Raindrop Size Distribution Model Research Articles

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

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.

Microphysics of Stratiform and Convective Precipitation During Meiyu Season in Eastern China

AbstractThe microphysical structure of Meiyu precipitation in Eastern China is investigated using two‐dimensional video disdrometer (2DVD) and S‐band polarimetric radar observations. The constrained‐gamma raindrop size distribution (DSD) model derived from 2DVD observations performs well in representing Meiyu DSDs. The vertical variability of polarimetric variables and retrieved DSD parameters are then investigated. The results show different patterns of vertical behavior for convective and stratiform rain due to different ice‐phase and precipitation microphysical processes. The radar reflectivity of stratiform rain presents a distinct bright band (with an average echo top between 6 and 7 km). In contrast, the convective rain shows a larger reflectivity with a relatively higher echo top at 8 km. Polarimetric signatures of convective rain above the 0°C isotherm imply the coexistence of rimed particles and aggregates, which is indispensable for the intense precipitation on the ground. However, with a bulk precipitation formed below the melting layer, warm rain processes are still critical pathways for the growth of raindrops and the subsequent generation of heavy rainfall. Furthermore, both convective and stratiform rain is dominated by raindrops <4 mm, and the increase in their rain intensity can mostly be attributed to the increase in raindrop concentration. The identified maritime nature of convective rain has a much higher (roughly more than two times) number concentration of raindrops than that of convection in a similar climate region. This study provides a more comprehensive picture of Meiyu precipitation microphysics in Eastern China.

Estimating raindrop size distributions using microwave link measurements: potential and limitations

Abstract. We present a novel method of using two or three collocated microwave link instruments to estimate the three parameters of a gamma raindrop size distribution (DSD) model. This allows path-average DSD measurements over a path length of several kilometers as opposed to the point measurements of conventional disdrometers. Our method is validated in a round-trip manner using simulated DSD fields as well as five laser disdrometers installed along a path. Different potential link combinations of frequency and polarization are investigated. We also present preliminary results from the application of this method to an experimental setup of collocated microwave links measuring at 26 and 38 GHz along a 2.2 km path. Simulations show that a DSD retrieval on the basis of microwave links can be accurate under idealized conditions. We found that a triple-link retrieval provides little added benefit over a dual-link retrieval in terms of accuracy or precision. In practice, the accuracy and success rate of any retrieval is highly dependent on the stability of the base power level as well as the precision of the instruments and in particular the quantization applied to the recorded power level.

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.

Attenuation relations for monsoonal rain at the X band from disdrometric measurements: Dependency on temperature, raindrop size distribution and drop shape models

Four years of disdrometric measurements made at Gadanki (13.5°N, 79.18°E), which receives rainfall during both southwest and northeast monsoons, have been used to (a) derive optimal attenuation relations for monsoonal rainfall at the X band, (b) study the impact of seasonal variation in raindrop size distribution (DSD) on attenuation relations and (c) analyze the dependency of these relations on the controlling parameters/models, such as temperature (T) and drop shape model. The results clearly show that the coefficients of these relations vary significantly with DSD (season and rain type), T and drop shape model, and are quite different for monsoonal rain than for those obtained elsewhere. The traditional relations that involve a specific attenuation (AH)‐reflectivity factor at horizontal polarization (ZH) and AH‐rain rate depend heavily on DSD and to some extent on T, while the relations involving a specific differential phase (KDP) and differential attenuation (ADP) show strong dependency on the drop shape model and DSD, but depend weakly on T. A detailed investigation has been carried out to decipher reasons for the observed intriguing seasonal variation in KDP‐based relations and their temperature dependency. The resonance scattering effects that are thought to be negligible at the X band in earlier studies appear to play a dominant role here and are primarily responsible for the observed features.

GNSS Measurement of Rain Rate by Polarimetric Phase Shift: Theoretical Analysis

In this paper, a novel method for rain rate estimation is researched by polarimetric phase shift of the Global Navigation Satellite System (GNSS). The physical process of GNSS signals propagating through rain-filled medium is investigated, by which the cause of polarimetric phase shift is explored. Then, a theoretical model between polarimetric phase shift Δ ϕ and rain rate R is established and simulated, which is based on the oblate spheroid raindrop model, four different popular raindrop size distribution models and raindrop canting angle distribution across the Space-Earth rain path. Additionally, effects of raindrop size distribution, rain path length, raindrop canting angle and temperature on the Δ ϕ -R relation are discussed systematically. Other factors in the slant path such as ice crystals, melting particles and ionosphere are also researched preliminarily. The results show that polarimetric phase shift of GNSS signals, which has a strong correlation with rain rate, can be used to estimate the rain rate, and these influencing factors, raindrop size distribution, rain path length, raindrop canting angle and temperature, are quite important in the process of rain rate measurement. It can be also found that the effect of ice crystals can be negligible, while that of melting particles should be considered, and though ionosphere effects are not obvious, the ionospheric anomalies cannot be neglected in future experiments. This method has potential applications in real-time, continuous, extreme precipitation reconnaissance and numerical weather prediction.

Estimation of Raindrop Size Distribution and Rainfall Rate from Polarimetric Radar Measurements at Attenuating Frequency Based on the Self-Consistency Principle

A method for estimating three parameters of a gamma raindrop size distribution (DSD) model and the rainfall rate from polarimetric radar at attenuating frequency was developed. The algorithm was developed based on the self-consistency principle but was expanded to consider the attenuation effect by describing the interrelation between polarimetric measurements along the range profile. The proposed method does not require any assumptions of relation among DSD parameters or simplifications of equations that describe the relation between the axis ratio and diameter of raindrops, which have been used in previous studies. Moreover, the proposed algorithm needs no external reference data such as two-dimensional video disdrometer measurements for attenuation corrections because it retrieves the co-polar and differential specific attenuation from the interrelation among the polarimetric measurements. The performance of this algorithm was evaluated by comparison with optical disdrometers and a weighing precipitation gauge. The evaluation of the algorithm showed that the retrieved three DSD parameters of raindrops, reflectivity, and differential reflectivity from actual C-band polarimetric radar data have fairly good agreement with those obtained by surface measurements. Moreover, rainfall rates retrieved using this algorithm have comparable precision with those estimated from the specific differential phase, and outperform those estimated through the so-called Z-R relation, particularly during heavy rainfall. Furthermore, the effects of raindrop temperature and shape parameter on the retrieval of the rainfall rate were examined. The results show that for radar operating at C-band, a raindrop temperature error of 10°C may be negligible in rainfall rate estimations, whereas a shape parameter error of 2 may increase the error of the rainfall rate estimation by 10 %.

A method for estimating rain rate from polarimetric GNSS measurements: Preliminary analysis

Rain rate is measured by a rain gauge, radar reflectivity and special differential phase shift traditionally. In this paper, a new way of estimating rain rate using rain-induced depolarization characteristics of Global Navigation Satellite System (GNSS) signals was studied. Using the cross-polarization discrimination (XPD) which is defined to describe the effect of depolarization, the relationship between XPD and rain rate (R) was presented based on the oblate spheroid raindrop model and Marshall–Palmer raindrop size distribution model. The sensibility of XPD with rain rate, rain path length and elevation of GNSS satellites was simulated systematically. Simulation results show that XPD is sensitive to rain rate and the XPD–R relation can be employed to evaluate the rain rate. The novel method for real-time, continuous, regional detection of rain rate explored in this paper will find applications in the nowcasting automated detection of global heavy rain reconnaissance.

OBTAINING RAINDROP SIZE MODEL USING METHOD OF MOMENT AND ITS APPLICATIONS FOR SOUTH AFRICA RADIO SYSTEMS

In this paper, the Raindrop Size Distribution (DSD) modeling and analysis are presented. Drop sizes are classifled into difierent rain types, namely: drizzle, widespread, shower and thunderstorm. The gamma and Lognormal distribution models are employed using the method of moments estimator, considering the third, fourth and sixth order moments. The results are compared with the existing raindrop size distribution models such as the three parameter lognormal distribution proposed by Ajayi and his colleagues and Singapore's modifled gamma and Lognormal models. This is then followed by the implementation of the proposed raindrop size distribution models on the computation of the speciflc rain attenuation. Finally, the paper suggests a suitable raindrop size distribution model for the region with its expressions. The proposed models are very useful for the determination of rain attenuation for terrestrial and satellite systems.

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.

Understanding the Variability of Z-R Relationships Caused by Natural Variations in Raindrop Size Distributions (DSD): Implication of Drop Size and Number

In the issue of rainfall estimation by radar through the necessary relationship between radar reflectivity Z and rain rate R (Z-R), the main limitation is attributed to the variability of this relationship. Indeed, several pre-vious studies have shown the great variability of this relationship in space and time, from a rainfall event to another and even within a single rainfall event. Recent studies have shown that the variability of raindrop size distributions and thereby Z-R relationships is therefore, more the result of complex dynamic, thermody-namic and microphysical processes within rainfall systems than a convective/stratiform classification of the ground rainfall signature. The raindrop number and size at ground being the resultant of various processes mentioned above, a suitable approach would be to analyze their variability in relation to that of Z-R relation-ship. In this study, we investigated the total raindrop concentration number NT and the median volume di-ameter D0 used in numerous studies, and have shown that the combination of these two ‘observed’ parame-ters appears to be an interesting approach to better understand the variability of the Z-R relationships in the rainfall events, without assuming a certain analytical raindrop size distribution model (exponential, gamma, or log-normal). The present study is based on the analysis of disdrometer data collected at different seasons and places in Africa, and aims to show the degree of the raindrop size and number implication in regard to the Z-R relationships variability.

Estimation of N*0 for the Two-Scale Gamma Raindrop Size Distribution Model and Its Statistical Properties at Several Locations in Asia

Abstract An automatic estimation method is developed to detect stepwise changes in the amplitude parameter of the normalized raindrop size distribution (DSD) N*0. To estimate N*0, it is also assumed that the variation of three DSD parameters follows the two-scale gamma DSD model; this is defined as a DSD model in which one DSD parameter is fixed, the second is allowed to vary rapidly, and the third is constant over a certain space or time domain and sometimes exhibits stepwise transitions. For this study, it is assumed that N*0 is the third DSD parameter. To estimate this stepwise-varying parameter automatically, a non-Gaussian state-space model is used for the time series of log10N*0. The smoothed time series of log10N*0 fit well to the stepwise transition of log10N*0 when it was assumed that the state transition probability follows a Cauchy distribution. By analyzing the long-term disdrometer data using this state-space model, statistical properties for log10N*0 are obtained at several Asian locations. It is confirmed that the N*0 thus estimated is useful to improve the rain-rate estimation from the measurement of radar reflectivity factor.

A relationship between rain radar reflectivity and height elevation variance of ringwaves due to the impact of rain on the sea surface

Raindrops impacting the rough sea modify its surface and its backscattering coefficient. This roughness change essentially depends on the rain content in very large drops, which is highly variable from one drop size distribution model to another. However, it has been observed that the radar reflectivity of raindrops has a drop size dependence very similar to that of the ringwaves induced by rain on the surface. From a numerical analysis on various drop size distributions, rain rates, and frequencies from 3 to 35 GHz, a relationship between the sea surface elevation variance of ringwaves resulting from drop impact and the rain radar reflectivity Z is established. It is found to be weakly dependent on the raindrop size distribution model. This link is expected to lead to better estimates of the surface roughness, and in turn, via electromagnetic scattering models, it could improve algorithms for near nadir rain radar retrieval.

Raindrop Size Distribution Modeling from a Statistical Rain Parameter Relation and Its Application to the TRMM Precipitation Radar Rain Retrieval Algorithm

AbstractA generalized method is presented to derive a “two scale” raindrop size distribution (DSD) model over a spatial or temporal domain in which a statistical rain parameter relation exists. The two-scale model is generally defined as a model in which one DSD parameter is allowed to vary rapidly and the other is constant over a certain space or time domain. The existence of a rain parameter relation such as the radar reflectivity–rainfall rate (Z–R) relation over a spatial or temporal domain is an example of such a two-scale DSD model. A procedure is described that employs a statistical rain parameter relation with an assumption of the gamma DSD model. An example using Z–R relations obtained at Kototabang, West Sumatra, is presented. The result shows that the resulting two-scale DSD model expressed by conventional DSD parameters depends on the assumed value of parameter μ while rain parameter relations such as k–Ze relations from those models using different μ values are very close to each other, indicating the stability of the model against the variation of μ and the validity of this method. The result is applied to the DSD model for the Tropical Rainfall Measuring Mission (TRMM) precipitation radar 2A25 (versions 5 and 6) algorithm. The derivation procedure of the 2A25 DSD model is described. Through the application of this model, it has become possible to make a logically well-organized rain profiling algorithm and reasonable rain attenuation correction and rainfall estimates, as described in an earlier paper by Iguchi et al.

Microphysical cross validation of spaceborne radar and ground polarimetric radar

Ground-based polarimetric radar observations along the beam path of the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), matched in resolution volume and aligned to PR measurements, are used to estimate the parameters of a gamma raindrop size distribution (RSD) model along the radar beam in the presence of rain. The PR operates at 13.8 GHz, and its signal returns can undergo significant attenuation due to rain, which requires compensation to adequately assess the rain rate. The current PR algorithm used for attenuation correction of the reflectivity is cross-validated using ground-based dual-polarization radar measurements. Data from the Texas and Florida Underflights (TEFLUN-B) campaign and TRMM Large-scale Biosphere Atmosphere (LBA) experiment are used in the analysis. The statistical behavior of the raindrop size distribution parameters are presented along the vertical profile through the rain layer, which is used to evaluate the PR attenuation correction and rainfall algorithms. The PR rain rate estimates are compared to ground radar estimates. The standard error of the difference between the rainfall estimates from PR and ground radar was within the error of the rainfall estimates from the two instruments. Though no systematic differences between PR attenuation-corrected reflectivity and ground radar reflectivity measurements are observed, there may exist some undercorrection and overcorrection on a beam-by-beam basis. Comparison of the normalized reflectivity versus rainfall relation between PR and ground polarimetric radar is also presented.

Estimation of Raindrop Size Distribution Parameters from Polarimetric Radar Measurements

Estimation of raindrop size distribution over large spatial and temporal scales has been a long-standing goal of polarimetric radar. Algorithms to estimate the parameters of a gamma raindrop size distribution model from polarimetric radar observations of reflectivity, differential reflectivity, and specific differential phase are developed. Differential reflectivity is the most closely related measurement to a parameter of the drop size distribution, namely, the drop median diameter (D0). The estimator for D0 as well as other parameters are evaluated in the presence of radar measurement errors. It is shown that the drop median diameter can be estimated to an accuracy of 10%, whereas the equivalent intercept parameter can be estimated to an accuracy of 6% in the logarithmic scale. The estimators for the raindrop size distribution parameters are also evaluated using disdrometer data based simulations. The disdrometer based evaluations confirm the accuracy of the algorithms developed herein.

A Methodology for Estimating the Parameters of a Gamma Raindrop Size Distribution Model from Polarimetric Radar Data: Application to a Squall-Line Event from the TRMM/Brazil Campaign

Abstract A methodology is proposed for estimating the parameters of a gamma raindrop size distribution model from radar measurements of Zh, Zdr, and Kdp at S band. Previously developed algorithms by Gorgucci et al. are extended to cover low rain-rate events where both Zdr and Kdp are noisy. Polarimetric data from the S-band Dual-Polarization Doppler Radar (S-Pol) during the Tropical Rainfall Measuring Mission (TRMM)/Brazil campaign are analyzed; specifically, the gamma parameters are retrieved for samples of convective and trailing stratiform rain during the 15 February 1999 squall-line event. Histograms of Nw and Do are retrieved from radar for each rain type and compared with related statistics reported in the literature. The functional behavior of Nw and Do versus rain rate retrieved from radar is compared against samples of 2D-video and RD-69 disdrometer data obtained during the campaign. The time variation of Nw, Do, and μ averaged over a 5 km × 5 km area (within which a network of gauges and a profi...

Tropical raindrop size distribution for the prediction of rain attenuation of microwaves in the 10-40 GHz band

This paper describes the measurement of microwave rain attenuation over a ten-year period (1988-1998) in Singapore. The rain attenuation of (vertically and horizontally polarized) microwaves at 15, 21, and 38 GHz propagating over a path length of approximately 1.1 km were recorded. A negative-exponential raindrop size distribution model is then developed by fitting of the experimental data with the total extinction cross sections of oblate spheroidal raindrops computed from the T-matrix approach. Graphs for attenuation versus rain rate (at selected frequencies) and for attenuation versus frequency (at selected rain rates) are also given.

Retrieval of Raindrop Size Distributions Using Two Doppler Wind Profilers: Model Sensitivity Testing

Abstract The behavior of precipitation is of great importance in obtaining a better understanding of heat transport estimates and global processes in the atmosphere. This paper discusses improvements in an earlier raindrop size distribution model that utilizes two Doppler wind profilers to obtain accurate measurements of rainfall. A UHF Doppler wind profiler provides a precipitation return while a VHF Doppler wind profiler provides vertical clear-air velocities. The model is tested using simulated data. Sensitivity tests examine the model's ability to estimate rainfall characteristics given typical (noisy) Doppler spectra, and the model's sensitivity to atmospheric parameters. Because it is necessary to estimate pressure, temperature, raindrop temperature, and water vapor pressure at the location of the radar volume, the sensitivity tests examine the effects of errors in the estimates of these parameters. Sensitivity testing of the raindrop size distribution model with simulated data indicates model accur...

Comment on raindrop size distribution model

The parameter set for the exponential raindrop size distribution model presented by Yeo, Kooi and Leong (see ibid. vol.41, P.709, 1993) was derived using a data set measured in Singapore. A limitation to the model is that it is accurate only for small rain rate or when the rain medium consists predominantly of small droplets with diameter D is >