M2: Systematic multi-scale modelling and analysis for geophysical flow

Mean systematic error of 500 hPa geopotential height fields (shading) for extended boreal winters (December–March) of the period 1962–2005. Errors are defined with regard to the observed mean field (contours), consisting of a combination of ERA-40 (1962–2001), and operational ECMWF analyses (2002–2005). (a) Systematic error in a numerical simulation with the ECMWF model IFS, version CY32R1, run at a horizontal resolution of T L 95 (about 210 km) and 91 vertical levels. (b) Systematic error in a simulation with a stochastic kinetic-energy backscatter scheme. Significant differences at the 95% confidence level based on a Student’s t -test are hatched (Franzke et al. 2015).

Principal investigators: Prof. Jens Rademacher (University of Bremen), Prof. Marcel Oliver (Jacobs University Bremen), Dr. Christian Franzke (Universität Hamburg)

We combine methods from formal asymptotics, mathematical analysis, dynamical systems, and stochastic analysis. Our primary focus lies on understanding phenomena and mechanisms – we believe that a better understanding of the nonlinear interactions between scales, waves and the flow regimes will be essential in evaluating and improving numerical weather and climate prediction models. Only in the nonlinear regime can we develop energy consistent schemes. Here we will approach this problem from 3 different directions:

  1. variational balanced model reduction,
  2. a dynamical systems approach of nonlinear waves and balance conditions and
  3. stochastic balanced model reduction.

While 1. and 3. will concentrate on foundational aspects of the problem, 2. will already check its validity using the ICON model in idealised set-ups.

5th Bremen Winter School and Symposium "Dynamical systems and fluids"

The 5th Winter School and Symposium on Dynamical systems and fluids is held at the Department of Mathematics of the University of Bremen. It is supported by the TRR 181.

The early registration deadline is January 31st 2017. The registration fee is 75 € per participant. For registration please email to Ebba Feldmann (ebba@math.uni-bremen.de).

The participants (especially students) are invited to present a poster at the poster session on the afternoon of the first day. Please submit your title and abstract to Ebba Feldmann (ebba@math.uni-bremen.de) before the registration deadline.

More information can be found here.

Invited guests

November 2016

Dr. Terence O'Kane (CSIRO Australia)

Dr. Terence O‘Kane from CSIRO Atmospheres and Ocean, Hobart, Australia, is an expert on stochastic subgrid modeling, coupled data assimilation, predictability, turbulence, geophysical fluid dynamics and advanced time series analysis. He has pionered subgrid modeling using statistical physics methods. His research is very relevant to project M2 but also projects M3 and M4.

As part of his visit he gave a TRR seminar entitled „Statistical Dynamical Subgrid Scale Parameterisation“. First he introduced the overall methodology and then he showed how this approach can be employed to atmospheric as well as ocean models with very good results. His seminar spark a lot of interest and subsequently Terry had many meetings with other TRR scientists but also non-TRR scientists from the Universität Hamburg and the Max-Planck-Institute.

Furthermore, we discussed energy consistent subgrid modeling and stochastic modeling approaches which are of particular importance to project M2. We started a joint project in which we will examine how stochastic subgrid scale parameterizations will affect coupled data assimilation and predictability.

We also finalized a book we are together editing on „Nonlinear and Stochastic Climate Dynamics“ to be published by Cambridge University Press later this year.

written by Dr. Christian Franzke

July 2016

Prof. Edgar Knobloch (UC Berkeley)

Prof. Edgar Knobloch from UC Berkeley visited Jens Rademacher in Bremen to discuss the M2 project related questions. An expert in nonlinear fluid phenomena, multiscale analysis and modelling, Prof. Knobloch's work is very relevant for the M2 area in general and project M2-2 in particular. His work on the influence of viscosity, scaling regimes and models in geophysical flow directly overlaps with the projects’ fundamental questions. Inviscid models fail to accont for the sometimes profound effect that viscous layers have on the bulk flow. Moreover, the energy flow through scales ultimately requires viscous dissipation and suitable driving. During the visit also the question of the role of nonlinear waves in the enery flow were discussed and it seems that many questions remain open at this point. This is especially true in the context of geostrophic balance.



Franzke, C. L., and O'Kane, T. J. (Eds.). (2017). Nonlinear and Stochastic Climate Dynamics. Cambridge University Press.

Gonchenko, S. V., and Ovsyannikov, I. I. (2017). Homoclinic tangencies to resonant saddles and discrete Lorenz attractors. Discrete and Continuous Dynamical Systems Series, Vol 10 (2), p. 273-288, doi: 10.3934/dcdss.2017013.

Franzke, C. L. (2017). Extremes in dynamic-stochastic systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(1), 012101.

Graves, T., Franzke, C. L., Watkins, N. W., Gramacy, R. B., & Tindale, E. (2017). Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models. Physica A: Statistical Mechanics and its Applications.


Ovsyannikov, I. I., & Turaev, D. V. (2016). Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model. Nonlinearity, 30(1), 115.