M5: Reducing Spurious Mixing and Energetic Inconsistencies in Realistic Ocean-Modelling Applications

Principal investigators: Prof. Sergey Danilov (Alfred Wegener Institute for Polar and Marine Research Bremerhaven/Jacobs University), Prof. Armin Iske (Universität Hamburg), Dr. Knut Klingbeil (Leibniz Institute for Baltic Sea Research Warnemünde)

The project investigates important aspects of the Arbitrary Lagrangian-Eulerian (ALE) layer motion framework and high-order weighted essentially non-oscillatory (WENO) advection schemes, in order to fully exploit the potential of these new concepts in realistic ocean climate modelling applications. During the first phase, these concepts have been identified as the most promising techniques to significantly reduce spurious mixing in ocean models. However, now the efforts in basic research have to be extended to address emerged challenges related to general robustness and efficiency as well as other further mandatory model adjustments. The main goals are:

  • Development of a robust generalized layer motion algorithm based on Lagrangian layer motion and a combination of different regridding strategies.
  • Adaptation and optimization of high-order numerical schemes for remapping, internal pressure gradient and WENO advection to the resulting unstructured mesh layout with sloping layers in FESOM.
  • Development of new diagnostics for diapycnal mixing and internal pressure gradient errors to assess the energetic consistency of the newly designed model components.

With these efforts, we aim for enabling a new era of energy-consistent climate simulations, which will not be dominated by spurious numerical mixing anymore, but by the advanced and wellcalibrated physically-motivated mixing parameterizations developed in other subprojects of this CRC.

The proposed project aims to further develop, assess and analyse numerical algorithms leading to reduction in spurious diapycnal mixing in ocean circulation models. This goal will be achieved by (i) the design and implementation of vertical mesh motion algorithms that reduce spurious mixing; (ii) use of advective schemes with isopycnal diffusion and special design of limiters; (iii) development and analysis of high-order advection algorithms relying on high-order flux evaluation.

Physical mixing (upper panels) and numerical mixing (lower panels) of temperature along a transect across the North Sea simulated with GETM using adaptive coordinates (left) and fixed (sigma in this case) coordinates (right). A reduction of numerical mixing and an according increase of physical mixing when using adaptive coordinates is clearly seen. This figure has been taken from Gräwe et al. (2015) (http://dx.doi.org/10.1016/j.ocemod.2015.05.008).

Reduction of spurious mixing by Lagrangian layer motion


  • realistic applications
  • with different dynamical regimes
  • combination of individual
  • layer motion techniques
  • triggering of regridding
  • efficient mesh regularization
  • analysis of diapycnal mixing
  • interpretation of mean
  • (thickness-weighted) quantities

Reduction of spurious mixing by new advection schemes and by stabilization with isoneutral dissipation


Improved understanding of solvers for generalized Riemann problems

Research gap:

Fast and robust solvers available, but only few rigorous analysis

Main questions:

What do approximate solvers

actually compute from an analytical perspective?

What is the common analytical structure of different solvers?


Our contribution:

Two new insights, important steps towards closing the gap

Analyzing Diapycnal Mixing in Ocean Models

The part of my supervisors and I in the M5, is to develop analysis tools to evaluate whether the new methods succeed in reducing the spurious mixing.

Erika Henell, PhD M5

Hi! My name is Erika and I work as a PhD student at the Leibniz-Institute for Baltic Sea Research Warnemünde (IOW) in Warnemünde, Rostock. I am supervised by Dr. Knut Klingbeil (IOW) and Prof. Dr. Hans Burchard (IOW) and am part of the TRR subproject M5 entitled “Reducing Spurious Mixing and Energetic Inconsistencies in Realistic Ocean-Modelling Applications”.

Before I joined the TRR, I pursued a Bachelor in Physics/Meteorology at the University of Stockholm (Sweden) and a Master in Atmosphere – Climate – Continental surfaces at the University Grenoble Alpes (France). My first connection with physical oceanography was made possible through two internships, during which I worked with the NEMO-eNATL60 model to (a) assess meddies (Mediterranean eddies) and Mediterranean overflow water, and (b) describe the dynamical interaction of internal tides and eddies.

The broad goal of the work in M5 is to implement new methods to reduce errors due to the so called spurious numerical mixing in current ocean models. The part of my supervisors and I in the M5 is to develop analysis tools to evaluate whether the new methods succeed in reducing the spurious mixing. The way we will go about this, is to extend existing tools and ideas about diahaline mixing to diapycnal mixing (mixing across isohalines to mixing across isopycnals).

I will work in particular with the GETM model (https://getm.eu/) which was developed in the working group at IOW that I am a part of. The analysis tools will thus be developed in GETM for idealized cases, extended to the Baltic Sea, and are later to be implemented and applied to global ocean models in collaboration with the Synthesis projects S1 and S2.

Reducing spurious diapycnal mixing in ocean models

My part of work is studying the newly proposed methods of rotating the diffusive part of the advection schemes into the isoneutral plane.

Margarita Smolentseva, PhD M5

Hi everyone, my name is Margarita and I’m a PhD student of the subproject M5 “Reducing spurious diapycnal mixing in ocean models.” This project is about development and analysis of algorithms leading to reducing spurious mixing in ocean models.

Particularly my part of work is studying the newly proposed methods of rotating the diffusive part of the advection schemes into the isoneutral plane. I work in AWI under supervision of Sergey Danilov.

By the moment adapted to triangular meshes with vertex-based and cell-based placement of scalar variables algorithm described by Lemarie at al. (2012) was implemented on the sea-ice model FESOM2.0. I started doing reference potential energy (RPE) analysis of the implemented harmonic version of the algorithm. Also biharmonic version is to be implemented soon. RPE analysis will be held for both versions and also on dissorted meshes. This analysis allows to determine spurious mixing depending on advection schemes and meshes type.

The future work includes analysis of spurious mixing with variance decay technique (by Knut Klingbeil et al.), analysis of regular and irregular meshes, carrying of realistic ocean simulations and analysis of spurious mixing under real conditions.