scholarly journals On Use of the Standard Deviation of the Mass Distribution as a Parameter in Raindrop Size Distribution Functions

2019 ◽  
Vol 58 (4) ◽  
pp. 787-796 ◽  
Author(s):  
Paul L. Smith ◽  
Roger W. Johnson ◽  
Donna V. Kliche
Keyword(s):  
Standard Deviation ◽  
Maximum Likelihood ◽  
Size Distribution ◽  
Mass Distribution ◽  
Shape Parameter ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Moment Methods ◽  
Raindrop Size Distribution ◽  
Raindrop Size

AbstractUse of the standard deviation σm of the drop mass distribution as one of the three parameters of raindrop size distribution (DSD) functions was introduced for application to disdrometer data supporting the Global Precipitation Measurement dual-frequency radar system. The other two parameters are a normalized drop number concentration Nw and the mass-weighted mean diameter Dm. This paper presents an evaluation of that formulation of the DSD functions, in two parts. First is a mathematical analysis showing that the procedure for estimating σm, along with the other DSD parameters, from disdrometer data is in essence another moment method. As such, it is subject to the biases and errors inherent in all moment methods. When the form of the DSD function is specified, it is inferior (like all moment methods) to the maximum likelihood technique for fitting parameters to sampled data. The second part is a series of sampling simulations illustrating the biases and errors involved in applying the formulation to the specific case of gamma DSDs. It leads to underestimates of σm and consequently to overestimates of the gamma shape parameter—with large root-mean-square errors. Comparison with maximum likelihood estimates shows the degree of improvement that could be obtained in the estimates of the shape parameter. The propensity to underestimate σm will be pervasive, and users of this DSD formulation should be cognizant of the biases and errors that can occur.

Estimation of raindrop size distribution parameters by maximum likelihood and L-moment methods: Effect of discretization

2012 ◽  
Vol 112 ◽  
pp. 1-11 ◽  
Author(s):  
Marzuki ◽  
Walter L. Randeu ◽  
Toshiaki Kozu ◽  
Toyoshi Shimomai ◽  
Michael Schönhuber ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Size Distribution ◽  
Moment Methods ◽  
Raindrop Size Distribution ◽  
Distribution Parameters ◽  
Raindrop Size

scholarly journals Raindrop Size Distribution and Radar Parameters in Coastal Tropical Rain Systems of Northeastern Brazil

2012 ◽  
Vol 51 (11) ◽  
pp. 1960-1970 ◽  
Author(s):  
Ricardo Sarmento Tenório ◽  
Marcia Cristina da Silva Moraes ◽  
Henri Sauvageot
Keyword(s):  
Size Distribution ◽  
Rain Rate ◽  
The Other ◽  
Northeastern Brazil ◽  
Drop Diameter ◽  
Coastal Site ◽  
Raindrop Size Distribution ◽  
The Mean ◽  
Raindrop Size ◽  
Bearing System

AbstractA dataset on raindrop size distribution (DSD) gathered in a coastal site of the Alagoas state in northeastern Brazil is used to analyze some differences between continental and maritime rainfall parameters. The dataset is divided into two subsets. One is composed of rainfall systems coming from the continent and moving eastward (i.e., offshore), representing the continental subset. The other is composed of rainfall systems that developed over the sea and are moving westward (i.e., inshore), representing the maritime subset. The mean conditional rain rate (i.e., for rain rate R > 0) is found to be higher for maritime (4.6 mm h−1) than for continental (3.2 mm h−1) conditions. The coefficient of variation of the conditional rain rate is lower for the maritime (1.75) than for the continental (2.25) subset. The continental and maritime DSDs display significant differences. For drop diameter D smaller than about 2 mm, the number of drops is higher for maritime rain than for continental rain. This reverses for D > 2 mm, in such a way that radar reflectivity factor Z for the maritime case is lower than for the continental case at the same rain rate. These results show that, to estimate precipitation by radar in the coastal area of northeastern Brazil, coefficients of the Z–R relation need to be adapted to the direction of motion of the rain-bearing system, inshore or offshore.

scholarly journals WRF Rainfall Modeling Post-Processing by Adaptive Parameterization of Raindrop Size Distribution: A Case Study on the United Kingdom

Atmosphere ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 36
Author(s):  
Qiqi Yang ◽  
Shuliang Zhang ◽  
Qiang Dai ◽  
Hanchen Zhuang
Keyword(s):  
United Kingdom ◽  
Size Distribution ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Rainfall Intensity ◽  
Post Processing ◽  
The United Kingdom ◽  
Raindrop Size Distribution ◽  
Double Moment ◽  
Raindrop Size

Raindrop size distribution (RSD) is a key parameter in the Weather Research and Forecasting (WRF) model for rainfall estimation, with gamma distribution models commonly used to describe RSD under WRF microphysical parameterizations. The RSD model sets the shape parameter (μ) as a constant of gamma distribution in WRF double-moment bulk microphysics schemes. Here, we propose to improve the gamma RSD model with an adaptive value of μ based on the rainfall intensity and season, designed using a genetic algorithm (GA) and the linear least-squares method. The model can be described as a piecewise post-processing function that is constant when rainfall intensity is <1.5 mm/h and linear otherwise. Our numerical simulation uses the WRF driven by an ERA-interim dataset with three distinct double-moment bulk microphysical parameterizations, namely, the Morrison, WDM6, and Thompson aerosol-aware schemes for the period of 2013–2017 over the United Kingdom at a 5 km resolution. Observations were made using a disdrometer and 241 rain gauges, which were used for calibration and validation. The results show that the adaptive-μ model of the gamma distribution was more accurate than the gamma RSD model with a constant shape parameter, with the root-mean-square error decreasing by averages of 23.62%, 11.33%, and 22.21% for the Morrison, WDM6, and Thompson aerosol-aware schemes, respectively. This model improves the accuracy of WRF rainfall simulation by applying adaptive RSD parameterization and can be integrated into the simulation of WRF double-moment microphysics schemes. The physical mechanism of the RSD model remains to be determined to improve its performance in WRF bulk microphysics schemes.

scholarly journals Evolution of the Shape of the Raindrop Size Distribution in Simulated Shallow Cumulus

2016 ◽  
Vol 73 (6) ◽  
pp. 2279-2297 ◽  
Author(s):  
Ann Kristin Naumann ◽  
Axel Seifert
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Cumulus Clouds ◽  
Microphysics Scheme ◽  
Space And Time ◽  
Shallow Cumulus ◽  
Raindrop Size Distribution ◽  
The Mean ◽  
Raindrop Size

Abstract In this paper, the evolution of the raindrop size distribution (RSD) is investigated for two isolated shallow cumulus clouds that are modeled with large-eddy simulations. For a two-moment bulk rain microphysics scheme that assumes the RSD to follow a gamma distribution, it is shown that the evolution of the rainwater content of an individual shallow cumulus cloud—in particular, its subcloud-layer rainwater amount and its surface precipitation rate—is highly sensitive to the choice of the shape parameter of the gamma distribution. To further investigate the shape of the RSD, a Lagrangian drop model is used to represent warm rain microphysics without a priori assumptions on the RSD. It is found that the shape parameter is highly variable in space and time and that existing closure equations, which are established from idealized studies of more heavily precipitating cases, are not appropriate for shallow cumulus. Although a relation of the shape parameter to the mean raindrop diameter is also found for individual shallow cumulus clouds, this relation differs already for the two clouds considered. It is therefore doubtful whether a two-moment scheme with a diagnostic parameterization of the shape parameter (i.e., a local closure in space and time) can be sufficient, especially when being applied across different cloud regimes. A three-moment bulk rain microphysics scheme is able to capture the general development of the relation of the shape parameter to the mean raindrop diameter for the two simulated clouds but misses some relevant features.

Vertical Variability of the Raindrop Size Distribution in Typhoons Observed at the Shenzhen 356-m Meteorological Tower

2020 ◽  
Vol 77 (12) ◽  
pp. 4171-4187
Author(s):  
Baojun Chen ◽  
Jun Yang ◽  
Ruiquan Gao ◽  
Keping Zhu ◽  
Chungen Zou ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Size Distribution ◽  
Weighted Mean ◽  
Meteorological Tower ◽  
Raindrop Size Distribution ◽  
Mean Diameter ◽  
Distribution Parameters ◽  
Low Altitude ◽  
Raindrop Size ◽  
Different Altitudes

AbstractRaindrop size distribution (DSD) characteristics at various altitudes in two landfalling typhoons in 2017 (Hato and Pakhar) were investigated by using laser-optical disdrometers mounted at four altitudes (10, 40, 160, and 320 m) of the Shenzhen 356-m meteorological tower. Significant differences of the DSD and derived parameters, mass-weighted mean diameter (Dm), normalized intercept parameter (NW), and standard deviation of the mass distribution σm, were observed at different altitudes for the two typhoons, while the rainwater content between the four altitudes had no statistically significant differences. The low-altitude DSDs had more midsize drops (1 < D < 3 mm), fewer large drops (D > 3 mm), and narrower distribution widths than the high-altitude ones, while the concentration of small drops varied nonlinearly with height. The value of NW decreased with height, while Dm and σm increased with height. The gamma distribution parameters N0, μ, and Λ are found to increase with decreasing height. Both the derived μ–Λ and Z–R relations were significantly varied in different altitudes.

scholarly journals Raindrop Size Distribution Measurements in Tropical Cyclones

2008 ◽  
Vol 136 (5) ◽  
pp. 1669-1685 ◽  
Author(s):  
Ali Tokay ◽  
Paul G. Bashor ◽  
Emad Habib ◽  
Takis Kasparis
Keyword(s):  
Size Distribution ◽  
Tropical Cyclones ◽  
Rain Rate ◽  
Liquid Water Content ◽  
The Other ◽  
Extratropical Cyclones ◽  
Raindrop Size Distribution ◽  
The Mean ◽  
High Concentrations ◽  
Raindrop Size

Abstract Characteristics of the raindrop size distribution in seven tropical cyclones have been studied through impact-type disdrometer measurements at three different sites during the 2004–06 Atlantic hurricane seasons. One of the cyclones has been observed at two different sites. High concentrations of small and/or midsize drops were observed in the presence or absence of large drops. Even in the presence of large drops, the maximum drop diameter rarely exceeded 4 mm. These characteristics of raindrop size distribution were observed in all stages of tropical cyclones, unless the storm was in the extratropical stage where the tropical cyclone and a midlatitude frontal system had merged. The presence of relatively high concentrations of large drops in extratropical cyclones resembled the size distribution in continental thunderstorms. The integral rain parameters of drop concentration, liquid water content, and rain rate at fixed reflectivity were therefore lower in extratropical cyclones than in tropical cyclones. In tropical cyclones, at a disdrometer-calculated reflectivity of 40 dBZ, the number concentration was 700 ± 100 drops m−3, while the liquid water content and rain rate were 0.90 ± 0.05 g m−3 and 18.5 ± 0.5 mm h−1, respectively. The mean mass diameter, on the other hand, was 1.67 ± 0.3 mm. The comparison of raindrop size distributions between Atlantic tropical cyclones and storms that occurred in the central tropical Pacific island of Roi-Namur revealed that the number density is slightly shifted toward smaller drops, resulting in higher-integral rain parameters and lower mean mass and maximum drop diameters at the latter site. Considering parameterization of the raindrop size distribution in tropical cyclones, characteristics of the normalized gamma distribution parameters were examined with respect to reflectivity. The mean mass diameter increased rapidly with reflectivity, while the normalized intercept parameter had an increasing trend with reflectivity. The shape parameter, on the other hand, decreased in a reflectivity range from 10 to 20 dBZ and remained steady at higher reflectivities. Considering the repeatability of the characteristics of the raindrop size distribution, a second impact disdrometer that was located 5.3 km away from the primary site in Wallops Island, Virginia, had similar size spectra in selected tropical cyclones.

scholarly journals Uncertainties in Profiler and Polarimetric DSD Estimates and Their Relation to Rainfall Uncertainties

2008 ◽  
Vol 25 (10) ◽  
pp. 1881-1887 ◽  
Author(s):  
Christopher R. Williams ◽  
Peter T. May
Keyword(s):  
Standard Deviation ◽  
Size Distribution ◽  
Power Law ◽  
Statistical Uncertainty ◽  
Radar Measurement ◽  
Estimation Algorithms ◽  
Weather Radars ◽  
Raindrop Size Distribution ◽  
Measurement Uncertainties ◽  
Raindrop Size

Abstract Polarimetric weather radars offer the promise of accurate rainfall measurements by including polarimetric measurements in rainfall estimation algorithms. Questions still remain on how accurately polarimetric measurements represent the parameters of the raindrop size distribution (DSD). In particular, this study propagates polarimetric radar measurement uncertainties through a power-law median raindrop diameter D0 algorithm to quantify the statistical uncertainties of the power-law regression. For this study, the power-law statistical uncertainty of D0 ranged from 0.11 to 0.17 mm. Also, the polarimetric scanning radar D0 estimates were compared with the median raindrop diameters retrieved from two vertically pointing profilers observing the same radar volume as the scanning radar. Based on over 900 observations, the standard deviation of the differences between the two radar estimates was approximately 0.16 mm. Thus, propagating polarimetric measurement uncertainties through D0 power-law regressions is comparable to uncertainties between polarimeteric and profiler D0 estimates.

A High-precision and Fast Solution Method of Gamma Raindrop Size Distribution based on 0-Moment and 3-Moment in South China

2021 ◽  
Author(s):  
XIANTONG LIU ◽  
HUIQI LI ◽  
SHENG Hu ◽  
QILIN WAN ◽  
HUI XIAO ◽  
...  
Keyword(s):  
Size Distribution ◽  
High Precision ◽  
South China ◽  
Solution Method ◽  
Shape Parameter ◽  
Weather Prediction ◽  
Order Moment ◽  
Raindrop Size Distribution ◽  
Fast Solution ◽  
Raindrop Size

AbstractAccording to the high accuracy linear shape-slope (μ-Λ) relationship observed by several 2-Dimensional-Video-Distrometers (2DVD) in South China, a high-precision and fast solution method of gamma (Γ) raindrop size distribution (RSD) function based on the zeroth order moment (M0) and the third order moment (M3) of RSD has been proposed. The 0-moment (M0) and 3-moment (M3) of RSD can be easily calculated from rain mass mixing ratio (Qr) and total number concentration (Ntr) simulated by the two-moment (2M) microphysical scheme, respectively. Three typical heavy rainfall processes and all RSD samples observed during 2019 in South China were selected to verify the accuracy of the method. Compared to the current widely used exponential RSD with a fixed shape parameter of zero in 2M microphysical scheme, the Γ RSD function using the linear constrained gamma (C-G) method agreed better with the Γ fit RSD from 2DVD observations. The characteristic precipitation parameters (e.g., rain rate, M2, M6 and M9) obtained by the proposed method are generally consistent with the parameters calculated by Γ fit RSD from 2DVD observations. The proposed method has effectively solved the problem that the shape parameter in the 2M microphysical scheme set to a constant, so that the Γ RSD functions are closer to the observations and have obviously smaller errors. This method has a good potential to be applied to the 2M microphysical schemes to improve the simulation of heavy precipitation in South China, but also paves the way for in-depth applications of radar data in numerical weather prediction models.

scholarly journals Regional variability of raindrop size distribution over Indonesia

2013 ◽  
Vol 31 (11) ◽  
pp. 1941-1948 ◽  
Author(s):  
M. Marzuki ◽  
H. Hashiguchi ◽  
M. K. Yamamoto ◽  
S. Mori ◽  
M. D. Yamanaka
Keyword(s):  
Size Distribution ◽  
Mesoscale Convective System ◽  
Radar Reflectivity ◽  
The Other ◽  
Convective System ◽  
Horizontal Scale ◽  
Regional Variability ◽  
Raindrop Size Distribution ◽  
Mesoscale Convective ◽  
Raindrop Size

Abstract. Regional variability of raindrop size distribution (DSD) along the Equator was investigated through a network of Parsivel disdrometers in Indonesia. The disdrometers were installed at Kototabang (KT; 100.32° E, 0.20° S), Pontianak (PT; 109.37° E, 0.00° S), Manado (MN; 124.92° E, 1.55° N) and Biak (BK; 136.10° E, 1.18° S). It was found that the DSD at PT has more large drops than at the other three sites. The DSDs at the four sites are influenced by both oceanic and continental systems, and majority of the data matched the maritime-like DSD that was reported in a previous study. Continental-like DSDs were somewhat dominant at PT and KT. Regional variability of DSD is closely related to the variability of topography, mesoscale convective system propagation and horizontal scale of landmass. Different DSDs at different sites led to different Z–R relationships in which the radar reflectivity at PT was much larger than at other sites, at the same rainfall rate.

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