Raindrop Size Distribution Parameters Research Articles

Comparison of Simulated Warm‐Rain Microphysical Processes in a Record‐Breaking Rainfall Event Using Polarimetric Radar Observations

AbstractDuring 6–7 May 2017, a record‐breaking nocturnal rainfall event occurred in Guangzhou, China, and it was a typical warm‐sector heavy rainfall event under weak synoptic forcing. A prior observational study by the authors revealed that warm‐rain microphysical processes were dominant and responsible for the record‐breaking precipitation. In this study, the double‐moment Morrison, Thompson and NSSL microphysics schemes in WRF are evaluated against polarimetric radar observations in their ability of reproducing observed microphysical characteristics. The Thompson scheme shows the greatest fidelity to the observed raindrop size distribution (RSD) median value, corresponding to the most amount of precipitation forecast. While the Morrison and NSSL simulations overestimate (underestimate) the raindrop size (number concentration), exhibiting continental‐type convective precipitation. The three experiments slightly overestimate differential reflectivity (ZDR), but significantly underestimate specific differential phase (KDP) and liquid water content by about 30%–50%, implying the undervaluation of number of medium‐sized raindrops. Examinations of the occurrence frequencies of ZDR, KDP, mass‐weighted diameter, and logarithmic normalized intercept parameter for rain suggest that all three schemes fail to reproduce the full variability of observed RSD for the extreme rainfall. The vertical variations of RSD parameters and the Kumjian‐Ryzhkov parameter space suggest that the collision–coalescence is the dominant warm‐rain microphysical process but the simulated process is too weak. This may be attributed to the misrepresented RSD near the melting layer, where the raindrops with lower number concentration and larger sizes cannot grow through the collision–coalescence process as actively.

Influence of raindrop size distribution variations on the rain specific attenuation coefficients

The raindrop size distribution is one of main term to evaluate microwave attenuation due to rainfall. In this paper, the lognormal distribution is introduced to represent the raindrop-size distribution based on the measurement performed at the Chungnam National University. Since the distribution parameters are strongly scattered around the fitted value, we developed a new statistical model for the lognormal distribution parameters. Based on the new statistical model for raindrop size distribution parameters we have estimated influence of raindrop size distribution variations on the rain specific attenuation coefficients.

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.

Characteristics of Raindrop Size Distribution in Typhoon Nida (2016) before and after Landfall in Southern China from 2D Video Disdrometer Data

During the passage of Typhoon Nida, the raindrop size distribution parameters, the raindrop spectra, the shape and slope (μ–Λ) relationship, the radar reflectivity factor, and rain rate (Z–R) relationship were investigated based on a two-dimensional (2D) video disdrometer in Guangdong, China, from August 1 to 2, 2016. Due to the underlying surface difference between the ocean and land, this process was divided into two distinct periods (before landfall and after landfall). The characteristics of raindrop size distribution between the period before landfall and the period after landfall were quite distinct. The period after landfall exhibited higher concentrations of each size bin (particularly small drops) and wider raindrop spectral width than the period before landfall. Compared with the period before landfall, the period after landfall had a higher average mass-weighted mean diameter Dm that was smaller than those of other TCs from the same ocean (the Pacific). The μ–Λ relationship and Z–R relationship in this study were also compared with other TCs from the same ocean (the Pacific). This investigation of the microphysical characteristics of Typhoon Nida before landfall and after landfall may improve radar quantitative precipitation estimation (QPE) products and microphysical schemes by providing useful information.

An Inverse Mapping Table Method for Raindrop Size Distribution Parameters Retrieval Using X-band Dual-Polarization Radar Observations

An inverse mapping table (IMT) method is proposed in this article to retrieve the raindrop size distribution (RSD) parameters from X-band polarimetric weather radar data. In the IMT method, a forward mapping database from three parameters of a gamma-type RSD to polarimetric radar variables is first built based on the scattering simulations under ideal atmospheric conditions, and then an inverse mapping database is derived. In particular, given a fixed shape parameter ( $\mu $ ) of RSD, the intersection of horizontal reflectivity ( $Z_{\text {H}}$ ) and differential reflectivity ( $Z_{\text {DR}}$ ) contour lines is first obtained in the domain of total number concentration ( $N_{\text {T}}$ ) and median volume diameter (MVD) $D_{0}$ ; and the inverse mapping relationship between $Z_{H}$ and $Z_{\text {DR}}$ to $N_{T}$ and $D_{0}$ at a fixed $\mu $ value is derived to form a single layer of IMT. Then, the monotonic relationship between $\mu $ and the specific differential propagation phase shift ( $K_{\text {DP}}$ ) or backscatter differential phase ( $\delta _{\text {CO}}$ ) can aid in determining $\mu $ and a single layer of IMT. Thus, the inverse mapping database from polarimetric observations to the three gamma-type RSD parameters $\mu $ , $N_{\text {T}}$ , and $D_{0}$ can be established. Demonstration studies during a convective rainfall event and a large-scale rainfall event which occurred in northeastern China are carried out to examine the performance of this IMT method compared to a constrained-gamma (C-G) method that uses empirical relations between RSD parameters. The results show that the IMT method has a better performance in the convective case and similar performance in the large-scale continuous rainfall case.

Use of polarimetric radar measurements to constrain simulated convective cell evolution: a pilot study with Lagrangian tracking

Abstract. To probe the potential value of a radar-driven field campaign to constrain simulation of isolated convection subject to a strong aerosol perturbation, convective cells observed by the operational KHGX weather radar in the vicinity of Houston, Texas, are examined individually and statistically. Cells observed in a single case study of onshore flow conditions during July 2013 are first examined and compared with cells in a regional model simulation. Observed and simulated cells are objectively identified and tracked from observed or calculated positive specific differential phase (KDP) above the melting level, which is related to the presence of supercooled liquid water. Several observed and simulated cells are subjectively selected for further examination. Below the melting level, we compare sequential cross sections of retrieved and simulated raindrop size distribution parameters. Above the melting level, we examine time series of KDP and radar differential reflectivity (ZDR) statistics from observations and calculated from simulated supercooled rain properties, alongside simulated vertical wind and supercooled rain mixing ratio statistics. Results indicate that the operational weather radar measurements offer multiple constraints on the properties of simulated convective cells, with substantial value added from derived KDP and retrieved rain properties. The value of collocated three-dimensional lightning mapping array measurements, which are relatively rare in the continental US, supports the choice of Houston as a suitable location for future field studies to improve the simulation and understanding of convective updraft physics. However, rapid evolution of cells between routine volume scans motivates consideration of adaptive scan strategies or radar imaging technologies to amend operational weather radar capabilities. A 3-year climatology of isolated cell tracks, prepared using a more efficient algorithm, yields additional relevant information. Isolated cells are found within the KHGX domain on roughly 40 % of days year-round, with greatest concentration in the northwest quadrant, but roughly 5-fold more cells occur during June through September. During this enhanced occurrence period, the cells initiate following a strong diurnal cycle that peaks in the early afternoon, typically follow a south-to-north flow, and dissipate within 1 h, consistent with the case study examples. Statistics indicate that ∼ 150 isolated cells initiate and dissipate within 70 km of the KHGX radar during the enhanced occurrence period annually, and roughly 10 times as many within 200 km, suitable for multi-instrument Lagrangian observation strategies. In addition to ancillary meteorological and aerosol measurements, robust vertical wind speed retrievals would add substantial value to a radar-driven field campaign.

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

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.

Modeling Radar Attenuation by a Low Melting Layer With Optimized Model Parameters at C-Band

At northern latitudes, it is not uncommon for a melting layer of precipitation to touch or be close to the ground. For a low elevation angle, radio waves from a surveillance weather radar scan can travel a long distance through a melting layer. The resulting attenuation can be significant and must be taken into account when radar observations are interpreted. In this paper, we use a melting layer model to derive the relations between the specific attenuation caused by propagation through a melting layer and the reflectivity factor associated with this layer. The relations derived in this paper are based on modeled attenuation values for a variety of conditions and input parameters, i.e., rain rate, snow density, and rain drop size distribution parameters. The model parameters were constrained by vertically pointing Doppler C-band radar measurements of two events. The fitting procedure is presented for two different cases, of unrimed and rimed snow, and case-specific estimates of the expected attenuation of the horizontal scanning are suggested. Based on measurements of precipitation collected on December 10, 2011, by the University of Helsinki Kumpula radar, we also demonstrate that radar signal attenuation due to propagation through a low melting layer can be on the order of 7 dB or higher over a distance of 40 km.

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.

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

Disdrometer has been widely used to estimate raindrop size distribution (DSD) for broad list of application. However, it classifies or bins drops automatically into size groups and provides the DSD at nominal drop diameters that correspond to the mean of bin width. Selection of the bin width may influence shape and parameterization of DSD since the exact size of individual drop in each bin, of course, is not the same as the mean of its bin size. Therefore, we present a comprehensive follow-up of a previous studyon the effect of bin width selection of 2D-Video Distrometer data. We applied the L-moment method, along with the moment and maximum likelihood methods, to samples taken from simulated and measured gamma raindrop populations. It is found that L-moment is less sensitive to bin width selection than maximum likelihood and moment methods. The bias due to bin width selection for L-moment and maximum likelihood methods is not much influenced by the mean sample size in comparison with that of moment method . With samples from the DSD having large number of raindrop or a larger shape parameter μ, the bias due to bin width selection can be small or negligible. Using the midsize of bin as the representative value for the class (bin) of binned data (ΔD) was acceptable because it gives the parameters closer to drop-by-drop data basis than using mean, mode and median of raindrop size.

Raindrop size distribution parameters estimated from polarimetric radar variables in convective cells around Okinawa Island during the Baiu period

Convective cells with low echo-top heights are commonly observed in the humid environments typical of the Baiu season around Okinawa Island. Representative convective cells with low echotop heights include convective cells in the stratiform and convective rain zones accompanying a precipitation system, as well as isolated convective cells. Raindrop size distribution (DSD) parameters (the median volume diameter D0 and the normalized intercept parameter Nw) for the three types of convective cells were clarified by estimation from polarimetric radar measurements. The estimated D0 values in the mature stages of a convective cell in a stratiform rain zone were approximately 1.2 mm, with radar reflectivity (Zh) of 40–45 dBZ, and the estimated Nw ranged from 32000–100000 mm−1 m−3. In contrast, for a convective cell in a convective rain zone, and also for an isolated convective cell, the estimated D0 was approximately 2 mm with Zh of 40–45 dBZ, and the estimated Nw values were in the range 1000–10000 mm−1 m−3. The variations in the estimated D0 and Nw within the lifetimes of the convective cells suggest the following microphysics: for the convective cell in the stratiform rain zone, a high number-concentration of small raindrops contributed to the increase in Zh, whereas for the convective cell in the convective rain zone and the isolated convective cell, large raindrops contributed to the increase in Zh, and raindrop coalescence processes were predominant at altitudes below 2 km ASL. This study characterized precipitation particle distributions for three convective cells, with low echo-top heights, representing the humid environment of Okinawa Island during the Baiu period. In particular, the precipitation particle distribution for the convective cell in the stratiform rain zone, which differs markedly from those of the convective cell in the convective rain zone and the isolated convective cell, was characterized.

Polarimetric Weather Radar Retrieval of Raindrop Size Distribution by Means of a Regularized Artificial Neural Network

The raindrop size distribution (RSD) is a critical factor in estimating rain intensity using advanced dual-polarized weather radars. A new neural-network algorithm to estimate the RSD from S-band dual-polarized radar measurements is presented. The corresponding rain rates are then computed assuming a commonly used raindrop diameter speed relationship. Numerical simulations are used to investigate the efficiency and accuracy of this method. A stochastic model based on disdrometer measurements is used to generate realistic range profiles of the RSD parameters, while a T-matrix solution technique is adopted to compute the corresponding polarimetric variables. The error analysis, which is performed in order to evaluate the expected errors of this method, shows an improvement with respect to other methodologies described in the literature. A further sensitivity evaluation shows that the proposed technique performs fairly well even for low specific differential phase-shift values

Rainfall rate retrieval in presence of path attenuation using C-band polarimetric weather radars

Abstract. Weather radar systems are very suitable tools for the monitoring of extreme rainfall events providing measurements with high spatial and temporal resolution over a wide geographical area. Nevertheless, radar rainfall retrieval at C-band is prone to several error sources, such as rain path attenuation which affects the accuracy of inversion algorithms. In this paper, the so-called rain profiling techniques (namely the surface reference method FV and the polarimetric method ZPHI) are applied to correct rain path attenuation and a new neural network algorithm is proposed to estimate the rain rate from the corrected measurements of reflectivity and differential reflectivity. A stochastic model, based on disdrometer measurements, is used to generate realistic range profiles of raindrop size distribution parameters while a T-matrix solution technique is adopted to compute the corresponding polarimetric variables. A sensitivity analysis is performed in order to evaluate the expected errors of these methods. It has been found that the ZPHI method is more reliable than FV, being less sensitive to calibration errors. Moreover, the proposed neural network algorithm has shown more accurate rain rate estimates than the corresponding parametric algorithm, especially in presence of calibration errors.

Development and evaluation of an expression for polydisperse particle scavenging coefficient for the below-cloud scavenging as a function of rain intensity using the moment method

An analytical expression for wet scavenging coefficient for below-cloud scavenging that is function of collision efficiency, raindrop terminal velocity, raindrop size distribution, and particle size distribution is obtained and tested. The parameters of raindrop size distribution are related with rain intensity since rain intensity can be easily measured. Then, the moment method is applied to the expression for scavenging coefficient to derive an analytical expression. Two widely used raindrop size distribution, Marshall-Palmer and lognormal distributions are considered and lognormal particle size distribution is assumed. The derived scavenging coefficient expression is applied to three model environments, urban, rural, and desert to demonstrate its applicability.

Correction for Rain Path Specific and Differential Attenuation of X-Band Dual-Polarization Observations

The accuracy of attenuation correction for X-band reflectivity (Z H) and differential reflectivity (ZDR) measurements in rainfall is analyzed using coincident X-band and S-band polarimetric radar observations collected during the International H2O Project in the period of May-June 2002 at northwestern Oklahoma. Two distinct attenuation correction techniques that use the differential propagation phase shift (PhiDP) information, which is not a power-dependent measurement, as a means to provide independent estimates of path-integrated attenuation are assessed. The study is facilitated by nonattenuated X-band ZH and ZDR profiles simulated based on raindrop size distribution parameters retrieved from matched multiparameter (ZH, ZDR, and KDP) S-band observations. The major outcome of this assessment is that PhiDP-based attenuation correction for both techniques can reach almost unbiased measurements (within 5% mean relative error) and low random error (15-20% relative standard deviation). The study shows moderate differences in the error statistics of the evaluated techniques. The sensitivity of attenuation correction uncertainty with respect to the assumed variability in raindrops' oblateness-size relation and the noise in PhiDP measurement is also shown

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.

Raindrop Size Distribution in Different Climatic Regimes from Disdrometer and Dual-Polarized Radar Analysis

The application of polarimetric radar data to the retrieval of raindrop size distribution parameters and rain rate in samples of convective and stratiform rain types is presented. Data from the Colorado State University (CSU), CHILL, NCAR S-band polarimetric (S-Pol), and NASA Kwajalein radars are analyzed for the statistics and functional relation of these parameters with rain rate. Surface drop size distribution measurements using two different disdrometers (2D video and RD-69) from a number of climatic regimes are analyzed and compared with the radar retrievals in a statistical and functional approach. The composite statistics based on disdrometer and radar retrievals suggest that, on average, the two parameters (generalized intercept and median volume diameter) for stratiform rain distributions lie on a straight line with negative slope, which appears to be consistent with variations in the microphysics of stratiform precipitation (melting of larger, dry snow particles versus smaller, rimed ice particles). In convective rain, “maritime-like” and “continental-like” clusters could be identified in the same two-parameter space that are consistent with the different multiplicative coefficients in the Z = aR1.5 relations quoted in the literature for maritime and continental regimes.

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.

Raindrop size distributions and radar reflectivity–rain rate relationships for radar hydrology

Abstract. The conversion of the radar reflectivity factor Z(mm6m-3) to rain rate R(mm h-1 ) is a crucial step in the hydrological application of weather radar measurements. It has been common practice for over 50 years now to take for this conversion a simple power law relationship between Z and R. It is the purpose of this paper to explain that the fundamental reason for the existence of such power law relationships is the fact that Z and R are related to each other via the raindrop size distribution. To this end, the concept of the raindrop size distribution is first explained. Then, it is demonstrated that there exist two fundamentally different forms of the raindrop size distribution, one corresponding to raindrops present in a volume of air and another corresponding to those arriving at a surface. It is explained how Z and R are defined in terms of both these forms. Using the classical exponential raindrop size distribution as an example, it is demonstrated (1) that the definitions of Z and R naturally lead to power law Z–R relationships, and (2) how the coefficients of such relationships are related to the parameters of the raindrop size distribution. Numerous empirical Z–R relationships are analysed to demonstrate that there exist systematic differences in the coefficients of these relationships and the corresponding parameters of the (exponential) raindrop size distribution between different types of rainfall. Finally, six consistent Z–R relationships are derived, based upon different assumptions regarding the rain rate dependence of the parameters of the (exponential) raindrop size distribution. An appendix shows that these relationships are in fact special cases of a general Z–R relationship that follows from a recently proposed scaling framework for describing raindrop size distributions and their properties. Keywords: radar hydrology, raindrop size distribution, radar reflectivity–rain rate relationship

Model for estimating rain attenuation at frequencies in range 6–30 GHz

The raindrop size distribution (RSD) for various types of rainfall over Guwahti, India is presented. The observed RSD parameters are compared with those given by other models. By employing the observed RSD, the values of a and b in the relation A = aRb for estimating the rain attenuation at frequencies from 6 to 30 GHz are given. The significance of the type of rainfall to controlling attenuation is described.