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Roland List and J. R. Gillespie

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No abstract available.

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R. List and D. M. Whelpdale

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A method is described by which the coalescence process can be examined for different drop and droplet sizes. Preliminary experiments show that factors such as the velocity of collision, the angle of impact, the surface tension, and the electric charges can affect coalescence. It is seen that the coalescence efficiency may be considerably less than unity.

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T. B. Low and R. List

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Roland List and J. R. Gillespie

Abstract

A numerical model was set up to study the evolution of raindrop spectra by collision-induced breakup as measured in the laboratory. The main conclusion is that drops with diameters larger than 2-3 mm, failing in a population of smaller drops typical of natural rain, break up in comparatively short times (1–5 min in rainfalls of 100 mm h−1). The presence of large drops (4–6 mm) in (cold) rain produced by the Wegener-Bergeron-Findeisen mechanism through melting of ice particles can be attributed to the short time available for large drops to break up in sufficient numbers during the time of fall after melting. Large drops are scarce in (steady-state) warm rain because they break up in collisions and rarely reach diameters larger than 2.5 mm. Hence, the standard notion of a critical diameter of 5–6 mm which raindrops are supposed to reach before breakup due to aerodynamic instability is no longer acceptable.

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Paul R. Harasti and Roland List

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This is the first in a three-part series of papers that present the first applications of principal component analysis (PCA) to Doppler radar data. Although this novel approach has potential applications to many types of atmospheric phenomena, the specific goal of this series is to describe and verify a methodology that establishes the position and radial extent of the core region of atmospheric vortices. The underlying assumption in the current application is that the streamlines of the nondivergent component of the horizontal wind are predominantly circular, which is a characteristic often observed in intense vortices such as tropical cyclones.

The method employs an S2-mode PCA on the Doppler velocity data taken from a single surveillance scan and arranged sequentially in a matrix according to the range and azimuth coordinates. Part I begins the series by examining the eigenvectors obtained from such a PCA applied to a Doppler velocity model for a modified, Rankine-combined vortex, where the ratio of the radius of maximum wind to the range from the radar to the circulation center is varied over a wide range of values typically encountered in the field. Results show that the first two eigenvectors within the eigenspace of range coordinates represent over 99% of the total variance in the data. It is also demonstrated that the coordinates of particular cusps in the curves of the eigenvector coefficients plotted against their indices are geometrically related to both the position of circulation center and the radius of maximum wind.

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Roland List, C. Fung, and R. Nissen

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Previous breakup experiments have been carried out at laboratory pressures (∼100 kPa). However, raindrop interactions mainly take place higher up in the atmosphere, even in the supercooled part of a cloud where drops can be initiated by shedding from hailstones. Thus, 50 kPa, corresponding to a height of ∼5.5 km in the atmosphere at a temperature of ∼−20°C, was selected to bracket the region of interest for rain. Six drop pairs were studied at 50 kPa and laboratory temperature (∼20°C), one of them with reduced surface tension.

The apparatus consists of drop-producing nozzles, acceleration systems, deflectors, a timing and selection control, a pressure regulator, and a photographic unit, mostly set up in a low-pressure chamber. After acceleration to terminal speed, a smaller drop is blown into the path of the larger one while an electronic timing system selects suitable drop pairs that may collide, thereby triggering eight subsequent flashes with a frequency of up to 100 kHz. The results are displayed in terms of a normalized fragment probability per size bin, ready for parameterization in the Part II of this paper.

Five drop pairs were studied in 772 individual events. Overall, 51% resulted in filament breakup, 22% in sheet breakup, 7% in disk breakup, and 20% ended in coalescence. No bag breakups were observed. When compared to the 100-kPa results, the fragment numbers increased at large collision kinetic energies (CKEs) by factors of between 2.64 and 4.37 with pressure decreasing from 100 to 50 kPa, and they remained unchanged at low CKE. Detailed diagrams and tables show the results for the different drop pairs and collision categories. Increasing the sensitivity of the optical measurements from 0.05 to 0.01 cm increased the number of recognized fragments by factors up to 4.4, but only for the two higher-CKE cases. The higher resolution did not increase the fragment numbers detected in the lower-CKE range.

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Roland List, R. Nissen, and C. Fung

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Fragment size distributions, experimentally obtained for six drop pairs colliding at 50 kPa, are parameterized similarly to the 100-kPa drop pair experiments by Low and List. This information is then introduced into a box model to allow assessment of the spectra evolution and a comparison of the two datasets taken at the two pressures. The differences in breakup patterns include the following: The contributions to mass transfer by breakup and coalescence are very similar at the two pressures, with larger values at lower pressure; the overall mass evolution is not particularly sensitive to pressure; and disk breakup plays an “erratic” role. The situation for the number concentration, however, is totally different and develops gradually. At 50 kPa there is also no three-peak equilibrium developing as for 100 kPa. The times to reach equilibrium are ∼12 h. Note that the box model does not include accretion of cloud droplets—which may well be more important than growth by accretion of fragments.

Application of the new parameterization is not beneficial for low rain rates, but it is strongly recommended for large rain rates (>50 mm h−1).

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R. List, N. R. Donaldson, and R. E. Stewart

Abstract

The evolution of raindrop spectra by collisional breakup is examined analytically and modelled in box and 1-dimensional shaft models, using the parameterization of Low and List. The significant analytical result shows that equilibrium drop size distributions occur in families that are multiples of one another:
fDRRD
where D is the drop diameter, R is the rainfall rate, f(D,R) the number density distribution in terms of D and R and ψ is a shape function.

For the Low-List breakup scheme the shapes are trimodal, with peaks in the number distributions at diameters of 264, 790, and 1760 μm. Similar structures were found by Valdez and Young, and Brown for box models. These peaks are expected to exist wherever spectra approach equilibrium, independently of the rainfall rate. In this paper the development of these peaks from non-equilibrium spectra is examined, together with the effect of periodically varying rainfall rates.

In box and one-dimensional shaft models, nonequilibrium spectra quickly develop features similar to those at equilibrium, but times and/or heights to reach true equilibrium are in excess of 30 minutes, or 3 km for all but the very heaviest rainfall rates. The peaks, however, should be identifiable in a matter of minutes, thus encouraging field verification under favorable conditions. In the absence of evaporation, spectral evolution below a cloud is dominated by the large drops, which produce the accompanying small drops by breakup.

Evaporation, while basically affecting the smallest drops, is quickly spread over the whole spectrum by the collision process and reduces the total liquid water content The drop spectrum shape however, remains unchanged.

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R. List, P. H. Schuepp, and R. G. J. Methot

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Calculations are presented of the relative contributions of heat exchange by conduction and convection, by evaporation, and by the supercooling of accreted drops to the total heat exchange of growing spherical hailstones. They reveal the regions of dominance of the different ratios for various icing conditions in a model cloud and in laboratory experiments. As an additional result, it can be shown that transfer ratios occurring in hail clouds can only partly be simulated in experiments at constant pressure, but a restricted imitation at constant pressure is possible. These ratios are also considered to represent new parameters for future experiments about the relationship between icing conditions and resulting hailstone shells.

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R. List, R. B. Charlton, and P. I. Buttuls

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Calculations are made on the growth of hailstone embryos of given size and concentration which are injected into a one-dimensional steady-state updraft, and grow while ascending, the updraft obeying the condition that ρ Vs is a constant. The growth was found to have a considerable effect on the free water content of the cloud due to depletion by the growing particles. The hailstones of this model generally reach biggest sizes if their concentration is low and if the embryos are as big as possible. Embryos of 5 mm diameter can grow to 2.5–3.0 cm in diameter within 8–12 min if the conditions are right.

It is further shown that thermal feedback is of great importance in calculating the cloud temperature since it greatly affects buoyancy and icing conditions; in this case, the frictional heating of the falling hydrometeors has to be included along with the heat of fusion. The buoyancy is investigated because it is necessary to decide which set of input parameters for the growth curves and the free water contents distributions is reasonable. For those hailclouds where hailstones grow while ascending, it may be concluded that the biggest updrafts do not necessarily produce the biggest hailstones. The icing conditions of the growing particles turned out to be such that the outermost layers of the biggest stones always grow non-spongy.

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