# Search Results

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- Author or Editor: R. Meneghini x

- Journal of Atmospheric and Oceanic Technology x

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## Abstract

Melting snow, graupel, and hail are often modeled as uniform mixtures of air–ice–water or ice–water. Two-layered models have also been proposed in which the particle consists of a dry snow or ice core surrounded by water or a wet snow mixture. For both types of particle models, the mixtures are characterized by effective dielectric constants. This information, along with particle shape, size, and orientation, provides the necessary data for calculating the scattering characteristics of the particles. The most commonly used formulas for the effective dielectric constant, ɛ_{eff}, are those of Maxwell Garnett and Bruggeman. To understand the applicability and limitations of these formulas, an expression for ɛ_{eff} is derived that depends on the mean internal electric fields within each component of the mixture. Using a conjugate gradient numerical method, the calculations are carried out for ice–water mixtures. Parameterization of the results in terms of the fractional water volume and the electromagnetic wavelength provides an expression for ɛ_{eff} for wavelengths between 3 and 28 mm. To circumvent the laborious task of parameterizing ɛ_{eff} with wavelength for air–ice–water mixtures, several approximate formulations are proposed. Tests of the accuracy of the formulas are made by calculating the mean and variance from different particle realizations and by comparison to a previous method. Tests of the applicability of the formulas for ɛ_{eff} are made by changing the shape, size, and orientations of the inclusions. While the formulas are adequate over a certain range of inclusion sizes and for a change in shape from cubic to spherical, they are not applicable to highly eccentric, aligned inclusions such as rods or plates.

## Abstract

Melting snow, graupel, and hail are often modeled as uniform mixtures of air–ice–water or ice–water. Two-layered models have also been proposed in which the particle consists of a dry snow or ice core surrounded by water or a wet snow mixture. For both types of particle models, the mixtures are characterized by effective dielectric constants. This information, along with particle shape, size, and orientation, provides the necessary data for calculating the scattering characteristics of the particles. The most commonly used formulas for the effective dielectric constant, ɛ_{eff}, are those of Maxwell Garnett and Bruggeman. To understand the applicability and limitations of these formulas, an expression for ɛ_{eff} is derived that depends on the mean internal electric fields within each component of the mixture. Using a conjugate gradient numerical method, the calculations are carried out for ice–water mixtures. Parameterization of the results in terms of the fractional water volume and the electromagnetic wavelength provides an expression for ɛ_{eff} for wavelengths between 3 and 28 mm. To circumvent the laborious task of parameterizing ɛ_{eff} with wavelength for air–ice–water mixtures, several approximate formulations are proposed. Tests of the accuracy of the formulas are made by calculating the mean and variance from different particle realizations and by comparison to a previous method. Tests of the applicability of the formulas for ɛ_{eff} are made by changing the shape, size, and orientations of the inclusions. While the formulas are adequate over a certain range of inclusion sizes and for a change in shape from cubic to spherical, they are not applicable to highly eccentric, aligned inclusions such as rods or plates.

## Abstract

Airborne dual-wavelength and dual-polarization radar data are analyzed for measurements taken in stratiform rain in the western Pacific during September 1990. The focus of the paper is on the vertical profiles of the linear depolarization ratio, LDR ( 10 GHz); the reflectivity factor, dBZ ( 10 GHz); and the dual-frequency ratio, DFR (10, 34.45 GHz). Statistical characterizations of the maxima of these quantities and the relative locations at which they occur suggest that the eccentricity of the melting particles is fairly large and that the shape and size of the particles are correlated. To try to explain these features, two types of simulation are presented. In the first, a set of measured drop size distributions is used in the context of a standard model of the melting layer. Variations in snow density, as well as shape, size, and orientation distributions are used to study the relationship between these parameters and the radar measurements. To reduce the amount of ambiguity in the estimation, a second type of simulation is described in which the size distribution of the snow is estimated. Comparisons between the simulated and measured profiles indicate that radar measurements can be used to derive certain characteristics of the particle size and shape distributions in the melting layer.

## Abstract

Airborne dual-wavelength and dual-polarization radar data are analyzed for measurements taken in stratiform rain in the western Pacific during September 1990. The focus of the paper is on the vertical profiles of the linear depolarization ratio, LDR ( 10 GHz); the reflectivity factor, dBZ ( 10 GHz); and the dual-frequency ratio, DFR (10, 34.45 GHz). Statistical characterizations of the maxima of these quantities and the relative locations at which they occur suggest that the eccentricity of the melting particles is fairly large and that the shape and size of the particles are correlated. To try to explain these features, two types of simulation are presented. In the first, a set of measured drop size distributions is used in the context of a standard model of the melting layer. Variations in snow density, as well as shape, size, and orientation distributions are used to study the relationship between these parameters and the radar measurements. To reduce the amount of ambiguity in the estimation, a second type of simulation is described in which the size distribution of the snow is estimated. Comparisons between the simulated and measured profiles indicate that radar measurements can be used to derive certain characteristics of the particle size and shape distributions in the melting layer.

## Abstract

The High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency conically scanning airborne radar provides estimates of the range-profiled mean Doppler and backscattered power from the precipitation and surface. A velocity–azimuth display analysis yields near-surface estimates of the mean horizontal wind vector *υ*
_{h} in cases in which precipitation is present throughout the scan. From the surface return, the normalized radar cross section (NRCS) is obtained, which, by a method previously described, can be corrected for path attenuation. Comparisons between *υ*
_{h} and the attenuation-corrected NRCS are used to derive transfer functions that provide estimates of the wind vector from the NRCS data under both rain and rain-free conditions. A reasonably robust transfer function is found by using the mean NRCS (⟨NRCS⟩) over the scan along with a filtering of the data based on a Fourier series analysis of *υ*
_{h} and the NRCS. The approach gives good correlation coefficients between *υ*
_{h} and ⟨NRCS⟩ at Ku band at incidence angles of 30° and 40°. The correlation degrades if the Ka-band data are used rather than the Ku band.

## Abstract

The High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency conically scanning airborne radar provides estimates of the range-profiled mean Doppler and backscattered power from the precipitation and surface. A velocity–azimuth display analysis yields near-surface estimates of the mean horizontal wind vector *υ*
_{h} in cases in which precipitation is present throughout the scan. From the surface return, the normalized radar cross section (NRCS) is obtained, which, by a method previously described, can be corrected for path attenuation. Comparisons between *υ*
_{h} and the attenuation-corrected NRCS are used to derive transfer functions that provide estimates of the wind vector from the NRCS data under both rain and rain-free conditions. A reasonably robust transfer function is found by using the mean NRCS (⟨NRCS⟩) over the scan along with a filtering of the data based on a Fourier series analysis of *υ*
_{h} and the NRCS. The approach gives good correlation coefficients between *υ*
_{h} and ⟨NRCS⟩ at Ku band at incidence angles of 30° and 40°. The correlation degrades if the Ka-band data are used rather than the Ku band.

## Abstract

An important objective in scatterometry is the estimation of near-surface wind speed and direction in the presence of rain. We investigate an attenuation correction method using data from the High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency scatterometer, which operates at Ku and Ka band with dual conical scans at incidence angles of 30° and 40°. The method relies on the fact that the differential normalized surface cross section, *δσ*
^{0} = *σ*
^{0}(Ka) − *σ*
^{0}(Ku), is relatively insensitive to wind speed and direction and that this quantity is closely related to the magnitude of the differential path attenuation, *δA* = *A*(Ka) − *A*(Ku), arising from precipitation, cloud, and atmospheric gases. As the method relies only on the difference between quantities measured in the presence and absence of rain, the estimates are independent of radar calibration error. As a test of the method’s accuracy, we make use of the fact that the radar rain reflectivities just above the surface, as seen along different incidence angles, are approximately the same. This yields constraint equations in the form of differences between pairs of path attenuations along different lines of sight to the surface. A second validation method uses the dual-frequency radar returns from the rain just above the surface where it can be shown that the difference between the Ku- and Ka-band-measured radar reflectivity factors provide an estimate of differential path attenuation. Comparisons between the path attenuations derived from the normalized surface cross section and those from these surface-independent methods generally show good agreement.

## Abstract

An important objective in scatterometry is the estimation of near-surface wind speed and direction in the presence of rain. We investigate an attenuation correction method using data from the High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency scatterometer, which operates at Ku and Ka band with dual conical scans at incidence angles of 30° and 40°. The method relies on the fact that the differential normalized surface cross section, *δσ*
^{0} = *σ*
^{0}(Ka) − *σ*
^{0}(Ku), is relatively insensitive to wind speed and direction and that this quantity is closely related to the magnitude of the differential path attenuation, *δA* = *A*(Ka) − *A*(Ku), arising from precipitation, cloud, and atmospheric gases. As the method relies only on the difference between quantities measured in the presence and absence of rain, the estimates are independent of radar calibration error. As a test of the method’s accuracy, we make use of the fact that the radar rain reflectivities just above the surface, as seen along different incidence angles, are approximately the same. This yields constraint equations in the form of differences between pairs of path attenuations along different lines of sight to the surface. A second validation method uses the dual-frequency radar returns from the rain just above the surface where it can be shown that the difference between the Ku- and Ka-band-measured radar reflectivity factors provide an estimate of differential path attenuation. Comparisons between the path attenuations derived from the normalized surface cross section and those from these surface-independent methods generally show good agreement.

## Abstract

A question arising from the recent interest in spaceborne weather radar is what methods can be used to estimate precipitation parameters from space. In this paper, dual-wavelength airborne radar data obtained from flights conducted during 1988 and 1989 are used to compare rain rates derived from backscattering and attenuation methods. We begin with a survey of path-averaged rain rates estimated from six methods over four flights. The fairly large number of high rain-rate cases encountered during these experiments allows for the first tests of the surface-reference method applied to the low-frequency (10-GHz) data. To help interpret the results the surface reference methods are studied by means of scatterplots of the surface cross sections at the two frequencies under rain and no-rain conditions. Approximate criteria are given on combining attenuation and backscattering methods to increase the effective dynamic range of the radar. The dual-wavelength capability of the radar is also used to examine the vertical structure of the precipitation: critical to the success of most methods is the ability to distinguish rain from mixed-phase precipitation. Another factor affecting the accuracy of the methods is the drop-size distribution. In the final section of the paper a procedure to estimate the profiled drop-size distribution is applied to the measured radar data.

## Abstract

A question arising from the recent interest in spaceborne weather radar is what methods can be used to estimate precipitation parameters from space. In this paper, dual-wavelength airborne radar data obtained from flights conducted during 1988 and 1989 are used to compare rain rates derived from backscattering and attenuation methods. We begin with a survey of path-averaged rain rates estimated from six methods over four flights. The fairly large number of high rain-rate cases encountered during these experiments allows for the first tests of the surface-reference method applied to the low-frequency (10-GHz) data. To help interpret the results the surface reference methods are studied by means of scatterplots of the surface cross sections at the two frequencies under rain and no-rain conditions. Approximate criteria are given on combining attenuation and backscattering methods to increase the effective dynamic range of the radar. The dual-wavelength capability of the radar is also used to examine the vertical structure of the precipitation: critical to the success of most methods is the ability to distinguish rain from mixed-phase precipitation. Another factor affecting the accuracy of the methods is the drop-size distribution. In the final section of the paper a procedure to estimate the profiled drop-size distribution is applied to the measured radar data.

## Abstract

For a spaceborne meteorological radar, the use of frequencies above 10 GHz may be necessary to attain sufficient spatial resolution. As the frequency increases, however, attenuation by rain becomes significant. To extend the range of rain rates that can be accurately estimated, methods other than the conventional *Z*-*R*, or backscattering method, are needed. In this paper, tests are made of two attenuation-based methods using data from a dual-wavelength airborne radar operating at 3 cm and 0.87 cm. For the conventional dual-wavelength method, the differential attenuation is estimated from the relative decrease in the signal level with range. For the surface reference method, the attenuation is determined from the difference of surface return powers measured in the absence and the presence of rain. For purposes of comparison, and as an indication of the relative accuracies of the techniques, the backscattering, (*Z*-*R*), method, as applied to the 3 cm data, is employed. As the primary sources of error for the *Z*-*R*, dual-wavelength, and surface reference methods are nearly independent, some confidence in the results is warranted when thew methods yield similar rain rates. Cases of good agreement occur most often in stratiform rain for rain rates between a few mm h^{−1} to about 15 mm h^{−1}; that is, where attenuation at the shorter wavelength is significant but not so severe as to result in a loss of signal. When the estimates disagree, it is sometimes possible to identify the likely error source by an examination of the return power profiles and a knowledge of the error sources.

## Abstract

For a spaceborne meteorological radar, the use of frequencies above 10 GHz may be necessary to attain sufficient spatial resolution. As the frequency increases, however, attenuation by rain becomes significant. To extend the range of rain rates that can be accurately estimated, methods other than the conventional *Z*-*R*, or backscattering method, are needed. In this paper, tests are made of two attenuation-based methods using data from a dual-wavelength airborne radar operating at 3 cm and 0.87 cm. For the conventional dual-wavelength method, the differential attenuation is estimated from the relative decrease in the signal level with range. For the surface reference method, the attenuation is determined from the difference of surface return powers measured in the absence and the presence of rain. For purposes of comparison, and as an indication of the relative accuracies of the techniques, the backscattering, (*Z*-*R*), method, as applied to the 3 cm data, is employed. As the primary sources of error for the *Z*-*R*, dual-wavelength, and surface reference methods are nearly independent, some confidence in the results is warranted when thew methods yield similar rain rates. Cases of good agreement occur most often in stratiform rain for rain rates between a few mm h^{−1} to about 15 mm h^{−1}; that is, where attenuation at the shorter wavelength is significant but not so severe as to result in a loss of signal. When the estimates disagree, it is sometimes possible to identify the likely error source by an examination of the return power profiles and a knowledge of the error sources.

## Abstract

A spaceborne precipitation radar samples the vertical structure of precipitating hydrometeors from the top down. The viewing geometry and operating frequency result in certain limitations and opportunities. Among the limitations is attenuation of the radar signal that can cause the measured radar reflectivity factor to be substantially less than the desired quantity, the true radar reflectivity factor. Another error source is the spatial variability in precipitation rates that occurs at scales smaller than the sensor field of view (FOV), giving rise to the nonuniform beamfilling (NUBF) effect. The opportunities arise when the radar return from the surface can be used to obtain constraints on the path-integrated attenuation (PIA) for use in hybrid attenuation correction algorithms. The surface return can also provide some information on the degree of NUBF at off-nadir viewing angles. In this paper ground-based radar data are used to simulate spaceborne radar data at nadir and off-nadir viewing angles at Ku band and Ka band and to test attenuation correction algorithms in the presence of nonuniform beamfilling. The cross-FOV gradient in PIA is found to be an important characteristic for describing the performance of attenuation correction algorithms.

## Abstract

A spaceborne precipitation radar samples the vertical structure of precipitating hydrometeors from the top down. The viewing geometry and operating frequency result in certain limitations and opportunities. Among the limitations is attenuation of the radar signal that can cause the measured radar reflectivity factor to be substantially less than the desired quantity, the true radar reflectivity factor. Another error source is the spatial variability in precipitation rates that occurs at scales smaller than the sensor field of view (FOV), giving rise to the nonuniform beamfilling (NUBF) effect. The opportunities arise when the radar return from the surface can be used to obtain constraints on the path-integrated attenuation (PIA) for use in hybrid attenuation correction algorithms. The surface return can also provide some information on the degree of NUBF at off-nadir viewing angles. In this paper ground-based radar data are used to simulate spaceborne radar data at nadir and off-nadir viewing angles at Ku band and Ka band and to test attenuation correction algorithms in the presence of nonuniform beamfilling. The cross-FOV gradient in PIA is found to be an important characteristic for describing the performance of attenuation correction algorithms.

## Abstract

The return from the ocean surface has a number of uses for airborne meteorological radar. The normalized surface cross section has been used for radar system calibration, estimation of surface winds, and in algorithms for estimating the path-integrated attenuation in rain. However, meteorological radars are normally optimized for observation of distributed targets that fill the resolution volume, and so a point target such as the surface can be poorly sampled, particularly at near-nadir look angles. Sampling the nadir surface return at an insufficient rate results in a negative bias of the estimated cross section. This error is found to be as large as 4 dB using observations from a high-altitude airborne radar. An algorithm for mitigating the error is developed that is based upon the shape of the surface echo and uses the returned signal at the three range gates nearest the peak surface echo.

## Abstract

The return from the ocean surface has a number of uses for airborne meteorological radar. The normalized surface cross section has been used for radar system calibration, estimation of surface winds, and in algorithms for estimating the path-integrated attenuation in rain. However, meteorological radars are normally optimized for observation of distributed targets that fill the resolution volume, and so a point target such as the surface can be poorly sampled, particularly at near-nadir look angles. Sampling the nadir surface return at an insufficient rate results in a negative bias of the estimated cross section. This error is found to be as large as 4 dB using observations from a high-altitude airborne radar. An algorithm for mitigating the error is developed that is based upon the shape of the surface echo and uses the returned signal at the three range gates nearest the peak surface echo.

## Abstract

Satellite weather radars that operate at attenuating wavelengths require an estimate of path attenuation to reconstruct the range profile of rainfall. One such method is the surface reference technique (SRT), by which attenuation is estimated as the difference between the surface cross section outside the rain and the apparent surface cross section measured in rain. This and the Hitschfeld–Bordan method are used operationally to estimate rain rate using data from the precipitation radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. To overcome some of the problems associated with the latest operational version of the SRT, a hybrid surface reference is defined that uses information from the along-track and cross-track variations of the surface cross sections in rain-free areas. Over ocean, this approach eliminates most of the discontinuities in the path-attenuation field. Self-consistency of the estimates is tested by processing the orbits backward as well as forward. Calculations from 2 weeks of PR data show that 90% of the rain events over ocean for which the SRT is classified as reliable or marginally reliable are such that the absolute difference between the forward and backward estimates is less than 1 dB.

## Abstract

Satellite weather radars that operate at attenuating wavelengths require an estimate of path attenuation to reconstruct the range profile of rainfall. One such method is the surface reference technique (SRT), by which attenuation is estimated as the difference between the surface cross section outside the rain and the apparent surface cross section measured in rain. This and the Hitschfeld–Bordan method are used operationally to estimate rain rate using data from the precipitation radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. To overcome some of the problems associated with the latest operational version of the SRT, a hybrid surface reference is defined that uses information from the along-track and cross-track variations of the surface cross sections in rain-free areas. Over ocean, this approach eliminates most of the discontinuities in the path-attenuation field. Self-consistency of the estimates is tested by processing the orbits backward as well as forward. Calculations from 2 weeks of PR data show that 90% of the rain events over ocean for which the SRT is classified as reliable or marginally reliable are such that the absolute difference between the forward and backward estimates is less than 1 dB.