The Parameterization of deep convection, Chapter 10 (pp 255-279) in The Physics and Parameterization of Moist Atmospheric Convection
Insights into the parameterization of convection from two decades of diagnostic studies are reviewed. The life cycle of a convective mesosystem mass flux is described using day 245 from the GARP Atlantic Tropical Experiment as example. The thermodynamic differences between non-precipitating convection and precipitating convection are discussed, as well as the importance of the mid-tropospheric freezing level in the tropics and the saturation pressure budget in the tropics. The strengths and weaknesses of the mass flux representation of deep convection is discussed. Diagnostic studies, which have identified three key vertical modes in the convective heating and drying structure, are outlined. Two are related deep modes associated with precipitation and deep tropospheric ascent, but a variable upward equivalent potential temperature (θE) flux. The other is a double mode structure with ascent in the upper troposphere over descent in the lower troposphere, coupled to inflow at the freezing level, with no net precipitation or transport of θE; the mode associated with deep mesoscale anvils. We discuss the mass flux formulation of convective updrafts and downdrafts. We outline the concepts (but not the details) behind the Betts-Miller parameterization and suggest two extensions. One is a formulation of the adjustment time in terms of grid-scale and gravity-wave propagation speed for the two primary modes. The second is an explicit parameterization of the mesoscale anvil mode.
This is the published version of a paper presented at the Kloster Seeon workshop Aug 4-16, 1996 in Bavaria, Germany.
It was also presented at a 1996 ECMWF workshop: and that version is a little more readable.
Another abbreviated talk version that skips details, but may be still easier to read is https://alanbetts.com/workspace/uploads/bettsmiller2004-1282913116.pdf
Betts, A.K.: 1997, The Parameterization of deep convection, Chapter 10 (pp 255-279) in The Physics and Parameterization of Moist Atmospheric Convection, Ed. R. K. Smith, NATO ASI Series C: Vol. 505, Kluwer Academic Publishers, Dordrecht, 498pp.