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- Author or Editor: Liang Liao x
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Abstract
An important objective for the dual-wavelength Ku-/Ka-band precipitation radar (DPR) that will be on board the Global Precipitation Measurement (GPM) core satellite is to identify the phase state of hydrometeors along the range direction. To assess this, radar signatures are simulated in snow and rain to explore the relation between the differential frequency ratio (DFR), defined as the difference of radar reflectivity factors between Ku and Ka bands, and the radar reflectivity factor at Ku band Z Ku for different hydrometeor types. Model simulations indicate that there is clear separation between snow and rain in the Z Ku–DFR plane assuming that the snow follows the Gunn–Marshall size distribution and rain follows the Marshall–Palmer size distribution. In an effort to verify the simulated results, the data collected by the Airborne Second-Generation Precipitation Radar (APR-2) in the Wakasa Bay Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) campaign are employed. Using the signatures of linear depolarization ratio at Ku band, the APR-2 data can be easily divided into the regions of snow, mixed phase, and rain for stratiform storms. These results are then superimposed onto the theoretical curves computed from the model in the Z Ku–DFR plane. For over 90% of the observations from a cold-season stratiform precipitation event, snow and rain can be distinguished if the Ku-band radar reflectivity exceeds 18 dBZ (the minimum detectable level of the GPM DPR at Ku band). This is also the case for snow and mixed-phase hydrometeors. Although snow can be easily distinguished from rain and melting hydrometeors by using Ku- and Ka-band radar, the rain and mixed-phase particles are not always separable. It is concluded that Ku- and Ka-band dual-wavelength radar might provide a potential means to identify the phase state of hydrometeors.
Abstract
An important objective for the dual-wavelength Ku-/Ka-band precipitation radar (DPR) that will be on board the Global Precipitation Measurement (GPM) core satellite is to identify the phase state of hydrometeors along the range direction. To assess this, radar signatures are simulated in snow and rain to explore the relation between the differential frequency ratio (DFR), defined as the difference of radar reflectivity factors between Ku and Ka bands, and the radar reflectivity factor at Ku band Z Ku for different hydrometeor types. Model simulations indicate that there is clear separation between snow and rain in the Z Ku–DFR plane assuming that the snow follows the Gunn–Marshall size distribution and rain follows the Marshall–Palmer size distribution. In an effort to verify the simulated results, the data collected by the Airborne Second-Generation Precipitation Radar (APR-2) in the Wakasa Bay Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) campaign are employed. Using the signatures of linear depolarization ratio at Ku band, the APR-2 data can be easily divided into the regions of snow, mixed phase, and rain for stratiform storms. These results are then superimposed onto the theoretical curves computed from the model in the Z Ku–DFR plane. For over 90% of the observations from a cold-season stratiform precipitation event, snow and rain can be distinguished if the Ku-band radar reflectivity exceeds 18 dBZ (the minimum detectable level of the GPM DPR at Ku band). This is also the case for snow and mixed-phase hydrometeors. Although snow can be easily distinguished from rain and melting hydrometeors by using Ku- and Ka-band radar, the rain and mixed-phase particles are not always separable. It is concluded that Ku- and Ka-band dual-wavelength radar might provide a potential means to identify the phase state of hydrometeors.
Abstract
The validity of the effective dielectric constant ɛ eff for nonspherical mixed-phase particles is tested by comparing the scattering parameters of ice–water mixtures for oblate and prolate spheroids obtained from the conjugate-gradient and fast Fourier transform (CGFFT) numerical scheme with those computed from the T matrix for a homogeneous particle with the derived ɛ eff with the same size, shape, and orientation as that of the mixed-phase particle. The accuracy of the effective dielectric constant is evaluated by examining whether the scattering parameters of interest can reproduce those of the direct computations, that is, the CGFFT results. Computations have been run over a range of prolate and oblate spheroids of different axial ratios up to size parameters of 4. It is found that the effective dielectric constant, obtained from realizations of small particles, can be applied to a class of particle types if the fractional water content remains the same. Analysis of the results indicates that the effective dielectric constant approach is useful in computing radar and radiometer polarimetric scattering parameters of nonspherical mixed-phase particles.
Abstract
The validity of the effective dielectric constant ɛ eff for nonspherical mixed-phase particles is tested by comparing the scattering parameters of ice–water mixtures for oblate and prolate spheroids obtained from the conjugate-gradient and fast Fourier transform (CGFFT) numerical scheme with those computed from the T matrix for a homogeneous particle with the derived ɛ eff with the same size, shape, and orientation as that of the mixed-phase particle. The accuracy of the effective dielectric constant is evaluated by examining whether the scattering parameters of interest can reproduce those of the direct computations, that is, the CGFFT results. Computations have been run over a range of prolate and oblate spheroids of different axial ratios up to size parameters of 4. It is found that the effective dielectric constant, obtained from realizations of small particles, can be applied to a class of particle types if the fractional water content remains the same. Analysis of the results indicates that the effective dielectric constant approach is useful in computing radar and radiometer polarimetric scattering parameters of nonspherical mixed-phase particles.
Abstract
A procedure to accurately resample spaceborne and ground-based radar data is described and then is applied to the measurements taken from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and the ground-based Weather Surveillance Radar-1988 Doppler (WSR-88D or WSR) for the validation of the PR measurements and estimates. Through comparisons with the well-calibrated, nonattenuated WSR at Melbourne, Florida, for the period 1998–2007, the calibration of the PR aboard the TRMM satellite is checked using measurements near the storm top. Analysis of the results indicates that the PR, after taking into account differences in radar reflectivity factors between the PR and WSR, has a small positive bias of 0.8 dB relative to the WSR, implying a soundness of the PR calibration in view of the uncertainties involved in the comparisons. Comparisons between the PR and WSR reflectivities are also made near the surface for evaluation of the attenuation-correction procedures used in the PR algorithms. It is found that the PR attenuation is accurately corrected in stratiform rain but is underestimated in convective rain, particularly in heavy rain. Tests of the PR estimates of rainfall rate are conducted through comparisons in the overlap area between the TRMM overpass and WSR scan. Analyses of the data are made both on a conditional basis, in which the instantaneous rain rates are compared only at those pixels at which both the PR and WSR detect rain, and an unconditional basis, in which the area-averaged rain rates are estimated independently for the PR and WSR. Results of the conditional rain comparisons show that the PR-derived rain is about 9% greater and 19% less than the WSR estimates for stratiform and convective storms, respectively. Overall, the PR tends to underestimate the conditional mean rain rate by 8% for all rain categories, a finding that conforms to the results of the area-averaged rain (unconditional) comparisons.
Abstract
A procedure to accurately resample spaceborne and ground-based radar data is described and then is applied to the measurements taken from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and the ground-based Weather Surveillance Radar-1988 Doppler (WSR-88D or WSR) for the validation of the PR measurements and estimates. Through comparisons with the well-calibrated, nonattenuated WSR at Melbourne, Florida, for the period 1998–2007, the calibration of the PR aboard the TRMM satellite is checked using measurements near the storm top. Analysis of the results indicates that the PR, after taking into account differences in radar reflectivity factors between the PR and WSR, has a small positive bias of 0.8 dB relative to the WSR, implying a soundness of the PR calibration in view of the uncertainties involved in the comparisons. Comparisons between the PR and WSR reflectivities are also made near the surface for evaluation of the attenuation-correction procedures used in the PR algorithms. It is found that the PR attenuation is accurately corrected in stratiform rain but is underestimated in convective rain, particularly in heavy rain. Tests of the PR estimates of rainfall rate are conducted through comparisons in the overlap area between the TRMM overpass and WSR scan. Analyses of the data are made both on a conditional basis, in which the instantaneous rain rates are compared only at those pixels at which both the PR and WSR detect rain, and an unconditional basis, in which the area-averaged rain rates are estimated independently for the PR and WSR. Results of the conditional rain comparisons show that the PR-derived rain is about 9% greater and 19% less than the WSR estimates for stratiform and convective storms, respectively. Overall, the PR tends to underestimate the conditional mean rain rate by 8% for all rain categories, a finding that conforms to the results of the area-averaged rain (unconditional) comparisons.
Physical Evaluation of GPM DPR Single- and Dual-Wavelength AlgorithmsAbstract
A physical evaluation of the rain profiling retrieval algorithms for the Dual-Frequency Precipitation Radar (DPR) on board the Global Precipitation Measurement (GPM) Core Observatory satellite is carried out by applying them to the hydrometeor profiles generated from measured raindrop size distributions (DSD). The DSD-simulated radar profiles are used as input to the algorithms, and their estimates of hydrometeors’ parameters are compared with the same quantities derived directly from the DSD data (or truth). The retrieval accuracy is assessed by the degree to which the estimates agree with the truth. To check the validity and robustness of the retrievals, the profiles are constructed for cases ranging from fully correlated (or uniform) to totally uncorrelated DSDs along the columns. Investigation into the sensitivity of the retrieval results to the model assumptions is made to characterize retrieval uncertainties and identify error sources. Comparisons between the single- and dual-wavelength algorithm performance are carried out with either a single- or dual-wavelength constraint of the path integral or differential path integral attenuation. The results suggest that the DPR dual-wavelength algorithm generally provides accurate range-profiled estimates of rainfall rate and mass-weighted diameter with the dual-wavelength estimates superior in accuracy to those from the single-wavelength retrievals.
Abstract
A physical evaluation of the rain profiling retrieval algorithms for the Dual-Frequency Precipitation Radar (DPR) on board the Global Precipitation Measurement (GPM) Core Observatory satellite is carried out by applying them to the hydrometeor profiles generated from measured raindrop size distributions (DSD). The DSD-simulated radar profiles are used as input to the algorithms, and their estimates of hydrometeors’ parameters are compared with the same quantities derived directly from the DSD data (or truth). The retrieval accuracy is assessed by the degree to which the estimates agree with the truth. To check the validity and robustness of the retrievals, the profiles are constructed for cases ranging from fully correlated (or uniform) to totally uncorrelated DSDs along the columns. Investigation into the sensitivity of the retrieval results to the model assumptions is made to characterize retrieval uncertainties and identify error sources. Comparisons between the single- and dual-wavelength algorithm performance are carried out with either a single- or dual-wavelength constraint of the path integral or differential path integral attenuation. The results suggest that the DPR dual-wavelength algorithm generally provides accurate range-profiled estimates of rainfall rate and mass-weighted diameter with the dual-wavelength estimates superior in accuracy to those from the single-wavelength retrievals.
Abstract
For air- and spaceborne weather radars, which typically operate at frequencies of 10 GHz and above, attenuation correction is usually an essential part of any rain estimation procedure. For ground-based radars, where the maximum range within the precipitation is usually much greater than that from air- or spaceborne radars, attenuation correction becomes increasingly important at frequencies above about 5 GHz. Although dual-polarization radar algorithms rely on the correlation between raindrop shape and size, while dual-wavelength weather radar algorithms rely primarily on non-Rayleigh scattering at the shorter wavelength, the equations for estimating parameters of the drop size distribution (DSD) are nearly identical in the presence of attenuation. Many of the attenuation correction methods that have been proposed can be classified as one of two types: those that employ a kZ (specific attenuation–radar reflectivity factor) relation, and those that use an integral equation formalism where the attenuation is obtained from the DSD parameters at prior gates, either stepping outward from the radar or inward toward the radar from some final range gate. The similarity is shown between the dual-polarization and dual-wavelength equations when either the kZ or the integral equation formulation is used. Differences between the two attenuation correction procedures are illustrated for simulated measurements from an X-band dual-polarization radar.
Abstract
For air- and spaceborne weather radars, which typically operate at frequencies of 10 GHz and above, attenuation correction is usually an essential part of any rain estimation procedure. For ground-based radars, where the maximum range within the precipitation is usually much greater than that from air- or spaceborne radars, attenuation correction becomes increasingly important at frequencies above about 5 GHz. Although dual-polarization radar algorithms rely on the correlation between raindrop shape and size, while dual-wavelength weather radar algorithms rely primarily on non-Rayleigh scattering at the shorter wavelength, the equations for estimating parameters of the drop size distribution (DSD) are nearly identical in the presence of attenuation. Many of the attenuation correction methods that have been proposed can be classified as one of two types: those that employ a kZ (specific attenuation–radar reflectivity factor) relation, and those that use an integral equation formalism where the attenuation is obtained from the DSD parameters at prior gates, either stepping outward from the radar or inward toward the radar from some final range gate. The similarity is shown between the dual-polarization and dual-wavelength equations when either the kZ or the integral equation formulation is used. Differences between the two attenuation correction procedures are illustrated for simulated measurements from an X-band dual-polarization radar.
Abstract
To overcome a deficiency in the standard Ku- and Ka-band dual-wavelength radar technique, a modified version of the method is introduced. The deficiency arises from ambiguities in the estimate of the mass-weighted diameter D m of the raindrop size distribution (DSD) derived from the differential frequency ratio (DFR), defined as the difference between the radar reflectivity factors (dB) at Ku and Ka band Z Ku − Z Ka. In particular, for DFR values less than zero, there are two possible solutions of D m , leading to ambiguities in the retrieved DSD parameters. It is shown that the double solutions to D m are effectively eliminated if the DFR is modified from Z Ku − Z Ka to Z Ku − γZ Ka (dB), where γ is a constant with a value less than 0.8. An optimal radar algorithm that uses the modified DFR for the retrieval of rain and D m profiles is described. The validity and accuracy of the algorithm are tested by applying it to radar profiles that are generated from measured DSD data. Comparisons of the rain rates and D m estimated from the modified DFR algorithm to the same hydrometeor quantities computed directly from the DSD spectra (or the truth) indicate that the modified DFR-based profiling retrievals perform fairly well and are superior in accuracy and robustness to retrievals using the standard DFR.
Abstract
To overcome a deficiency in the standard Ku- and Ka-band dual-wavelength radar technique, a modified version of the method is introduced. The deficiency arises from ambiguities in the estimate of the mass-weighted diameter D m of the raindrop size distribution (DSD) derived from the differential frequency ratio (DFR), defined as the difference between the radar reflectivity factors (dB) at Ku and Ka band Z Ku − Z Ka. In particular, for DFR values less than zero, there are two possible solutions of D m , leading to ambiguities in the retrieved DSD parameters. It is shown that the double solutions to D m are effectively eliminated if the DFR is modified from Z Ku − Z Ka to Z Ku − γZ Ka (dB), where γ is a constant with a value less than 0.8. An optimal radar algorithm that uses the modified DFR for the retrieval of rain and D m profiles is described. The validity and accuracy of the algorithm are tested by applying it to radar profiles that are generated from measured DSD data. Comparisons of the rain rates and D m estimated from the modified DFR algorithm to the same hydrometeor quantities computed directly from the DSD spectra (or the truth) indicate that the modified DFR-based profiling retrievals perform fairly well and are superior in accuracy and robustness to retrievals using the standard DFR.
Abstract
W-band (3.2-mm) radars are seeing increasing utilization as a result of improving microwave technologies and the increased research emphasis being given to nonprecipitating clouds. This niche is exemplified by the study of the radiatively important stratus and cirrus clouds, which essentially require the application of Rayleigh and nonspherical scattering solutions, respectively. To increase the utility of such studies, the authors provide the following relations derived from empirical and model-derived particle size distributions that rely on a combination of Rayleigh and conjugate gradient-fast Fourier transform scattering theory approaches to relate (equivalent) radar reflectivity factors (Ze) Z (mm6 m−3) to liquid water content (LWC, g m−3) and ice water content (IWC, mg m−3): Z = (3.6/Nd)LWC1.8 for stratus clouds, where Nd (cm−3) is the droplet concentration, and IWC = 21.7 Ze0.83 for cirrus clouds using the dielectric constant appropriate for ice, which is valid over a IWC range of 3–100 mg m−3. Sources of 95-GHz attenuation are also discussed.
In addition, radar estimates of the lidar volume extinction coefficient σl (m−1) are derived using the exponential ice particle size distributions, yielding σl = 6.5 × 10−4Ze0.86 for solid ice particles, or 9.65 × 10−4Ze0.81 if an ice density of 0.5 g cm−3 is used to approximate the effects of hollow ice crystals in cirrus clouds.
Abstract
W-band (3.2-mm) radars are seeing increasing utilization as a result of improving microwave technologies and the increased research emphasis being given to nonprecipitating clouds. This niche is exemplified by the study of the radiatively important stratus and cirrus clouds, which essentially require the application of Rayleigh and nonspherical scattering solutions, respectively. To increase the utility of such studies, the authors provide the following relations derived from empirical and model-derived particle size distributions that rely on a combination of Rayleigh and conjugate gradient-fast Fourier transform scattering theory approaches to relate (equivalent) radar reflectivity factors (Ze) Z (mm6 m−3) to liquid water content (LWC, g m−3) and ice water content (IWC, mg m−3): Z = (3.6/Nd)LWC1.8 for stratus clouds, where Nd (cm−3) is the droplet concentration, and IWC = 21.7 Ze0.83 for cirrus clouds using the dielectric constant appropriate for ice, which is valid over a IWC range of 3–100 mg m−3. Sources of 95-GHz attenuation are also discussed.
In addition, radar estimates of the lidar volume extinction coefficient σl (m−1) are derived using the exponential ice particle size distributions, yielding σl = 6.5 × 10−4Ze0.86 for solid ice particles, or 9.65 × 10−4Ze0.81 if an ice density of 0.5 g cm−3 is used to approximate the effects of hollow ice crystals in cirrus clouds.
Abstract
As shown by Takahashi et al., multiple path attenuation estimates over the field of view of an airborne or spaceborne weather radar are feasible for off-nadir incidence angles. This follows from the fact that the surface reference technique, which provides path attenuation estimates, can be applied to each radar range gate that intersects the surface. This study builds on this result by showing that three of the modified Hitschfeld–Bordan estimates for the attenuation-corrected radar reflectivity factor can be generalized to the case where multiple path attenuation estimates are available, thereby providing a correction to the effects of nonuniform beamfilling. A simple simulation is presented showing some strengths and weaknesses of the approach.
Abstract
As shown by Takahashi et al., multiple path attenuation estimates over the field of view of an airborne or spaceborne weather radar are feasible for off-nadir incidence angles. This follows from the fact that the surface reference technique, which provides path attenuation estimates, can be applied to each radar range gate that intersects the surface. This study builds on this result by showing that three of the modified Hitschfeld–Bordan estimates for the attenuation-corrected radar reflectivity factor can be generalized to the case where multiple path attenuation estimates are available, thereby providing a correction to the effects of nonuniform beamfilling. A simple simulation is presented showing some strengths and weaknesses of the approach.
Abstract
A framework based on measured raindrop size distribution (DSD) data has been developed to assess uncertainties in DSD models employed in Ku- and Ka-band dual-wavelength radar retrievals. In this study, the rain rates and attenuation coefficients from DSD parameters derived by dual-wavelength algorithms are compared with those directly obtained from measured DSD spectra. The impact of the DSD gamma parameterizations on rain estimation from the Global Precipitation Measurement mission (GPM) Dual-Frequency Precipitation Radar (DPR) is examined for the cases of a fixed shape factor μ as well as for a constrained μ—that is, a μ–Λ relation (a relationship between the shape parameter and slope parameter Λ of the gamma DSD)—by using 11 Particle Size and Velocity (Parsivel) disdrometer measurements with a total number of about 50 000 one-minute spectra that were collected during the Iowa Flood Studies (IFloodS) experiment. It is found that the DPR-like dual-wavelength techniques provide fairly accurate estimates of rain rate and attenuation if a fixed-μ gamma DSD model is used, with the value of μ ranging from 3 to 6. Comparison of the results reveals that the retrieval errors from the μ–Λ relations are generally small, with biases of less than ±10%, and are comparable to the results from a fixed-μ gamma model with μ equal to 3 and 6. The DSD evaluation procedure is also applied to retrievals in which a lognormal DSD model is used.
Abstract
A framework based on measured raindrop size distribution (DSD) data has been developed to assess uncertainties in DSD models employed in Ku- and Ka-band dual-wavelength radar retrievals. In this study, the rain rates and attenuation coefficients from DSD parameters derived by dual-wavelength algorithms are compared with those directly obtained from measured DSD spectra. The impact of the DSD gamma parameterizations on rain estimation from the Global Precipitation Measurement mission (GPM) Dual-Frequency Precipitation Radar (DPR) is examined for the cases of a fixed shape factor μ as well as for a constrained μ—that is, a μ–Λ relation (a relationship between the shape parameter and slope parameter Λ of the gamma DSD)—by using 11 Particle Size and Velocity (Parsivel) disdrometer measurements with a total number of about 50 000 one-minute spectra that were collected during the Iowa Flood Studies (IFloodS) experiment. It is found that the DPR-like dual-wavelength techniques provide fairly accurate estimates of rain rate and attenuation if a fixed-μ gamma DSD model is used, with the value of μ ranging from 3 to 6. Comparison of the results reveals that the retrieval errors from the μ–Λ relations are generally small, with biases of less than ±10%, and are comparable to the results from a fixed-μ gamma model with μ equal to 3 and 6. The DSD evaluation procedure is also applied to retrievals in which a lognormal DSD model is used.
A Generalized Dual-Frequency Ratio (DFR) Approach for Rain RetrievalsAbstract
The dual-frequency ratio of radar reflectivity factors (DFR) has been shown to be a useful quantity as it is independent of the number concentration of the particle size distribution and primarily a function of the mass-weighted particle diameter Dm . A drawback of DFR-related methods for rain estimation, however, is the nonunique relationship between Dm and DFR. At Ku- and Ka-band frequencies, two solutions for Dm exist when DFR is less than zero. This ambiguity generates multiple solutions for the range profiles of the particle size parameters. We investigate characteristics of these solutions for both the initial-value (forward) and final-value (backward) forms of the equations. To choose one among many possible range profiles of Dm , number concentration, and rain rate R, independently measured path attenuations are used. For the backward approach, the possibility exists of dispensing with externally measured path attenuations by achieving consistency between the input and output path attenuations. The methods are tested by means of a simulation based on disdrometer-measured raindrop size distributions and the results are compared with a simplified version of the operational R–Dm method.
Abstract
The dual-frequency ratio of radar reflectivity factors (DFR) has been shown to be a useful quantity as it is independent of the number concentration of the particle size distribution and primarily a function of the mass-weighted particle diameter Dm . A drawback of DFR-related methods for rain estimation, however, is the nonunique relationship between Dm and DFR. At Ku- and Ka-band frequencies, two solutions for Dm exist when DFR is less than zero. This ambiguity generates multiple solutions for the range profiles of the particle size parameters. We investigate characteristics of these solutions for both the initial-value (forward) and final-value (backward) forms of the equations. To choose one among many possible range profiles of Dm , number concentration, and rain rate R, independently measured path attenuations are used. For the backward approach, the possibility exists of dispensing with externally measured path attenuations by achieving consistency between the input and output path attenuations. The methods are tested by means of a simulation based on disdrometer-measured raindrop size distributions and the results are compared with a simplified version of the operational R–Dm method.
