Assessment of the z ∼ time‐filtered arbitrary Lagrangian‐Eulerian coordinate in a global eddy‐permitting ocean model

A recognized deficiency of ocean models with a constant-depth vertical coordinate is for truncation errors in the vertical advection scheme to result in spurious numerical mixing of tracers, which can be substantially stronger than that prescribed by the model's mixing scheme. The z∼ vertical coordinate allows vertical levels to displace in a Lagrangian fashion on time scales shorter than a few days, but reverts to fixed levels on longer timescales, and is intended to reduce numerical mixing from transient vertical motions such as internal waves and tides. An assessment of z∼ in a 1/4° global implementation of the Nucleus for European Modeling of the Ocean model is presented. It is shown that, in the presence of near-inertial gravity waves in the North Atlantic, z∼ significantly reduces Eulerian vertical velocities with respect to those in a simulation with the default z* vertical coordinate; that the vertical coordinate approaches an isopycnal, or adiabatic, surface on short timescales; and that both tendencies are enhanced when the z∼ timescale parameters are lengthened with respect to the default settings. Analysis based on density transformation rates shows that numerical mixing is consistently reduced by of order 10% as the z∼ timescales are lengthened. The realism of the model simulation with different timescale parameters is assessed in the global domain, and it is shown that drifts in temperature and salinity, and the spindown in z* of the Antarctic Circumpolar Current, are reduced with z∼, without incurring significant drawbacks in other metrics such as the strength of the overturning circulation or sea ice cover.