A Micro-Macro Parareal Implementation for the Ocean-Circulation Model FESOM2

TL;DR

This work investigates applying a micro-macro Parareal variant to the state-of-the-art ocean model FESOM2, using a coarse PI mesh and a refined FPI mesh to accelerate time integration while targeting diagnostic variables. It details the mesh-generation and interpolation workflow, including topology-preserving refinement, CDO-based conservative velocity interpolation, and a lifting/restriction framework between meshes. Numerical experiments indicate that convergence of diagnostics to the fine-mesh reference is achievable only with near-full iteration counts, and interpolation/overheads prevent meaningful wall-clock speedups under current configurations; stability issues also arise for longer runs. The study identifies key bottlenecks such as interpolation schemes for vertical velocity and restart-file handling and proposes concrete steps—extend conservative interpolation, optimize pipelines, and test CORE as the fine mesh—to advance practical Parareal deployment in climate models. Overall, it provides a detailed, end-to-end blueprint for applying micro-macro Parareal to unstructured-grid ocean models and clarifies the substantial challenges that must be overcome to realize real-time reductions in climate simulations.

Abstract

A micro-macro variant of the parallel-in-time algorithm Parareal has been applied to the ocean-circulation and sea-ice model model FESOM2. The state-of-the-art software in climate research has been developed by the Alfred-Wegener-Institut (AWI) in Bremen, Germany. The algorithm requires two meshes of low and high spatial resolution to define the coarse and fine propagator. As a first assessment we refined the PI mesh, increasing its resolution by factor 4. The main objective of this study was to demonstrate that micro-macro Parareal can provide convergence in diagnostic variables in complex climate research problems. After the introduction to FESOM2 we show how to generate the refined mesh and which interpolation methods were chosen. With the convergence results presented we discuss the success of this attempt and which steps have to be taken to extend the approach to current research problems.

Figures (66)

• Figure 1: Illustration of variable placement on the horizontal plane. The horizontal velocities are located at the cell centers (red) and scalar quantities at the nodes (blue).
• Figure 2: Illustration of the vertical discretization of the ocean. The staggered placement of variables is demonstrated for one top-to-bottom column. FESOM2 allows for use of partial cells and variation in thickness and amount of layers by applying the Arbitrary Lagrangian Euler (ALE) method.
• Figure 3: Illustration of the vertical discretization with the linear free-surface (linfs) approach. The layer thickness and the volumes of the cells remain constant during the simulation. Cells and nodes outside the boundary (blue line) are part of the mesh but neglected during computations.
• Figure 4: Examples of triangluar skewness: a) triangle with equal angles. b) slightly distorted triangle $SKEW = 0.182$ c) distorted triangle $SKEW = 0.583$
• Figure 5: Illustration of skewness in triangles and their impact on the mesh quality. The dotted, gray lines represent connections between cell centers and edge midpoints, colored lines the direct link between centers. Optimally, those lines should overlap or be as close as possible.