A02 - Multiscale data and asymptotic model assimilation for atmospheric flows
Head(s): Prof. Dr.-Ing. Rupert Klein (FU Berlin), Prof. Dr.-Ing. Sebastian Reich (U Potsdam), Prof. Dr. Claudia Schillings (FU Berlin)
Project member(s): Dr. Cesar Ali Ojeda Marin (Potsdam), Ruben Harris (FU Berlin)
Participating institution(s): FU Berlin, U Potsdam
Computational models can only resolve part of the vast range of spatio-temporal scales found in the atmosphere. Consequently, their numerical discretizations modify scale interactions through associated truncation errors, and parameterizations of the net effects of unresolved scales introduce further model errors. At the same time, insight into the current state of the atmosphere is limited by the sparsity of meteorological observations. To cope with the resulting
uncertainties, data assimilation (DA) enables controlled adjustments of model-based forward simulations using incoming observational data by minimizing the model-to-data distances in suitable norms. DA algorithms require explicit consideration of the multi-scale nature of atmospheric flows to be applicable in the presence of limited data and poor statistical resolution.
This project aims at DA methods connecting scale analysis, computational fluid dynamics, and advanced data filtering. Methodologically speaking, we address the predictive modeling of weather systems whose root model is known but computationally inaccessible due to a cascade of partially unresolvable scales.
During the second funding period, we have (i) laid the theoretical foundation for the robust filtering and parameter estimation of multi-scale systems, (ii) combined multi-scale numerics with localized DA in order to produce balanced analysis ensembles, and (iii) contributed in manifold ways to the theory and algorithmic implementation of mean-field approaches for
Bayesian inference and control.
We will further advance these three main lines of research during the final funding period. Specifically, we will (i) build a comprehensive theory of robust multi-scale data assimilation using rough path theory, (ii) extend and apply balanced data assimilation to the prediction of atmospheric blocking regimes, and (iii) further expand our mean-field control-perspective on
change of measures to applications from machine learning, molecular dynamics, and Bayesian inference.