# B7 - Identification of robust cloud patterns via inverse methods

*Principal investigators: Prof. Dr. Peter Spichtinger, Prof. Dr. Martin Hanke-Bourgeois*

*Other researcher: Nikolas Porz (PhD)*

Cloud patterns and structures in clouds depend crucially on the atmospheric flow field as well as thermodynamic conditions at cloud formation. However, it is not clear how robust these structures are in terms of variations in environmental conditions (e.g., humidity, temperature, etc.) as well as parameters in cloud parameterizations. Since cloud patterns on the order of few tens of kilometers can in turn influence the atmospheric flow via organized latent heat release or radiation feedbacks, the robustness of cloud structures is an important feature.

In this project we will investigate variations in cloud variables and cloud structures due to different sources of uncertainties. First, variations in cloud variables are driven by parameters in cloud parameterizations (i.e. in the representation of cloud processes in the cloud models). Second, variations in environmental conditions might lead to different pathways of cloud formation and evolution.

In order to determine the variations due to different sources of uncertainties, we will apply inverse methods. We will setup a simple but realistic analytical cloud model, consisting of a set of ordinary differential equations, which will subsequently be coupled to hyperbolic conservation laws associated to sedimentation processes. This model will be coupled to simple dynamics in the sense of kinematic frameworks. We will use a Bayesian approach to obtain confidence intervals for the unknown model parameters, in combination with sparsity enhancing priors. This analysis will also point out potentials for further reduction of the model complexity.

In order to assess the variations of initial cloud conditions, we will use two different but complementary methods. As first method, we will use the analytical cloud model coupled to simple dynamics for time-reversal calculations, integrating the model backward in time and evaluating its variation due to perturbed 'initial' conditions. The method will lead to a full spread in variations, but might break down at bifurcations in the system.

Complementary to the first approach, we will develop an adjoint model for the analytical cloud model, to be employed for an iterative solution of the inverse problem. This sophisticated approach will provide possible initial cloud configurations under the assumption of convergence, but will not address possible pathways and not detect different initial states that give similar "observations at weather stations". Finally, we will collect results from the different but complementary methods in order to determine in a synthesis the variability of cloud variables and cloud patterns due to variations in model parameter as well as cloud environmental conditions.