Head(s): Prof. Dr.-Ing. Rupert Klein (FU Berlin), Hon.-Prof. Hans-Christian Hege (ZIB), Prof. Dr. Stephan Pfahl (FU Berlin), Dr. Lisa Schielicke (FU Berlin)
Project member(s): Tom Dörffel, Natalia Mikula (née Ernst), Gottfried Hastermann, George Pacey
Participating institution(s): FU Berlin, ZIB

Project Summary

This project aims at a multiscale theory for the intensification of tropical storms as well as for the interaction of fronts and convection in the midlatitudes. The analysis of tropical storms builds upon the asymptotic analysis of nearly axisymmetric vortices with large tilt in dry air by Päschke et al., J. Fluid Mech. 701, 137–170, (2012). This theory incorporates the multiscale effects of clouds and precipitation in a simplified way as prescribed external heat sources. It predicts that certain arrangements of non-axisymmetric heating and vortex tilt can induce vortex amplification.
During the first funding period this theory was corroborated by idealised three-dimensional numerical simulations, and vortex formation under moist aerothermodynamics was studied using a regional weather forecast code. In extending the asymptotic theory to self-consistently include moist processes, we first studied deep convective “hot towers”, which play a central role in vortex intensification, and revealed a new mechanism for their self-sustainance. In parallel, the well-posedness of the moisture transport model was proven rigorously.
From the application perspective, the project will next include key multiscale processes neglected in the theory so far. These concern the energy supply through the near-surface boundary layer, vortex stabilisation by vortex Rossby waves, and the interaction of cloud tower ensembles with the bulk vortex. The result will be a discrete-continuous hybrid multiscale model.
One methodological challenge arises from the need to combine matched asymptotic expansions, multiple scales techniques, and stochastic analysis to capture the boundary layer, the vortex Rossby waves, and the ensembles of randomly triggered cloud towers, respectively.
A second methodological challenge lies in testing the increasingly complex theoretical model. To do so, advanced data analysis and visualisation techniques shall be utilised and extended were needed. The theory will be tested against observational data and high resolution numerical simulations, pursued, e.g., by the ministry-funded   HD(CP)²   project. The challenge is to verify the theoretically predicted asymptotic scalings from the complex three-dimensional, nonstationary data. After extracting the characteristic scales and space-time structure of the boundary layer flow and of individual convection events, data analysis methods shall be developed that allow us to assess the validity of their asymptotic description, given observations and detailed flow simulations. An additional challenge is to define techniques by which the (stochastic) organisation of convection within the simulated bulk vortex can be characterised in sufficient detail for comparison with a related idealized stochastic model.

An extension of the project started in March 2020 focusing on the scale interactions between cold fronts and convective cells in the midlatitudes. As a basis for the development of a reduced theoretical model for frontal dynamics in a moist atmosphere, an empirical analysis of the interaction between cold fronts and convection was first performed by analyzing convective cells tracks obtained from radar data and automatically detected fronts in atmospheric reanalysis data. One key finding from the empirical analysis was that on average around twice as many convective cells develop on cold-frontal convective cell days compared to non-frontal convective cell days. This result highlights the importance large-scale synoptic cold fronts have on the development of smaller-scale convective cells. The empirical analysis has also indicated that different forcing mechanisms have varying importance on the development of convective cells depending on the convective cell location relative to the front. A regression model will be developed to quantify which forcing mechanisms are most important for each cell-front location. Subsequently, the feedback of convective processes on the frontal structure will be investigated in case studies by artificially triggering or suppressing convection in a weather prediction model. Finally, these statistical results from the observational analysis and the process-based insights from the numerical experiments will be used as a starting point for the theoretical model development using methods of multiscale asymptotics. 

Publications C06