• Arakawa, A., 1969: Parameterization of cumulus convection. Proc. of the WMO/IUGG Symposium of Numerical Weather Prediction, Tokyo, Japan, Japan Meteorological Society, 1–6.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment. Part I:. J. Atmos. Sci., 31 , 674701.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., 1973: Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Meteor. Soc., 99 , 178196.

  • Betts, A. K., 1974: Thermodynamic classification of tropical convective soundings. Mon. Wea. Rev., 102 , 760764.

  • Emanuel, K. A., J. D. Neelin, and C. S. Bretherton, 1994: On large-scale circulations in convecting atmospheres. Quart. J. Roy. Meteor. Soc., 120 , 11111143.

    • Search Google Scholar
    • Export Citation
  • Randall, D. A., D-M. Pan, P. Ding, and D. G. Cripe, 1997: Quasi-equilibrium. The Physics and Parameterization of Moist Atmospheric Convection, NATO ASI Series, R. Smith, Ed., Kluwer Academic, 359–385.

    • Search Google Scholar
    • Export Citation
  • Rennó, N. O., and A. P. Ingersoll, 1996: Natural convection as a heat engine: A theory for CAPE. J. Atmos. Sci., 53 , 572585.

  • Yano, J. I., 1999: Scale-separation and quasi-equilibrium principles in Arakawa and Schubert's cumulus parameterization. J. Atmos. Sci., 56 , 38213823.

    • Search Google Scholar
    • Export Citation
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Remarks on Quasi-Equilibrium Theory

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  • 1 Department of Atmospheric Sciences, The University of Arizona, Tucson, Arizona
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Abstract

A recent article by J. I. Yano has indicated that there is an inconsistency in the original formulation of the quasi-equilibrium theory of Arakawa and Schubert. He argues that this inconsistency results from a contradiction in the two asymptotic limits of the theory; that is, the fractional area covered by convection, and the ratio of the convective adjustment and large-scale timescales cannot simultaneously go to zero, σ → 0 and τADJ/τLS → 0. Yano cites the heat engine theory proposed by Rennó and Ingersoll as “formally establishing” this contradiction. It is demonstrated in this paper that the quasi-equilibrium framework originally developed by Arakawa and Schubert is perfectly consistent with the heat engine theory for steady-state convection, that is, when the timescale associated with the large-scale forcing τLS approximates the effective adjustment timescale of the large-scale ensemble of convective clouds τEFF. Indeed, the quasi-equilibrium framework states that, on the large scale, the atmosphere is in quasi steady state.

Corresponding author address: Prof. Nilton O. Rennó, Department of Atmospheric Sciences, The University of Arizona, P.O. Box 210081, Tucson, AZ 85721. Email: renno@atmo.arizona.edu

Abstract

A recent article by J. I. Yano has indicated that there is an inconsistency in the original formulation of the quasi-equilibrium theory of Arakawa and Schubert. He argues that this inconsistency results from a contradiction in the two asymptotic limits of the theory; that is, the fractional area covered by convection, and the ratio of the convective adjustment and large-scale timescales cannot simultaneously go to zero, σ → 0 and τADJ/τLS → 0. Yano cites the heat engine theory proposed by Rennó and Ingersoll as “formally establishing” this contradiction. It is demonstrated in this paper that the quasi-equilibrium framework originally developed by Arakawa and Schubert is perfectly consistent with the heat engine theory for steady-state convection, that is, when the timescale associated with the large-scale forcing τLS approximates the effective adjustment timescale of the large-scale ensemble of convective clouds τEFF. Indeed, the quasi-equilibrium framework states that, on the large scale, the atmosphere is in quasi steady state.

Corresponding author address: Prof. Nilton O. Rennó, Department of Atmospheric Sciences, The University of Arizona, P.O. Box 210081, Tucson, AZ 85721. Email: renno@atmo.arizona.edu

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