A recognized deficiency of ocean models with a constant-depth vertical coordinate is for truncation errors in the advection scheme to result in spurious numerical mixing of tracers, which can be substantial larger 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 ¼° global implementation of the NEMO 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 control simulation with the default z* vertical coordinate; that the vertical coordinate approaches an isopycnal, or adiabatic, surface on short timescales; and that both tendences are enhanced when the z~ timescale parameters are lengthened with respect to the default settings. Evaluation of an effective diapycnal diffusivity, based on density transformation rates, shows that numerical mixing is consistently reduced 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 penalties in other metrics such as the strength of the overturning circulation or sea ice cover.

As the sea-ice modeling community is shifting to advanced numerical frameworks, developing new sea-ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea-ice models. Initiated at the Forum for Arctic Modelling and Observational Synthesis (FAMOS), the Sea Ice Rheology Experiment (SIREx) aims at evaluating current state-of-the-art sea-ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea-ice physics (rheology) and by model configuration. Part I of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea-ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the Viscous-Plastic (and the Elastic-Viscous-Plastic variant), Elastic-Anisotropic-Plastic, and Maxwell-Elasto-Brittle rheologies are compared in a single study. We find that both plastic and brittle sea-ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi-fractality. Model configuration (e.g. numerical convergence, atmospheric forcing, spatial resolution) and physical parameterizations (e.g. ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea-ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features (LKFs) in a SIREx Part II companion paper.