Title: Property Preserving Remap and Transport for Earth System Models

Abstract: Earth system models are complex frameworks that couple atmosphere, ocean, land, and ice components to simulate the Earth's climate. These models must maintain stability over long integration times, conserve key physical quantities, and accurately pass information between components. In the atmosphere and ocean, the transport of tracer quantities is often handled using semi-Lagrangian algorithms, which allow for large timesteps but require a remapping step to project advected quantities back onto the computational grid.

Remapping algorithms need to balance accuracy, efficiency, and the preservation of physical properties such as mass conservation, positivity, and local bounds. In this talk, I will present an optimization-based remap algorithm that explicitly enforces conservation and local bounds as constraints within a quadratic programming framework. This approach ensures property preservation while minimizing numerical error and maintaining linear relationships between tracer fields.  

The algorithm is applied to tracer transport using semi-Lagrangian methods for both cell-averaged quantities and high-order nodal representations. I will also discuss the extension of this approach to remapping between Lagrangian particles and Eulerian grids, motivated by a particle-based sea ice model. Numerical results will be presented on spherical geometries, including standard benchmark problems such as solid body rotation and deformational flow tests, highlighting the algorithm’s accuracy, conservation properties, and robustness.