The simplest QTCM, referred to as QTCM1.0, occurs when we
carry only a single temperature basis function typical of deep convection
effects. Two leading basis functions are carried for the velocity field:
for the barotropic mode and 
given by (
) for the baroclinic
mode associated with 
variations. Projecting on these gives equations
that need be solved only in (x,y) for 
and 
.