Abstract: This paper is focused on the numerical and computational issues associated to ocean-atmosphere coupling. It is shown that usual coupling methods do not provide the solution to the correct problem, but to an approaching one since they are equivalent to performing one single iteration of an iterative coupling method. The stability analysis of these ad-hoc methods is presented, and we motivate and propose the adaptation of a Schwarz domain decomposition method to ocean-atmosphere coupling to obtain a stable and consistent coupling method.

Abstract: As atmospheric models are pushed towards non-hydrostatic resolutions, there is a growing need for new numerical discretizations that are accurate, robust and effective at these scales. In this paper we describe a new arbitrary-order staggered nodal finite-element method (SNFEM) vertical discretization motivated by the flux reconstruction formulation. The SNFEM formulation generalizes traditional second-order vertical discretizations, including Lorenz and Charney-Phillips discretizations, to arbitrary order-of-accuracy while preserving desirable properties such as energy conservation. Preliminary results from application of this method to an idealized baroclinic instability are given, demonstrating the effect of improvements in order of accuracy on the structure of the instability.

Abstract: We examine a High Order / Low Order (HOLO) approach for a z-level ocean model and show that the traditional semi-implicit and split-explicit methods, as well as a recent preconditioning strategy, can easily be cast in the framework of HOLO methods. The HOLO formulation admits an implicit-explicit method that is algorithmically scalable and second-order accurate, allowing timesteps much larger than the barotropic time scale. We show how HOLO approaches, in particular the implicit-explicit method, can provide a solid route for ocean simulation to heterogeneous computing and exascale environments.

Abstract: Sandia National Laboratories is developing a new global atmosphere model named Aeras that is performance portable and supports the quantification of uncertainties. These next-generation capabilities are enabled by building Aeras on top of Albany, a code base that supports the rapid development of scientific application codes while leveraging Sandia's foundational mathematics and computer science packages in Trilinos and Dakota. Embedded uncertainty quantification is an original design capability of Albany, and performance portability is a recent upgrade for Albany. Other required features, such as shell-type elements, spectral elements, efficient explicit and semi-implicit time-stepping, transient sensitivity analysis, and concurrent ensembles, were not components of Albany as the project began, and have been (or are being) added by the Aeras team. We present early sensitivity analysis and performance portability results for the shallow water equations.