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A Warm Rain Microphysics Parameterization that Includes the Effect of Turbulence

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  • 1 Centre for Australian Weather and Climate Research,* Melbourne, Victoria, Australia
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Abstract

A warm rain parameterization has been developed by solving the stochastic collection equation with the use of turbulent collision kernels. The resulting parameterizations for the processes of autoconversion, accretion, and self-collection are functions of the turbulent intensity of the flow and are applicable to turbulent cloud conditions ranging in dissipation rates of turbulent kinetic energy from 100 to 1500 cm2 s−3. Turbulence has a significant effect on the acceleration of the drop size distribution and can reduce the time to the formation of raindrops. When the stochastic collection equation is solved with the gravitational collision kernel for an initial distribution with a liquid water content of 1 g m−3 and 240 drops cm−3 with a mean volume radius of 10 μm, the amount of mass that is transferred to drop sizes greater than 40 μm in radius after 20 min is 0.9% of the total mass. When the stochastic collection equation is solved with a turbulent collision kernel for collector drops in the range of 10–30 μm with a dissipation rate of turbulent kinetic energy equal to 100 cm2 s−3, this percentage increases to 21.4. Increasing the dissipation rate of turbulent kinetic energy to 500, 1000, and 1500 cm2 s−3 further increases the percentage of mass transferred to radii greater than 40 μm after 20 min to 41%, 52%, and 58%, respectively, showing a substantial acceleration of the drop size distribution when a turbulent collision kernel that includes both turbulent and gravitational forcing replaces the purely gravitational kernel. The warm rain microphysics parameterization has been developed from direct numerical simulation (DNS) results that are characterized by Reynolds numbers that are orders of magnitude smaller than those of atmospheric turbulence. The uncertainty involved with the extrapolation of the results to high Reynolds numbers, the use of gravitational collision efficiencies, and the range of the droplets for which the effect of turbulence has been included should all be considered when interpreting results based on these new microphysics parameterizations.

Corresponding author address: Dr. Charmaine Franklin, CSIRO Marine and Atmospheric Research, Private Bag No. 1, Aspendale, VIC 3195, Australia. Email: charmaine.franklin@csiro.au

Abstract

A warm rain parameterization has been developed by solving the stochastic collection equation with the use of turbulent collision kernels. The resulting parameterizations for the processes of autoconversion, accretion, and self-collection are functions of the turbulent intensity of the flow and are applicable to turbulent cloud conditions ranging in dissipation rates of turbulent kinetic energy from 100 to 1500 cm2 s−3. Turbulence has a significant effect on the acceleration of the drop size distribution and can reduce the time to the formation of raindrops. When the stochastic collection equation is solved with the gravitational collision kernel for an initial distribution with a liquid water content of 1 g m−3 and 240 drops cm−3 with a mean volume radius of 10 μm, the amount of mass that is transferred to drop sizes greater than 40 μm in radius after 20 min is 0.9% of the total mass. When the stochastic collection equation is solved with a turbulent collision kernel for collector drops in the range of 10–30 μm with a dissipation rate of turbulent kinetic energy equal to 100 cm2 s−3, this percentage increases to 21.4. Increasing the dissipation rate of turbulent kinetic energy to 500, 1000, and 1500 cm2 s−3 further increases the percentage of mass transferred to radii greater than 40 μm after 20 min to 41%, 52%, and 58%, respectively, showing a substantial acceleration of the drop size distribution when a turbulent collision kernel that includes both turbulent and gravitational forcing replaces the purely gravitational kernel. The warm rain microphysics parameterization has been developed from direct numerical simulation (DNS) results that are characterized by Reynolds numbers that are orders of magnitude smaller than those of atmospheric turbulence. The uncertainty involved with the extrapolation of the results to high Reynolds numbers, the use of gravitational collision efficiencies, and the range of the droplets for which the effect of turbulence has been included should all be considered when interpreting results based on these new microphysics parameterizations.

Corresponding author address: Dr. Charmaine Franklin, CSIRO Marine and Atmospheric Research, Private Bag No. 1, Aspendale, VIC 3195, Australia. Email: charmaine.franklin@csiro.au

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