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A simple equilibrium model for shallow-cumulus-topped mixed layers

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Abstract

A new equilibrium model for shallow-cumulus-topped mixed layers is presented. A variant on the w * closure for the shallow-cumulus mass flux is applied that retains the convective area-fraction in its formulation. As opposed to being constant, the fraction is explicitly modeled using a statistical closure as a function of the saturation deficit and humidity variance at cloud base. As a consequence, important new interactions are introduced between the convective transport, humidity, and depth of the mixed layer. This mechanism, which we call the mass-flux humidity feedback, helps determine the character of the equilibrium state such that the mixed-layer top is maintained close to the cloud-base height. Due to the strong sensitivity of the mass flux to the area fraction, the latter thus acts as a regulator or valve mechanism on moist convective transport. As a consequence, the mixed-layer model is able to explain the robustness of many aspects of the shallow-cumulus boundary layer that is typically found in observations and large-eddy simulations (LESs). The model is evaluated for a single-LES case as well as for global climatology obtained from a 40-year reanalysis of meteorological data by the European Centre for Medium-range Weather Forecasts (ECMWF). LES characteristics of convective mass flux, cloud fraction, humidity variance, cloud-base height, and surface fluxes of heat and humidity are reproduced. The solution on reanalysis fields reproduces the spatial structure of mixed-layer temperature and humidity and their associated surface fluxes in the subtropical Atlantic and Pacific trade wind regions. Furthermore, the spatial structure of the convective area-fraction matches that of synoptic surface observations of frequency of occurrence of shallow cumulus. Particularly striking is the smooth onset of the convective area-fraction and mass flux along the trade-wind trajectory that is reproduced, from zero to typical trade-wind values. The cumulus onset represents the necessity for shallow-cumulus mass flux to occur in order to close the mixed-layer budgets of heat, moisture, and mass, as a response to the changing magnitude of large-scale subsidence and free tropospheric humidity along the trajectory. Finally, the mass flux model is implemented in an intermediate-complexity tropical climate model to study its behavior when fully interactive with the larger-scale flow. A climate run then shows that the model is stable, due to the mass-flux humidity feedback acting to keep the shallow-cumulus boundary layer close to its equilibrium state for long, climatological timescales.

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Author notes

  1. Roel Neggers

    Present address: European Centre for Medium-range Weather Forecasts (ECMWF), Shinfield Park, Reading, Berkshire, RG2 9AX, UK

Authors and Affiliations

  1. Department of Atmospheric and Oceanic Sciences, University of California at Los Angeles (UCLA), Los Angeles, CA, USA

    Roel Neggers, Bjorn Stevens & J. David. Neelin

Authors
  1. Roel Neggers
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  2. Bjorn Stevens
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  3. J. David. Neelin
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Correspondence to Roel Neggers.

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Communicated by R. Klein.

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Neggers, R., Stevens, B. & Neelin, J.D. A simple equilibrium model for shallow-cumulus-topped mixed layers. Theor. Comput. Fluid Dyn. 20, 305–322 (2006). https://doi.org/10.1007/s00162-006-0030-1

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  • DOI: https://doi.org/10.1007/s00162-006-0030-1

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