# A2 - Impact of structured heat sources on larger scales in atmospheric dynamics

*Project leaders: Prof. Dr. Maria Lukacova, Prof. Dr. Peter Spichtinger*

*Other researchers: Bettina Wiebe (PhD student), Kai Werth (scientific programmer)*

The aim of this interdisciplinary project is to investigate how structured heat sources, e.g., driven by cloud processes, on the small scale influence the atmospheric processes on larger scales. Clearly, it is a challenging task to describe consistently both from the mathematical as well as physical point of view the propagation of small scale "stochastic errors" and their influence on the large scale dynamics. For this purpose we will extend and generalize high-resolution numerical simulations combined with uncertainty quantification as started in Phase 1.

This project is a collaboration between applied mathematics and cloud physics. The numerical strategy proposed in this context is the generalized polynomial chaos stochastic Galerkin method, which belongs to the state-of-art methods in uncertainty quantification, though it has not yet been so popular in atmospheric sciences. Here lies the novelty of our project. We will introduce several random parameters, e.g., model parameters but also parameters describing the environmental conditions. The stochastic Galerkin method allows to reconstruct all solutions from a few chosen basis representations, since the simulation in the stochastic space is realized on-the-fly together with the space-time approximations. This is complementary to a standard Monte Carlo approach, where a huge ensemble of model simulations with randomly perturbed parameters/environmental conditions must be used as input for statistical investigations. The Galerkin approach reduces the amount of computational effort using sophisticated mathematical methods, the spectral Galerkin method for the approximation in the stochastic space.

We will use this approach to investigate the predictability of atmospheric flows in a sophisticated way. In the proposed project we concentrate on two relevant atmospheric scenarios: (i) the initiation of convection driven by turbulent and structured planetary boundary layer, and (ii) the impact of structured heat sources, e.g., mimicking structures in cirrocumulus, in the tropopause region on larger scale dynamics. The parameters of heat sources will be perturbed and the sensitivity of flow due to perturbations will be studied. The aim is to investigate the question of predictability for these two scenarios in terms of stochastic representation.