  The paper is concerned with a nonlinear system of partial differential
equations with parameters and the random external force. This system describes
the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a
rotating two-dimensional sphere. The stationary measures for the Markov
semigroup defined by the solutions of the Cauchy problem for this problem is
considered. One parameter of the system is highlighted - the coefficient of
kinematic viscosity. The sufficient conditions on the random right-hand side
and the other parameters are derived for the existence of a limiting nontrivial
point for any sequence of the stationary measures for this system when any
sequence of the kinematic viscosity coefficients goes to zero. As it is well
known, this coefficient in practice is extremely small. A number of integral
properties are proved for the limiting measure. In addition, these results are
obtained for one similar baroclinic atmosphere system.
