Adaptive Monte Carlo Sampling for Cloud and Microphysics Calculations

Abstract

An important problem in large-scale modeling of the atmosphere is the parametrization of clouds and microphysics on subgrid scales. The framework Cloud Layers Unified By Binormals (CLUBB) was developed to improve the parametrization of subgrid variability. Monte Carlo sampling is used to couple the different physical processes, which improves the grid average of subgrid tendencies. In this Thesis we develop an adaptive Monte Carlo sampling algorithm that re-uses sample points of the previous time step by re-weighting them according to the change of the underlying distribution. This process is called 'what-if sampling' and is an application of importance sampling. An example illustrates that what-if sampling converges slowly when the atmospheric conditions change too much. Therefore, the algorithm was extended by adaptive criteria. These prohibit re-weighting if the atmospheric conditions change too fast and allow the re-weighting method to converge to the right solution. We studied five test cases for different atmospheric conditions and found that the computation of the what-if weights is too expensive and suffers from bad importance sampling. The high-dimensional distribution of CLUBB that evolves in time makes re-weighting difficult. The simulation results of what-if sampling are similar to the standard Monte Carlo method or even worse considering the higher computational costs. Therefore, the algorithm was simplified such that old tendencies are re-used without any re-weighting. This approximation removes the overhead and reduces the extra noise. However, simple re-using does not improve the accuracy of the model for the same computation time for general application. Only in the special case of very few sample points, this method can improve the performance without increasing the error significantly. The standard Monte Carlo sampler of CLUBB works very efficiently by applying well suited importance sampling. For normal simulations, using fewer sample points is better than applying any re-using algorithm to a larger number of sample points.