This paper is Part II of a two-part paper that documents the CM4X (Climate Model version 4X) hierarchy of coupled climate models developed at the Geophysical Fluid Dynamics Laboratory (GFDL). Part I of this paper is presented in \citeA{CM4X_partI}. Here we present a suite of case studies that examine ocean and sea ice features that are targeted for further research, which include sea level, eastern boundary upwelling, Arctic and Southern Ocean sea ice, Southern Ocean circulation, and North Atlantic circulation. The case studies are based on experiments that follow the protocol of version 6 from the Coupled Model Intercomparison Project (CMIP6). The analysis reveals a systematic improvement in the simulation fidelity of CM4X relative to its CM4.0 predecessor, as well as an improvement when refining the ocean/sea ice horizontal grid spacing from the $0.25^{\circ}$ of CM4X-p25 to the $0.125^{\circ}$ of CM4X-p125. Even so, there remain many outstanding biases, thus pointing to the need for further grid refinements, enhancements to numerical methods, and/or advances in parameterizations, each of which target long-standing model biases and limitations.

A document by Brandon G Reichl. Click on the document to view its contents.

Due to their limited resolution, numerical ocean models need to be interpreted as representing filtered or averaged equations. How to interpret models in terms of formally averaged equations, however, is not always clear, particularly in the case of hybrid or generalized vertical coordinate models. We derive the averaged hydrostatic Boussinesq equations in generalized vertical coordinates for an arbitrary thickness weighted-average. We then consider various special cases and discuss the extent to which the averaged equations are consistent with existing model formulations. As previously discussed, the momentum equations in existing depth-coordinate models are best interpreted as representing Eulerian averages (i.e., averages taken at fixed depth), while the tracer equations can be interpreted as either Eulerian or thickness-weighted isopycnal averages. Instead we find that no averaging is fully consistent with existing formulations of the parameterizations in semi-Lagrangian discretizations of generalized vertical coordinate ocean models. Perhaps the most natural interpretation of generalized vertical coordinate models is to assume that the average follows the model’s coordinate surfaces. However, the existing model formulations are generally not consistent with coordinate-following averages, which would require “coordinate-aware” parameterizations that can account for the changing nature of the eddy terms as the coordinate changes. Alternatively, the model variables can be interpreted as representing either Eulerian or (thickness-weighted) isopycnal averages, independent of the model coordinate that is being used for the numerical discretization. Existing parameterizations in generalized vertical coordinate models, however, are usually not fully consistent with either of these interpretations. We discuss what changes are needed to achieve consistency.

We present the GFDL-CM4X (Geophysical Fluid Dynamics Laboratory Climate Model version 4X) coupled climate model hierarchy. The primary application for CM4X is to investigate ocean and sea ice physics as part of a realistic coupled Earth climate model. CM4X utilizes an updated MOM6 (Modular Ocean Model version 6) ocean physics package relative to CM4.0, and there are two members of the hierarchy: one that uses a horizontal grid spacing of $0.25^{\circ}$ (referred to as CM4X-p25) and the other that uses a $0.125^{\circ}$ grid (CM4X-p125). CM4X also refines its atmospheric grid from the nominally 100~km (cubed sphere C96) of CM4.0 to 50~km (C192). Finally, CM4X simplifies the land model to allow for a more focused study of the role of ocean changes to global mean climate.   CM4X-p125 reaches a global ocean area mean heat flux imbalance of $-0.02~\mbox{W}~\mbox{m}^{-2}$ within $\mathcal{O}(150)$ years in a pre-industrial simulation, and retains that thermally equilibrated state over the subsequent centuries. This 1850 thermal equilibrium is characterized by roughly $400~\mbox{ZJ}$ less ocean heat than present-day, which corresponds to estimates for anthropogenic ocean heat uptake between 1850 and present-day. CM4X-p25 approaches its thermal equilibrium only after more than 1000 years, at which time its ocean has roughly $1100~\mbox{ZJ}$ {\it more} heat than its early 21st century ocean initial state. Furthermore, the root-mean-square sea surface temperature bias for historical simulations is roughly 20\% smaller in CM4X-p125 relative to CM4X-p25 (and CM4.0). We offer the {\it mesoscale dominance hypothesis} for why CM4X-p125 shows such favorable thermal equilibration properties.

A document by Nora Loose. Click on the document to view its contents.

The mechanical interaction between ice floes in the polar sea-ice packs plays an important role in the state and predictibility of the ice cover. Using a Lagrangian-based numerical model we investigate the mechanics of sea ice floe-floe interactions. Our simulations show that elastic and reversible deformation offers significant resistance to compression before ice floes yield with brittle failure. When pressure ridges start to form, compressional strength dramatically decreases, implying thicker sea ice is not necessarily stronger compared to thinner ice. These effects are not accounted for in current sea-ice models that describe ice strength by thickness alone. As our results show, the observed transition in mechanical state during ridging initiation may lead to biases in simulated ridge building rates and sea-ice thickness. We propose a parameterization that describes failure mechanics from fracture toughness and Coulomb sliding, improving the representation of ridge building dynamics in particle-based and continuum sea-ice models.

We examine the role of transient and standing eddies in an idealized model with a Southern Ocean analog and two basins in the Southern hemisphere. We use the new MOM6 code base in an entirely adiabatic configuration, which allows for full equilibrium integration in only 100 years of simulation time. Fine resolution eddy-resolving simulations at 1/16- and 1/8-degree resolutions are performed in cases with and without continental barriers and/or bottom roughness. A time- and zonal-Reynolds averaging approach is used to decompose eddy fluxes into transient eddies and standing meanders. For a flat bottom channel the wind driven overturning circulation is balanced by transient eddies, consistent with previous studies. However, when continental barriers or bottom roughness are present, we find that standing meanders are dominant in the Southern Ocean.