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Abstract This paper is Part II of a two‐part paper that documents the Climate Model version 4X (CM4X) hierarchy of coupled climate models developed at the Geophysical Fluid Dynamics Laboratory. Part I of this paper is presented in Griffies et al. (2025a,https://doi.org/10.1029/2024MS004861). 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. 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 of CM4X‐p25 to the 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. 

Abstract 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 (referred to as CM4X‐p25) and the other that uses a grid (CM4X‐p125). CM4X also refines its atmospheric grid from the nominally 100 km (cubed sphere C96) of CM4.0–50 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 within years in a pre‐industrial simulation, and retains that thermally equilibrated state over the subsequent centuries. This 1850 thermal equilibrium is characterized by roughly less ocean heat than present‐day, which corresponds to estimates for anthropogenic ocean heat uptake between 1870 and present‐day. CM4X‐p25 approaches its thermal equilibrium only after more than 1000 years, at which time its ocean has roughlymoreheat 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 themesoscale dominance hypothesisfor why CM4X‐p125 shows such favorable thermal equilibration properties. 

Abstract. We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable.The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography.The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing.We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence. 

Abstract There are two distinct parameterizations for the restratification effect of mesoscale eddies: the Greatbatch and Lamb (1990, GL90,https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485_1990_020_1634_opvmom_2_0_co_2.xml?tab_body=abstract-display) parameterization, which mixes horizontal momentum in the vertical, and the Gent and McWilliams (1990, GM90,https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485_1990_020_0150_imiocm_2_0_co_2.xml) parameterization, which flattens isopycnals adiabatically. Even though these two parameterizations are effectively equivalent under the assumption of quasi‐geostrophy, GL90 has been used much less than GM90, and exclusively inz‐coordinate models. In this paper, we compare the GL90 and GM90 parameterizations in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. From a theoretical perspective, GL90 is more attractive than GM90 for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness‐weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The striking resemblance between the GL90 and GM90 simulations persists from non‐eddying through eddy‐permitting resolution. We conclude that GL90 is a promising alternative to GM90 for isopycnal coordinate models, where it is more consistent with theory, computationally more efficient, easier to implement, and numerically more stable. Assessing the applicability of GL90 in realistic global ocean simulations with hybrid coordinate schemes should be a priority for future work.