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.

Comparison of Two Raindrop Size Distribution Retrieval Algorithms for X-Band Dual Polarization Observations

2008 ◽  
Vol 9 (3) ◽  
pp. 589-600 ◽  
Author(s):  
Marios N. Anagnostou ◽  
Emmanouil N. Anagnostou ◽  
Jothiram Vivekanandan ◽  
Fred L. Ogden
Keyword(s):  
Size Distribution ◽  
Empirical Relation ◽  
Shape Parameters ◽  
Dual Polarization ◽  
Axis Ratio ◽  
Differential Phase Shift ◽  
Drop Shape ◽  
Raindrop Size Distribution ◽  
X Band ◽  
Raindrop Size

Abstract In this study the authors evaluate two algorithms, the so-called beta (β) and constrained methods, proposed for retrieving the governing parameters of the “normalized” gamma drop size distribution (DSD) from dual-polarization radar measurements. The β method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase shift (KDP). The constrained method assumes that the axis-ratio relation is fixed and computes DSD parameters from ZH, ZDR, and an empirical relation between the DSD slope and shape parameters. The two techniques are evaluated for polarimetric X-band radar observations by comparing retrieved DSD parameters with disdrometer observations and examining simulated radar parameters for consistency. Error effects on the β method and constrained method retrievals are analyzed. The β approach is found to be sensitive to errors in KDP and to be less consistent with observations. Large retrieved β values are found to be associated with large retrieved DSD shape parameters and small median drop diameters. The constrained method provides reasonable rain DSD retrievals that agree better with disdrometer observations.

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.

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 Raindrop Size Distribution and Rain Characteristics during the 2013 Great Colorado Flood

2015 ◽  
Vol 17 (1) ◽  
pp. 53-72 ◽  
Author(s):  
Katja Friedrich ◽  
Evan A. Kalina ◽  
Joshua Aikins ◽  
Matthias Steiner ◽  
David Gochis ◽  
...  
Keyword(s):  
Drop Size ◽  
Doppler Radar ◽  
Liquid Water Content ◽  
Size Distributions ◽  
Intense Rainfall ◽  
Wind Fields ◽  
Raindrop Size Distribution ◽  
Median Volume ◽  
Drop Size Distributions ◽  
Analysis System

Abstract Drop size distributions observed by four Particle Size Velocity (PARSIVEL) disdrometers during the 2013 Great Colorado Flood are used to diagnose rain characteristics during intensive rainfall episodes. The analysis focuses on 30 h of intense rainfall in the vicinity of Boulder, Colorado, from 2200 UTC 11 September to 0400 UTC 13 September 2013. Rainfall rates R, median volume diameters D0, reflectivity Z, drop size distributions (DSDs), and gamma DSD parameters were derived and compared between the foothills and adjacent plains locations. Rainfall throughout the entire event was characterized by a large number of small- to medium-sized raindrops (diameters smaller than 1.5 mm) resulting in small values of Z (<40 dBZ), differential reflectivity Zdr (<1.3 dB), specific differential phase Kdp (<1° km−1), and D0 (<1 mm). In addition, high liquid water content was present throughout the entire event. Raindrops observed in the plains were generally larger than those in the foothills. DSDs observed in the foothills were characterized by a large concentration of small-sized drops (d < 1 mm). Heavy rainfall rates with slightly larger drops were observed during the first intense rainfall episode (0000–0800 UTC 12 September) and were associated with areas of enhanced low-level convergence and vertical velocity according to the wind fields derived from the Variational Doppler Radar Analysis System. The disdrometer-derived Z–R relationships reflect how unusual the DSDs were during the 2013 Great Colorado Flood. As a result, Z–R relations commonly used by the operational NEXRAD strongly underestimated rainfall rates by up to 43%.

scholarly journals Evaluation of Gamma Raindrop Size Distribution Assumption through Comparison of Rain Rates of Measured and Radar-Equivalent Gamma DSD

2014 ◽  
Vol 53 (6) ◽  
pp. 1618-1635 ◽  
Author(s):  
Elisa Adirosi ◽  
Eugenio Gorgucci ◽  
Luca Baldini ◽  
Ali Tokay
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Rain Rate ◽  
Hydrological Cycle ◽  
Drop Size Distribution ◽  
Dual Polarization ◽  
Raindrop Size Distribution ◽  
Radar Measurements ◽  
Raindrop Size ◽  
Rain Rates

AbstractTo date, one of the most widely used parametric forms for modeling raindrop size distribution (DSD) is the three-parameter gamma. The aim of this paper is to analyze the error of assuming such parametric form to model the natural DSDs. To achieve this goal, a methodology is set up to compare the rain rate obtained from a disdrometer-measured drop size distribution with the rain rate of a gamma drop size distribution that produces the same triplets of dual-polarization radar measurements, namely reflectivity factor, differential reflectivity, and specific differential phase shift. In such a way, any differences between the values of the two rain rates will provide information about how well the gamma distribution fits the measured precipitation. The difference between rain rates is analyzed in terms of normalized standard error and normalized bias using different radar frequencies, drop shape–size relations, and disdrometer integration time. The study is performed using four datasets of DSDs collected by two-dimensional video disdrometers deployed in Huntsville (Alabama) and in three different prelaunch campaigns of the NASA–Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM) ground validation program including the Hydrological Cycle in Mediterranean Experiment (HyMeX) special observation period (SOP) 1 field campaign in Rome. The results show that differences in rain rates of the disdrometer DSD and the gamma DSD determining the same dual-polarization radar measurements exist and exceed those related to the methodology itself and to the disdrometer sampling error, supporting the finding that there is an error associated with the gamma DSD assumption.

scholarly journals STUDY ON SUMMER RAINDROP SIZE DISTRIBUTION AND RETRIEVED POLARIMETRIC RADAR PARAMETER OVER LEIZHOU PENINSULA

2019 ◽  
Vol XLII-3/W9 ◽  
pp. 245-250
Author(s):  
Z. B. Zhou ◽  
J. J. Lv ◽  
S. J. Niu
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Least Squares Method ◽  
Convective Precipitation ◽  
Polarimetric Radar ◽  
Leizhou Peninsula ◽  
Raindrop Size Distribution ◽  
Precipitation Estimation ◽  
Raindrop Size ◽  
Subtropical Monsoon Climate

Abstract. Leizhou peninsula is located in the south of Guangdong Province, near South China Sea, and has a tropical and subtropical monsoon climate. Based on observed drop size distribution (DSD) data from July 2007 to August 2007 with PARSIVEL disdrometers deployed at Zhanjiang and Suixi, the characterists of DSDs are studied. Non-linear least squares method is used to fit Gamma distribution. Convective and stratiform averaged DSDs are in good agreement with Gamma distribution, especially in stratiform case. Convective average DSDs have a wider spectrum and higher peak. Microphysical parameter differences between convective and stratiform are discussed, convective precipitation has a higher mass-weighted mean diameter (Dm) and generalized intercepts (Nw) in both areas. The constrained relations between Gamma distribution parameter (μ, Λ, N0) is derived. The retrieved polarimetric radar parameter (KDP, ZDR, Zh) have a good self-consistency, which can be used to improve the accuracy of KDP calculation. R-KDP-ZDR is superior to the R-KDP, R-ZDR-Zh in quantitative precipitation estimation (QPE), with a correlation coefficient higher than 0.98.

scholarly journals The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws

2010 ◽  
Vol 10 (4) ◽  
pp. 9121-9151 ◽  
Author(s):  
H. Leijnse ◽  
R. Uijlenhoet
Keyword(s):  
High Velocity ◽  
Drop Size ◽  
Doppler Radar ◽  
Probability Distributions ◽  
Power Laws ◽  
Size Distributions ◽  
Optical Links ◽  
Gamma Distributions ◽  
Raindrop Size Distribution ◽  
Drop Size Distributions

Abstract. It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of recently broken-up larger drops. In this paper we quantify the effect of this phenomenon on raindrop size distribution measurements from a Joss-Waldvogel disdrometer, a 2-D Video Distrometer, and a vertically-pointing Doppler radar. Probability distributions of fall velocities have been parameterized, where the parameters are functions of both rainfall intensity and drop size. These parameterizations have been used to correct Joss-Waldvogel disdrometer measurements for this phenomenon. The effect of these corrections on fitted scaled drop size distributions are apparent but not major. Fitted gamma distributions for three different types of rainfall have been used to simulate drop size measurements. The effect of the high-velocity small drops is shown to be minor. Especially for the purpose of remote sensing of rainfall using radar, microwave links, or optical links, the errors caused by using the slightly different retrieval relations will be masked completely by other error sources.

scholarly journals Small-Scale Variability of the Raindrop Size Distribution and Its Effect on Areal Rainfall Retrieval

2016 ◽  
Vol 17 (7) ◽  
pp. 2077-2104 ◽  
Author(s):  
Timothy H. Raupach ◽  
Alexis Berne
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Integration Time ◽  
Small Scale ◽  
Drop Diameter ◽  
Weather Model ◽  
Raindrop Size Distribution ◽  
Areal Rainfall ◽  
Raindrop Size ◽  
Microphysical Processes

Abstract The drop size distribution (DSD) describes the microstructure of liquid precipitation. The high variability of the DSD reflects the variety of microphysical processes controlling raindrop properties and affects the retrieval of rainfall. An analysis of the effects of DSD subgrid variability on areal estimation of precipitation is presented. Data used were recorded with a network of disdrometers in Ardèche, France. DSD variability was studied over two typical scales: 5 km × 5 km, similar to the ground footprint size of the Global Precipitation Measurement (GPM) spaceborne weather radar, and 2.8 km × 2.8 km, an operational pixel size of the Consortium for Small-Scale Modeling (COSMO) numerical weather model. Stochastic simulation was used to generate high-resolution grids of DSD estimates over the regions of interest, constrained by experimental DSDs measured by disdrometers. From these grids, areal DSD estimates were derived. The error introduced by assuming a point measurement to be representative of the areal DSD was quantitatively characterized and was shown to increase with the size of the considered area and with drop size and to decrease with the integration time. The controlled framework allowed for the accuracy of retrieval algorithms to be investigated. Rainfall variables derived by idealized simulations of GPM- and COSMO-style algorithms were compared to subgrid distributions of the same variables. While rain rate and radar reflectivity were well represented, the estimated drop concentration and mass-weighted mean drop diameter were often less representative of subgrid values.

scholarly journals The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws

2010 ◽  
Vol 10 (14) ◽  
pp. 6807-6818 ◽  
Author(s):  
H. Leijnse ◽  
R. Uijlenhoet
Keyword(s):  
High Velocity ◽  
Drop Size ◽  
Doppler Radar ◽  
Probability Distributions ◽  
Power Laws ◽  
Size Distributions ◽  
Optical Links ◽  
Gamma Distributions ◽  
Raindrop Size Distribution ◽  
Drop Size Distributions

Abstract. It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of recently broken-up larger drops. In this paper we quantify the effect of this phenomenon on raindrop size distribution measurements from a Joss-Waldvogel disdrometer, a 2-D Video Distrometer, and a vertically-pointing Doppler radar. Probability distributions of fall velocities have been parameterized, where the parameters are functions of both rainfall intensity and drop size. These parameterizations have been used to correct Joss-Waldvogel disdrometer measurements for this phenomenon. The effect of these corrections on fitted scaled drop size distributions are apparent but not major. Fitted gamma distributions for three different types of rainfall have been used to simulate drop size measurements. The effect of the high-velocity small drops is shown to be minor. Especially for the purpose of remote sensing of rainfall using radar, microwave links, or optical links, the errors caused by using the slightly different retrieval relations will be masked completely by other error sources.

scholarly journals Raindrop size distributions and radar reflectivity–rain rate relationships for radar hydrology

2001 ◽  
Vol 5 (4) ◽  
pp. 615-628 ◽  
Author(s):  
R. Uijlenhoet
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Rain Rate ◽  
Radar Reflectivity ◽  
Size Distributions ◽  
Raindrop Size Distribution ◽  
Special Cases ◽  
Fundamental Reason ◽  
Radar Measurements ◽  
Raindrop Size

Abstract. The conversion of the radar reflectivity factor Z(mm6m-3) to rain rate R(mm h-1 ) is a crucial step in the hydrological application of weather radar measurements. It has been common practice for over 50 years now to take for this conversion a simple power law relationship between Z and R. It is the purpose of this paper to explain that the fundamental reason for the existence of such power law relationships is the fact that Z and R are related to each other via the raindrop size distribution. To this end, the concept of the raindrop size distribution is first explained. Then, it is demonstrated that there exist two fundamentally different forms of the raindrop size distribution, one corresponding to raindrops present in a volume of air and another corresponding to those arriving at a surface. It is explained how Z and R are defined in terms of both these forms. Using the classical exponential raindrop size distribution as an example, it is demonstrated (1) that the definitions of Z and R naturally lead to power law Z–R relationships, and (2) how the coefficients of such relationships are related to the parameters of the raindrop size distribution. Numerous empirical Z–R relationships are analysed to demonstrate that there exist systematic differences in the coefficients of these relationships and the corresponding parameters of the (exponential) raindrop size distribution between different types of rainfall. Finally, six consistent Z–R relationships are derived, based upon different assumptions regarding the rain rate dependence of the parameters of the (exponential) raindrop size distribution. An appendix shows that these relationships are in fact special cases of a general Z–R relationship that follows from a recently proposed scaling framework for describing raindrop size distributions and their properties. Keywords: radar hydrology, raindrop size distribution, radar reflectivity–rain rate relationship

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