Two additional convective closure assumptions are implemented in the
current version (qtcm.f.mconvct2). One is called the
`unshifted- 
scheme' or `U- scheme',
which assumes that the convective temperature profile, , arises
following a moist adiabat from the boundary layer without the shift
used in the original Betts-Miller scheme to match the moisture sinks.
This condition is indeed applied to the moisture sink term.
It avoids explicitly specifying convective moisture profile.
Simulations with this scheme produce similar
results to the standard version. Implications of this scheme are
discussed in detail in Su et al. [10].
Another scheme is called the `nonlinear 
' scheme. It is in principle
the same as the standard scheme but retains the nonlinear Clausius-Clapeyron
dependence of 
(the convective moisture profile) on
temperature in horizontal variations as well as vertical. In the standard
version, linearization is used about a reference profile at each level, which
holds well through the tropics, but is beyond its range of validity in
mid-latitudes in winter.
This scheme significantly reduces the excessive mid-latitude
precipitation shown in the standard model and prevents occurrence of negative
humidity in mid-latitudes. Comparison of the model results from
different convective schemes is shown in Su et al. [10].