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Abstract
A method is proposed for estimating the area-average rain-rate distribution from attenuating-wavelength spaceborne or airborne radar data. Because highly attenuated radar returns yield unreliable estimates of the rain rate, these are eliminated by means of a proxy variable, Q, derived from the apparent radar reflectivity factors and a power law relating the attenuation coefficient and the reflectivity factor. In determining the probability distribution function of areawide rain rates, the elimination of attenuated measurements at high rain rates and the loss of data at light rain rates, because of low signal-to-noise ratios, leads to truncation of the distribution at the low and high ends. To estimate it over all rain rates, a lognormal distribution is assumed, the parameters of which are obtained from a nonlinear least squares fit to the truncated distribution. Implementation of this type of threshold method depends on the method used in estimating the high-resolution rain-rate estimates (e.g., either the standard Z–R or the Hitschfeld–Bordan estimate) and on the type of rain-rate estimate (either point or path averaged). To test the method, measured drop size distributions are used to characterize the rain along the radar beam. Comparisons with the standard single-threshold method or with the sample mean, taken over the high-resolution estimates, show that the present method usually provides more accurate determinations of the area-averaged rain rate if the values of the threshold parameter, Q T , are chosen in the range from 0.2 to 0.4.
Abstract
A method is proposed for estimating the area-average rain-rate distribution from attenuating-wavelength spaceborne or airborne radar data. Because highly attenuated radar returns yield unreliable estimates of the rain rate, these are eliminated by means of a proxy variable, Q, derived from the apparent radar reflectivity factors and a power law relating the attenuation coefficient and the reflectivity factor. In determining the probability distribution function of areawide rain rates, the elimination of attenuated measurements at high rain rates and the loss of data at light rain rates, because of low signal-to-noise ratios, leads to truncation of the distribution at the low and high ends. To estimate it over all rain rates, a lognormal distribution is assumed, the parameters of which are obtained from a nonlinear least squares fit to the truncated distribution. Implementation of this type of threshold method depends on the method used in estimating the high-resolution rain-rate estimates (e.g., either the standard Z–R or the Hitschfeld–Bordan estimate) and on the type of rain-rate estimate (either point or path averaged). To test the method, measured drop size distributions are used to characterize the rain along the radar beam. Comparisons with the standard single-threshold method or with the sample mean, taken over the high-resolution estimates, show that the present method usually provides more accurate determinations of the area-averaged rain rate if the values of the threshold parameter, Q T , are chosen in the range from 0.2 to 0.4.
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
This paper briefly reviews several single-frequency rain profiling methods for an airborne or spaceborne radar. The authors describe the different methods from a unified point of view starting from the basic differential equation. This facilitates the comparisons between the methods and also provides a better understanding of the physical and mathematical basis of the methods. The application of several methods to airborne radar data taken during the Convective and Precipitation/Electrification Experiment is shown. Finally, the authors consider a hybrid method that provides a smooth transition between the Hitschfeld-Bordan method, which performs well at low attenuations, and the surface reference method, for which the relative error decreases with increasing path attenuation.
Abstract
This paper briefly reviews several single-frequency rain profiling methods for an airborne or spaceborne radar. The authors describe the different methods from a unified point of view starting from the basic differential equation. This facilitates the comparisons between the methods and also provides a better understanding of the physical and mathematical basis of the methods. The application of several methods to airborne radar data taken during the Convective and Precipitation/Electrification Experiment is shown. Finally, the authors consider a hybrid method that provides a smooth transition between the Hitschfeld-Bordan method, which performs well at low attenuations, and the surface reference method, for which the relative error decreases with increasing path attenuation.
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
In the case of a nadir-looking spaceborne or aircraft radar in the presence of rain the return power corresponding to secondary surface scattering may provide information on the properties of the surface and the precipitation. The object of the study is to evaluate a method for determining simultaneously the rainfall rate and the back-scattering coefficient of the surface, σ0. The method is based upon the mirror-reflected power, Pm , which corresponds to the portion of the incident power scattered from the surface to the precipitation, intercepted by the precipitation, and again returned to the surface where it is scattered a final time back to the antenna. Two approximations are obtained for Pm depending on whether the held of view at the surface is either much greater or much less than the height of the reflection layer. Since the dependence of Pm on the backscattering coefficient of the surface differs in the two cases, two algorithms are given by which the path-averaged rain rate and σ0 can be deduced. We also discuss the delectability of Pm , the relative strength of other contributions to the return power arriving simultaneously with Pm , and the validity of the approximations used in deriving Pm .
Abstract
In the case of a nadir-looking spaceborne or aircraft radar in the presence of rain the return power corresponding to secondary surface scattering may provide information on the properties of the surface and the precipitation. The object of the study is to evaluate a method for determining simultaneously the rainfall rate and the back-scattering coefficient of the surface, σ0. The method is based upon the mirror-reflected power, Pm , which corresponds to the portion of the incident power scattered from the surface to the precipitation, intercepted by the precipitation, and again returned to the surface where it is scattered a final time back to the antenna. Two approximations are obtained for Pm depending on whether the held of view at the surface is either much greater or much less than the height of the reflection layer. Since the dependence of Pm on the backscattering coefficient of the surface differs in the two cases, two algorithms are given by which the path-averaged rain rate and σ0 can be deduced. We also discuss the delectability of Pm , the relative strength of other contributions to the return power arriving simultaneously with Pm , and the validity of the approximations used in deriving Pm .
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.
