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- Author or Editor: Toshio Iguchi x
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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
In this study, the authors used Tropical Rainfall Measuring Mission precipitation radar (TRMM PR) data to investigate changes in the actual (attenuation corrected) surface backscattering cross section (σ 0 e ) due to changes in surface conditions induced by rainfall, the effects of changes in σ 0 e on the path integrated attenuation (PIA) estimates by surface reference techniques (SRTs), and the effects on rain-rate estimates by the TRMM PR standard rain-rate retrieval algorithm.
Over land, σ 0 e is statistically higher under rainfall than under no rainfall conditions (soil moisture effect) unless the land surface is densely covered by vegetation. Over ocean, the dependence of σ 0 e on the incident angle differs under rainfall and no-rainfall conditions (wind speed effect). The alongtrack spatial reference (ATSR) method, one of the SRTs used in the standard algorithm, partially considers these effects, while the temporal reference (TR) method, another SRT, never involves these effects; its PIA estimates thus have negative biases over land. In the hybrid spatial reference (HSR) method used over ocean, different incident angles create different biases in PIA estimates. If the TR method is replaced by the ATSR method, the monthly rainfall amount in July 2001 all over the land within the TRMM coverage increases by 0.70%. The bias in the HSR method over ocean can be mitigated by fitting a σ 0–θ curve separately to smaller incident angles and to larger incident angles. This improvement increases or decreases the monthly rainfall amounts in individual incident angle regions by up to 10%.
Abstract
In this study, the authors used Tropical Rainfall Measuring Mission precipitation radar (TRMM PR) data to investigate changes in the actual (attenuation corrected) surface backscattering cross section (σ 0 e ) due to changes in surface conditions induced by rainfall, the effects of changes in σ 0 e on the path integrated attenuation (PIA) estimates by surface reference techniques (SRTs), and the effects on rain-rate estimates by the TRMM PR standard rain-rate retrieval algorithm.
Over land, σ 0 e is statistically higher under rainfall than under no rainfall conditions (soil moisture effect) unless the land surface is densely covered by vegetation. Over ocean, the dependence of σ 0 e on the incident angle differs under rainfall and no-rainfall conditions (wind speed effect). The alongtrack spatial reference (ATSR) method, one of the SRTs used in the standard algorithm, partially considers these effects, while the temporal reference (TR) method, another SRT, never involves these effects; its PIA estimates thus have negative biases over land. In the hybrid spatial reference (HSR) method used over ocean, different incident angles create different biases in PIA estimates. If the TR method is replaced by the ATSR method, the monthly rainfall amount in July 2001 all over the land within the TRMM coverage increases by 0.70%. The bias in the HSR method over ocean can be mitigated by fitting a σ 0–θ curve separately to smaller incident angles and to larger incident angles. This improvement increases or decreases the monthly rainfall amounts in individual incident angle regions by up to 10%.
Abstract
A method is studied to make a nonuniform beamfilling (NUBF) correction for the path-integrated attenuation (PIA) derived from spaceborne radar measurement. The key of this method is to estimate rain-rate variability within a radar field of view from the local statistics of a radar-measurable quantity (〈Q〉) such as PIA derived from the surface reference technique. Statistical analyses are made on spatial variabilities of the radar-measurable quantities using a shipborne radar dataset over the tropical Pacific obtained during the TOGA COARE field campaign. It is found that there are reasonably good correlations between the coarse-scale variability of 〈Q〉 and the finescale variability of rain rate, and the regression coefficient (slope) of these two quantities depends somewhat upon rain types. Based on the statistical analyses, the method is tested with a simulation using the same dataset. The test result indicates that this method is effective in reducing bias errors in the estimation of rain-rate statistics. Although it is also effective to make the NUBF correction on an individual instantaneous field-of-view basis, one must account for the variability of local rainfall statistical characteristics that may cause significant errors in the NUBF correction.
Abstract
A method is studied to make a nonuniform beamfilling (NUBF) correction for the path-integrated attenuation (PIA) derived from spaceborne radar measurement. The key of this method is to estimate rain-rate variability within a radar field of view from the local statistics of a radar-measurable quantity (〈Q〉) such as PIA derived from the surface reference technique. Statistical analyses are made on spatial variabilities of the radar-measurable quantities using a shipborne radar dataset over the tropical Pacific obtained during the TOGA COARE field campaign. It is found that there are reasonably good correlations between the coarse-scale variability of 〈Q〉 and the finescale variability of rain rate, and the regression coefficient (slope) of these two quantities depends somewhat upon rain types. Based on the statistical analyses, the method is tested with a simulation using the same dataset. The test result indicates that this method is effective in reducing bias errors in the estimation of rain-rate statistics. Although it is also effective to make the NUBF correction on an individual instantaneous field-of-view basis, one must account for the variability of local rainfall statistical characteristics that may cause significant errors in the NUBF correction.
Abstract
A new attenuation correction method has been developed for the dual-frequency precipitation radar (DPR) on the core satellite of the Global Precipitation Measurement (GPM) mission. The new method is based on Hitschfeld and Bordan’s attenuation correction method (HB method), but the relationship between the specific attenuation k and the effective radar reflectivity factor Z e (k–Z e relationship) is modified by using the dual-frequency ratio (DFR) of Z e and the surface reference technique (SRT). Therefore, the new method is called the HB-DFR-SRT method (H-D-S method). The previous attenuation correction method, called the HB-DFR method (H-D method), results in an underestimation of precipitation rates for heavy precipitation, but the H-D-S method mitigates the negative bias by means of the SRT. When only a single-frequency measurement is available, the H-D-S method is identical to the HB-SRT method (H-S method).
The attenuation correction methods were tested with a simple synthetic DPR dataset. As long as the SRT gives perfect estimates of path-integrated attenuation and the adjustment factor of the k–Z e relationship (denoted by ε) is vertically constant, the H-S method is much better than the dual-frequency methods. Tests with SRT error and vertical variation in ε showed that the H-D method was better than the H-S method for weak precipitation, whereas the H-S method was better than the H-D method for heavy precipitation. The H-D-S method did not produce the best results for both weak and heavy precipitation, but the results are stable. Quantitative evaluation should be done with real DPR measurement datasets.
Abstract
A new attenuation correction method has been developed for the dual-frequency precipitation radar (DPR) on the core satellite of the Global Precipitation Measurement (GPM) mission. The new method is based on Hitschfeld and Bordan’s attenuation correction method (HB method), but the relationship between the specific attenuation k and the effective radar reflectivity factor Z e (k–Z e relationship) is modified by using the dual-frequency ratio (DFR) of Z e and the surface reference technique (SRT). Therefore, the new method is called the HB-DFR-SRT method (H-D-S method). The previous attenuation correction method, called the HB-DFR method (H-D method), results in an underestimation of precipitation rates for heavy precipitation, but the H-D-S method mitigates the negative bias by means of the SRT. When only a single-frequency measurement is available, the H-D-S method is identical to the HB-SRT method (H-S method).
The attenuation correction methods were tested with a simple synthetic DPR dataset. As long as the SRT gives perfect estimates of path-integrated attenuation and the adjustment factor of the k–Z e relationship (denoted by ε) is vertically constant, the H-S method is much better than the dual-frequency methods. Tests with SRT error and vertical variation in ε showed that the H-D method was better than the H-S method for weak precipitation, whereas the H-S method was better than the H-D method for heavy precipitation. The H-D-S method did not produce the best results for both weak and heavy precipitation, but the results are stable. Quantitative evaluation should be done with real DPR measurement datasets.
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.
Abstract
Digitized signals for a spaceborne weather radar are generated to inspect a Doppler signal processor, in which the digital signals are converted to analog through an arbitrary wave generator. A conventional Rice harmonic analysis is applied to include fluctuations of Fourier coefficients explicitly in a time series rather than in an ensemble. The accuracy of Doppler velocity is studied through this simulation for a mean estimator of contiguous pulse-pair operation in a space mission, characterized by a low signal-to-noise ratio (SNR) and a short coherence time. A linear perturbation formula is shown to deviate from the simulation as the SNR decreases and the pulse-pair interval increases. Furthermore, a theoretical limit in measurement accuracy is derived, beyond which the correlation signal is to be practically regarded as white noise, losing the physical meaning of measurement.
Abstract
Digitized signals for a spaceborne weather radar are generated to inspect a Doppler signal processor, in which the digital signals are converted to analog through an arbitrary wave generator. A conventional Rice harmonic analysis is applied to include fluctuations of Fourier coefficients explicitly in a time series rather than in an ensemble. The accuracy of Doppler velocity is studied through this simulation for a mean estimator of contiguous pulse-pair operation in a space mission, characterized by a low signal-to-noise ratio (SNR) and a short coherence time. A linear perturbation formula is shown to deviate from the simulation as the SNR decreases and the pulse-pair interval increases. Furthermore, a theoretical limit in measurement accuracy is derived, beyond which the correlation signal is to be practically regarded as white noise, losing the physical meaning of measurement.
Abstract
Validating the results from the spaceborne Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) requires comparisons with well-calibrated ground-based radar measurements. At altitudes near the storm top, where effects of PR signal attenuation are small, the data are used to check the relative calibration accuracy of the radars. Near the surface, where attenuation effects at the PR frequency of 13.8 GHz can be significant, the data provide an assessment of the performance of the PR attenuation correction algorithm. The ground-based data are taken from the Doppler Weather Surveillance (WSR-88D) radar located at Melbourne, Florida. In 1998, 24 overpasses of the TRMM satellite over the Melbourne site occurred during times when significant precipitation was present in the overlap region of the PR and WSR-88D. Resampling the ground-based and spaceborne datasets to a common grid provides a means by which the radar reflectivity factors (dBZ) can be compared at different heights and for different rain types over ocean and land. The results from 1998 show that the dBZ fields derived from the PR data after attenuation correction agree to within about 1 dB of those obtained from the WSR-88D with relatively minor variations (0.3 dB) in this difference with height. Comparisons of rain rates also yield good agreement with the conditional mean rain rate from the PR and WSR-88D of 8.5 and 7.6 mm h−1, respectively. The agreement improves in the comparison of area-averaged rain rates where the PR and WSR-88D yield values of 1.25 and 1.21 mm h−1, respectively, with a correlation coefficient for the 24 overpasses of 0.95.
Abstract
Validating the results from the spaceborne Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) requires comparisons with well-calibrated ground-based radar measurements. At altitudes near the storm top, where effects of PR signal attenuation are small, the data are used to check the relative calibration accuracy of the radars. Near the surface, where attenuation effects at the PR frequency of 13.8 GHz can be significant, the data provide an assessment of the performance of the PR attenuation correction algorithm. The ground-based data are taken from the Doppler Weather Surveillance (WSR-88D) radar located at Melbourne, Florida. In 1998, 24 overpasses of the TRMM satellite over the Melbourne site occurred during times when significant precipitation was present in the overlap region of the PR and WSR-88D. Resampling the ground-based and spaceborne datasets to a common grid provides a means by which the radar reflectivity factors (dBZ) can be compared at different heights and for different rain types over ocean and land. The results from 1998 show that the dBZ fields derived from the PR data after attenuation correction agree to within about 1 dB of those obtained from the WSR-88D with relatively minor variations (0.3 dB) in this difference with height. Comparisons of rain rates also yield good agreement with the conditional mean rain rate from the PR and WSR-88D of 8.5 and 7.6 mm h−1, respectively. The agreement improves in the comparison of area-averaged rain rates where the PR and WSR-88D yield values of 1.25 and 1.21 mm h−1, respectively, with a correlation coefficient for the 24 overpasses of 0.95.
Detection of Intense Ice Precipitation with GPM/DPRAbstract
Detection of ice precipitation is one of the objectives in the Global Precipitation Measurement (GPM) mission. The dual-frequency precipitation radar (DPR) can provide precipitation echoes at two different frequencies, which may enable differentiating solid precipitation echoes from liquid precipitation echoes. A simple algorithm that flags the pixels that contain intense ice precipitation above the height of 
Abstract
Detection of ice precipitation is one of the objectives in the Global Precipitation Measurement (GPM) mission. The dual-frequency precipitation radar (DPR) can provide precipitation echoes at two different frequencies, which may enable differentiating solid precipitation echoes from liquid precipitation echoes. A simple algorithm that flags the pixels that contain intense ice precipitation above the height of
Correction of Path-Integrated Attenuation Estimates Considering the Soil Moisture Effect for the GPM Dual-Frequency Precipitation RadarAbstract
Spaceborne precipitation radars, including the Tropical Rainfall Measuring Mission’s Precipitation Radar (PR) and the Global Precipitation Measurement Mission’s Dual-Frequency Precipitation Radar (DPR), measure not only precipitation echoes but surface echoes as well, the latter of which are used to estimate the path-integrated attenuation (PIA) in the surface reference technique (SRT). In our previous study based on analyzing PR measurements, we found that attenuation-free surface backscattering cross sections (denoted by
Abstract
Spaceborne precipitation radars, including the Tropical Rainfall Measuring Mission’s Precipitation Radar (PR) and the Global Precipitation Measurement Mission’s Dual-Frequency Precipitation Radar (DPR), measure not only precipitation echoes but surface echoes as well, the latter of which are used to estimate the path-integrated attenuation (PIA) in the surface reference technique (SRT). In our previous study based on analyzing PR measurements, we found that attenuation-free surface backscattering cross sections (denoted by
Abstract
Use of dual-wavelength radar, with properly chosen wavelengths, will significantly lessen the ambiguities in the retrieval of microphysical properties of hydrometeors. In this paper, a dual-wavelength algorithm is described to estimate the characteristic parameters of the snow size distributions. An analysis of the computational results, made at X and Ka bands (T-39 airborne radar) and at S and X bands (CP-2 ground-based radar), indicates that valid estimates of the median volume diameter of snow particles, D 0, should be possible if one of the two wavelengths of the radar operates in the non-Rayleigh scattering region. However, the accuracy may be affected to some extent if the shape factors of the gamma distribution used for describing the particle distribution are chosen far from the true values or if cloud water attenuation is significant. To examine the validity and accuracy of the dual-wavelength radar algorithms, the algorithms are applied to the data taken from the Convective and Precipitation-Electrification Experiment (CaPE) in 1991, in which the dual-wavelength airborne radar was coordinated with in situ aircraft particle observations and ground-based radar measurements. Having carefully coregistered the data obtained from the different platforms, the airborne radar-derived size distributions are then compared with the in situ measurements and ground-based radar. Good agreement is found for these comparisons despite the uncertainties resulting from mismatches of the sample volumes among the different sensors as well as spatial and temporal offsets.
Abstract
Use of dual-wavelength radar, with properly chosen wavelengths, will significantly lessen the ambiguities in the retrieval of microphysical properties of hydrometeors. In this paper, a dual-wavelength algorithm is described to estimate the characteristic parameters of the snow size distributions. An analysis of the computational results, made at X and Ka bands (T-39 airborne radar) and at S and X bands (CP-2 ground-based radar), indicates that valid estimates of the median volume diameter of snow particles, D 0, should be possible if one of the two wavelengths of the radar operates in the non-Rayleigh scattering region. However, the accuracy may be affected to some extent if the shape factors of the gamma distribution used for describing the particle distribution are chosen far from the true values or if cloud water attenuation is significant. To examine the validity and accuracy of the dual-wavelength radar algorithms, the algorithms are applied to the data taken from the Convective and Precipitation-Electrification Experiment (CaPE) in 1991, in which the dual-wavelength airborne radar was coordinated with in situ aircraft particle observations and ground-based radar measurements. Having carefully coregistered the data obtained from the different platforms, the airborne radar-derived size distributions are then compared with the in situ measurements and ground-based radar. Good agreement is found for these comparisons despite the uncertainties resulting from mismatches of the sample volumes among the different sensors as well as spatial and temporal offsets.
