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- Author or Editor: Guifu Zhang x
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Abstract
There have been debates and differences of opinion over the validity of using drop size distribution (DSD) models to characterize precipitation microphysics and to retrieve DSD parameters from multiparameter radar measurements. In this paper, simulated and observed rain DSDs are used to evaluate moment estimators. Seven estimators for gamma DSD parameters are evaluated in terms of the biases and fractional errors of five integral parameters: radar reflectivity (ZH ), differential reflectivity (Z DR), rainfall rate (R), mean volume diameter (Dm ), and total number concentration (NT ). It is shown that middle-moment estimators such as M234 (using the second-third-fourth moments) produce smaller errors than lower- and higher-moment estimators if the DSD follows the gamma distribution. However, if there are model errors, the performance of M234 degrades. Even though the DSD parameters can be biased in moment estimators, integral parameters are usually not. Maximum likelihood (ML) and L-moment (LM) estimators perform similarly to low-moment estimators such as M012. They are sensitive to both model error and the measurement errors of the low ends of DSDs. The overall differences among M234, M246, and M346 are not substantial for the five evaluated parameters. This study also shows that the discrepancy between the radar and disdrometer observations cannot be reduced by using these estimators. In addition, the previously found constrained-gamma model is shown not to be exclusively determined by error effects. Rather, it is equivalent to the mean function of normalized DSDs derived through Testud’s approach, and linked to precipitation microphysics.
Abstract
There have been debates and differences of opinion over the validity of using drop size distribution (DSD) models to characterize precipitation microphysics and to retrieve DSD parameters from multiparameter radar measurements. In this paper, simulated and observed rain DSDs are used to evaluate moment estimators. Seven estimators for gamma DSD parameters are evaluated in terms of the biases and fractional errors of five integral parameters: radar reflectivity (ZH ), differential reflectivity (Z DR), rainfall rate (R), mean volume diameter (Dm ), and total number concentration (NT ). It is shown that middle-moment estimators such as M234 (using the second-third-fourth moments) produce smaller errors than lower- and higher-moment estimators if the DSD follows the gamma distribution. However, if there are model errors, the performance of M234 degrades. Even though the DSD parameters can be biased in moment estimators, integral parameters are usually not. Maximum likelihood (ML) and L-moment (LM) estimators perform similarly to low-moment estimators such as M012. They are sensitive to both model error and the measurement errors of the low ends of DSDs. The overall differences among M234, M246, and M346 are not substantial for the five evaluated parameters. This study also shows that the discrepancy between the radar and disdrometer observations cannot be reduced by using these estimators. In addition, the previously found constrained-gamma model is shown not to be exclusively determined by error effects. Rather, it is equivalent to the mean function of normalized DSDs derived through Testud’s approach, and linked to precipitation microphysics.
Abstract
A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squall-line system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.
Abstract
A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squall-line system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.
Abstract
The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity Z DR, specific differential phase K DP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using ZH alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more helpful when the parameter estimation is not very successful with ZH alone. Between Z DR and K DP, K DP is found to produce larger positive impacts on parameter estimation in general while Z DR is more useful in the estimation of the intercept parameter of hail. In the experiments that attempt to correct errors in all five parameters, the filter fails to correctly estimate the snow intercept parameter and the density with or without polarimetric data, seemingly due to the small sensitivity of the observations to these parameters and complications involving the observation operator error. When these two snow parameters are not corrected during the estimation process, the estimations of the other three parameters and of all of the state variables are significantly improved and the positive impacts of polarimetric data are larger than that of a five-parameter estimation. These results reveal the significant complexity of the estimation problem for a highly nonlinear system and the need for careful sensitivity analysis. The problem is potentially more challenging with real-data cases when unknown sources of model errors are inevitable.
Abstract
The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity Z DR, specific differential phase K DP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using ZH alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more helpful when the parameter estimation is not very successful with ZH alone. Between Z DR and K DP, K DP is found to produce larger positive impacts on parameter estimation in general while Z DR is more useful in the estimation of the intercept parameter of hail. In the experiments that attempt to correct errors in all five parameters, the filter fails to correctly estimate the snow intercept parameter and the density with or without polarimetric data, seemingly due to the small sensitivity of the observations to these parameters and complications involving the observation operator error. When these two snow parameters are not corrected during the estimation process, the estimations of the other three parameters and of all of the state variables are significantly improved and the positive impacts of polarimetric data are larger than that of a five-parameter estimation. These results reveal the significant complexity of the estimation problem for a highly nonlinear system and the need for careful sensitivity analysis. The problem is potentially more challenging with real-data cases when unknown sources of model errors are inevitable.
Abstract
The theory of measuring crossbeam wind, shear, and turbulence within the radar’s resolution volume V6 is described. Spaced-antenna weather radar interferometry is formulated for such measurements using phased-array weather radar. The formulation for a spaced-antenna interferometer (SAI) includes shear of the mean wind, allows turbulence to be anisotropic, and allows receiving beams to have elliptical cross sections. Auto- and cross-correlation functions are derived based on wave scattering by randomly distributed particles. Antenna separation, mean wind, shear, and turbulence all contribute to signal decorrelation. Crossbeam wind cannot be separated from shear, and thus crossbeam wind measurements are biased by shear. It is shown that SAI measures an apparent crossbeam wind (i.e., the angular shear of the radial wind component). Whereas the apparent crossbeam wind and turbulence within V6 cannot be separated using monostatic Doppler techniques, angular shear and turbulence can be separated using the SAI.
Abstract
The theory of measuring crossbeam wind, shear, and turbulence within the radar’s resolution volume V6 is described. Spaced-antenna weather radar interferometry is formulated for such measurements using phased-array weather radar. The formulation for a spaced-antenna interferometer (SAI) includes shear of the mean wind, allows turbulence to be anisotropic, and allows receiving beams to have elliptical cross sections. Auto- and cross-correlation functions are derived based on wave scattering by randomly distributed particles. Antenna separation, mean wind, shear, and turbulence all contribute to signal decorrelation. Crossbeam wind cannot be separated from shear, and thus crossbeam wind measurements are biased by shear. It is shown that SAI measures an apparent crossbeam wind (i.e., the angular shear of the radial wind component). Whereas the apparent crossbeam wind and turbulence within V6 cannot be separated using monostatic Doppler techniques, angular shear and turbulence can be separated using the SAI.
Detection of Ground Clutter for Dual-Polarization Weather Radar Using a Novel 3D Discriminant FunctionAbstract
A novel 3D discriminant function is introduced as part of a ground clutter detection algorithm for improving weather radar observations. The 3D discriminant function utilizes the phase fluctuations of the received signals for horizontal and vertical polarizations and the dual-scan cross-correlation coefficient. An optimal decision based on the 3D discriminant function is made using a simple Bayesian classifier to distinguish clutter from weather signals. For convenience of use, a multivariate Gaussian mixture model is used to represent the probability density functions of discriminant functions. The model parameters are estimated based on the maximum likelihood using the expectation–maximization (ML-EM) method. The performance improvements are demonstrated by applying the proposed detection algorithm to radar data collected by the polarimetric Norman, Oklahoma (KOUN), weather radar. This algorithm is compared to other clutter detection algorithms and the results indicate that, using the proposed detection algorithm, a better probability of detection can be achieved.
Abstract
A novel 3D discriminant function is introduced as part of a ground clutter detection algorithm for improving weather radar observations. The 3D discriminant function utilizes the phase fluctuations of the received signals for horizontal and vertical polarizations and the dual-scan cross-correlation coefficient. An optimal decision based on the 3D discriminant function is made using a simple Bayesian classifier to distinguish clutter from weather signals. For convenience of use, a multivariate Gaussian mixture model is used to represent the probability density functions of discriminant functions. The model parameters are estimated based on the maximum likelihood using the expectation–maximization (ML-EM) method. The performance improvements are demonstrated by applying the proposed detection algorithm to radar data collected by the polarimetric Norman, Oklahoma (KOUN), weather radar. This algorithm is compared to other clutter detection algorithms and the results indicate that, using the proposed detection algorithm, a better probability of detection can be achieved.
Abstract
A new general polarimetric radar simulator for nonhydrostatic numerical weather prediction (NWP) models has been developed based on rigorous scattering calculations using the T-matrix method for reflectivity, differential reflectivity, specific differential phase, and copolar cross-correlation coefficient. A continuous melting process accounts for the entire spectrum of varying density and dielectric constants. This simulator is able to simulate polarimetric radar measurements at weather radar frequency bands and can take as input the prognostic variables of high-resolution NWP model simulations using one-, two-, and three-moment microphysics schemes. The simulator was applied at 10.7-cm wavelength to a model-simulated supercell storm using a double-moment (two moment) bulk microphysics scheme to examine its ability to simulate polarimetric signatures reported in observational studies. The simulated fields exhibited realistic polarimetric signatures that include Z DR and K DP columns, Z DR arc, midlevel Z DR and ρhυ rings, hail signature, and K DP foot in terms of their general location, shape, and strength. The authors compared the simulation with one employing a single-moment (SM) microphysics scheme and found that certain signatures, such as Z DR arc, midlevel Z DR, and ρhυ rings, cannot be reproduced with the latter. It is believed to be primarily caused by the limitation of the SM scheme in simulating the shift of the particle size distribution toward larger/smaller diameters, independent of mixing ratio. These results suggest that two- or higher-moment microphysics schemes should be used to adequately describe certain important microphysical processes. They also demonstrate the utility of a well-designed radar simulator for validating numerical models. In addition, the simulator can also serve as a training tool for forecasters to recognize polarimetric signatures that can be reproduced by advanced NWP models.
Abstract
A new general polarimetric radar simulator for nonhydrostatic numerical weather prediction (NWP) models has been developed based on rigorous scattering calculations using the T-matrix method for reflectivity, differential reflectivity, specific differential phase, and copolar cross-correlation coefficient. A continuous melting process accounts for the entire spectrum of varying density and dielectric constants. This simulator is able to simulate polarimetric radar measurements at weather radar frequency bands and can take as input the prognostic variables of high-resolution NWP model simulations using one-, two-, and three-moment microphysics schemes. The simulator was applied at 10.7-cm wavelength to a model-simulated supercell storm using a double-moment (two moment) bulk microphysics scheme to examine its ability to simulate polarimetric signatures reported in observational studies. The simulated fields exhibited realistic polarimetric signatures that include Z DR and K DP columns, Z DR arc, midlevel Z DR and ρhυ rings, hail signature, and K DP foot in terms of their general location, shape, and strength. The authors compared the simulation with one employing a single-moment (SM) microphysics scheme and found that certain signatures, such as Z DR arc, midlevel Z DR, and ρhυ rings, cannot be reproduced with the latter. It is believed to be primarily caused by the limitation of the SM scheme in simulating the shift of the particle size distribution toward larger/smaller diameters, independent of mixing ratio. These results suggest that two- or higher-moment microphysics schemes should be used to adequately describe certain important microphysical processes. They also demonstrate the utility of a well-designed radar simulator for validating numerical models. In addition, the simulator can also serve as a training tool for forecasters to recognize polarimetric signatures that can be reproduced by advanced NWP models.
Abstract
Observations and analysis of an ice–liquid phase precipitation event, collected with an S-band polarimetric KOUN radar and a two-dimensional video disdrometer (2DVD) in central Oklahoma on 20 January 2007, are presented. Using the disdrometer measurements, precipitation is classified either as ice pellets or rain/freezing rain. The disdrometer observations showed fast-falling and slow-falling particles of similar size. The vast majority (>99%) were fast falling with observed velocities close to those of raindrops with similar sizes. In contrast to the smaller particles (<1 mm in diameter), bigger ice pellets (>1.5 mm) were relatively easy to distinguish because their shapes differ from the raindrops. The ice pellets were challenging to detect by looking at conventional polarimetric radar data because of the localized and patchy nature of the ice phase and their occurrence close to the ground. Previously published findings referred to cases in which ice pellet areas were centered on the radar location and showed a ringlike structure of enhanced differential reflectivity Z DR and reduced copolar correlation coefficient ρ hv and horizontal reflectivity Z H in PPI images. In this study, a new, unconventional way of looking at polarimetric radar data is introduced: slanted vertical profiles (SVPs) at low (0°–1°) radar elevations. From the analysis of the localized and patchy structures using SVPs, the polarimetric refreezing signature, reflected in local enhancement in Z DR and reduction in Z H and ρ hv, became much more evident. Model simulations of sequential drop freezing using Marshall–Palmer DSDs along with the observations suggest that preferential freezing of small drops may be responsible for the refreezing polarimetric signature, as suggested in previous studies.
Abstract
Observations and analysis of an ice–liquid phase precipitation event, collected with an S-band polarimetric KOUN radar and a two-dimensional video disdrometer (2DVD) in central Oklahoma on 20 January 2007, are presented. Using the disdrometer measurements, precipitation is classified either as ice pellets or rain/freezing rain. The disdrometer observations showed fast-falling and slow-falling particles of similar size. The vast majority (>99%) were fast falling with observed velocities close to those of raindrops with similar sizes. In contrast to the smaller particles (<1 mm in diameter), bigger ice pellets (>1.5 mm) were relatively easy to distinguish because their shapes differ from the raindrops. The ice pellets were challenging to detect by looking at conventional polarimetric radar data because of the localized and patchy nature of the ice phase and their occurrence close to the ground. Previously published findings referred to cases in which ice pellet areas were centered on the radar location and showed a ringlike structure of enhanced differential reflectivity Z DR and reduced copolar correlation coefficient ρ hv and horizontal reflectivity Z H in PPI images. In this study, a new, unconventional way of looking at polarimetric radar data is introduced: slanted vertical profiles (SVPs) at low (0°–1°) radar elevations. From the analysis of the localized and patchy structures using SVPs, the polarimetric refreezing signature, reflected in local enhancement in Z DR and reduction in Z H and ρ hv, became much more evident. Model simulations of sequential drop freezing using Marshall–Palmer DSDs along with the observations suggest that preferential freezing of small drops may be responsible for the refreezing polarimetric signature, as suggested in previous studies.
Abstract
This study presents a two-dimensional variational approach to retrieving raindrop size distributions (DSDs) from polarimetric radar data in the presence of attenuation. A two-parameter DSD model, the constrained-gamma model, is used to represent rain DSDs. Three polarimetric radar measurements—reflectivity ZH, differential reflectivity ZDR, and specific differential phase KDP—are optimally used to correct for the attenuation and retrieve DSDs by taking into account measurement error effects. Retrieval results with simulated data demonstrate that the proposed algorithm performs well. Applications to real data collected by the X-band Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) radars and the C-band University of Oklahoma–Polarimetric Radar for Innovations in Meteorology and Engineering (OU-PRIME) also demonstrate the efficacy of this approach.
Abstract
This study presents a two-dimensional variational approach to retrieving raindrop size distributions (DSDs) from polarimetric radar data in the presence of attenuation. A two-parameter DSD model, the constrained-gamma model, is used to represent rain DSDs. Three polarimetric radar measurements—reflectivity ZH, differential reflectivity ZDR, and specific differential phase KDP—are optimally used to correct for the attenuation and retrieve DSDs by taking into account measurement error effects. Retrieval results with simulated data demonstrate that the proposed algorithm performs well. Applications to real data collected by the X-band Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) radars and the C-band University of Oklahoma–Polarimetric Radar for Innovations in Meteorology and Engineering (OU-PRIME) also demonstrate the efficacy of this approach.
Abstract
Raindrop size distribution (DSD) retrieval from remote radar measurements or from in situ disdrometer measurements is an important area of research. If the shape (μ) and slope (Λ) of a three-parameter gamma distribution n(D) = N 0 D μ exp(−ΛD) are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified to a two-parameter DSD, that is, a constrained gamma DSD. An empirical relation between the μ and Λ was derived using moments estimated from video-disdrometer measurements. Here, the effects of DSD truncation on a μ and Λ relation were analyzed. It was shown that characteristic size and variance of size of a constrained gamma DSD depend only on the shape parameter μ. Assuming that a constrained gamma DSD is valid, S-band polarimetric radar–based estimators for rain rate, median volume diameter, specific propagation phase, attenuation, and differential attenuation were derived. The radar-based estimators were used to obtain the spatial distribution of DSD parameters corresponding to a range–height indicator of radar measurements. Self-consistency among polarization radar measurements is used to indirectly verify constrained gamma DSD-based polarization radar estimators.
Abstract
Raindrop size distribution (DSD) retrieval from remote radar measurements or from in situ disdrometer measurements is an important area of research. If the shape (μ) and slope (Λ) of a three-parameter gamma distribution n(D) = N 0 D μ exp(−ΛD) are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified to a two-parameter DSD, that is, a constrained gamma DSD. An empirical relation between the μ and Λ was derived using moments estimated from video-disdrometer measurements. Here, the effects of DSD truncation on a μ and Λ relation were analyzed. It was shown that characteristic size and variance of size of a constrained gamma DSD depend only on the shape parameter μ. Assuming that a constrained gamma DSD is valid, S-band polarimetric radar–based estimators for rain rate, median volume diameter, specific propagation phase, attenuation, and differential attenuation were derived. The radar-based estimators were used to obtain the spatial distribution of DSD parameters corresponding to a range–height indicator of radar measurements. Self-consistency among polarization radar measurements is used to indirectly verify constrained gamma DSD-based polarization radar estimators.
