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QTCM Approach

All QTCM versions are derived from the nonlinear primitive equations





where temperature T and specific humidity q are in energy units, tex2html_wrap_inline2352 are the long-wave radiative fluxes depending on T, q and cloudiness over the column, and surface temperature tex2html_wrap_inline1960 . Shortwave fluxes S are positive downward. The operators tex2html_wrap_inline2362 , tex2html_wrap_inline2364 and tex2html_wrap_inline2366 include horizontal diffusion and horizontal advection terms. The vertical fluxes of sensible heat and moisture by nonconvective, diffusive transport, tex2html_wrap_inline2368 and tex2html_wrap_inline2370 , and stress tex2html_wrap_inline2372 , vanish at the top and have drag laws at the surface for tex2html_wrap_inline2374 , evaporation E, and tex2html_wrap_inline2378 . The hydrostatic equation has been used for baroclinic pressure gradients in the momentum equation (3), where tex2html_wrap_inline2380 is the geopotential at the lowest pressure level, tex2html_wrap_inline2382 .

An important subsidiary relation that holds for all convective parameterizations is the ``convective heating'' and ``moistening'' terms tex2html_wrap_inline1990 and tex2html_wrap_inline2386 cannot change the vertically integrated moist static energy budget, i.e. tex2html_wrap_inline2388 or


where tex2html_wrap_inline2392 , tex2html_wrap_inline2394 , absorbing tex2html_wrap_inline2396 into all fluxes for brevity, and tex2html_wrap_inline2398 denotes vertical averaging over the troposphere, from the surface, tex2html_wrap_inline2400 , to the tropopause, tex2html_wrap_inline2402 .

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