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Drop Shapes, Model Comparisons, and Calculations of Polarimetric Radar Parameters in Rain

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  • 1 Colorado State University, Fort Collins, Colorado
  • | 2 Graz University of Technology, Graz, Austria
  • | 3 Joanneum Research, Graz, Austria
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Abstract

Drop shapes derived from a previously conducted artificial rain experiment using a two-dimensional video disdrometer (2DVD) are presented. The experiment involved drops falling over a distance of 80 m to achieve their terminal velocities as well as steady-state oscillations. The previous study analyzed the measured axis ratios (i.e., ratio of maximum vertical to maximum horizontal chord) as a function of equivolumetric spherical drop diameter (D eq) for over 115 000 drops ranging from 1.5 to 9 mm. In this paper, the actual contoured shapes of the drops are reported, taking into account the finite quantization limits of the instrument. The shapes were derived from the fast line-scanning cameras of the 2DVD. The drops were categorized into D eq intervals of 0.25-mm width and the smoothed contours for each drop category were superimposed on each other to obtain their most probable shapes and their variations due to drop oscillations. The most probable shapes show deviation from oblate spheroids for D eq > 4 mm, the larger drops having a more flattened base, in good agreement with the equilibrium (nonoblate) shape model of Beard and Chuang. Deviations were noted from the Beard and Chuang model shapes for diameters larger than 6 mm. However, the 2DVD measurements of the most probable contour shapes are the first to validate the Beard and Chuang model shapes for large drops, and further to demonstrate the differences from the equivalent oblate shapes. The purpose of this paper is to document the differences in radar polarization parameters and the range of error incurred when using the equivalent oblate shapes versus the most probable contoured shapes measured with the 2DVD especially for drop size distributions (DSDs) with large median volume diameters (>2 mm).

The measured contours for D eq > 1.5 mm were fitted to a modified conical equation, and scattering calculations were performed to derive the complex scattering amplitudes for forward and backscatter for H and V polarizations primarily at 5.34 GHz (C band) but also at 3 GHz (S band) and 9 GHz (X band). Calculations were also made to derive the relevant dual-polarization radar parameters for measured as well as model-based drop size distributions. When comparing calculations using the contoured shapes against the equivalent oblate spheroid shapes, good agreement was obtained for cases with median volume diameter (D 0) less than around 2 mm. Small systematic differences in the differential reflectivity (Z dr) values of up to 0.3 dB were seen for the larger D 0 values when using the oblate shapes, which can be primarily attributed to the shape differences in the resonance region, which occurs in the 5.5–7-mm-diameter range at C band. Lesser systematic differences were present in the resonance region at X band (3–4 mm). At S band, the impact of shape differences in the polarimetric parameters were relatively minor for D 0 up to 2.5 mm. Unusual DSDs with very large D 0 values (>3 mm) (e.g., as can occur along the leading edge of severe convective storms or aloft due localized “big drop” zones) can accentuate the Z dr difference between the contoured shape and the oblate spheroid equivalent, especially at C band. For attenuation-correction schemes based on differential propagation phase, it appears that the equivalent oblate shape approximation is sufficient using a fit to the axis ratios from the 80-m fall experiment given in this paper. For high accuracy in developing algorithms for predicting D 0 from Z dr, it is recommended that the fit to the most probable contoured shapes as given in this paper be used especially at C band.

Corresponding author address: Merhala Thurai, Dept. of ECE, Colorado State University, Fort Collins, CO 80523-1373. Email: merhala@engr.colostate.edu

Abstract

Drop shapes derived from a previously conducted artificial rain experiment using a two-dimensional video disdrometer (2DVD) are presented. The experiment involved drops falling over a distance of 80 m to achieve their terminal velocities as well as steady-state oscillations. The previous study analyzed the measured axis ratios (i.e., ratio of maximum vertical to maximum horizontal chord) as a function of equivolumetric spherical drop diameter (D eq) for over 115 000 drops ranging from 1.5 to 9 mm. In this paper, the actual contoured shapes of the drops are reported, taking into account the finite quantization limits of the instrument. The shapes were derived from the fast line-scanning cameras of the 2DVD. The drops were categorized into D eq intervals of 0.25-mm width and the smoothed contours for each drop category were superimposed on each other to obtain their most probable shapes and their variations due to drop oscillations. The most probable shapes show deviation from oblate spheroids for D eq > 4 mm, the larger drops having a more flattened base, in good agreement with the equilibrium (nonoblate) shape model of Beard and Chuang. Deviations were noted from the Beard and Chuang model shapes for diameters larger than 6 mm. However, the 2DVD measurements of the most probable contour shapes are the first to validate the Beard and Chuang model shapes for large drops, and further to demonstrate the differences from the equivalent oblate shapes. The purpose of this paper is to document the differences in radar polarization parameters and the range of error incurred when using the equivalent oblate shapes versus the most probable contoured shapes measured with the 2DVD especially for drop size distributions (DSDs) with large median volume diameters (>2 mm).

The measured contours for D eq > 1.5 mm were fitted to a modified conical equation, and scattering calculations were performed to derive the complex scattering amplitudes for forward and backscatter for H and V polarizations primarily at 5.34 GHz (C band) but also at 3 GHz (S band) and 9 GHz (X band). Calculations were also made to derive the relevant dual-polarization radar parameters for measured as well as model-based drop size distributions. When comparing calculations using the contoured shapes against the equivalent oblate spheroid shapes, good agreement was obtained for cases with median volume diameter (D 0) less than around 2 mm. Small systematic differences in the differential reflectivity (Z dr) values of up to 0.3 dB were seen for the larger D 0 values when using the oblate shapes, which can be primarily attributed to the shape differences in the resonance region, which occurs in the 5.5–7-mm-diameter range at C band. Lesser systematic differences were present in the resonance region at X band (3–4 mm). At S band, the impact of shape differences in the polarimetric parameters were relatively minor for D 0 up to 2.5 mm. Unusual DSDs with very large D 0 values (>3 mm) (e.g., as can occur along the leading edge of severe convective storms or aloft due localized “big drop” zones) can accentuate the Z dr difference between the contoured shape and the oblate spheroid equivalent, especially at C band. For attenuation-correction schemes based on differential propagation phase, it appears that the equivalent oblate shape approximation is sufficient using a fit to the axis ratios from the 80-m fall experiment given in this paper. For high accuracy in developing algorithms for predicting D 0 from Z dr, it is recommended that the fit to the most probable contoured shapes as given in this paper be used especially at C band.

Corresponding author address: Merhala Thurai, Dept. of ECE, Colorado State University, Fort Collins, CO 80523-1373. Email: merhala@engr.colostate.edu

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