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- Author or Editor: Alexander V. Ryzhkov x
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Abstract
In the presence of partial beam blockage (PBB), weather radar measurements can experience significant bias that directly compromises the accuracy of the hydrologic applications. Techniques for the calibration of the radar reflectivity factor Z and differential reflectivity Z DR, measured with dual-polarization weather radars in the presence of partial beam obstruction, are examined in this paper.
The proposed Z DR calibration technique utilizes radar measurements of Z DR in light rain and dry aggregated snow at unblocked and blocked elevations. This calibration technique was tested for the National Severe Storms Laboratory’s (NSSL’s) Cimarron radar that suffers from PBB, and a polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) that does not experience PBB. Results indicate that the Z DR bias that is associated with PBB can be calibrated with an accuracy of 0.2–0.3 dB, provided that the dataset is sufficiently large.
Calibration of Z in the presence of PBB is based on the idea of self-consistency among Z, Z DR, and the specific differential phase K DP in rain. The self-consistency calibration of Z from the Cimarron radar is performed following an area–time integral method. Integration is partitioned into small azimuthal sectors to assess the azimuthal modulation of the Z bias. The suggested technique is validated by direct comparisons of reflectivity factors that are measured by the Cimarron radar and the unobstructed operational WSR-88D radar. It is shown that the azimuthal modulation of Z that is caused by PBB is well captured, and the accuracy of the Z calibration is within 2–3 dB.
Abstract
In the presence of partial beam blockage (PBB), weather radar measurements can experience significant bias that directly compromises the accuracy of the hydrologic applications. Techniques for the calibration of the radar reflectivity factor Z and differential reflectivity Z DR, measured with dual-polarization weather radars in the presence of partial beam obstruction, are examined in this paper.
The proposed Z DR calibration technique utilizes radar measurements of Z DR in light rain and dry aggregated snow at unblocked and blocked elevations. This calibration technique was tested for the National Severe Storms Laboratory’s (NSSL’s) Cimarron radar that suffers from PBB, and a polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) that does not experience PBB. Results indicate that the Z DR bias that is associated with PBB can be calibrated with an accuracy of 0.2–0.3 dB, provided that the dataset is sufficiently large.
Calibration of Z in the presence of PBB is based on the idea of self-consistency among Z, Z DR, and the specific differential phase K DP in rain. The self-consistency calibration of Z from the Cimarron radar is performed following an area–time integral method. Integration is partitioned into small azimuthal sectors to assess the azimuthal modulation of the Z bias. The suggested technique is validated by direct comparisons of reflectivity factors that are measured by the Cimarron radar and the unobstructed operational WSR-88D radar. It is shown that the azimuthal modulation of Z that is caused by PBB is well captured, and the accuracy of the Z calibration is within 2–3 dB.
Abstract
Chaff contaminates estimates of precipitation amounts; hence, it is important to remove (or censor) its presence from the fields of radar reflectivity. It is demonstrated that efficient and direct identification of chaff is possible with a polarimetric radar. Specifically considered are the horizontal and vertical polarization basis and covariances of corresponding returned signals. Pertinent polarimetric variables are the copolar correlation coefficient, differential reflectivity, and the linear depolarization ratio. Two models are used to compute the expected values of these variables. In one, chaff is approximated with a Hertzian dipole and, in the other, with a thin wire antenna. In these models chaff is assumed to have a uniform distribution of flutter angles (angle between the horizontal plane and chaff axis). The two models produce nearly equivalent results. Also shown are polarimetric signatures of chaff observed in the presence of precipitation. Inferences about chaff's orientation are made from comparisons between measured and observed differential reflectivity and the cross-correlation coefficient.
Abstract
Chaff contaminates estimates of precipitation amounts; hence, it is important to remove (or censor) its presence from the fields of radar reflectivity. It is demonstrated that efficient and direct identification of chaff is possible with a polarimetric radar. Specifically considered are the horizontal and vertical polarization basis and covariances of corresponding returned signals. Pertinent polarimetric variables are the copolar correlation coefficient, differential reflectivity, and the linear depolarization ratio. Two models are used to compute the expected values of these variables. In one, chaff is approximated with a Hertzian dipole and, in the other, with a thin wire antenna. In these models chaff is assumed to have a uniform distribution of flutter angles (angle between the horizontal plane and chaff axis). The two models produce nearly equivalent results. Also shown are polarimetric signatures of chaff observed in the presence of precipitation. Inferences about chaff's orientation are made from comparisons between measured and observed differential reflectivity and the cross-correlation coefficient.
Abstract
Rainfall estimation from specific differential phases in meteorological situations with significant anomalous propagation (AP) is discussed. It is shown that the correlation coefficient between horizontally and vertically polarized backscatter signals and local variability of the total differential phase can be good identifiers of ground clutter–contaminated data. Further, it is suggested how to estimate rainfall in regions of ground clutter caused by AP.
Abstract
Rainfall estimation from specific differential phases in meteorological situations with significant anomalous propagation (AP) is discussed. It is shown that the correlation coefficient between horizontally and vertically polarized backscatter signals and local variability of the total differential phase can be good identifiers of ground clutter–contaminated data. Further, it is suggested how to estimate rainfall in regions of ground clutter caused by AP.
Abstract
The authors contrast rainfall in two Oklahoma squall lines: one with deep convection occurred in the spring and the other with shallower convection in the winter. Both passed over a micronetwork of densely spaced rain gauges and were observed with the National Severe Storm Laboratory's polarimetric weather radar. Polarimetric measurements reveal differences in storm structure that in turn imply that microphysical processes caused the drop size distributions to be quite distinct for the two events. In the winter squall line the conventional R(Z) algorithm for estimating rainfall fails badly, whereas in the summer squall line it performs well. The method based on specific differential phase measurements, however, yields a very good match between radar-derived areal precipitation amount and rain depth obtained from the micronetwork of densely located rain gauges for both events.
Abstract
The authors contrast rainfall in two Oklahoma squall lines: one with deep convection occurred in the spring and the other with shallower convection in the winter. Both passed over a micronetwork of densely spaced rain gauges and were observed with the National Severe Storm Laboratory's polarimetric weather radar. Polarimetric measurements reveal differences in storm structure that in turn imply that microphysical processes caused the drop size distributions to be quite distinct for the two events. In the winter squall line the conventional R(Z) algorithm for estimating rainfall fails badly, whereas in the summer squall line it performs well. The method based on specific differential phase measurements, however, yields a very good match between radar-derived areal precipitation amount and rain depth obtained from the micronetwork of densely located rain gauges for both events.
This paper is an overview of weather radar polarimetry emphasizing surveillance applications. The following potential benefits to operations are identified: improvement of quantitative precipitation measurements, discrimination of hail from rain with possible determination of sizes, identification of precipitation in winter storms, identification of electrically active storms, and distinction of biological scatterers (birds vs insects). Success in rainfall measurements is attributed to unique properties of differential phase. Referrals to fields of various polarimetric variables illustrate the signatures associated with different phenomena. It is argued that classifying hydrometeors is a necessary step prior to proper quantification of the water substance. The promise of polarimetry to accomplish classification is illustrated with an application to a hailstorm.
This paper is an overview of weather radar polarimetry emphasizing surveillance applications. The following potential benefits to operations are identified: improvement of quantitative precipitation measurements, discrimination of hail from rain with possible determination of sizes, identification of precipitation in winter storms, identification of electrically active storms, and distinction of biological scatterers (birds vs insects). Success in rainfall measurements is attributed to unique properties of differential phase. Referrals to fields of various polarimetric variables illustrate the signatures associated with different phenomena. It is argued that classifying hydrometeors is a necessary step prior to proper quantification of the water substance. The promise of polarimetry to accomplish classification is illustrated with an application to a hailstorm.
Abstract
This study describes, illustrates, and validates hail detection by a simplified version of the National Severe Storms Laboratory’s fuzzy logic polarimetric hydrometeor classification algorithm (HCA). The HCA uses four radar variables: reflectivity, differential reflectivity, cross-correlation coefficient, and “reflectivity texture” to classify echoes as rain mixed with hail, ground clutter–anomalous propagation, biological scatterers (insects, birds, and bats), big drops, light rain, moderate rain, and heavy rain. Diagnostic capabilities of HCA, such as detection of hail, are illustrated for a variety of storm environments using polarimetric radar data collected mostly during the Joint Polarimetric Experiment (JPOLE; 28 April–13 June 2003). Hail classification with the HCA is validated using 47 rain and hail reports collected by storm-intercept teams during JPOLE. For comparison purposes, probability of hail output from the Next-Generation Weather Radar Hail Detection Algorithm (HDA) is validated using the same ground truth. The anticipated polarimetric upgrade of the Weather Surveillance Radar-1988 Doppler network drives this direct comparison of performance. For the four examined cases, contingency table statistics show that the HCA outperforms the HDA. The superior performance of the HCA results primary from the algorithm’s lack of false alarms compared to the HDA. Statistical significance testing via bootstrapping indicates that differences in the probability of detection and critical success index between the algorithms are statistically significant at the 95% confidence level, whereas differences in the false alarm rate and Heidke skill score are statistically significant at the 90% confidence level.
Abstract
This study describes, illustrates, and validates hail detection by a simplified version of the National Severe Storms Laboratory’s fuzzy logic polarimetric hydrometeor classification algorithm (HCA). The HCA uses four radar variables: reflectivity, differential reflectivity, cross-correlation coefficient, and “reflectivity texture” to classify echoes as rain mixed with hail, ground clutter–anomalous propagation, biological scatterers (insects, birds, and bats), big drops, light rain, moderate rain, and heavy rain. Diagnostic capabilities of HCA, such as detection of hail, are illustrated for a variety of storm environments using polarimetric radar data collected mostly during the Joint Polarimetric Experiment (JPOLE; 28 April–13 June 2003). Hail classification with the HCA is validated using 47 rain and hail reports collected by storm-intercept teams during JPOLE. For comparison purposes, probability of hail output from the Next-Generation Weather Radar Hail Detection Algorithm (HDA) is validated using the same ground truth. The anticipated polarimetric upgrade of the Weather Surveillance Radar-1988 Doppler network drives this direct comparison of performance. For the four examined cases, contingency table statistics show that the HCA outperforms the HDA. The superior performance of the HCA results primary from the algorithm’s lack of false alarms compared to the HDA. Statistical significance testing via bootstrapping indicates that differences in the probability of detection and critical success index between the algorithms are statistically significant at the 95% confidence level, whereas differences in the false alarm rate and Heidke skill score are statistically significant at the 90% confidence level.
Abstract
This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (Nt ) and mean volume diameters (Dm ) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only, Nt (Dm ) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only, Dm increases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations for Nt and Dm . The solutions to these coupled equations are generalized power-law functions of height z for Dm (z) and Nt (z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles of Nt and Dm within 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimate Nt and Dm below radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.
Significance Statement
While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.
Abstract
This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (Nt ) and mean volume diameters (Dm ) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only, Nt (Dm ) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only, Dm increases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations for Nt and Dm . The solutions to these coupled equations are generalized power-law functions of height z for Dm (z) and Nt (z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles of Nt and Dm within 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimate Nt and Dm below radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.
Significance Statement
While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.
Abstract
A new polarimetric melting layer detection algorithm (MLDA) is utilized to estimate the top (melting level) and bottom boundaries of the melting layer and is tailored for operational deployment. Melting layer designations from a polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) in central Oklahoma are validated using radiosonde and model temperature analysis. It is demonstrated that the MLDA estimates the top of the melting layer with a root-mean-square error of about 200 m within 60 km of the radar. There is evidence that the polarimetric radar might yield better spatial and temporal designation of the melting layer within the storm than that obtained from existing numerical model output and soundings.
Abstract
A new polarimetric melting layer detection algorithm (MLDA) is utilized to estimate the top (melting level) and bottom boundaries of the melting layer and is tailored for operational deployment. Melting layer designations from a polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) in central Oklahoma are validated using radiosonde and model temperature analysis. It is demonstrated that the MLDA estimates the top of the melting layer with a root-mean-square error of about 200 m within 60 km of the radar. There is evidence that the polarimetric radar might yield better spatial and temporal designation of the melting layer within the storm than that obtained from existing numerical model output and soundings.
Abstract
Backscatter differential phase δ within the melting layer has been identified as a reliably measurable but still underutilized polarimetric variable. Polarimetric radar observations at X band in Germany and S band in the United States are presented that show maximal observed δ of 8.5° at X band but up to 70° at S band. Dual-frequency observations at X and C band in Germany and dual-frequency observations at C and S band in the United States are compared to explore the regional frequency dependencies of the δ signature. Theoretical simulations based on usual assumptions about the microphysical composition of the melting layer cannot reproduce the observed large values of δ at the lower-frequency bands and also underestimate the enhancements in differential reflectivity Z DR and reductions in the cross-correlation coefficient ρ hυ . Simulations using a two-layer T-matrix code and a simple model for the representation of accretion can, however, explain the pronounced δ signatures at S and C bands in conjunction with small δ at X band. The authors conclude that the δ signature bears information about microphysical accretion and aggregation processes in the melting layer and the degree of riming of the snowflakes aloft.
Abstract
Backscatter differential phase δ within the melting layer has been identified as a reliably measurable but still underutilized polarimetric variable. Polarimetric radar observations at X band in Germany and S band in the United States are presented that show maximal observed δ of 8.5° at X band but up to 70° at S band. Dual-frequency observations at X and C band in Germany and dual-frequency observations at C and S band in the United States are compared to explore the regional frequency dependencies of the δ signature. Theoretical simulations based on usual assumptions about the microphysical composition of the melting layer cannot reproduce the observed large values of δ at the lower-frequency bands and also underestimate the enhancements in differential reflectivity Z DR and reductions in the cross-correlation coefficient ρ hυ . Simulations using a two-layer T-matrix code and a simple model for the representation of accretion can, however, explain the pronounced δ signatures at S and C bands in conjunction with small δ at X band. The authors conclude that the δ signature bears information about microphysical accretion and aggregation processes in the melting layer and the degree of riming of the snowflakes aloft.
Abstract
A new synthesis of information forming the foundation for rule-based systems to deduce dominant bulk hydrometeor types and amounts using polarimetric radar data is presented. The information is valid for a 10-cm wavelength and consists of relations that are based on an extensive list of previous and recent observational and modeling studies of polarimetric signatures of hydrometeors. The relations are expressed as boundaries and thresholds in a space of polarimetric radar variables. Thus, the foundation is laid out for identification of hydrometeor types (species), estimation of characteristics of hydrometeor species (size, concentrations, etc.), and quantification of bulk hydrometeor contents (amounts). A fuzzy classification algorithm that builds upon this foundation will be discussed in a forthcoming paper.
Abstract
A new synthesis of information forming the foundation for rule-based systems to deduce dominant bulk hydrometeor types and amounts using polarimetric radar data is presented. The information is valid for a 10-cm wavelength and consists of relations that are based on an extensive list of previous and recent observational and modeling studies of polarimetric signatures of hydrometeors. The relations are expressed as boundaries and thresholds in a space of polarimetric radar variables. Thus, the foundation is laid out for identification of hydrometeor types (species), estimation of characteristics of hydrometeor species (size, concentrations, etc.), and quantification of bulk hydrometeor contents (amounts). A fuzzy classification algorithm that builds upon this foundation will be discussed in a forthcoming paper.
