Search Results
You are looking at 1 - 10 of 15 items for
- Author or Editor: S. Joseph Munchak x
- Refine by Access: All Content x
Abstract
Observations of raindrop size distributions (DSDs) have validated the use of three-parameter distribution functions in representing the observed spectra. However, dual-frequency radar measurements are limited to retrieving two independent parameters of the DSD, thus requiring a constraint on a three-parameter distribution. In this study, disdrometer observations from a variety of climate regions are employed to develop constraints on the gamma distribution that are optimized for dual-frequency radar rainfall retrievals. These observations are composited by reflectivity, and then gamma parameters are fit to the composites. The results show considerable variability in shape parameter between regions and within a region at different reflectivities. Most notable is that oceanic regions exhibit maxima in shape parameter at 13.6-GHz reflectivities between 40 and 50 dBZ, in contrast to continental regions. The shape parameter and slope parameter of all composite DSDs are poorly correlated. Thus, constraints of a constant shape parameter or shape parameter–slope parameter relationship are inadequate to represent the observed variability. However, the shape and slope parameters are highly correlated at a given reflectivity. Constraints of a fixed shape parameter and relationships between a shape parameter m and slope parameter Λ, both of which are given as functions of 13.6-GHz reflectivity, are applied to retrieve rain rate, liquid water content, and mean mass diameter from the composites. The m–Λ relationships perform best at high reflectivity (dBZ 13.6 > 35), whereas the fixed shape parameter generally results in lower error at medium and low reflectivities (dBZ 13.6 < 35). All calculations have been made under the assumption that the reflectivity measurements have been corrected for attenuation.
Abstract
Observations of raindrop size distributions (DSDs) have validated the use of three-parameter distribution functions in representing the observed spectra. However, dual-frequency radar measurements are limited to retrieving two independent parameters of the DSD, thus requiring a constraint on a three-parameter distribution. In this study, disdrometer observations from a variety of climate regions are employed to develop constraints on the gamma distribution that are optimized for dual-frequency radar rainfall retrievals. These observations are composited by reflectivity, and then gamma parameters are fit to the composites. The results show considerable variability in shape parameter between regions and within a region at different reflectivities. Most notable is that oceanic regions exhibit maxima in shape parameter at 13.6-GHz reflectivities between 40 and 50 dBZ, in contrast to continental regions. The shape parameter and slope parameter of all composite DSDs are poorly correlated. Thus, constraints of a constant shape parameter or shape parameter–slope parameter relationship are inadequate to represent the observed variability. However, the shape and slope parameters are highly correlated at a given reflectivity. Constraints of a fixed shape parameter and relationships between a shape parameter m and slope parameter Λ, both of which are given as functions of 13.6-GHz reflectivity, are applied to retrieve rain rate, liquid water content, and mean mass diameter from the composites. The m–Λ relationships perform best at high reflectivity (dBZ 13.6 > 35), whereas the fixed shape parameter generally results in lower error at medium and low reflectivities (dBZ 13.6 < 35). All calculations have been made under the assumption that the reflectivity measurements have been corrected for attenuation.
Abstract
Although zonal mean rain rates from the Tropical Rainfall Measuring Mission (TRMM) are in good (<10%) agreement between the TRMM Microwave Imager (TMI) and precipitation radar (PR) rainfall algorithms, significant uncertainties remain in some regions where these estimates differ by as much as 30% over the period of record. Previous comparisons of these algorithms with ground validation (GV) rainfall have shown significant (>10%) biases of differing sign at various GV locations. Reducing these biases is important in the context of developing a database of cloud profiles for passive microwave retrievals that is based upon the PR-measured profiles. A retrieval framework based upon optimal estimation theory is proposed wherein three parameters describing the raindrop size distribution (DSD), ice particle size distribution, and cloud water path (cLWP) are retrieved for each radar profile. The modular nature of the framework provides the opportunity to test the sensitivity of the retrieval to the inclusion of different measurements, retrieved parameters, and models for microwave scattering properties of hydrometeors. The retrieved rainfall rate is found to be strongly sensitive to the a priori constraints in DSD and cLWP; thus, these parameters are tuned to match polarimetric radar estimates of rainfall near Kwajalein, Republic of Marshall Islands. An independent validation against gauge-tuned radar rainfall estimates at Melbourne, Florida, shows agreement within 2%, which exceeds previous algorithms’ ability to match rainfall at these two sites. Errors between observed and simulated brightness temperatures are reduced and climatological features of the DSD, as measured by disdrometers at these two locations, are also reproduced in the output of the combined algorithm.
Abstract
Although zonal mean rain rates from the Tropical Rainfall Measuring Mission (TRMM) are in good (<10%) agreement between the TRMM Microwave Imager (TMI) and precipitation radar (PR) rainfall algorithms, significant uncertainties remain in some regions where these estimates differ by as much as 30% over the period of record. Previous comparisons of these algorithms with ground validation (GV) rainfall have shown significant (>10%) biases of differing sign at various GV locations. Reducing these biases is important in the context of developing a database of cloud profiles for passive microwave retrievals that is based upon the PR-measured profiles. A retrieval framework based upon optimal estimation theory is proposed wherein three parameters describing the raindrop size distribution (DSD), ice particle size distribution, and cloud water path (cLWP) are retrieved for each radar profile. The modular nature of the framework provides the opportunity to test the sensitivity of the retrieval to the inclusion of different measurements, retrieved parameters, and models for microwave scattering properties of hydrometeors. The retrieved rainfall rate is found to be strongly sensitive to the a priori constraints in DSD and cLWP; thus, these parameters are tuned to match polarimetric radar estimates of rainfall near Kwajalein, Republic of Marshall Islands. An independent validation against gauge-tuned radar rainfall estimates at Melbourne, Florida, shows agreement within 2%, which exceeds previous algorithms’ ability to match rainfall at these two sites. Errors between observed and simulated brightness temperatures are reduced and climatological features of the DSD, as measured by disdrometers at these two locations, are also reproduced in the output of the combined algorithm.
Abstract
The scattering properties of aggregates are studied herein. Early aggregates (<7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.
Abstract
The scattering properties of aggregates are studied herein. Early aggregates (<7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.
A Consistent Treatment of Microwave Emissivity and Radar Backscatter for Retrieval of Precipitation over Water SurfacesAbstract
The Global Precipitation Measurement (GPM) Microwave Imager (GMI) and dual-frequency precipitation radar (DPR) are designed to provide the most accurate instantaneous precipitation estimates currently available from space. The GPM Combined Radar–Radiometer Algorithm (CORRA) plays a key role in this process by retrieving precipitation profiles that are consistent with GMI and DPR measurements; therefore, it is desirable that the forward models in CORRA use the same geophysical input parameters. This study explores the feasibility of using internally consistent emissivity and surface backscatter cross-sectional (
Abstract
The Global Precipitation Measurement (GPM) Microwave Imager (GMI) and dual-frequency precipitation radar (DPR) are designed to provide the most accurate instantaneous precipitation estimates currently available from space. The GPM Combined Radar–Radiometer Algorithm (CORRA) plays a key role in this process by retrieving precipitation profiles that are consistent with GMI and DPR measurements; therefore, it is desirable that the forward models in CORRA use the same geophysical input parameters. This study explores the feasibility of using internally consistent emissivity and surface backscatter cross-sectional (
Abstract
Rainfall retrieval algorithms for passive microwave radiometers often exploit the brightness temperature depression due to ice scattering at high-frequency channels (≥85 GHz) over land. This study presents an alternate method to estimate the daily rainfall amount using the emissivity temporal variation (i.e., Δe) under rain-free conditions at low-frequency channels (19, 24, and 37 GHz). Emissivity is derived from 10 passive microwave radiometers, including the Global Precipitation Measurement (GPM) Microwave Imager (GMI), the Advanced Microwave Scanning Radiometer 2 (AMSR2), three Special Sensor Microwave Imager/Sounders (SSMIS), the Advanced Technology Microwave Sounder (ATMS), and four Advanced Microwave Sounding Units-A (AMSU-A). Four different satellite combination schemes are used to derive the Δe for daily rainfall estimates. They are all 10 satellites, 5 imagers, 6 satellites with very different equator crossing times, and GMI only. Results show that Δe from all 10 satellites has the best performance with a correlation of 0.60 and RMSE of 6.52 mm, compared with the Integrated Multisatellite Retrievals for GPM (IMERG) Final run product. The 6-satellites scheme has comparable performance with the all-10-satellites scheme. The 5-imagers scheme performs noticeably worse with a correlation of 0.49 and RMSE of 7.28 mm, while the GMI-only scheme performs the worst with a correlation of 0.25 and RMSE of 11.36 mm. The inferior performance from the 5-imagers and GMI-only schemes can be explained by the much longer revisit time, which cannot accurately capture the emissivity temporal variation.
Abstract
Rainfall retrieval algorithms for passive microwave radiometers often exploit the brightness temperature depression due to ice scattering at high-frequency channels (≥85 GHz) over land. This study presents an alternate method to estimate the daily rainfall amount using the emissivity temporal variation (i.e., Δe) under rain-free conditions at low-frequency channels (19, 24, and 37 GHz). Emissivity is derived from 10 passive microwave radiometers, including the Global Precipitation Measurement (GPM) Microwave Imager (GMI), the Advanced Microwave Scanning Radiometer 2 (AMSR2), three Special Sensor Microwave Imager/Sounders (SSMIS), the Advanced Technology Microwave Sounder (ATMS), and four Advanced Microwave Sounding Units-A (AMSU-A). Four different satellite combination schemes are used to derive the Δe for daily rainfall estimates. They are all 10 satellites, 5 imagers, 6 satellites with very different equator crossing times, and GMI only. Results show that Δe from all 10 satellites has the best performance with a correlation of 0.60 and RMSE of 6.52 mm, compared with the Integrated Multisatellite Retrievals for GPM (IMERG) Final run product. The 6-satellites scheme has comparable performance with the all-10-satellites scheme. The 5-imagers scheme performs noticeably worse with a correlation of 0.49 and RMSE of 7.28 mm, while the GMI-only scheme performs the worst with a correlation of 0.25 and RMSE of 11.36 mm. The inferior performance from the 5-imagers and GMI-only schemes can be explained by the much longer revisit time, which cannot accurately capture the emissivity temporal variation.
Cross Validation of Rainfall Characteristics Estimated from the TRMM PR, a Combined PR–TMI Algorithm, and a C-POL Ground Radar during the Passage of Tropical Cyclone and Nontropical Cyclone Events over Darwin, AustraliaAbstract
This study cross validates the radar reflectivity Z; the rainfall drop size distribution parameter (median volume diameter D o ); and the rainfall rate R estimated from the Tropical Rainfall Measuring Mission (TRMM) satellite Precipitation Radar (PR), a combined PR and TRMM Microwave Imager (TMI) algorithm (COM), and a C-band dual-polarized ground radar (GR) for TRMM overpasses during the passage of tropical cyclone (TC) and non-TC events over Darwin, Australia. Two overpass events during the passage of TC Carlos and 11 non-TC overpass events are used in this study, and the GR is taken as the reference. It is shown that the correspondence is dependent on the precipitation type whereby events with more (less) stratiform rainfall usually have a positive (negative) bias in the reflectivity and the rainfall rate, whereas in the D o the bias is generally positive but small (large). The COM reflectivity estimates are similar to the PR, but it has a smaller bias in the D o for most of the greater stratiform events. This suggests that combining the TMI with the PR adjusts the D o toward the “correct” direction if the GR is taken as the reference. Moreover, the association between the TRMM estimates and the GR for the two TC events, which are highly stratiform in nature, is similar to that observed for the highly stratiform non-TC events (there is no significant difference), but it differs considerably from that observed for the majority of the highly convective non-TC events.
Abstract
This study cross validates the radar reflectivity Z; the rainfall drop size distribution parameter (median volume diameter D o ); and the rainfall rate R estimated from the Tropical Rainfall Measuring Mission (TRMM) satellite Precipitation Radar (PR), a combined PR and TRMM Microwave Imager (TMI) algorithm (COM), and a C-band dual-polarized ground radar (GR) for TRMM overpasses during the passage of tropical cyclone (TC) and non-TC events over Darwin, Australia. Two overpass events during the passage of TC Carlos and 11 non-TC overpass events are used in this study, and the GR is taken as the reference. It is shown that the correspondence is dependent on the precipitation type whereby events with more (less) stratiform rainfall usually have a positive (negative) bias in the reflectivity and the rainfall rate, whereas in the D o the bias is generally positive but small (large). The COM reflectivity estimates are similar to the PR, but it has a smaller bias in the D o for most of the greater stratiform events. This suggests that combining the TMI with the PR adjusts the D o toward the “correct” direction if the GR is taken as the reference. Moreover, the association between the TRMM estimates and the GR for the two TC events, which are highly stratiform in nature, is similar to that observed for the highly stratiform non-TC events (there is no significant difference), but it differs considerably from that observed for the majority of the highly convective non-TC events.
Abstract
Raindrop size distribution (DSD) retrievals from two years of data gathered by the Tropical Rainfall Measuring Mission (TRMM) satellite and processed with a combined radar–radiometer algorithm over the oceans equatorward of 35° are examined for relationships with variables describing properties of the vertical precipitation profile, mesoscale organization, and background environment. In general, higher freezing levels and relative humidities (tropical environments) are associated with smaller reflectivity-normalized median drop size (ϵ DSD) than in the extratropics. Within the tropics, the smallest ϵ DSD values are found in large, shallow convective systems where warm rain formation processes are thought to be predominant, whereas larger sizes are found in the stratiform regions of organized deep convection. In the extratropics, the largest ϵ DSD values are found in the scattered convection that occurs when cold, dry continental air moves over the much warmer ocean after the passage of a cold front. These relationships are formally attributed to variables describing the large-scale environment, mesoscale organization, and profile characteristics via principal component (PC) analysis. The leading three PCs account for 23% of the variance in ϵ DSD at the individual profile level and 45% of the variance in 1°-gridded mean values. The geographical distribution of ϵ DSD is consistent with many of the observed regional reflectivity–rainfall (Z–R) relationships found in the literature as well as discrepancies between the TRMM radar-only and radiometer-only precipitation products. In particular, midlatitude and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Ocean intertropical convergence zone.
Abstract
Raindrop size distribution (DSD) retrievals from two years of data gathered by the Tropical Rainfall Measuring Mission (TRMM) satellite and processed with a combined radar–radiometer algorithm over the oceans equatorward of 35° are examined for relationships with variables describing properties of the vertical precipitation profile, mesoscale organization, and background environment. In general, higher freezing levels and relative humidities (tropical environments) are associated with smaller reflectivity-normalized median drop size (ϵ DSD) than in the extratropics. Within the tropics, the smallest ϵ DSD values are found in large, shallow convective systems where warm rain formation processes are thought to be predominant, whereas larger sizes are found in the stratiform regions of organized deep convection. In the extratropics, the largest ϵ DSD values are found in the scattered convection that occurs when cold, dry continental air moves over the much warmer ocean after the passage of a cold front. These relationships are formally attributed to variables describing the large-scale environment, mesoscale organization, and profile characteristics via principal component (PC) analysis. The leading three PCs account for 23% of the variance in ϵ DSD at the individual profile level and 45% of the variance in 1°-gridded mean values. The geographical distribution of ϵ DSD is consistent with many of the observed regional reflectivity–rainfall (Z–R) relationships found in the literature as well as discrepancies between the TRMM radar-only and radiometer-only precipitation products. In particular, midlatitude and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Ocean intertropical convergence zone.
The GPM Combined AlgorithmAbstract
In this paper, the operational Global Precipitation Measurement (GPM) mission combined radar–radiometer algorithm is thoroughly described. The operational combined algorithm is designed to reduce uncertainties in GPM Core Observatory precipitation estimates by effectively integrating complementary information from the GPM Dual-Frequency Precipitation Radar (DPR) and the GPM Microwave Imager (GMI) into an optimal, physically consistent precipitation product. Although similar in many respects to previously developed combined algorithms, the GPM combined algorithm has several unique features that are specifically designed to meet the GPM objectives of deriving, based on GPM Core Observatory information, accurate and physically consistent precipitation estimates from multiple spaceborne instruments, and ancillary environmental data from reanalyses. The algorithm features an optimal estimation framework based on a statistical formulation of the Gauss–Newton method, a parameterization for the nonuniform distribution of precipitation within the radar fields of view, a methodology to detect and account for multiple scattering in Ka-band DPR observations, and a statistical deconvolution technique that allows for an efficient sequential incorporation of radiometer information into DPR precipitation retrievals.
Abstract
In this paper, the operational Global Precipitation Measurement (GPM) mission combined radar–radiometer algorithm is thoroughly described. The operational combined algorithm is designed to reduce uncertainties in GPM Core Observatory precipitation estimates by effectively integrating complementary information from the GPM Dual-Frequency Precipitation Radar (DPR) and the GPM Microwave Imager (GMI) into an optimal, physically consistent precipitation product. Although similar in many respects to previously developed combined algorithms, the GPM combined algorithm has several unique features that are specifically designed to meet the GPM objectives of deriving, based on GPM Core Observatory information, accurate and physically consistent precipitation estimates from multiple spaceborne instruments, and ancillary environmental data from reanalyses. The algorithm features an optimal estimation framework based on a statistical formulation of the Gauss–Newton method, a parameterization for the nonuniform distribution of precipitation within the radar fields of view, a methodology to detect and account for multiple scattering in Ka-band DPR observations, and a statistical deconvolution technique that allows for an efficient sequential incorporation of radiometer information into DPR precipitation retrievals.
Abstract
Previous studies showed that conical scanning radiometers greatly outperform cross-track scanning radiometers for precipitation retrieval over ocean. This study demonstrates a novel approach to improve precipitation rates at the cross-track scanning radiometers’ observation time by propagating the conical scanning radiometers’ retrievals to the cross-track scanning radiometers’ observation time. The improved precipitation rate is a weighted average of original cross-track radiometers’ retrievals and retrievals propagated from a conical scanning radiometer. The cross-track scanning radiometers include the Advanced Technology Microwave Sounder (ATMS) on board the SNPP satellite and four Microwave Humidity Sounders (MHSs). The conical scanning radiometers include the Advanced Microwave Scanning Radiometer 2 (AMSR2) and three Special Sensor Microwave Imager/Sounders (SSMISs), while the precipitation retrievals from the Global Precipitation Measurement (GPM) Microwave Imager (GMI) are taken as the reference. Results show that the morphed precipitation rates agree much better with the reference. The degree of improvement depends on several factors, including the propagated precipitation source, the time interval between the cross-track scanning radiometer and the conical scanning radiometer, the precipitation type (convective versus stratiform), the precipitation events’ size, and the geolocation. The study has potential to greatly improve high-impact weather systems monitoring (e.g., hurricanes) and multisatellite precipitation products. It may also enhance the usefulness of future satellite missions with cross-track scanning radiometers on board.
Abstract
Previous studies showed that conical scanning radiometers greatly outperform cross-track scanning radiometers for precipitation retrieval over ocean. This study demonstrates a novel approach to improve precipitation rates at the cross-track scanning radiometers’ observation time by propagating the conical scanning radiometers’ retrievals to the cross-track scanning radiometers’ observation time. The improved precipitation rate is a weighted average of original cross-track radiometers’ retrievals and retrievals propagated from a conical scanning radiometer. The cross-track scanning radiometers include the Advanced Technology Microwave Sounder (ATMS) on board the SNPP satellite and four Microwave Humidity Sounders (MHSs). The conical scanning radiometers include the Advanced Microwave Scanning Radiometer 2 (AMSR2) and three Special Sensor Microwave Imager/Sounders (SSMISs), while the precipitation retrievals from the Global Precipitation Measurement (GPM) Microwave Imager (GMI) are taken as the reference. Results show that the morphed precipitation rates agree much better with the reference. The degree of improvement depends on several factors, including the propagated precipitation source, the time interval between the cross-track scanning radiometer and the conical scanning radiometer, the precipitation type (convective versus stratiform), the precipitation events’ size, and the geolocation. The study has potential to greatly improve high-impact weather systems monitoring (e.g., hurricanes) and multisatellite precipitation products. It may also enhance the usefulness of future satellite missions with cross-track scanning radiometers on board.
Abstract
Parameters of the normalized gamma particle size distribution (PSD) have been retrieved from the Precipitation Image Package (PIP) snowfall observations collected during the International Collaborative Experiment–PyeongChang Olympic and Paralympic winter games (ICE-POP 2018). Two of the gamma PSD parameters, the mass-weighted particle diameter D mass and the normalized intercept parameter NW , have median values of 1.15–1.31 mm and 2.84–3.04 log(mm−1 m−3), respectively. This range arises from the choice of the relationship between the maximum versus equivalent diameter, D mx–D eq, and the relationship between the Reynolds and Best numbers, Re–X. Normalization of snow water equivalent rate (SWER) and ice water content W by NW reduces the range in NW , resulting in well-fitted power-law relationships between SWER/NW and D mass and between W/NW and D mass. The bulk descriptors of snowfall are calculated from PIP observations and from the gamma PSD with values of the shape parameter μ ranging from −2 to 10. NASA’s Global Precipitation Measurement (GPM) mission, which adopted the normalized gamma PSD, assumes μ = 2 and 3 in its two separate algorithms. The mean fractional bias (MFB) of the snowfall parameters changes with μ, where the functional dependence on μ depends on the specific snowfall parameter of interest. The MFB of the total concentration was underestimated by 0.23–0.34 when μ = 2 and by 0.29–0.40 when μ = 3, whereas the MFB of SWER had a much narrower range (from −0.03 to 0.04) for the same μ values.
Abstract
Parameters of the normalized gamma particle size distribution (PSD) have been retrieved from the Precipitation Image Package (PIP) snowfall observations collected during the International Collaborative Experiment–PyeongChang Olympic and Paralympic winter games (ICE-POP 2018). Two of the gamma PSD parameters, the mass-weighted particle diameter D mass and the normalized intercept parameter NW , have median values of 1.15–1.31 mm and 2.84–3.04 log(mm−1 m−3), respectively. This range arises from the choice of the relationship between the maximum versus equivalent diameter, D mx–D eq, and the relationship between the Reynolds and Best numbers, Re–X. Normalization of snow water equivalent rate (SWER) and ice water content W by NW reduces the range in NW , resulting in well-fitted power-law relationships between SWER/NW and D mass and between W/NW and D mass. The bulk descriptors of snowfall are calculated from PIP observations and from the gamma PSD with values of the shape parameter μ ranging from −2 to 10. NASA’s Global Precipitation Measurement (GPM) mission, which adopted the normalized gamma PSD, assumes μ = 2 and 3 in its two separate algorithms. The mean fractional bias (MFB) of the snowfall parameters changes with μ, where the functional dependence on μ depends on the specific snowfall parameter of interest. The MFB of the total concentration was underestimated by 0.23–0.34 when μ = 2 and by 0.29–0.40 when μ = 3, whereas the MFB of SWER had a much narrower range (from −0.03 to 0.04) for the same μ values.
