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

Yefim L. Kogan NorthWest Research Associates, Seattle, Washington

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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 was simulated by an LES model initialized with soundings from the Rain in Cumulus over the Ocean (RICO) field project. In Part I, 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 the evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H. This function can be quite accurately approximated by the third-order polynomials of z and H. It is suggested that the 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.

Significance Statement

This study investigated condensation/evaporation processes in tropical cumulus clouds. The energy exchanged during these processes is an important driving force behind a wide range of atmospheric phenomena. It was found that the vertical distribution of this energy source can be expressed as a linear function of cloud updrafts. This finding suggests a new approach to calculate cloud energy transformations in numerical weather prediction models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content 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 was simulated by an LES model initialized with soundings from the Rain in Cumulus over the Ocean (RICO) field project. In Part I, 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 the evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H. This function can be quite accurately approximated by the third-order polynomials of z and H. It is suggested that the 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.

Significance Statement

This study investigated condensation/evaporation processes in tropical cumulus clouds. The energy exchanged during these processes is an important driving force behind a wide range of atmospheric phenomena. It was found that the vertical distribution of this energy source can be expressed as a linear function of cloud updrafts. This finding suggests a new approach to calculate cloud energy transformations in numerical weather prediction models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yefim Kogan, ykogan@nwra.com
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  • Barker, H. W., 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part I: Methodology and homogeneous biases. J. Atmos. Sci., 53, 22892303, https://doi.org/10.1175/1520-0469(1996)053<2289:APFCGA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bogenschutz, P. A., and S. K. Krueger, 2013: A simplified PDF parameterization of subgrid-scale clouds and turbulence for cloud-resolving models. J. Adv. Model. Earth Syst., 5, 195211, https://doi.org/10.1002/jame.20018.

    • Search Google Scholar
    • Export Citation
  • Bony, S., and K. A. Emanuel, 2001: A parameterization of the cloudiness associated with cumulus convection; evaluation using TOGA COARE data. J. Atmos. Sci., 58, 31583183, https://doi.org/10.1175/1520-0469(2001)058<3158:APOTCA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., 1982: Cloud-ensemble relations based on the gamma probability distribution for the higher-order models of the planetary boundary layer. J. Atmos. Sci., 39, 26912700, https://doi.org/10.1175/1520-0469(1982)039<2691:CERBOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cheng, A., and K.-M. Xu, 2009: A PDF-based microphysics parameterization for simulation of drizzling boundary layer clouds. J. Atmos. Sci., 66, 23172334, https://doi.org/10.1175/2009JAS2944.1.

    • Search Google Scholar
    • Export Citation
  • Cooper, W. A., 1989: Effects of variable droplet growth histories on droplet size distributions. Part I: Theory. J. Atmos. Sci., 46, 13011311, https://doi.org/10.1175/1520-0469(1989)046%3C1301:EOVDGH%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cuijpers, J. W. M., and P. Bechtold, 1995: A simple parameterization of cloud water related variables for use in boundary layer models. J. Atmos. Sci., 52, 24862490, https://doi.org/10.1175/1520-0469(1995)052<2486:ASPOCW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Davis, A., A. Marshak, W. Wiscombe, and R. Cahalan, 1996: Scale invariance of liquid water distributions in marine stratocumulus. Part I: Spectral properties and stationarity issues. J. Atmos. Sci., 53, 15381558, https://doi.org/10.1175/1520-0469(1996)053<1538:SIOLWD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Del Genio, A. D., M.-S. Yao, W. Kovari, and K. K.-W. Lo, 1996: A prognostic cloud water parameterization for global climate models. J. Climate, 9, 270304, https://doi.org/10.1175/1520-0442(1996)009<0270:APCWPF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Golaz, J.-C., V. E. Larson, and W. R. Cotton, 2002: A PDF-based model for boundary layer clouds. Part I: Method and model description. J. Atmos. Sci., 59, 35403551, https://doi.org/10.1175/1520-0469(2002)059<3540:APBMFB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60, 607625, https://doi.org/10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kogan, Y., 2013: A cumulus cloud microphysics parameterization for cloud-resolving models. J. Atmos. Sci., 70, 14231436, https://doi.org/10.1175/JAS-D-12-0183.1.

    • Search Google Scholar
    • Export Citation
  • Kogan, Y., 2022: Estimating phase transition rates in shallow cumulus clouds from mass flux. Part I: Theory and numerical simulations. J. Atmos. Sci., 79, 29832999, https://doi.org/10.1175/JAS-D-22-0060.1.

    • Search Google Scholar
    • Export Citation
  • Kogan, Y., and D. B. Mechem, 2014: A PDF-based microphysics parameterization for shallow cumulus clouds. J. Atmos. Sci., 71, 10701089, https://doi.org/10.1175/JAS-D-13-0193.1.

    • Search Google Scholar
    • Export Citation
  • Kogan, Y., and D. B. Mechem, 2016: A PDF-based formulation of microphysical variability in cumulus congestus clouds. J. Atmos. Sci., 73, 167184, https://doi.org/10.1175/JAS-D-15-0129.1.

    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., and I. P. Mazin, 2003: Supersaturation of water vapor in clouds. J. Atmos. Sci., 60, 29572974, https://doi.org/10.1175/1520-0469(2003)060<2957:SOWVIC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lappen, C.-L., and D. A. Randall, 2001: Toward a unified parameterization of the boundary layer and moist convection. Part I: A new type of mass-flux model. J. Atmos. Sci., 58, 20212036, https://doi.org/10.1175/1520-0469(2001)058<2021:TAUPOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Larson, V. E., and J.-C. Golaz, 2005: Using probability density functions to derive consistent closure relationships among higher-order moments. Mon. Wea. Rev., 133, 10231042, https://doi.org/10.1175/MWR2902.1.

    • Search Google Scholar
    • Export Citation
  • Larson, V. E., R. Wood, P. R. Field, J.-C. Golaz, T. H. Vonder Harr, and W. R. Cotton, 2001a: Systematic biases in the microphysics and thermodynamics of numerical models that ignore subgrid-scale variability. J. Atmos. Sci., 58, 11171128, https://doi.org/10.1175/1520-0469(2001)058<1117:SBITMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Larson, V. E., R. Wood, P. R. Field, J.-C. Golaz, T. H. Vonder Harr, and W. R. Cotton, 2001b: Small-scale and mesoscale variability of scalars in cloudy boundary layers: One-dimensional probability density functions. J. Atmos. Sci., 58, 19781994, https://doi.org/10.1175/1520-0469(2001)058<1978:SSAMVO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lewellen, W. S., and S. Yoh, 1993: Binormal model of ensemble partial cloudiness. J. Atmos. Sci., 50, 12281237, https://doi.org/10.1175/1520-0469(1993)050<1228:BMOEPC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lohmann, U., and E. Roeckner, 1996: Design and performance of a new cloud microphysics scheme developed for the ECHAM general circulation model. Climate Dyn., 12, 557572, https://doi.org/10.1007/BF00207939.

    • Search Google Scholar
    • Export Citation
  • Nelson, E. L., and T. S. L’Ecuyer, 2018: Global character of latent heat release in oceanic warm rain systems. J. Geophys. Res. Atmos., 123, 47974817, https://doi.org/10.1002/2017JD027844.

    • Search Google Scholar
    • Export Citation
  • Oreopoulos, L., N. Cho, and D. Lee, 2017: New insights about cloud vertical structure from CloudSat and CALIPSO observations. J. Geophys. Res. Atmos., 122, 92809300, https://doi.org/10.1002/2017JD026629.

    • Search Google Scholar
    • Export Citation
  • Paluch, I. R., and C. A. Knight, 1984: Mixing and the evolution of cloud droplet size spectra in a vigorous continental cumulus. J. Atmos. Sci., 41, 18011815, https://doi.org/10.1175/1520-0469(1984)041<1801:MATEOC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., I. P. Mazin, A. Korolev, and A. Khain, 2013: Supersaturation and diffusional droplet growth in liquid clouds. J. Atmos. Sci., 70, 27782793, https://doi.org/10.1175/JAS-D-12-077.1.

    • Search Google Scholar
    • Export Citation
  • Politovich, M. K., and W. A. Cooper, 1988: Variability of the supersaturation in cumulus clouds. J. Atmos. Sci., 45, 16511664, https://doi.org/10.1175/1520-0469(1988)045<1651:VOTSIC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rauber, R. M., and Coauthors, 2007: Rain in shallow cumulus over the ocean: The RICO campaign. Bull. Amer. Meteor. Soc., 88, 19121928, https://doi.org/10.1175/BAMS-88-12-1912.

    • Search Google Scholar
    • Export Citation
  • Schneider, S. H., W. M. Washington, and R. M. Chervin, 1978: Cloudiness as a climatic feedback mechanism: Effects on cloud amounts of prescribed global and regional surface temperature changes in the NCAR GCM. J. Atmos. Sci., 35, 22072221, https://doi.org/10.1175/1520-0469(1978)035<2207:CAACFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Siebert, H., and R. A. Shaw, 2017: Supersaturation fluctuations during the early stage of cumulus formation. J. Atmos. Sci., 74, 975988, https://doi.org/10.1175/JAS-D-16-0115.1.

    • Search Google Scholar
    • Export Citation
  • Slingo, J. M., 1987: The development and verification of a cloud prediction scheme for the ECMWF model. Quart. J. Roy. Meteor. Soc., 113, 899927, https://doi.org/10.1002/qj.49711347710.

    • Search Google Scholar
    • Export Citation
  • Sommeria, G., and J. W. Deardorff, 1977: Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34, 344355, https://doi.org/10.1175/1520-0469(1977)034<0344:SSCIMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Soong, S.-T., and Y. Ogura, 1973: A comparison between axisymmetric and slab-symmetric cumulus cloud models. J. Atmos. Sci., 30, 879893, https://doi.org/10.1175/1520-0469(1973)030<0879:ACBAAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677690, https://doi.org/10.1002/qj.49710444110.

    • Search Google Scholar
    • Export Citation
  • Tomassini, L., 2020: The interaction between moist convection and the atmospheric circulation in the tropics. Bull. Amer. Meteor. Soc., 101, E1378E1396, https://doi.org/10.1175/BAMS-D-19-0180.1.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A. M., 2002: A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci., 59, 19171942, https://doi.org/10.1175/1520-0469(2002)059<1917:APPFTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • VanZanten, M. C., and Coauthors, 2011: Controls on precipitation and cloudiness in simulations of trade-wind cumulus as observed during RICO. J. Adv. Model. Earth Syst., 3, M06001, https://doi.org/10.1029/2011MS000056.

    • Search Google Scholar
    • Export Citation
  • Wielicki, B. A., and L. Parker, 1994: Frequency distributions of cloud liquid water path in oceanic boundary layer cloud as a function of regional cloud fraction. Preprints, Eighth Conf. on Atmospheric Radiation, Nashville, TN, Amer. Meteor. Soc., 415–417.

  • Wood, R., and P. R. Field, 2000: Relationships between total water, condensed water, and cloud fraction in stratiform clouds examined using aircraft data. J. Atmos. Sci., 57, 18881905, https://doi.org/10.1175/1520-0469(2000)057<1888:RBTWCW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Xu, K.-M., and S. K. Krueger, 1991: Evaluation of cloudiness parameterizations using a cumulus ensemble model. Mon. Wea. Rev., 119, 342367, https://doi.org/10.1175/1520-0493(1991)119<0342:EOCPUA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Xu, K.-M., and D. A. Randall, 1996: A semiempirical cloudiness parameterization for use in climate models. J. Atmos. Sci., 53, 30843102, https://doi.org/10.1175/1520-0469(1996)053<3084:ASCPFU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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