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- Author or Editor: R. C. Srivastava x

- Journal of Atmospheric and Oceanic Technology x

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## Abstract

For an exponential drop size distribution, the mean Doppler velocity at vertical incidence, after correction for vertical air motion, depends only on the slope of the distribution. The intercept of the distribution can then be deduced from the radar reflectivity and the slope and the intercept can be used to compute the rainwater content and the rainfall rate. The necessity of correcting for the vertical air motion limits the method to stratiform rain where it may be obtained by VAD methods or may be small enough to be neglected. Two examples of the use of the method are presented.

## Abstract

For an exponential drop size distribution, the mean Doppler velocity at vertical incidence, after correction for vertical air motion, depends only on the slope of the distribution. The intercept of the distribution can then be deduced from the radar reflectivity and the slope and the intercept can be used to compute the rainwater content and the rainfall rate. The necessity of correcting for the vertical air motion limits the method to stratiform rain where it may be obtained by VAD methods or may be small enough to be neglected. Two examples of the use of the method are presented.

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## Abstract

The authors describe a method for the measurement of specific attenuation using two radars operating at virtually the same wavelength at which the attenuation is desired. Use of the same wavelength avoids confounding between differences in received powers due to attenuation and wavelength dependence of reflectivity factors. A governing equation for the specific attenuation and an analytical solution of the equation are derived. The analytical solution gives an explicit expression for the specific attenuation in terms of the specific attenuation at an initial point and the second derivative of estimates of the difference between ensemble average received powers for the two radars along and near the characteristics of the governing equation. An error analysis shows that error in the computed attenuation is due to error in the attenuation coefficient at the initial point and errors in the estimates of the ensemble average received powers. Unless the initial point is poorly chosen, the error due to the initial condition is approximately of the same magnitude as the error in the initial value of the specific attenuation. The error due to errors in estimates of the ensemble average received powers accumulate along the characteristics; the error increases rapidly near the radars and is smaller away from the radars. The error decreases with distance between the radars, the number of independent pulses averaged to find estimates of ensemble average power, the number of independent radar pulse volumes used in smoothing the observed reflectivities, and the angular intervals used in performing the numerical differentiation for the calculation of the above-mentioned second derivative. Using typical radar parameters, it is found that the standard error of the two-way specific attenuation can be less than a tenth or a few tenths of a decibel per kilometer if the number of independent pulses exceeds about 10, smoothing is performed over hundreds of independent radar pulse volumes, and the angular intervals for the differentiation are about 3° or greater.

## Abstract

The authors describe a method for the measurement of specific attenuation using two radars operating at virtually the same wavelength at which the attenuation is desired. Use of the same wavelength avoids confounding between differences in received powers due to attenuation and wavelength dependence of reflectivity factors. A governing equation for the specific attenuation and an analytical solution of the equation are derived. The analytical solution gives an explicit expression for the specific attenuation in terms of the specific attenuation at an initial point and the second derivative of estimates of the difference between ensemble average received powers for the two radars along and near the characteristics of the governing equation. An error analysis shows that error in the computed attenuation is due to error in the attenuation coefficient at the initial point and errors in the estimates of the ensemble average received powers. Unless the initial point is poorly chosen, the error due to the initial condition is approximately of the same magnitude as the error in the initial value of the specific attenuation. The error due to errors in estimates of the ensemble average received powers accumulate along the characteristics; the error increases rapidly near the radars and is smaller away from the radars. The error decreases with distance between the radars, the number of independent pulses averaged to find estimates of ensemble average power, the number of independent radar pulse volumes used in smoothing the observed reflectivities, and the angular intervals used in performing the numerical differentiation for the calculation of the above-mentioned second derivative. Using typical radar parameters, it is found that the standard error of the two-way specific attenuation can be less than a tenth or a few tenths of a decibel per kilometer if the number of independent pulses exceeds about 10, smoothing is performed over hundreds of independent radar pulse volumes, and the angular intervals for the differentiation are about 3° or greater.

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## Abstract

Retrievals of specific attenuation at 5.5-cm wavelength from dual-radar observations of a summer convective storm in Florida are presented. The retrieved specific attenuation is positive except in regions near the radars where the observed reflectivity factors suffered from contamination by ground clutter. The specific attenuations ranged between 0.0 and 2.0 dB km^{−1}; they are small at higher levels of the storm, and high reflectivity cores are generally associated with higher specific attenuations. A plot of the retrieved specific attenuation against reflectivity factor at 10-cm wavelength shows that a majority of the retrieved values agree with those calculated from empirical relationships between reflectivity factor and specific attenuation. A small fraction of the points having high reflectivity factors have smaller than empirically predicted attenuations; these are attributed to dry ice particles. A larger fraction of the points having low reflectivity factors, less than about 30 dB*Z,* have higher than empirically predicted attenuations; these are attributed to attenuation by cloud liquid water and mixed-phase hydrometeors. A scatterplot of the differential reflectivity factor at 10-cm wavelength against the ratio of the retrieved specific attenuation to the reflectivity factor at 10-cm wavelength agrees generally with a theoretically expected relationship between the two parameters for horizontally oriented deformed raindrops, giving credence to the retrievals. However, the points scatter rather widely around the theoretical curve and the scatter is attributed to 1) signal fluctuations; 2) physical factors, namely, cloud water, ice particles, and mixed-phase particles of various shapes; 3) instrumental factors, namely, ground clutter, finite pulse volume, mismatched radar antenna patterns, and sidelobes; and 4) numerical procedures used in the retrievals, namely, data interpolation, smoothing, and differentiation.

## Abstract

Retrievals of specific attenuation at 5.5-cm wavelength from dual-radar observations of a summer convective storm in Florida are presented. The retrieved specific attenuation is positive except in regions near the radars where the observed reflectivity factors suffered from contamination by ground clutter. The specific attenuations ranged between 0.0 and 2.0 dB km^{−1}; they are small at higher levels of the storm, and high reflectivity cores are generally associated with higher specific attenuations. A plot of the retrieved specific attenuation against reflectivity factor at 10-cm wavelength shows that a majority of the retrieved values agree with those calculated from empirical relationships between reflectivity factor and specific attenuation. A small fraction of the points having high reflectivity factors have smaller than empirically predicted attenuations; these are attributed to dry ice particles. A larger fraction of the points having low reflectivity factors, less than about 30 dB*Z,* have higher than empirically predicted attenuations; these are attributed to attenuation by cloud liquid water and mixed-phase hydrometeors. A scatterplot of the differential reflectivity factor at 10-cm wavelength against the ratio of the retrieved specific attenuation to the reflectivity factor at 10-cm wavelength agrees generally with a theoretically expected relationship between the two parameters for horizontally oriented deformed raindrops, giving credence to the retrievals. However, the points scatter rather widely around the theoretical curve and the scatter is attributed to 1) signal fluctuations; 2) physical factors, namely, cloud water, ice particles, and mixed-phase particles of various shapes; 3) instrumental factors, namely, ground clutter, finite pulse volume, mismatched radar antenna patterns, and sidelobes; and 4) numerical procedures used in the retrievals, namely, data interpolation, smoothing, and differentiation.