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Temperature and Moisture Equations

For the simplest QTCM, we use a version of the Betts-Miller (1986) moist convective adjustment scheme, with convection restoring toward convective profiles in both T and q. The convective profile for moisture need not be purely a subsaturation parameterization, but is assumed to have a dominant vertical dependence tex2html_wrap_inline2494 . After some rearrangement this implies tex2html_wrap_inline2496 where we use tex2html_wrap_inline2498 , with tex2html_wrap_inline2500 the time scale of convection in strongly convecting regions and tex2html_wrap_inline2502 a smoothed Heaviside function depending on tex2html_wrap_inline2504 , a quantity related to CAPE projected on retained structures. The quantity tex2html_wrap_inline1964 is a projection of moisture onto basis function tex2html_wrap_inline2508 .

The thermodynamic equation and moisture equations are then




where the dry stability tex2html_wrap_inline2516 and the gross moisture stratification tex2html_wrap_inline2518 are the contributions of s and q to tex2html_wrap_inline2306 in (11). The sum of these equations yields the moist static energy equations (10) with the q terms simplified to tex2html_wrap_inline2528 .

Johnny Wei-Bing Lin
Wed Aug 26 16:58:31 PDT 1998