1 Analysis of Raindrop Shapes , Fall Velocities , and 2 Scattering Calculations during Tropical Storm Nate

Tropical storm Nate, which was a powerful hurricane prior to landfall along the 12 Alabama coast, traversed north towards our instrumented site in Hunstville, AL. The rain bands 13 lasted 18 h and the 2D-video disdrometer (2DVD) captured the event which was shallow and 14 indicative of pure warm rain processes. Measurements of raindrop size, shape and velocity 15 distributions are quite rare in pure warm rain and are expected to differ from cold rain processes. 16 In particular, asymmetric shapes due to drop oscillations and their impact on polarimetric radar 17 signatures in warm rain have not been studied so far. Recently, the 2DVD data has been used for 18 3D reconstruction of asymmetric raindrop shapes but their fraction (relative to the more common 19 oblate shapes) in warm rain has yet to be ascertained. Here we compute the scattering matrix 20 drop-by-drop using Computer Simulation Technology integral equation solver for drop sizes>2.5 21 mm. From the scattering matrix elements, the polarimetric radar observables are simulated by 22 integrating over 1 minute consecutive segments of the event. These simulated values are compared 23 with dual-polarized C-band radar data located at 15 km range from the 2DVD site to evaluate the 24 contribution of the asymmetric drop shapes. 25


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One of the important applications of polarimetric radar is the measurement of rainfall whose 30 accuracy depends critically on the assumed drop shape model which under equilibrium (i.e., 31 balance of aerodynamic, surface tension and gravitational forces) was derived numerically by Beard 32 and Chuang [1]. However, rain drops (with D>0.7 mm or so) do oscillate due to wake instabilities or 33 time-varying drag but the oscillation modes (axisymmetric or asymmetric) and the distribution of

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[11]. However, in less intense convection or in pure warm rain process (coalescence) dominated 54 events, the frequency of occurrence of asymmetric drops shapes and their impact on rain rate 55 retrieval algorithms is not known. While it is known that small drops dominate the size 56 distributions in tropical rain with active warm rain processes relative to ice dominated deeper 57 convection at the same rain rate, it has been speculated that in the ice dominated cases, asymmetric 58 shapes due to oscillations can be dampened by residual tiny ice cores in the nearly fully melted 59 drops (originating as graupel or tiny hail aloft). On the other hand, pure warm rain processes have 60 no such damping mechanism and thus might exhibit more frequent occurrence of asymmetric

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The paper is organized as follows. In section 2, we give an overview of tropical storm (TS) Nate 68 and an outline of the specific instruments and measurements pertaining to this study. In section 3, 69 processing of the 2DVD-based images is presented, together with drop horizontal velocities which 70 are obtained as a by-product of the de-skwing procedure of the drop images. Section 4 outlines the 71 scattering calculation procedure and section 5 presents the single particle radar cross-sections 72 calculated for all drops with D > 2.5 mm as well as their differential relectivities. In section 6, the 73 computed reflecitivity and differential reflectivity based on the scattering calculations over a 74 1-minute interval are compared with the C-band radar measurements over the instrument site, for 75 the entire duration of the Nate event at the instrument site. The main conclusions are summarized in 76 section 7 as well as discussion on each of the main conclusion points.

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Tropical system Nate originated as a fast moving hurricane which made landfall on the US Gulf 3 of 16 temperature at 2-m height was around 73-75 deg F (23-24 deg C) during much of the storm period 93 (02 to 20 hr UTC). A X-band vertically-pointing Doppler radar [15] located a few meters also made 94 observations over the entire storm event, and a C-band dual-polarization radar (ARMOR) [16]     shapes for each drop but also its horizontal velocities along the x and y axes, which in turn enables 111 the magnitude and direction to be determined. Along the z-axis, the matching procedure from the 112 2DVD's two camera images (A and B) enables the fall speeds to be determined on a drop-by-drop 113 basis. However, due to a number of limitations, the velocity and shape information can only be 114 retrieved for relatively large drops, in particular for drops with equi-volume diameter larger than 115 1.5 or 2 mm. When performing scattering calculations, it is the larger drops which will have the 116 highest contributions to the polarimetric radar variables such as differential reflectivity and copolar 117 correlation coefficient and differential backscatter phase.

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The 2DVD measurements during the entire Nate event revealed that the drop diameters (Deq) 119 did not exceed 4 mm. There were 601 drops with Deq > 2.5 mm out of 1,467,540 drops in total; out of 120 these, only 79 drops exceeded 3 mm and only 12 drops exceeded 3.5 mm. One of the biggest drops

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The 3D shapes of each raindrop was reconstructed with Matlab-software using the procedure

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Since the shape is fixed for a given drop size, the scattering amplitude will be expected to be a single 194 curve for a given polarization. Furthermore, the rotational symmetry of the drop shape will result in 195 RCS being independent of the look angle. The scatter in the RCS values for the reconstructed drops 196 is of course due to both variation in shapes and the variation with look angle, but even so they 197 appear to lie evenly scattered on both sides of the two (solid black and dashed black) curves.

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The differential reflectivity of each reconstructed drop is obtained from the difference between 199 the horizontal and vertical polarization radar cross-sections. Because both the H and V radar cross 200 sections for any given drop will vary with the look angle, its differential reflectivity will also have a

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The set of panels in Fig. 6

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The 1-minute based calculations for the entire 18 hour event period is shown in Fig. 9 and 300 compared with the C-band ARMOR radar data over and in the vicinity of the disdrometer site.

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In terms of the differential backscatter phase, the scattering calculations for the >2.