M3: Toward consistent subgrid momentum closures

Principal investigator: Prof. Marcel Oliver (Jacobs University Bremen), Dr. Sergey Danilov (Alfred Wegener Institute for Polar and Marine Research Bremerhaven)

This project addresses energy backscatter from sub-grid scale motion, both theoretically and in the context of state-of-the-art global ocean circulation models at “eddy permitting” or barely eddy resolving resolutions.  We systematically explore remedies by quantifying the energy budget near the grid scale in situations close to geostrophic turbulence, evaluating existing closure schemes, investigating new approaches to minimally dissipative sub-grid closures, and transferring the best approaches to full primitive equation ocean and earth system models.

Highlights Phase I

Result I: Ocean kinetic energy backscatter

Ocean kinetic energy backscatter reinjects overdissipated kinetic energy via subgrid energy equation into resolved flow to reduce total (unphysical) energy dissipation via classical viscosity closures.

➢ 10% to 50% reduced SSH mean and variability biases (Fig. 1), as well as temperature and salinity mean biases in global ¼° simulations with the FESOM2 model

Figure 1: Bias reduction in sea surface height (SSH) due to backscatter: (top) temporal standard deviation of SSH anomalies from the AVISO observational estimates (1993-2009); (bottom) ratio of SSH standard deviation between AVISO and (left) the reference simulation and (right) the simulation with the new backscatter parametrization; Red corresponds to an underestimation of the variability by the simulation, blue to an overestimation. (Adapted from Juricke et al., 2020).

Result II: Stochastic atmosphere-ocean coupling for climate models

A stochastic coupling scheme is introduced communicate underestimated surface fluxvariability between the ocean and atmosphere. Fluxes are based on randomly drawn ocean surface fields for meshes with higher resolution in the ocean compared to the atmosphere.

➢ 10% to 50% reduced pricipitation mean and variability biases in the tropical Pacific

Seasonal ENSO phase locking of temperature anomalies. Black dots indicate the standard deviation of the observed Niño3.4 index (1870–2018) per month as provided by NOAA; the standard deviations of the simulated Niño3.4 indices are plotted as orange and blue bars (from Rackow et al., 2019).

Result III: Spurious waves and spectral artifacts on unstructured meshes

Differences in continuous, structured and unstructured models are clearly seen on, e.g., Floquet-Bloch dispersion diagrams for a 1D shallow water model (w, k, ℎ are frequency, wavenumber and discretization step, respectively):

➢ Spectral gaps need to be estimated since they imply absence of normal propagating waves at frequencies lying in the gaps. Such gaps create unwanted directional bias, spurious waves and other undesirable artefacts.

➢ Some structured, e.g., triangular, meshes also lead to spectral gaps.

Next phase outlook:

➢ Spurious interfacial waves on unstructured meshes

The union of different grids (B) and the local inclusions of refined mesh areas (C) imply the appearance of a new type of waves, namely guided waves propagating at the interface, and local waves. These types of waves, sometimes called Rayleigh-Stoneley waves, considered to be "spurious" in the current context and should be muffled, since there are no such waves in the original uniform grid (A) reflecting the homogeneity of real models.

Result IV: Local diagnostics of entropy production

Diagnosed rates of entropy production calculated from resolved wind fluctuations take positive or negative signs, with only a slight bias to positive values (part of M4). The dynamics is therefore, on average, thermodynamically consistent.

➢ Restrictions to the dynamic Smagorinsky model arise that also take into account the need for model stability.

No guests available.

Research Stay in Pusan by Ekaterina Bagaeva (Sep 23)

Since the end of 2022, the topic of research stay slowly began to appear in our discussions with my supervisor.  We were considering various research groups studying eddies' modeling but overall decided to contact Prof. Dr. Christian Franzke, an expert in atmospheric stochastic modeling. As I found out later during the research stay he has a broad range of scientific interests, but first things first. We reached out to Prof. Franzke, who confirmed his interest in hosting a guest PhD student. And I haven’t told you yet about the destination. South Korea, Pusan National University, what an exotic place for the research stay! 

I began preparations. Timing was settled (right after the summer break), duration was defined (3 weeks) and the tickets to cross the entire Eurasia  were bought. Pleasant little things have remained: to have online meetings to discuss the working plan for these 3 weeks, to find the perfect Airbnb near the university, to plan the weekend trips…  

On September 1st, when all the students in my home country started the new academic year, I  moved to the East. Everything went very smoothly and on Monday we were already having the meeting with Prof. Franzke. On the same day, I was introduced to the working group of young scientists, and we had lunch together in the Korean mensa. I think after these three weeks, the concentration of kimchi in my stomach reached a critical amount.

I am very grateful to Prof. Franzke, who found time to meet and discuss intermediate results every second day and also was always available by phone, despite the high workload. We ended up with the idea that I’m currently implementing in FESOM2. And what is also great is that we are in contact after the research stay and keep meeting biweekly. During the last week, I had the opportunity to give a talk about my PhD work in front of an ocean modelling group. I believe it went well, because there were quite some questions.  

It's time to come up with the summary. During this short time South Korea gave me a chance to get to know it. The working environment, the urban design, the Korean weather with sunny and rainy days, delicious food and the most important for me - people there. As a nice bonus I did weekend trips to Seoul, to the DMZ between two Koreas, did several hikes to the temples and around Pusan.

First Steps in Stochastic Ocean Modelling

To find a good stochastic kinetic energy backscatter parameterization is my local aim so far.

Ekaterina Bagaeva, PhD M3

My name is Ekaterina and I’m a PhD Student of project M3 “Towards Consistent Subgrid Momentum Closures”. I work at Jacobs University in Bremen and at AWI in Bremerhaven as well. Due to Corona pandemic the personal contacts are quite limited, but I was lucky enough to meet already my colleagues in AWI and also regularly meet the colleagues in Jacobs University.

Before joining to TRR I’ve got a master degree in Mathematical Modelling following an Erasmus Program in Europe. My master thesis was related to stochastic modelling of the evolution of an epidemic. The stochastic area of my thesis brings me to the current work in TRR.

My global aim in the projects is to improve the representation of ocean variability that represents by ocean eddies. Some ocean eddies are already resolved for certain degrees of resolution, but still there are variations where explicit simulation is not possible. Some of these variabilities could be resolved by bringing back to the model kinetic energy, so called kinetic energy backscatter, obtained through the stochastic parametrization. And to find a good stochastic kinetic energy backscatter parameterization is my local aim so far.

To date, we are on the second stage of the project, so the first months of my work were devoted to acquaintance with the FESOM model, its configurations and code itself. The other significant part was related to understanding of papers which were published by members of M3 during the first stage of the project. Currently I start to implement the idea of identifying the process based on EOF (Empirical Orthogonal Functions) analysis of kinetics energy difference between realization of the model on the fine and coarse grids.

I see the evolution of my work in the application of smarter and more sophisticated approached of stochastic parametrization, preserving the model intuitively understandable and available for computation.