Raindrop Size Distribution Retrieval Research Articles

Raindrop Size Distribution Retrieval Model for X-Band Dual-Polarization Radar in China Incorporating Various Climatic and Geographical Elements

The X-band dual-polarization radar can provide raindrop size distribution (DSD) data at a continuous spatiotemporal scale; however, the traditional empirical-formula-based DSD retrieval methods for X-band radar are limited by high uncertainty and poor generality such as differences due to rainfall type, seasons, and geographical environment. This study identified strong correlations between polarimetric radar variables and various climatic and geographical elements. Two random-forest-based DSD retrieval models, one using only X-band radar parameters as the model input (RF-DSD) and the other containing multielement inputs as well (RF-M-DSD), were established using datasets from 18 sites in China. This study also evaluated the proposed models using different error indices over three test sites. Compared with the traditional DSD retrieval model for X-band dual-polarization radar, RF-DSD and RF-M-DSD showed improved predictive ability for all DSD parameters. The root-mean-square error (RMSE) values for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D_{0}$ </tex-math></inline-formula> (median volume diameter parameter), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\text {log}}_{10}N_{w}$ </tex-math></inline-formula> (normalized intercept parameter), and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> (shape parameter) were 27%, 55%, and 39% lower, respectively, for RF-DSD, and 48%, 68%, and 43% lower, respectively, for RF-M-DSD. Finally, the DSD retrieval models were applied on one CLA-12A X-band radar in the Jiangsu Province. The DSD retrieval results suggest that the proposed models perform well on radar observation data with low uncertainty especially for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D_{0}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\text {log}}_{10}N_{w}$ </tex-math></inline-formula> . Summary reveals that the RF-M-DSD performs superior and has stable DSD retrieval capabilities across different geographical areas, which can provide reliable radar-DSD retrieval data for areas with scarce disdrometer data.

Retrieval of Raindrop Size Distribution Using Dual-Polarized Microwave Signals from LEO Satellites: A Feasibility Study through Simulations.

In this paper, a novel approach for raindrop size distribution retrieval using dual-polarized microwave signals from low Earth orbit satellites is proposed. The feasibility of this approach is studied through modelling and simulating the retrieval system which includes multiple ground receivers equipped with signal-to-noise ratio estimators and a low Earth orbit satellite communicating with the receivers using both vertically and horizontally polarized signals. Our analysis suggests that the dual-polarized links offer the opportunity to estimate two independent raindrop size distribution parameters. To achieve that, the vertical and horizontal polarization attenuations need to be measured at low elevation angles where the difference between them is more distinct. Two synthetic rain fields are generated to test the performance of the retrieval. Simulation results suggest that the specific attenuations for both link types can be retrieved through a least-squares algorithm. They also confirm that the specific attenuation ratio of vertically to horizontally polarized signals can be used to retrieve the slope and intercept parameters of raindrop size distribution.

Analysis of the Vertical Air Motions and Raindrop Size Distribution Retrievals of a Squall Line Based on Cloud Radar Doppler Spectral Density Data

A squall line is a type of strongly organized mesoscale convective system that can cause severe weather disasters. Thus, it is crucial to explore the dynamic structure and hydrometeor distributions in squall lines. This study analyzed a squall line over Guangdong Province on 6 May 2016 that was observed using a Ka-band millimeter-wave cloud radar (CR) and an S-band dual-polarization radar (PR). Doppler spectral density data obtained by the CR were used to retrieve the vertical air motions and raindrop size distribution (DSD). The results showed the following: First, the CR detected detailed vertical profiles and their evolution before and during the squall line passage. In the convection time segment (segment B), heavy rain existed with a reflectivity factor exceeding 35 dBZ and a velocity spectrum width exceeding 1.3 m s−1. In the PR detection, the differential reflectivity factor (Zdr) was 1–2 dB, and the large specific differential phase (Kdp) also represented large liquid water content. In the transition and stratiform cloud time segments (segments B and C), the rain stabilized gradually, with decreasing cloud tops, stable precipitation, and a 0 °C layer bright band. Smaller Kdp values (less than 0.9) were distributed around the 0 °C layer, which may have been caused by the melting of ice crystal particles. Second, from the CR-retrieved vertical air velocity, before squall line passage, downdrafts dominated in local convection and weak updrafts existed in higher-altitude altostratus clouds. In segment B, the updraft air velocity reached more than 8 m s−1 below the 0 °C layer. From segments C to D, the updrafts changed gradually into weak and wide-ranging downdrafts. Third, in the comparison of DSD values retrieved at 1.5 km and DSD values on the ground, the retrieved DSD line was lower than the disdrometer, the overall magnitude of the DSD retrieved was smaller, and the difference decreased from segments C to D. The standardized intercept parameter (Nw) and shape parameter (μ) of the DSD retrieved at 1.8 km showed good agreement with the disdrometer results, and the mass-weighted mean diameter (Dm) was smaller than that on the ground, but very close to the PR-retrieved Dm result at 2 km. Therefore, comparing with the DSD retrieved at around 2 km, the overall number concentration remained unchanged and Dm got larger on the ground, possibly reflecting the process of raindrop coalescence. Lastly, the average vertical profiles of several quantities in all segments showed that, first of all, the decrease of Nw and Dm with height in segments C and D was similar, reflecting the collision effect of falling raindrops. The trends were opposite in segment B, indicating that raindrops underwent intense mixing and rapid collision and growth in this segment. Then, PR-retrieved Dm profiles can verify the rationality of the CR-retrieved Dm. Finally, a vertical velocity profile peak generated a larger Dm especially in segments C and D.

Optimized raindrop size distribution retrieval and quantitative rainfall estimation from polarimetric radar

A variational approach for optimized drop size distribution (DSD) retrieval, attenuation correction, and rainfall estimation from polarimetric radar measurements (horizontal reflectivity factor ZH, differential reflectivity ZDR, and differential phase shift ΦDP) is proposed in this study. The spatial continuity of rain is guaranteed by introducing the radial B-spine filter and azimuthal Kalman filter, which helps to mitigate the impact of the random errors in ZDR and ΦDP. The approach is evaluated using a simulated experiment and two real cases observed by a mobile C-band and an operational S-band polarimetric radar in south China. The comparative results demonstrate that the proposed variational approach can correct attenuation more accurately than the conventional method using assumed linear relationships between specific attenuation and specific differential phase. The rainfalls derived from the DSD estimates based on this proposed approach agree well with the rain gauge measurements. It is also shown that the proposed method has a better performance than the existing variational retrieval and the composite estimator.

Recent Progress in Dual-Polarization Radar Research and Applications in China

Dual-polarization (dual-pol) radar can measure additional parameters that provide more microphysical information of precipitation systems than those provided by conventional Doppler radar. The dual-pol parameters have been successfully utilized to investigate precipitation microphysics and improve radar quantitative precipitation estimation (QPE). The recent progress in dual-pol radar research and applications in China is summarized in four aspects. Firstly, the characteristics of several representative dual-pol radars are reviewed. Various approaches have been developed for radar data quality control, including calibration, attenuation correction, calculation of specific differential phase shift, and identification and removal of non-meteorological echoes. Using dual-pol radar measurements, the microphysical characteristics derived from raindrop size distribution retrieval, hydrometeor classification, and QPE is better understood in China. The limited number of studies in China that have sought to use dual-pol radar data to validate the microphysical parameterization and initialization of numerical models and assimilate dual-pol data into numerical models are summarized. The challenges of applying dual-pol data in numerical models and emerging technologies that may make significant impacts on the field of radar meteorology are discussed.

Raindrop Size Distribution Retrieval Using Joint Dual-Frequency and Dual-Polarization Microwave Links

Estimation of raindrop size distribution (DSD) is essential in many meteorological and hydrologic fields. This paper proposes a method for retrieving path-averaged DSD parameters using joint dual-frequency and dual-polarization microwave links of the telecommunication system. Detailed analyses of the rain-induced attenuation calculation are performed based on the T-matrix method. A forward model is established for describing the relation between the DSD and the rain-induced attenuation. Then, the method is proposed to retrieve propagation path DSD parameters based on Levenberg–Marquardt optimization algorithm. The numerical simulation for path-averaged DSD retrieval shows that the RMSEs of three gamma DSD parameters are 0.34 mm−1, 0.81, and 3.21×103 m−3·mm−1, respectively, in rainfall intensity above 30 mm/h. Meanwhile, the method can retrieve the rainfall intensity without the influence of variational DSD. Theoretical analyses and numerical simulations confirm that the method for retrieving path-averaged DSD parameters is promising. The method can complement existing DSD monitoring systems such as the disdrometer and provide high-resolution rainfall measurements with widely distributed microwave links without additional cost.

High-Precision Measurements of the Copolar Correlation Coefficient: Non-Gaussian Errors and Retrieval of the Dispersion Parameter μ in Rainfall

AbstractThe copolar correlation coefficient ρhv has many applications, including hydrometeor classification, ground clutter and melting-layer identification, interpretation of ice microphysics, and the retrieval of raindrop size distributions (DSDs). However, the quantitative error estimates that are necessary if these applications are to be fully exploited are currently lacking. Previous error estimates of ρhv rely on knowledge of the unknown “true” ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. Frequency distributions of ρhv estimates are in fact shown to be highly negatively skewed. A new variable, = log10(1 − ρhv), is defined that does have Gaussian error statistics and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, the manner in which the imperfect collocation of the horizontal and vertical polarization sample volumes may be accounted for is demonstrated. The possibility of using L to estimate the dispersion parameter μ in the gamma drop size distribution is investigated. Including drop oscillations is found to be essential for this application; otherwise, there could be biases in retrieved μ of up to approximately 8. Preliminary results in rainfall are presented. In a convective rain case study, the estimates presented herein show μ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

High-Resolution Raindrop Size Distribution Retrieval Based on the Doppler Spectrum in the Case of Slant Profiling Radar

AbstractDoppler spectra from vertically profiling radars are usually considered to retrieve the raindrop size distribution (DSD). However, to exploit both fall velocity spectrum and polarimetric measurements, Doppler spectra acquired in slant profiling mode should be explored. Rain DSD samples are obtained from simultaneously measured vertical and slant profile Doppler spectra and evaluated. In particular, the effect of the horizontal wind and the averaging time are investigated.The Doppler spectrum provides a way to retrieve the DSD, the radial wind, and a spectral broadening factor by means of a nonlinear optimization technique. For slant profiling of light rain when the horizontal wind is strong, the DSD results can be affected. Such an effect is demonstrated on a study case of stratiform light rain. Adding a wind profiler mode to the radar simultaneously supplies the horizontal wind and Doppler spectra. Before the retrieval procedure, the Doppler spectra are shifted in velocity to remove the mean horizontal wind contribution. The DSD results are considerably improved.Generally, averaged Doppler spectra are input into this type of algorithm. Instead, high-resolution, low-averaged Doppler spectra are chosen in order to take into account the small-scale variability of the rainfall. Investigating the linear relations at fixed median volume diameter, measured reflectivity-retrieved rainfall rate, for a slant beam, the consistency of the integrated parameters is established for two averaging periods. Nevertheless, the corresponding DSD parameter distributions reveal differences attributed to the averaging of the Doppler spectra.The new aspects are to obtain the same retrieval quality as vertically profiling and highly averaged spectra in an automated way.

Analysis of the microphysical properties of a stratiform rain event using an L-Band profiler radar

This paper investigates spatial and temporal distributions of the microphysical properties of precipitating stratiform clouds based on Doppler spectra of rain particles observed by an L-band profiler radar. The retrieval of raindrop size distributions (RSDs) is accomplished through eliminating vertical air motion and isolating the terminal fall velocity of raindrops in the observed Doppler velocity spectrum. The microphysical properties of raindrops in a broad stratiform region with weak convective cells are studied using data collected from a 1320-MHz wind profiler radar in Huayin, Shaanxi Province on 14 May 2009. RSDs and gamma function parameters are retrieved at altitudes between 700 and 3000 m above the surface, below a melting layer. It is found that the altitude of the maximum number of raindrops was closely related to the surface rain rate. The maximum number of large drops was observed at lower altitudes earlier in the precipitation event but at higher altitudes in later periods, suggesting decreases in the numbers of large and medium size raindrops. These decreases may have been caused by the breakup of larger drops and evaporation of smaller drops as they fell. The number of medium size drops decreased with increasing altitude. The relationship between reflectivity and liquid water content during this precipitation event was Z = 1.69×104 M 1.5, and the relationship between reflectivity and rain intensity was Z = 256I 1.4.

Raindrop Size Distribution Retrieval From Dual-Frequency and Dual-Polarization Radar

Differential reflectivity from dual-polarization radars at frequencies such as S- and C-bands has been used to estimate the median drop diameter. Similarly, the dual-frequency ratio (DFR) can also be used to estimate median drop diameter. This paper presents an algorithm for estimating the raindrop size distribution parameters of median drop diameter ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) and equivalent intercept parameter ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nw</i> ) using a dual-polarization dual-frequency ground radar operating at Ku- and Ka-bands. The retrieval philosophy is based on combining attributes of the DFR, historically used in spaceborne radar systems and dual-polarization approaches used in ground radar algorithms. The estimator of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> as well as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nw</i> (in the logarithmic scale) are evaluated using simulated radar observations in the presence of different error sources. It is shown that normalized bias and standard error for two estimators are both within ±2% and 16% when system noise is added. The situation when Ka-band observations are extinct during heavy precipitation is also considered.

POTENTIAL ROLE OF DUAL-POLARIZATION RADAR IN THE VALIDATION OF SATELLITE PRECIPITATION MEASUREMENTS

Dual-polarization weather radars have evolved significantly in the last three decades culminating in operational deployment by the National Weather Service. In addition to operational applications in the weather service, dual-polarization radars have shown significant potential in contributing to the research fields of ground-based remote sensing of rainfall microphysics, the study of precipitation evolution, and hydrometeor classification. Microphysical characterization of precipitation and quantitative precipitation estimation are important applications that are critical in the validation of satellite-borne precipitation measurements and also serve as valuable tools in algorithm development. This paper presents the important role played by dual-polarization radar in validating spaceborne precipitation measurements. Examples of raindrop size distribution retrievals and hydrometeor-type classification are discussed. The quantitative precipitation estimation is a product of direct relevance to spaceborne o...

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

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.

Raindrop Size Distribution Retrievals from a VHF Boundary Layer Profiler

Abstract The retrieval of raindrop size distributions (DSDs) in precipitation using boundary layer wind profiler operating at VHF is described. To make the retrievals, a Fourier transform–based deconvolution technique, optimized to run with little human input, is used. The sensitivities of the technique and its overall accuracy are investigated using simulated spectra. The retrievals have an error that depends on the drop diameter, with relative errors varying between ∼10% and 35%. An overall average negative bias of about ∼20% is also found. The magnitude and direction of this bias depend on the spectral width of the input spectrum. The radar and methodology are applied to a case study of a convective cell. Retrievals are made with ∼300 m resolution between 800 and 4600 m. The temporal resolution is 2 min. Comparisons with a rain gauge show that both the magnitude and timing of the precipitation are well captured by the radar. The relationship between the observed rain rate and exponential fits applied t...

A General Approach to the Retrieval of Raindrop Size Distributions from Wind Profiler Doppler Spectra: Modeling Results

Abstract A technique is described that allows estimates of the raindrop size distribution to be obtained from the Doppler spectra measured by wind-profiling radars. The method makes no a priori assumptions regarding the shape of the drop size distributions. To test the accuracy of the technique, artificial data with realistic statistical properties have been generated and the shape of the model drop size distribution varied, The analysis technique obtains an accuracy of around 10% in the drop size range between 1 and 4 mm for data consistent with typical 50-MHz observations averaged over 5–10 min. There are limitations outside this range and the physical reasons for these are discussed. Simulations with multiple-peaked distributions show that the technique can also well resolve complicated distributions