Protat
Keyword(s):  
Drop Size ◽  
Size Distributions ◽  
Correction Factors ◽  
Distribution Parameters ◽  
Radar Measurements ◽  
Nonzero Mean ◽  
Polarimetric Weather Radar ◽  
Drop Size Distributions ◽  
Differential Reflectivity ◽  
Ship Movement

Abstract The effect of ship motion on shipborne polarimetric radar measurements is considered at C band. Calculations are carried out by (i) varying the “effective” mean canting angle and (ii) separately examining the elevation dependence. Scattering from a single oblate hydrometeor is considered at first. Equations are derived (i) to convert the measured differential reflectivity for nonzero mean canting angles to those for zero mean canting angle and (ii) to do the corresponding corrections for nonzero elevation angles. Scattering calculations are also performed using the T-matrix method with measured drop size distributions as input. Dependence on mean volume diameter is examined as well as variations of the four main polarimetric parameters. The results show that as long as the ship movement is limited to a roll of less than about 10°–15°, the effects are tolerable. Furthermore, the results from the scattering simulations have been used to provide equations for correction factors that can be applied to compensate for the “apparent” nonzero canting angles and nonzero elevation angles, so that drop size distribution parameters and rainfall rates can be estimated without any bias.

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

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.

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>

scholarly journals Fidelity of Analytic Drop Size Distributions in Drizzling Stratiform Clouds Based on Large-Eddy Simulations

2009 ◽  
Vol 66 (8) ◽  
pp. 2335-2348 ◽  
Author(s):  
Yefim L. Kogan ◽  
Zena N. Kogan ◽  
David B. Mechem
Keyword(s):  
Gamma Distribution ◽  
Drop Size ◽  
Accurate Estimate ◽  
Radar Reflectivity ◽  
Size Distributions ◽  
Eddy Simulation ◽  
Analytical Functions ◽  
Large Eddy ◽  
Stratiform Clouds ◽  
Drop Size Distributions

Abstract Cloud microphysical parameterizations and retrievals rely heavily on knowledge of the shape of drop size distributions (DSDs). Many investigations assume that DSDs in the entire or partial drop size range may be approximated by known analytical functions. The most frequently employed approximations of function are of the type of gamma, lognormal, Khrgian–Mazin, and Marshall–Palmer. At present, little is known about the accuracy of these approximations. The authors employ a DSD dataset generated by the Cooperative Institute for Mesoscale Meteorological Studies Large-Eddy Simulation (CIMMS LES) explicit microphysics model for stratocumulus cases observed during the Atlantic Stratocumulus Transition Experiment (ASTEX) field project. The fidelity of analytic lognormal- and gamma-type DSD functions is evaluated according to how well they represent the higher-order moments of the drop spectra, such as precipitation flux and radar reflectivity. It is concluded that for boundary layer marine drizzling stratocumuli, a DSD based on the two-mode gamma distribution provides a more accurate estimate of precipitation flux and radar reflectivity than the DSD based on the lognormal distribution. The gamma distribution also provides a more accurate radar reflectivity field in two- and three-moment bulk microphysical models compared to the conventional Z–R relationship.

scholarly journals Profiles of Raindrop Size Distributions as Retrieved by Microrain Radars

2005 ◽  
Vol 44 (12) ◽  
pp. 1930-1949 ◽  
Author(s):  
Gerhard Peters ◽  
Bernd Fischer ◽  
Hans Münster ◽  
Marco Clemens ◽  
Andreas Wagner
Keyword(s):  
Baltic Sea ◽  
Drop Size ◽  
Size Distributions ◽  
The Baltic Sea ◽  
Weather Radars ◽  
Height Dependence ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
The Baltic ◽  
Rain Rates

Abstract Data of vertically pointing microrain radars (MRRs), located at various sites around the Baltic Sea, were analyzed for a period of several years. From the Doppler spectra profiles of drop size distributions (DSDs) are obtained. A significant height dependence of the shape of the DSDs—and thus of the Z–R relations—is observed at high rain rates. This implies, for the considered sites, that ground-based Z–R relations lead to underestimation of high rain rates by weather radars.

scholarly journals Do We Observe Aerosol Impacts on DSDs in Strongly Forced Tropical Thunderstorms?

2011 ◽  
Vol 68 (9) ◽  
pp. 1902-1910 ◽  
Author(s):  
P. T. May ◽  
V. N. Bringi ◽  
M. Thurai
Keyword(s):  
Drop Size ◽  
Probability Distributions ◽  
Size Distributions ◽  
Cloud Properties ◽  
Median Volume ◽  
Rain Drop ◽  
Distribution Parameters ◽  
Radar Measurements ◽  
Ice Multiplication ◽  
Drop Size Distributions

Abstract Rain drop size distributions retrieved from polarimetric radar measurements over regularly occurring thunderstorms over the islands north of Darwin, Australia, are used to test if aerosol contributions to the probability distributions of the drop size distribution parameters (median volume diameter and normalized intercept parameter) are detectable. The observations reported herein are such that differences in cloud properties arising from thermodynamic differences are minimized but even so may be a factor. However, there is a clear signature that high aerosol concentrations are correlated with smaller number concentrations and larger drops. This may be associated with enhanced ice multiplication processes for low aerosol concentration storms or other processes such as invigoration of the updrafts.

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