Drop Size Distribution Model Research Articles

Rain Attenuations Based on Drop Size Distribution (DSD) Model and Empirical Model at Low THz Frequencies

Rain attenuation based on the drop size distribution (DSD) with different rainfall rates (R) at low THz frequencies is investigated in this paper. The rain attenuation is calculated using the DSD measured for one year and the extinction cross-section (ECS) by the Mie scattering theory. Moreover, the obtained specific rain attenuation is verified by the empirical model using the measurement system consisting of a transmitter, a receiver, and weather measurement units. We measured the received power against the uniform transmitted power at 240, 270, and 300 GHz on the rooftop of the National Radio Research Agency (RRA) in Korea during the same period as the DSD measurement period. After curve fitting by regression analysis, we compared both rain attenuations obtained in two methods with the recommendation International Telecommunication Union Radiocommunication Sector (ITU-R) P.838-3. The root mean square errors (RMSEs) of the DSD model are 2.8977, 2.8646, and 2.8331 at 240, 270, and 300 GHz, respectively. The calculated result using the Mie scattering and the measured DSD methods shows the best fit to the data of the ITU-R recommendation for a rainfall rate of up to 5 mm/h. On the other hand, the empirical results using the T/Rx antenna system are slightly higher compared to the data of the ITU-R recommendation. As the rainfall rate increases, the difference between our results and ITU-R recommendation increases. This study will be useful for predicting rain attenuation for terrestrial wireless links operating at low THz frequencies.

Development of Drop Size Distribution Model for Dropwise Condensation on a Superhydrophobic Surface

This study presents a mathematical model of drop size distribution during dropwise condensation on a superhydrophobic surface. The model is developed by combining a power law growth model, an exponentially decaying population model, and a Gaussian probability model for growth variations. The model is validated against experiment data, with correlations ranging from 88% to 94%. The growth model is shown to sufficiently describe the growth of drops from 0.02 mm to 0.1 mm but may be extrapolated to describe the growth of even smaller drops. The experiment data show that drop size distribution or frequency distribution of drops of different sizes varies significantly with time and may be considered pseudo-cyclic. The developed model, together with the sweep rate of drops, sufficiently describes this behavior and, consequently, may also be used to better estimate the heat transfer rate due to dropwise condensation.

Can DSD Assumptions Explain the Differences in Satellite Estimates of Warm Rain?

Abstract Satellite-based oceanic precipitation estimates, particularly those derived from the Global Precipitation Measurement (GPM) satellite and CloudSat, suffer from significant disagreement over regions of the globe where warm rain processes are dominant. GPM estimates of average rain rate tend to be lower than CloudSat estimates, due in part to GPM being less sensitive to shallow and/or light precipitation. Using coincident observations between GPM and CloudSat, we find that the GPM_2BCMB product misses about two-thirds of total accumulated warm rain compared to the CloudSat 2C-RAIN-PROFILE product. This difference becomes much smaller when products are compared at 1000 m above the surface (mitigating surface clutter issues) and when forcing the frequency of rain from CloudSat to match the frequency from GPM (mitigating sensitivity issues). However, even then a gap of about 25% remains. Using an optimal estimation retrieval algorithm on the underlying data, we retrieve a similar result, but find that the remaining difference between the GPM and CloudSat retrieved rain rates can be almost entirely accounted for by inconsistent assumptions about the shape of the drop size distribution (DSD) that are made in the two retrievals. We conclude that DSD assumptions contribute significantly to the relative underestimation of warm rain by GPM compared to CloudSat. Because the choice of DSD model has such a large effect on retrieved rain rates, more work is needed to determine whether the DSD models assumed by either the GPM_2BCMB or 2C-RAIN-PROFILE algorithms are actually appropriate for warm rain.

How Accurately Can Warm Rain Realistically Be Retrieved with Satellite Sensors? Part I: DSD Uncertainties

Abstract A significant part of the uncertainty in satellite-based precipitation products stems from differing assumptions about drop size distributions (DSDs). Satellite radar-based retrieval algorithms rely on DSD assumptions that may be overly simplistic, whereas radiometers further struggle to distinguish cloud water from rain. We utilize the Ocean Rainfall and Ice-phase Precipitation Measurement Network (OceanRAIN), version 1.0, dataset to examine the impact of DSD variability on the ability of satellite measurements to accurately estimate rates of warm rainfall. We use the binned disdrometer counts and a simple model of the atmosphere to simulate observations for three satellite architectures. Two are similar to existing instrument combinations on the GPM Core Observatory and CloudSat, and the third is a theoretical triple-frequency radar–radiometer architecture. Using an optimal estimation framework, we find that the assumed DSD shape can have a large impact on retrieved rain rate. A three-parameter normalized gamma DSD model is sufficient for describing and retrieving the DSDs observed in the OceanRAIN dataset. Assuming simpler single-moment DSD models can lead to significant biases in retrieved rain rate, on the order of 100%. Differing DSD assumptions could thus plausibly explain a large portion of the disagreement in satellite-based precipitation estimates.

Analysis of Rain-Induced Attenuation at Ku-V Band Using Gamma Drop Size Distribution Model Over a Tropical Region

Analysis of Rain-Induced Attenuation at Ku-V Band Using Gamma Drop Size Distribution Model Over a Tropical Region

Impact of integration time steps of rain drop size distribution on their structuring and their modelling: a case study in northern Benin

This paper focused on modelling rain drop size distributions (DSDs) of various integration time steps using unimodal DSD models (gamma and lognormal). Rain DSD data considered are those collected from 2005 to 2007 near Djougou city in the north-western region of Benin Republic. The efficiency of these models was characterized by statistical criteria, mainly Nash and KGE. These criteria are used to assess the level of fitting of rain DSD spectra. Superimposed rain DSDs were then parameterized with the rainfall rate, using the scaling law formalism. Results show that there is an improvement in the structuring of the rain DSDs according to their measurement duration. Analysis of the occurrence statistics of the structuring of the spectra reveals that the Spectra ill adjusted by a unimodal DSD model represents 5 to 15% of the population of 1 min rain DSDs. This population decreases according to the measurement duration of the spectra. The optimal measurement time is found to be 10 min. Furthermore, parameters of the shape functions (gamma and lognormal) increase or decrease markedly according to the measurement duration of the rain DSD spectra. For applications using the relationships deduced from the rain DSDs, results suggested that the measurement time scale must be taken into account when choosing appropriate relationships.

A Case Study on Microphysical Characteristics of Mesoscale Convective System Using Generalized DSD Parameters Retrieved from Dual-Polarimetric Radar Observations

The microphysical characteristics of a mesoscale convective system (MCS) during a summer monsoon of South Korea are investigated using the generalized drop size distributions (DSD) that are derived from S-band dual-polarization radar data. The characteristics parameters of generalized DSDs (generalized number concentration, N0′ and generalized mean diameter, Dm) are directly calculated from DSD’s two moments without any assumption on the DSD model. Relationships between ZDR and generalized DSD parameters normalized by ZH are derived in the form of the polynomial equation. Verification of the retrieved DSD parameters is conducted with the 2-D video disdrometer (2DVD) located about 23 km from the radar. The standard deviations (SD) of retrieved DSD parameters are about 0.26 for log N0′, and about 0.11 for Dm because of the variability of DSDs. The SD of the retrieved log N0′ from the dual-polarimetric measurement reaches to about 0.46 (almost double) for 11 rain events while the accuracy of retrieved Dm is quite higher (~0.19). This higher error in retrieved log N0′ is likely attributed to the larger discrepancy in radar-observed and DSD-calculated ZDR when ZH is low. This retrieval technique is applied to a mesoscale convective system (MCS) case to investigate the Lagrangian characteristics of the microphysical process. The MCS is classified into the leading edge and trailing stratiform region by using the storm classification algorithm. The leading edge dominated by strong updraft showed the broad DSD spectra with a steady temporal increase of Dm throughout the event, likely because of the dominant drop growth by the collision-coalescence process. On the other hand, the drop growth is less significant in the trailing stratiform region as shown by the nearly constant Dm for the entire period. The DSD variation is also controlled by the new generation of drops in the leading edge and less extent in the trailing stratiform during the early period when precipitation systems grow. When the system weakens, the characteristic number concentration decreases with time, indicating the new generation of drops becomes less significant in both regions.

Optimized rain drop size distribution model for microwave propagation for equatorial Africa

In radio propagation, modelling of rainfall rate, rain attenuation and drop size distribution is highly location-dependent and thus requires availability of reliable data from various locations. Models and mathematical predictions obtained based on data from one location often prove inadequate when applied to another location with either slightly or radically different rainfall pattern. In this paper, the focus is to develop a new rainfall drop size distribution model for equatorial Africa using disdrometer data obtained in Butare, Rwanda (2°35’53.88”S and 29° 44’ 31.5” E). Rainfall data was classified into annual, monthly and rainfall regimes which are drizzle, widespread, shower and thunderstorm, based on their rainfall rates. The maximum likelihood estimation technique was applied to construct estimates of input Drop Size Distribution (DSD) fit parameters of the developed statistical distribution for rainfall DSD in Butare. The newly obtained distribution was compared to the existing rainfall DSD models, namely, Lognormal, Gamma, Marshall-Palmer and Weibull distributions, and found to be an improvement over the existing ones. The Mie Scattering technique is employed to derive the scattering parameters. Thereafter, the derived scattering parameters with DSD models are used for the estimation of rainfall attenuation for the Central African region.

Raindrop size distribution and microphysical characteristics of a great rainstorm in 2016 in Beijing, China

This paper analyzes the characteristics of rain drop size distributions (DSDs) and vertical profiles of hydrometeors for a severe rainstorm event that occurred in Beijing, northern China, from 19 to 21 July 2016 using in situ measurements from two disdrometers (OTT-Parsivel2 and 2D-Video-Distrometer) and remote sensing data collected by a second-generation Micro Rain Radar (MRR2). This rainstorm was characterized by stratiform precipitation with embedded strong convection on 19 July and widespread, intense mixed convective-stratified rainfall resulting in persistent rainfall between 20 and 21 July. The temporal and spatial variations in rainfall rate R, liquid water content W, reflectivity Z, DSDs and the gamma DSD parameters in different precipitation episodes of this event are derived and compared between two meteorological stations in Beijing. Rainfall throughout the entire event was characterized by large concentrations of small- to medium-sized raindrops (diameters between 2 and 4 mm) and few larger particles (D > 4 mm), resulting in small values of reflectivity Z (<40 dBZ) and liquid water content W (<1.0 g m−3). In addition, the log10Nw-Dm scatter pairs recorded during the convective phase of this rainstorm indicate maritime-like convection. The time evolution of DSDs shows that most single peak DSDs occurred during stratiform rainfall, and bimodal DSDs were observed when the convective rainfall cells passed by and collisional breakups occurred. The gamma DSD model with a single peak in the stratiform phase of the storm and the bimodal DSD in the convective episode of the storm are quantitatively evaluated. In addition, in each precipitation episode, the differences in exponent b and coefficient A of the Z-R relationship between the two stations are smaller for stratiform rainfall than for convective rainfall due to the more evident variability of drop size and number concentration in convective rain. The physical nature of this relationship and the possible mechanisms leading to diverse characteristics in different phases of this heavy rainstorm are discussed.

Modeling of Raindrop Size Distribution Observed Using Micro Rain Radar Over Darjeeling (27.05oN, 88.26oE): An Eastern Himalayan Region

Micro rain radar (MRR-2) provides the measurement of the drop size distribution DSD with altitude and rain rates. In this paper, we show a new form of gamma drop size distribution (DSD) model. MRR-2 is based on the principle of Radar spectrum measurement of continuous-wave of frequency modulation. DSD measurements for the rain rates ~ 0–25 mm/h and the height from 150 to 2000 m during the south-west monsoon season for the period 2009 and 2010 are used in this study. From the variance of DSD ( $$\sigma^{2}$$ ) and mass-weighted mean drop diameter as well as after the mathematical calculation, two parameters ( $$\varLambda$$ and µ) are obtained for the use of lower-order moments. Both the moments are utilized for the best suitable of gamma DSD. Measured DSD for the different rain rates and different altitudes below the melting layer height (~ 2–3 km) compared among the exponential, lognormal and gamma DSD model over Darjeeling in the Eastern Himalaya. The correlation between best fit measured DSD and gamma distribution indicate that they correlate well for both lower and higher order moments for the heights 150 m and 1050 m. Whereas they correlated only for higher order moments for the 450 m, 1500 m and 1950 m. Thus, it is found that the observed pattern of DSD agrees well to the gamma DSD model.

Simulation of Drop-Size Distribution During Dropwise and Jumping Drop Condensation on a Vertical Surface: Implications for Heat Transfer Modeling.

Accurate models for condensation heat transfer are necessary to improve condenser design. Drop-size distribution is an important aspect of heat transfer modeling that is difficult to measure for small drop sizes. The present work uses a numerical simulation of condensation which incorporates the possibility of coalescence and coalescence-induced jumping over a range of drop sizes. Results of the simulation are compared with previous theoretical models and the impact of the assumptions used in those models is explored. In particular, previous drop-size distribution models may predict heat transfer rates less accurately for high contact angles and for coalescence-induced jumping since coalescence occurs over a range of drop sizes and does not always result in departure. The influence of various input parameters (nucleation site distribution approach, nucleation site density, contact angle, maximum drop size, heat transfer modeling to individual drops, and minimum jumping size) on the drop-size distribution and overall heat transfer rate is explored. Assignment of the nucleation site spatial distribution and heat transfer model affect both the drop-size distribution and predicted overall heat transfer rate. Results from the simulation suggest that, when the contact angle is large (as on superhydrophobic surfaces) and no coalescence-induced jumping occurs, the heat transfer may not be as sensitive to the maximum drop-size as previously supposed. Furthermore, this work suggests that when coalescence-induced jumping occurs, reducing the maximum drop size may not always increase heat transfer since drops similar in size to those removed by coalescence-induced jumping can contribute significantly to the overall heat transfer rate.

Characterization and Simulation of a Low-Pressure Rotator Spray Plate Sprinkler Used in Center Pivot Irrigation Systems

Spray sprinklers enable to operate at low pressures (&lt;103 kPa) in self-propelled irrigation machines. A number of experiments were performed to characterize the water distribution pattern of an isolated rotator spray plate sprinkler operating at very low pressure under different experimental conditions. The experiments were performed under two pressures (69 kPa and 103 kPa) and in calm and windy conditions. The energy losses due to the impact of the out-going jet with the sprinkler plate were measured using an optical technique. The adequacy to reproduce the measured water distribution pattern under calm conditions of two drop size distribution models was evaluated. A ballistic model was used to simulate the water distribution pattern under wind conditions evaluating three different drag models: (1) considering solid spherical drops; (2) a conventional model based on wind velocity and direction distortion pattern, and (3) a new drag coefficient model independent of wind speed. The energy losses measured with the optical method range from 20% to 60% from higher to lower nozzle sizes, respectively, for both evaluated working pressures analyzing over 16,500 droplets. For the drop size distribution selected, Weibull accurately reproduced the water application with a maximum root mean square error (RMSE) of 19%. Up to 28% of the RMSE could be decreased using the wind-independent drag coefficient model with respect to the conventional model; the difference with respect to the spherical model was 4%.

Rain Statistics Investigation and Rain Attenuation Modeling for Millimeter Wave Short-Range Fixed Links

Millimeter wave (mmWave) communication is a key technology for fifth generation (5G) and beyond communication networks. However, the communication quality of the radio link can be largely affected by rain attenuation, which should be carefully taken into consideration when calculating the link budget. In this paper, we present results of weather data collected with a PWS100 disdrometer and mmWave channel measurements at 25.84 GHz (K band) and 77.52 GHz (E band) using a custom-designed channel sounder. The rain statistics, including rain intensity, rain events, and rain drop size distribution (DSD) are investigated for one year. The rain attenuation is predicted using the DSD model with Mie scattering and from the model in ITU-R P.838-3. The distance factor in ITU-R P.530-17 is found to be inappropriate for a short-range link. The wet antenna effect is investigated and additional protection of the antenna radomes is demonstrated to reduce the wet antenna effect on the measured attenuation.

Invariance of the Double-Moment Normalized Raindrop Size Distribution through 3D Spatial Displacement in Stratiform Rain

AbstractDouble-moment normalization of the drop size distribution (DSD) summarizes the DSD in a compact way, using two of its statistical moments and a “generic” double-moment normalized DSD function. Results are presented of an investigation into the invariance of the double-moment normalized DSD through horizontal and vertical displacement in space, using data from disdrometers, vertically pointing K-band Micro Rain Radars, and an X-band polarimetric weather radar. The invariance of the double-moment normalized DSD is tested over a vertical range of up to 1.8 km and a horizontal range of up to approximately 100 km. The results suggest that for practical use, with well-chosen input moments, the double-moment normalized DSD can be assumed invariant in space in stratiform rain. The choice of moments used to characterize the DSD affects the amount of DSD variability captured by the normalization. It is shown that in stratiform rain, it is possible to capture more than 85% of the variability in DSD moments zero to seven using the technique. Most DSD variability in stratiform rain can thus be explained through the variability of two of its statistical moments. The results suggest similar behavior exists in transition and convective rain, but the limited data samples available do not allow for robust conclusions for these rain types. The results have implications for practical uses of double-moment DSD normalization, including the study of DSD variability and microphysics, DSD-retrieval algorithms, and DSD models used in rainfall retrieval.

Raindrop size distribution and rainfall attenuation modeling in equatorial and subtropical Africa: the critical diameters

Raindrop sizes were obtained from Butare, Rwanda (2.6°S, 29.74°E) and Durban, South Africa (29°52′S, 30°58′E) using the Joss–Waldvogel RD-80 disdrometer. The obtained data is used for the analysis of the drop size distribution (DSD) and specific rainfall attenuation modeling in these African countries identified as equatorial (Butare) and subtropical (Durban) regions. The influence of the raindrop diameters that are critical to the DSD and specific rain attenuation at operating frequencies of 10–150 GHz is investigated using the estimated R0.01 values for Butare and Durban. Parameter fittings for the proposed DSD models at these locations for different rain rate values are investigated. The proposed drop size distribution models are also compared with those of other countries. At operating frequency range 10 ≤ f ≤ 40 GHz, the specific attenuation in Rwanda tends to be higher when compared to Durban. However, at frequency above 40 GHz, Durban shows a higher specific attenuation than Rwanda. The largest contributions to the overall specific rain attenuation are formed by drop diameters in the range 1.5 ≤ D ≤ 3.5 and 1.0 ≤ D ≤ 3.0 mm for Rwanda and South Africa, respectively, especially at higher frequencies. A minimal contribution is observed at the larger diameters. The influence of the disdrometer bins on the attenuation due to rain is also analyzed for these locations. The estimation will be useful to properly design adequate fade margin levels and for the purpose of link budget design by service providers and system engineers in the regions.

THE CRITICAL DIAMETERS FOR RAINFALL ATTENUATION IN SOUTHERN AFRICA

This paper investigates the in∞uence of critical raindrop diameters on the speciflc rain attenuation in Durban (29 - 52 0 S, 30 - 58 0 E), South Africa. The total rainfall attenuation is evaluated by integrating over all the raindrop sizes and the difierential change in the attenuation is observed over a given range of drop size diameters. The major contribution to the speciflc attenuation for the drop size distribution (DSD) models considered is created by the raindrop diameters not exceeding 2mm especially at higher frequencies. The three parameter lognormal and gamma distribution models are employed for the purpose of analysis. For the DSD models considered in this work, the total percentage fraction created by raindrops in the diameter range 0:5mmD • 2:5mm and 1mmD • 3mm to the total speciflc attenuation is found to be critical for the overall and seasonal rainfall attenuation at 2.5GHz{ 100GHz in Durban. It is observed that the total speciflc attenuation increases with increased frequencies and a higher rainfall rate produces high rain attenuation. In this paper, both the overall and seasonal values of R0:01 determined for Durban are used.

Tree-based genetic programming approach to infer microphysical parameters of the DSDs from the polarization diversity measurements

The use of polarization diversity measurements to infer the microphysical parametrization has remained an active goal in the radar remote sensing community. In view of this, the tree-based genetic programming (GP) as a novel approach has been presented for retrieving the governing microphysical parameters of a normalized gamma drop size distribution model D0 (median drop diameter), Nw (concentration parameter), and μ (shape parameter) from the polarization diversity measurements. A large number of raindrop spectra acquired from a Joss–Waldvogel disdrometer has been utilized to develop the GP models, relating the microphysical parameters to the T-matrix scattering simulated polarization measurements. Several functional formulations retrieving the microphysical parameters-D0 [f(ZDR), f(ZH, ZDR)], log10Nw [f(ZH, D0), f(ZH, ZDR, D0), and μ[f(ZDR, D0), f(ZH, ZDR, D0)], where ZH represents reflectivity and ZDR represents differential reflectivity, have been investigated, and applied to a S-band polarimetric radar (CAMRA) for evaluation. It has been shown that the GP model retrieved microphysical parameters from the polarization measurements are in a reasonable agreement with disdrometer observations. The calculated root mean squared errors (RMSE) are noted as 0.23–0.25mm for D0, 0.74–0.85 for log10Nw (Nw in mm−1 mm−3), and 3.30–3.36 for μ. The GP model based microphysical retrieval procedure is further compared with a physically based constrained gamma model for D0 and log10Nw estimates. The close agreement of the retrieval results between the GP and the constrained gamma models supports the suitability of the proposed genetic programming approach to infer microphysical parameterization.

Rain attenuation measurement and prediction on parallel 860-nm free space optical and 58-GHz millimeter-wave paths

Attenuation of electromagnetic waves at 860 nm and 58 GHz due to scattering in rain is measured on the terrestrial paths simultaneously with rain intensity. The relationship between rain intensity and rain attenuation of light is analyzed using the Marshal-Palmer drop size distribution model and the Mie scattering theory. The pertinent power law model is derived from drop size distribution parameters. An empirical composite power law model is proposed and fitted to the dataset extracted from rain attenuation events recorded during a seven-year experiment in Prague. Observed average rain attenuation of light at intensities larger than about 5 mm/h is lower than attenuation predicted by standard models. Rain attenuation measured at 58 GHz is larger than attenuation at 860 nm for rain intensities in the range from 0.1 to 100 mm/h.

Characteristics of raindrop spectra as normalized gamma distribution from a Joss–Waldvogel disdrometer

The raindrop spectra observed in a precipitation system is a complex phenomenon that can help to explain the underlying physical processes of rainfall. This paper explores the characteristics of raindrop spectra in terms of drop size distributions (DSD) using seven years of Joss–Waldvogel disdrometer data within the mid-latitude UK region climatology. A total of 162,415 one-minute “filtered” raindrop spectra obtained from the disdrometer are fitted into a normalized gamma DSD model describing DSDs by the concentration parameter (Nw), the drop diameter (Dm and D0), and the shape parameter (μ). The results show that the rain rates retrieved from the normalized gamma DSD model are in good agreement with the disdrometer measured rain rates, implying the appropriateness of the raindrop spectra as normalized gamma distributions. The DSD characteristics are studied in different seasonal (“cold” and “warm”), atmospheric (“dry” and “wet”) as well as rain type (“stratiform” and “convective”) contexts in a long-term perspective. It has been revealed that the normalized gamma DSD parameters are very sensitive to the rain intensities. The mass weighted mean drop diameter Dm clearly increases exponentially with respect to the rain intensities. Variation of the DSDs in different contexts is also exposed reflecting seasonal, atmospheric and rain type consequence on raindrop spectra. Particularly, the scatterplot between the concentration parameter log10Nw and the median drop diameter D0 exhibits clear separation index between stratiform and convective DSDs. There is a large difference in averaged mass weighted mean drop diameters among stratiform and convective segments (stratiform <Dm>=0.988mm versus convective <Dm>=1.99mm). The DSD inconsistency in different contexts have been further examined in terms of the Z–R relationships (Z=aRb) variability. Additionally, 10 selected events taken place during the study period are also investigated, in which each of the events has shown unique DSD characteristics.

REGIONAL VARIABILITY OF RAIN DROP SIZE DISTRIBUTION MODEL IN INDIA

Present study shows the development of integrated rain drop size distribution (DSD) model and gives a comparative study with DSDs of difierent regions in India. This work is useful for estimation of rain induced attenuation. Rain data of flve difierent regions (Ahmedabad, Shillong, Thiruvananthapuram, Kharagpur and Hasan) was used for this work. Attenuation characteristics are difierent for difierent regions because DSD varies according to the climatic conditions. Development of DSD model for each location is not feasible. It is a demand to develop a integrated DSD model which gives the tolerable error in DSD for difierent regions, so that, it can be adjusted in fade margin of the communication system. The result of this work shows the good correlation between the proposed integrated DSD model and DSDs of difierent regions.