The growth of ice particles by riming is one of the central problems in cloud physics and has great impacts on many other atmospheric processes. This is the dominant process that forms graupel and hail. It occurs in deep convective clouds and it influences the further development of such clouds due to its thermodynamic and dynamic effects. It is also one of the most important processes leading to the electrification of thunderclouds. Quantitative knowledge of this process is necessary for accurate weather and climate predictions. Despite the critical importance of the riming growth process, there are only limited field and laboratory experimental data on riming growth available, and only very simplistic theoretical treatments of the process. In order to increase understanding of the process, a numerical study will be conducted on the growth of ice particles by accreting supercooled droplets, starting from a pristine ice crystal and following its growth to become a graupel. Two numerical models will be developed, one for simulating the fall behavior of the falling ice particles while accreting droplets (hence changing its shape); the other for determining the collision efficiency of the supercooled droplet hitting the ice particle. The first model involves solving numerically the relevant Navier-Stokes equations to obtain the flow field around the falling particle. Using these flow fields, solutions will be found to the equations of motion of supercooled droplets around the falling ice particle so as to determine their trajectories and hence their collision efficiency. Computations of the ventilation coefficients of the falling rimed particles will be performed as well. These numerical models will be used to perform computations to determine the collision efficiencies for a wide range of ice crystal/droplet size combinations and atmospheric conditions. This will yield an extensive data set of quantitative collisional growth rates of graupel in different conditions.

The intellectual merit of the proposed work is that the results from this study will fill a large gap in available knowledge in this fundamental area of cloud physics and provide necessary quantitative information on how the riming growth process operates in clouds. Such information can be used to design better graupel riming parameterizations for use in storm-scale numerical models to understand better the convective cloud dynamics. It can also be used by larger scale weather/climate models to improve their large scale precipitation parameterizations. The experience gained and the numerical flow fields obtained from this study also will also be useful for the future study of ice-ice collisional growth.

The broader impacts of the results of the study include their use to enhance our capability to predict weather and climate evolution through the use of numerical prediction models. The research activity will help train graduate students and young scientists who will contribute to atmospheric science research. The research results will be disseminated in scientific journals, meetings, and public lectures so that wider audience becomes aware of them. Recent research results are regularly incorporated into survey-level courses (aiming at college freshmen) by the principal investigator. They convey to the younger generation the excitement of scientific discoveries and their great contributions to society.

Project Report

Graupel (also called soft hail) is the predecessor of hail. It is formed when an ice crystal collides with supercooled (temperature colder than 0°C) water droplets in clouds and the droplets freeze on the ice, a process called riming. When a graupel grows by riming to exceed 5 mm in diameter, it is called a hail. It is well known that large hailstorms cause extensive damages to crops and properties but until recently there wasn’t accurate knowledge on how fast graupel rimes to form hail. How fast graupel rime depends mainly on the flow pattern, called flow field, of air around the falling graupel. The flow field influences how small cloud droplets move around the graupel, sometimes causing the droplet to collide with the graupel but sometimes causing the droplet to miss the graupel. The most common shape of graupel is conical, having a round bottom and relatively sharp top and there wasn’t any quantitative knowledge about the flow fields around falling conical particles of the graupel size range. Our first step was to obtain such flow fields. We used numerical techniques and utilized a commercial numerical package called ANSYS Fluent to solve the equation governing the flow of air around falling graupel. That equation is called the Navier-Stokes equation. The flow fields are different when particles fall at different inclination angles. Fig. 1 is an example of the velocity, vorticity and pressure distribution fields around a graupel of 3.62 mm diameter falling at 30° inclination. The vortices produced by the falling graupel can be clearly seen in this figure. In this figure, the arrows represent the velocity vectors projected on the central x-z cross-section, white contours the pressure deviation from the unperturbed field, and color the vorticity. After the flow field was determined, we proceeded to solve the equation of motion of a small cloud droplet moving in this field, which was also done numerically. The solution of this equation determines the trajectory of the droplet and hence indicates whether or not the droplet collides with the graupel. From the trajectory that resulted in grazing collision, we determined the collision efficiency of the graupel in collecting the supercooled droplets to form rime. We have completed the calculations of a series of collision efficiencies of graupel of various sizes collecting supercooled droplets of various sizes. We will summarize these results for publication in the near future. Naturally, these collision efficiencies will be useful in understanding how fast graupel will grow to become hail. The techniques we used here can also be applied to determine how efficient graupel and hail can sweep out dust particles in air, which is an important problem in air pollution studies. The flow fields obtained in this project can be used to determine the collision efficiency between the graupel and ice crystals which is said to play a central role on how electric charges are generated in thunderstorms. The project also helped training a postdoctoral fellow and a few graduate students in the field of computational fluid dynamics.

National Science Foundation (NSF)
Division of Atmospheric and Geospace Sciences (AGS)
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Chungu Lu
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University of Wisconsin Madison
United States
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