  We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud
system that models dynamics of warm clouds. Our goal is to explicitly describe
the evolution of uncertainties that arise due to unknown input data, such as
model parameters and initial or boundary conditions. The developed stochastic
Galerkin method combines the space-time approximation obtained by a suitable
finite volume method with a spectral-type approximation based on the
generalized polynomial chaos expansion in the stochastic space. The resulting
numerical scheme yields a second-order accurate approximation in both space and
time and exponential convergence in the stochastic space. Our numerical results
demonstrate the reliability and robustness of the stochastic Galerkin method.
We also use the proposed method to study the behavior of clouds in certain
perturbed scenarios, for examples, the ones leading to changes in macroscopic
cloud pattern as a shift from hexagonal to rectangular structures.
