scholarly journals One, No One, and One Hundred Thousand: The Paradigm of the Z–R Relationship

2020 ◽  
Vol 21 (6) ◽  
pp. 1161-1169
Author(s):  
Massimiliano Ignaccolo ◽  
Carlo De Michele
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Rain Rate ◽  
Scaling Law ◽  
Drop Size Distribution ◽  
Physical Relationship ◽  
Simple Realization ◽  
Linear Fit ◽  
State Of Affairs

AbstractThe Z–R relationship is a scaling-law formulation, Z = ARb, connecting the radar reflectivity Z to the rain rate R. However, more than 100 Z–R relationships, with different values of the parameters, have been reported in literature. This abundance of relationships is in itself a strong indication that no one “physical” relationship exists, a state of affairs that we find similar to that of the protagonist of Luigi Pirandello’s novel One, No One and One Hundred Thousand. Nevertheless the “elevation” of a simple linear fit in the (logR, logZ) space to the role of “scaling law” is such a widespread tenet in literature that it eclipses the simple realization that the abundance of different intercepts and slopes reflects the inhomogeneous nature of rain, and, in ultimate analysis, the statistical variability existing between the number of drops and drop size distribution. Here, we “eliminate” the contribution of the number of drops by rescaling both reflectivity and rainfall rate to per unit drop variables, (Z, R) → (z, r), so that the remaining variability is due only to the variability of the drop size distribution. We use a worldwide database of disdrometer data to show that for the rescaled variables (z, r) only “one,” albeit approximate, scaling law exists.

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 Disdrometer measurements under Sense-City rainfall simulator

2019 ◽  
Author(s):  
Auguste Gires ◽  
Philippe Bruley ◽  
Anne Ruas ◽  
Daniel Schertzer ◽  
Ioulia Tchiguirinskaia
Keyword(s):  
Kinetic Energy ◽  
Size Distribution ◽  
Drop Size ◽  
Rain Rate ◽  
Drop Size Distribution ◽  
Climatic Chamber ◽  
Sampling Area ◽  
Data Set ◽  
Raw Data ◽  
Rainfall Simulator

Abstract. The Hydrology, Meteorology and Complexity laboratory of Ecole des Ponts ParisTech (hmco.enpc.fr) and the Sense-City consortium (http://sense-city.ifsttar.fr/) make available a data set of optical disdrometers measurements coming from a cam-paign that took place in September 2017 under the rainfall simulator of the Sense-City climatic chamber which is located near Paris. Two OTT Parsivel2 were used. The size and velocity of drops falling through the sampling area of the devices of roughly few tens of cm2 is computed by disdrometers. This enables to estimate the drop size distribution and further study rainfall micro-physics or kinetic energy for example. Raw data, i.e. basically a matrix containing a number of drops according to classes of size and velocity, along with more aggregated ones such rain rate or drop size distribution with filtering is available. Link to the data set (Gires et al., 2019): http://doi.org/10.5281/zenodo.3347051.

DROP IMPACT EXPERIMENT AS A MODEL EXPERIMENT TO INVESTIGATE THE ROLE OF OIL-IN-WATER EMULSIONS IN CONTROLLING THE DROP SIZE DISTRIBUTION OF AN AGRICULTURAL SPRAY

2016 ◽  
Vol 26 (8) ◽  
pp. 827-851 ◽  
Author(s):  
Clara Vernay ◽  
Laurence Ramos ◽  
Jean-Paul Douzals ◽  
Rajesh Goyal ◽  
Jean-Christophe Castaing ◽  
...  
Keyword(s):  
Size Distribution ◽  
Model Experiment ◽  
Drop Size ◽  
Drop Impact ◽  
Drop Size Distribution ◽  
Oil In Water ◽  
Impact Experiment

Modeling volatilization of trichloroethylene from a domestic shower spray: the role of drop-size distribution

1992 ◽  
Vol 26 (8) ◽  
pp. 1602-1606 ◽  
Author(s):  
Nicholas Giardino ◽  
Nurtan A. Esmen ◽  
Julian B. Andelman
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution

scholarly journals Effect of sampling variation on error of rainfall variables measured by optical disdrometer

2012 ◽  
Vol 5 (6) ◽  
pp. 8895-8924 ◽  
Author(s):  
X. C. Liu ◽  
T. C. Gao ◽  
L. Liu
Keyword(s):  
Size Distribution ◽  
Relative Error ◽  
Drop Size ◽  
Rain Rate ◽  
Marked Point ◽  
Water Concentration ◽  
Drop Size Distribution ◽  
Short Side ◽  
Mean Diameter ◽  
Sampling Variation

Abstract. During the sampling process of precipitation particles by optical disdrometers, the randomness of particles and sampling variability has great impact on the accuracy of precipitation variables. Based on a marked point model of raindrop size distribution, the effect of sampling variation on drop size distribution and velocity distribution measurement using optical disdrometers are analyzed by Monte Carlo simulation. The results show that the samples number, rain rate, drop size distribution, and sampling size have different influences on the accuracy of rainfall variables. The relative errors of rainfall variables caused by sampling variation in a descending order as: water concentration, mean diameter, mass weighed mean diameter, mean volume diameter, radar reflectivity factor, and number density, which are independent with samples number basically; the relative error of rain variables are positively correlated with the margin probability, which is also positively correlated with the rain rate and the mean diameter of raindrops; the sampling size is one of the main factors that influence the margin probability, with the decreasing of sampling area, especially the decreasing of short side of sample size, the probability of margin raindrops is getting greater, hence the error of rain variables are getting greater, and the variables of median size raindrops have the maximum error. To ensure the relative error of rainfall variables measured by optical disdrometer less than 1%, the width of light beam should be at least 40 mm.

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