Estimating Phase Transition Rates in Shallow Cumulus Clouds from Mass Flux. Part II: Vertically dependent formulation

Yefim L. Kogan NorthWest Research Associates, Seattle, WA. USA

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Abstract

This work continued the investigation of the relationship between phase transition rates and mass flux in trade wind cumulus clouds. The latter were simulated by an LES model initialized with soundings from the RICO field project. In Part I (Kogan, 2022) we demonstrated that a very high correlation exists between integral phase transition rates and upward mass flux. In this study we focused on the vertically dependent variables and showed that a similar high correlation exists between the condensation rate 𝒞 (z) and the upward mass flux ℳ (z).

Based on condensation theory, we showed that under quasi-steady approximation condensation rates can be calculated by a linear function of ℳ with the slope coefficient dependent only on temperature and pressure. The model data showed that the error of such approximation is less than a few tenths of a percent.

The parameterization of the evaporation process is more complex, mostly because of the slow evaporation of raindrops as they fall through the cloud’s unsaturated areas. Nevertheless, it was possible to define the fraction of evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H. This function can be quite accurately approximated by the 3rd order polynomials of z and H. It is suggested that proposed formulation of evaporation together with the quasi-steady formulation of condensation can serve as a parameterization of water phase transition rates in shallow cumulus clouds.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yefim Kogan (ykogan@nwra.com)

Abstract

This work continued the investigation of the relationship between phase transition rates and mass flux in trade wind cumulus clouds. The latter were simulated by an LES model initialized with soundings from the RICO field project. In Part I (Kogan, 2022) we demonstrated that a very high correlation exists between integral phase transition rates and upward mass flux. In this study we focused on the vertically dependent variables and showed that a similar high correlation exists between the condensation rate 𝒞 (z) and the upward mass flux ℳ (z).

Based on condensation theory, we showed that under quasi-steady approximation condensation rates can be calculated by a linear function of ℳ with the slope coefficient dependent only on temperature and pressure. The model data showed that the error of such approximation is less than a few tenths of a percent.

The parameterization of the evaporation process is more complex, mostly because of the slow evaporation of raindrops as they fall through the cloud’s unsaturated areas. Nevertheless, it was possible to define the fraction of evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H. This function can be quite accurately approximated by the 3rd order polynomials of z and H. It is suggested that proposed formulation of evaporation together with the quasi-steady formulation of condensation can serve as a parameterization of water phase transition rates in shallow cumulus clouds.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yefim Kogan (ykogan@nwra.com)
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