L2: Quantifying Dynamical Regimes in the Ocean and the Atmosphere

Principal investigators: Prof. Marcel Oliver (Catholic University of Eichstätt-Ingolstadt), Prof. Nedjeljka Žagar (University of Hamburg), Dr. Manita Chouksey (Leibniz Institute for Baltic Sea Research Warnemünde), Dr. Sergiy Vasylkevych (University of Hamburg)

Objectives

Dynamical regimes are flows that share common and uniform dynamical or statistical properties, often within a well-defined region of space or time. More generally, we speak of dynamical regimes in the sense of a flow decomposition into constituents with uniform properties, most prominently Rossby waves or “balanced flow” on the one hand and inertia-gravity waves (or, for short, gravity waves) on the other. In order to understand couplings between these processes and the two wave regimes, this subproject aims at their separation and quantification.

The need to quantify the individual constituents of different dynamical regimes arises, first, from the wish to understand their overall dynamics and interactions and their roles in the energy pathways in the atmosphere and ocean. Second, dynamical regimes give rise to bulk properties of the flow, such as vertical momentum fluxes in the atmosphere and spectral characteristics of mesoscale and submesoscale currents in the ocean, which can be learned from high-resolution models but need to be parameterized in relatively low-resolution simulations as are used in climate models. Third, we need to develop tools to detect the remnants of unresolved dynamical regimes from properties of the large scale flow, for example to couple gravity wave parameterizations to the dynamical core.

We approach the regime quantification problem using sophisticated mathematical tools applied to high-resolution primitive equation models, atmospheric analyses and climate simulations. We shall

(a) apply the so-called optimal balance algorithm to realistic primitive equation models, and
(b) systematically evaluate the vertical momentum fluxes associated with Rossby and inertia-gravity waves using 3D linear wave theory with a focus on the tropics.

The results will provide, among others, a novel scale-dependent quantification of the vertical momentum fluxes associated with different atmospheric regimes in analyses and climate models, as a guide for their improved parameterization in climate models. In addition, we will not only provide new and improved diagnostics but also obtain a deeper understanding of the concept of balance itself, especially in the context of global and complex models. For this, a Telescope-ocean-simulation, which has the focus in the Walvis Ridge and simulates not only sub-mesoscale and mesoscale eddies but also internal tides, will be carried out in a joint effort with other subprojects, especially with L4 and W2.

Reports

Research Stay in Brest by Mariana Lage (Dec 22)

One of the best parts of being a scientist in my opinion is to go abroad, meet new researchers and discuss ideas. It is amazing to see what other scientists are doing and how different the institutes are. Last year I had the opportunity to go to Ifremer (Institut français de recherche pour l'exploitation de la mer), in Brest, Brittany, France, and all started with a simple email to Claire Ménesguen introducing myself and asking whether I could visit the institute.

Claire is one of the team leaders of the Ocean Scale Interactions group at the Laboratory for Ocean Physics and Satellite remote sensing (LOPS) together with Jonathan Gula. The main focus of the group is to study ocean dynamics with a particular interest in small horizontal and temporal scales. Once the collaboration was settled and I arrived in Brest, we had several meetings to start planning the structure of the upcoming work. The infrastructure at Ifremer is great, and I met many PhD students and posdocs. As the time and work progressed, we decide to slightly modify our initial plan. Science is highly non-linear, so we had to adapt given the results we obtained with some of the analyses. The good part about that is that I was able to constantly discuss not only with Claire (and Jeff), but also with a lot of people from both Ifremer and LOPS. Because people have different backgrounds, we were able to approach my research topic from many different angles, which led to many nice ideas.

Apart from work (because it would be a shame not to enjoy Brittany’s landscape), I enjoyed the weekends hiking and traveling to small cities around Brest, and, of course, eating! Brittany is very well-known for crêpes, sea food (oysters!) and caramel, which are musts to try when you are there. Brest is on the west coast of France and the landscape is just stunning! The color of the water, the lighthouses and the shape of the coast make this city quite unique. There is also an Aquarium which is really worth visiting. One curiosity from there is that they have their own language (Breton, or Brezhoneg), although nowadays French is the main language spoken. Another curiosity is that it rains a lot, and the weather can easily change from heavy storm to shining sun in a matter of hours.

After my return, Claire and I are still in close contact and we are already planning the next steps regarding our collaborative research. My time there was really pleasant and fruitful and a second research stay is planned in October 2023. I really recommend sometime abroad for everyone especially because the TRR provides the most difficult thing to get: money. This is a unique opportunity to gather different opinions about one’s research topic and to get people to know you too. I left behind many open doors and I am really excited to continue working with all the people I met!

Decomposition of Vertical Momentum Fluxes in the Tropical Atmosphere

Based on MODES we will develop a tool for the computation of vertical momentum fluxes from high-resolution ERA5 data.
Valentino Neduhal, PhD L2

Greetings dear reader! My name is Valentino and I work as a PhD student at the University of Hamburg under the supervision of Dr. Nedjeljka Žagar (Universität Hamburg). I am a part of the TRR subproject L2 named “Quantifying Dynamical Regimes in the Ocean and the Atmosphere”. I am originally from Croatia where I spent all of my education years. I have Bachelor in Physics/Geophysics from the University of Zagreb and a Masters in Meteorology and Physical Oceanography that I acquired with the thesis on “Implementation of the empirical orthogonal functions analysis to determine nonstationarity of time series” from the University of Zagreb.

I started my work as a part of TRR in May of 2021. with the goal of my work being the quantification of vertical momentum fluxes in the tropical atmosphere. To do this we will employ normal mode decomposition ( NMD ) to decompose atmospheric motions to different dynamical regimes. More precisely we will be using the MODES NMD package developed by Žagar et al., for the horizontal velocity and an associated novel spectral approach for the vertical velocity decomposition. Based on MODES we will develop a tool for the computation of vertical momentum fluxes from high-resolution ERA5 data.

Then, we will analyze climate models in the same way and compare the results with those for reanalysis to quantify missing momentum fluxes across scales. The results will be then used to quantify the missing momentum fluxes in climate models that are still running at a much lower resolution. The quantification of vertical momentum fluxes associated with the inertiagravity waves in analysis data can become valuable validation metrics of new parameterizations and upscale transfers in ICON-a and other climate models. The results will provide, among others, a novel scaledependent quantification of the vertical momentum fluxes associated with different atmospheric regimes in analyses and climate models.

Publications

Fedele, F., Chandre, C. , Horvat, M. & Žagar, N. (2024): Hamiltonian Lorenz-like models. Physica D: Nonlinear Phenomena, 134494. doi: https://doi.org/10.1016/j.physd.2024.134494
Neduhal, V., Žagar, N., Lunkeit, F., Polichtchouk, I. & Zaplotnik, Ž. (2024). Decomposition of the Horizontal Wind Divergence Associated With the Rossby, Mixed Rossby-Gravity, Inertia-Gravity, and Kelvin Waves on the Sphere. Journal of Geophysical Research: Atmospheres, 129, e2023JD040427, doi: https://doi.org/10.1029/2023JD040427.
Oliver, M. & Tiofack Kenfack, M.A. (2024). Deterministic and stochastic surrogate models for a slowly driven fast oscillator. SIAM J. Appl. Dyn. Syst. 23(2), 1090-1107, doi: https://doi.org/10.1137/23M1602176.
Žagar, N., Neduhal, V., Vasylkevych, S. et al. (2023). Decomposition of vertical velocity and its zonal wavenumber kinetic energy spectra in the hydrostatic atmosphere. J. Atmos. Sci. 80(11), 2747–2767, doi: https://doi.org/10.1175/JAS-D-23-0090.1.
Chouksey, M., Eden, C., Masur, G. & Oliver, M. (2023). A comparison of methods to balance geophysical flows. J. Fluid Mech. 971, A2, doi: https://doi.org/10.1017/jfm.2023.602.
Denamiel, C., Vasylkevych, S., Žagar, N., Zemunik, P. & Vilibić, I. (2023). Destructive potential of planetary meteotsunami waves beyond the Hunga Tonga–Hunga Ha’apai volcano eruption. B. Am. Meteorol. Soc. 104(1), E178–E191, doi: https://doi.org/10.1175/BAMS-D-22-0164.1.
Masur, G.T., Mohamad, H. & Oliver, M. (2023). Quasi-convergence of an implementation of optimal balance by backward-forward nudging. Multiscale Model. Simul. 21, 624–640, doi: https://doi.org/10.1137/22M1506018.
Mohamad, H. & Oliver, M. (2021). Numerical integration of functions of a rapidly rotating phase. SIAM J. Num. Anal. 59, 2310–2319, doi: https://doi.org/10.1137/19M128658X.
Li, Z. & von Storch, J.-S. (2020). M2 internal-tide generation in STORMTIDE2. J. Geophys. Res. - Oceans 125, e2019JC01545, doi: https://doi.org/10.1029/2019JC015453.
Masur, G. T., & Oliver, M. (2020). Optimal balance for rotating shallow water in primitive variables, Geophys. & Astrophys. Fluid Dyn., doi: https://doi.org/10.1080/03091929.2020.1745789.
Badin, G., Behrens, J., Franzke, C., Oliver, M. & Rademacher, J. (2019). Introduction, Geophys. Astro. Fluid, 113:5-6, 425-427, DOI: 10.1080/03091929.2019.1655259.
Gutjahr, O., Putrasahan, D., Lohmann, K., Jungclaus, J. H., von Storch, J. S., Brüggemann, N., Haak, H., & Stössel, A. (2019). Max Planck Institute Earth System Model (MPI-ESM1. 2) for High-Resolution Model Intercomparison Project (HighResMIP). Geophys. Mod. Develop., 12, 3241-3281, doi.org/10.5194/gmd-12-3241-2019.
Oliver, M. & Vasylkevych, S. (2019). Geodesic motion on groups of diffeomorphisms with H¹ metric as geometric generalised Lagrangian mean theory. Geophys. Astrophys. Fluid Dyn. 113, 466–490, doi: https://doi.org/10.1080/03091929.2019.1639697.
Conti, G. and G. Badin (2019). Velocity statistics for point vortices in the local α-models of turbulence, Geophys. Astro. Fluid., doi: 10.1080/03091929.2019.1572750.
von Storch, J. S., Badin, G. & Oliver, M. (2019). The Interior Energy Pathway: Inertia-Gravity Wave Emission by Oceanic Flows. In Energy Transfers in Atmosphere and Ocean (pp. 53-85). Springer, Cham., doi: https://doi.org/10.1007/978-3-030-05704-6_2.
Franzke, C. L., Oliver, M., Rademacher, J. D., & Badin, G. (2019). Multi-scale methods for geophysical flows. In Energy Transfers in Atmosphere and Ocean (pp. 1-51). Springer, Cham., doi: https://doi.org/10.1007/978-3-030-05704-6_1.
Mohamad, H., and Oliver, M. (2019). A direct construction of a slow manifold for a semilinear wave equation of Klein–Gordon type. J. Differ. Eq., doi: https://doi.org/10.1016/j.jde.2019.01.001.
Oliver, M. (2018). An estimate on the Bedrosian commutator in Sobolev space. J. Inequal. Appl. 348(4), doi: https://doi.org/10.1186/s13660-018-1940-3.
Badin, G., Oliver, M. & Vasylkevych, S. (2018). Geometric Lagrangian averaged Euler-Boussinesq and Primitive Equations, J. Phys. A-Math. Theor., 51, 455501, doi: 10.1088/1751-8121/aae1cb.
Dräger-Dietel, J., Jochumsen, K., Griesel, A. & Badin, G. (2018). Relative dispersion of surface drifters in the Benguela upwelling region. J. Phys. Oceanogr., doi: https://doi.org/10.1175/JPO-D-18-0027.1.
Badin, G. and Barry, A. (2018). Collapse of generalized Euler and surface quasi-geostrophic point-vortices. Phys. Rev. E, 98, 023110, doi.org/10.1103/PhysRevE.98.023110.
Domeisen, D.I.V. , Badin, G. & Koszalka, I. (2018). How predictable are the Arctic and North Atlantic Oscillations? Exploring the variability and predictability of the Northern Hemisphere, J. Climate, 31, 997-1014, doi.org/10.1175/JCLI-D-17-0226.1.
Conti, G. & Badin, G. (2017). Hyperbolic Covariant Coherent Structures in Two Dimensional Flows. Fluids, 2017, 2(4), 50., doi.org/10.3390/fluids2040050.
Gottwald, G.A., Mohamad, H. & Oliver, M. (2017). Optimal balance via adiabatic invariance of approximate slow manifolds. Multiscale Model. Simul. 15, 1404–1422, doi: https://doi.org/10.48550/arXiv.2206.13068.
Blender, R. & Badin, G. (2017).Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations. Fluids 2017, 2 (2), doi:10.3390/fluids2020024.
Blender, R. & Badin, G. (2017). Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation. Eur. Phys. J. Plus, 132(3), 137, doi: 10.1140/epjp/i2017-11440-x.