An adaptive vertical coordinate for idealised and global ocean modelling

Abstract

Numerical models of ocean circulation are used in a wide variety of applications, for which speed, accuracy and memory requirements are a trade-off. The representations of physical flow features, such as deep ocean heat uptake and the meridional overturning circulation, are sensitive to the density structure of the ocean, which is determined by mixing and advection. While mixing itself is a physical phenomenon that is represented in the models, another source of mixing is numerical truncation errors, also known as spurious mixing. As a consequence, models with significant spurious mixing may poorly represent the flows being modelled. We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which can be used to estimate mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITgcm and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel. Evaluating the independent contributions to spurious mixing in a model motivated development of a new vertical coordinate for ocean modelling. The goal of this coordinate is to provide local layers of approximately constant density to reduce numerical truncation errors in lateral advection, while maintaining sufficient vertical resolution to resolve surface interactions and vertical modes in weakly-stratified regions. This coordinate was then evaluated in two ways. First, spurious mixing was evaluated using the new split RPE diagnostic in idealised test cases. Using the new coordinate, spurious mixing was reduced in many of the idealised test cases compared to more commonly used coordinates, and in no cases was the spurious mixing increased. Second, the coordinate was evaluated in a more realistic global-scale simulation, comparing key physical metrics against pre-existing coordinates used in ocean modelling. This evaluation demonstrates the potential for the new coordinate to be used in ocean modelling, improving accuracy without a significant computational overhead.