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.

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

Studies of ocean surface transport often invoke the “Eulerian-mean hypothesis”: that wave-agnostic general circulation models neglecting explicit surface waves effects simulate the Eulerian-mean ocean velocity time-averaged over surface wave oscillations. Acceptance of the Eulerian-mean hypothesis motivates reconstructing the total, Lagrangian-mean surface velocity by adding Stokes drift to model output. Here, we show that the Eulerian-mean hypothesis is inconsistent, because wave-agnostic models cannot accurately simulate the Eulerian-mean velocity if Stokes drift is significant compared to the Eulerian-mean or Lagrangian-mean velocity. We conclude that Stokes drift should not be added to ocean general circulation model output. We additionally show the viability of the alternative “Lagrangian-mean hypothesis” using a theoretical argument and by comparing a wave-agnostic global ocean simulation with an explicitly wave-averaged simulation. We find that our wave-agnostic model accurately simulates the Lagrangian-mean velocity even though the Stokes drift is significant.

High-frequency wind speed and wave variability influence the air-sea CO2 flux by modulating the gas transfer velocity. Traditional gas transfer velocity formulations scale solely with wind speed and ignore wave activity, including wave breaking and bubble-mediated transfers. In this study, we quantify the effects of wave-induced spatiotemporal variability on the CO2 flux and the ocean carbon storage using a wind-wave-dependent gas transfer velocity formulation in an ocean general circulation model (MOM6-COBALTv2). We find that wave activity introduces a hemispheric asymmetry in ocean carbon storage, with gain in the southern hemisphere where wave activity is robust year-round and loss in the northern hemisphere where continental sheltering reduces carbon uptake. Compared to a traditional wind-dependent formulation, the wind-wave-dependent formulation yields a modest global increase in ocean carbon storage of 4.3 PgC over 1959-2018 (~4%), but on average, enhances the CO2 gas transfer velocity and flux variability by 5-30% on high-frequency and seasonal timescales in the extratropics and up to 200-300% during storms (>15 m s-1 wind speed). This wave-induced spatiotemporal variability in CO2 flux is comparable to the flux expected from marine carbon dioxide removal (mCDR) techniques, such that neglecting wind-wave variability in modeled CO2 fluxes could hinder distinguishing between natural variability and human-induced changes, undermining mCDR verification and monitoring efforts.

We argue that ocean general circulation models and observations based on Ekman or geostrophic balance provide estimates of the Lagrangian-mean ocean velocity field averaged over surface waves — the total time-averaged velocity that advects oceanic tracers, particles, and water parcels. This interpretation contradicts an assumption often made in ocean transport studies that numerical models and observations based on dynamical balances estimate the Eulerian-mean velocity — the velocity time-averaged at a fixed position and only _part_ of the total ocean velocity. Our argument uses the similarity between the wave-averaged Lagrangian-mean momentum equations appropriate at large oceanic scales, and the momentum equations solved by “wave-agnostic” general circulation models that neglect surface wave effects. We further our case by comparing a realistic, global, “wave-agnostic” general circulation ocean model to a wave-averaged Lagrangian-mean general circulation ocean model at eddy-permitting 1/4-degree resolution, and find that the wave-agnostic velocity field is almost identical to the wave-averaged Lagrangian-mean velocity.