Numerical simulations and uncertainty quantification for cloud simulation
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Abstract
Clouds are one of the most important and at the same time one of the most uncer-
tain components in the Earth-atmosphere system. In this thesis, we first consider a
deterministic model for warm clouds derived from physical principles. This cloud model
consists of the Navier-Stokes equations describing weakly compressible flows coupled to
evolution equations for liquid water phases. In addition, we investigate two stochastic
models which are derived from the deterministic one. The first stochastic model exhibits
uncertainties in the cloud representations which do not propagate to the flow variables,
whereas the second model is fully stochastic. Since cloud models are associated with very
rich dynamics, especially due to their multi-scale behavior, and since a quantification of
their uncertainties is computationally expensive, their numerical simulation requires so-
phisticated methods. In this work, we develop and study finite volume schemes with
implicit-explicit time discretization combined with a spectral expansion in the stochastic
space. We conduct extensive numerical benchmarking for both the deterministic and the
stochastic models and compare the accuracy of the developed stochastic method for the
fully stochastic model against a standard sampling method. In numerical experiments of
two and three-dimensional Rayleigh-Bénard convection we further demonstrate the appli-
cability of our stochastic methods for uncertainty quantification in complex atmospheric
models.