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Temperature and Moisture Equations

The thermodynamic equation and moisture equations, for temperature and moisture projections tex2html_wrap_inline1573 and tex2html_wrap_inline1491 associated with basis functions tex2html_wrap_inline1951 and tex2html_wrap_inline2013 are:

  equation945

  equation950

For QTCM1, we use a version of the Betts-Miller (1986) moist convective adjustment scheme, with convection restoring temperature toward convective profile tex2html_wrap_inline1863 . The moisture sink and convective heating terms are given by

equation955

where tex2html_wrap_inline2017 , with tex2html_wrap_inline2019 the time scale of convection in strongly convecting regions and tex2html_wrap_inline2021 a smoothed Heaviside function depending on tex2html_wrap_inline2023 , given in square brackets, a quantity related to CAPE projected on retained structures. The convective profile of temperature is given as tex2html_wrap_inline2025 a reference profile independent of space, plus departures tex2html_wrap_inline2027 following a moist adiabat from the boundary layer with vertical profile of tex2html_wrap_inline1951 . An additional closure assumption is required, which links tex2html_wrap_inline2027 to tex2html_wrap_inline1573 and tex2html_wrap_inline1491 after some manipulation. Examples of this closure are discussed in  [1] and  [10], where the dry stability tex2html_wrap_inline2037 and the gross moisture stratification tex2html_wrap_inline2039 are the contributions of s and q to tex2html_wrap_inline1833 in (gif). The sum of these equations yields the moist static energy equations (gif) with the q terms simplified to tex2html_wrap_inline2049 .



Johnny Wei-Bing Lin
Thu Sep 9 13:11:12 PDT 1999