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

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.

Solving equations faster and more accurately

Designing high-order numerical methods needs a good understanding of the mathematical equations we want to solve.

Claus Götz, Postdoc in M5

Hi, I’m Claus and I am a PostDoc in Project M5. The focus of my research in this project is the development and analysis of high-order advection methods and high-oder flux evaluation techniques for ocean models. Our goal is to reduce spurious diapycnal mixing in ocean models and I’m working on the intersection between mathematical analysis and numerical methods to help with that.

High-order numerical methods for flow computations are becoming increasingly more popular in computational engineering, but may be not as widespread in climate and ocean science. So what’s the deal with high and low order?

Classical finite differences and finite volume methods for the discretization of partial differential equations use one piece of information in each cell (say, a function value at the cell-center or an integral average over the cell) and put this information into a discrete version of the PDE. This allows for fast and robust algorithms, but in order to resolve small scale features, we often need very fine grids. On the other hand, the high-order methods we are interested in, use higher degree polynomials or other nonlinear functions in each cell. This extra information allow us resolve more features of the solution, even on coarser girds. In many computational fluid dynamics applications this leads to a smaller overall computational time and we would like to show that this is also true for problems in ocean science.

However, carelessly throwing high-order polynomials at your problem is a sure recipe for failure. If we want to include more features of the analytical solution in our numerical solution, we need a good understanding of the analytical properties and how they can be translated into our numerical scheme. For our particular application, e.g., we want tight control over diffusion properties and need to tune our methods to avoid artificial diffusion without losing stability properties that numerical diffusion brings.

In short, designing high-order numerical methods needs a good understanding of the mathematical equations we want to solve. I’m happy to be involved with learning more about the equations in ocean science, so that we can solve them faster and more accurately.