A02  Multiscale data and asymptotic model assimilation for atmospheric flows
Head(s): Prof. Dr.Ing. Sebastian Reich (U Potsdam), Prof. Dr.Ing. Rupert Klein (FU Berlin)
Project member(s): Ray Chew, Gottfried Hastermann, Dr. Nikolas Nüsken
Participating institution(s): FU Berlin, U Potsdam
Project Summary
Computational flow models can only resolve part of the vast range of spatiotemporal scales found in the atmosphere. Consequently, their numerical discretisations modify scale interactions through associated truncation errors, and parameterisations 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 modelbased forward simulations using incoming observational data by minimizing the modeltodata distances in suitable norms. DA algorithms require explicit use of the multiscale 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 modelling of weather systems whose root model is known but computationally inaccessible due to a cascade of partially unresolvable scales.
More specifically, we will exploit observational data and asymptotic characterisations of both the root model and the DA procedures, to (i) derive efficient and robust data assimilation techniques, to (ii) extend the DA approach from the first funding period for providing physically consistent analysis fields to meteorological applications, and to (iii) provide a mathematical and computational framework for multilevel DA applicable to model hierarchies involving moist atmospheric processes.
Project publications

Nüsken, N. and Richter, L. (2020) Solving highdimensional HamiltonJacobiBellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. SFB 1114 Preprint in arXiv . pp. 140. (Submitted)

Duncan, A. and Nüsken, N. and Szpruch, L. (2019) On the geometry of Stein variational gradient descent. SFB 1114 Preprint in arXiv:1912.00894 . (Unpublished)

Garbuno Inigo, A. and Nüsken, N. and Reich, S. (2019) Affine invariant interacting Langevin dynamics for Bayesian inference. SFB 1114 Preprint in arXiv:1912.02859 . pp. 129. (Unpublished)

Leung, T.Y. and Leutbecher, M. and Reich, S. and Shepherd, Th.G. (2019) Atmospheric Predictability: Revisiting the Inherent FiniteTime Barrier. Journal of the Atmospheric Sciences, 76 (12). pp. 38833892. ISSN Online: 15200469 Print: 00224928

Benacchio, T. and Klein, R. (2019) A semiimplicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics. Monthly Weather Review, 147 (11). pp. 42214240. ISSN Online: 15200493; Print: 00270644

Hittmeir, Sabine and Klein, Rupert and Li, Jinkai and Titi, Edriss (2019) "Global wellposedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes" by Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss. Analysis of PDEs . pp. 128. ISSN 1907.11199 (Submitted)

Nüsken, N. and Reich, S. and Rozdeba, P.J. (2019) State and parameter estimation from observed signal increments. Entropy, 21 (5). 505. ISSN 10994300

Kühnlein, C. and Deconinck, W. and Klein, R. and Malardel, S. and Piotrowski, Z. and Smolarkiewicz, P.K. and Szmelter, J. and Wedi, N. (2019) FVM 1.0: a nonhydrostatic finitevolume dynamical core for the IFS. Geosci. Model Dev., 12 (2). pp. 651676. ISSN 1991959X, ESSN: 19919603

Vater, S. and Klein, R. (2018) A SemiImplicit Multiscale Scheme for Shallow Water Flows at Low Froude Number. Communications in Applied Mathematics & Computational Science, 13 (2). pp. 303336. ISSN 15593940

Müller, A. and Névir, P. and Klein, R. (2018) Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the QuasiGeostrophic Theory. Mathematics of Climate and Weather Forecasting, 4 (1). pp. 122. ISSN 23536438 (online)

Taghvaei, A. and de Wiljes, J. and Mehta, P.G. and Reich, S. (2017) Kalman Filter and Its Modern Extensions for the ContinuousTime Nonlinear Filtering Problem. J. Dyn. Sys., Meas., Control, 140 (3). 030904.

Acevedo, W. and de Wiljes, J. and Reich, S. (2017) Secondorder accurate ensemble transform particle filters. SIAM J. Sci. Comput., 39 (5). A1834A1850. ISSN 10957197 (online)

Hittmeir, S. and Klein, R. and Li, J. and Titi, E. (2017) Global wellposedness for passively transported nonlinear moisture dynamics with phase changes. Nonlinearity, 30 (10). pp. 36763718. ISSN 09517715

Reinhardt, M. and Hastermann, G. and Klein, R. and Reich, S. (2017) Balanced data assimilation for highlyoscillatory mechanical systems. Journal of Nonlinear Science . pp. 123. (Submitted)

O'Kane, T.J. and Monselesan, D.P. and Risbey, J.S. and Horenko, I. and Franzke, Ch.L.E. (2017) On memory, dimension, and atmospheric teleconnection patterns. Math. Clim. Weather Forecast, 3 (1). pp. 127.