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.

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

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

The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length-scale of interest. To carry out a length-scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially filtered by employing the coarse-graining technique. At length-scales greater than 10o (or roughly 1000 km), the dynamics closely follow the Topographic-Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length-scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic-Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of Ο(10-100) km in size, and the associated bottom pressure anomalies in local vorticity balances at length-scales smaller than 1000 km. Overall, there is a transition from the Topographic-Nonlinear regime at scales smaller than 10o to the Topographic-Sverdrup regime at length-scales greater than 10o. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea-land boundaries, where bottom stress and horizontal friction generally peak.

We expand on a recent determination of the first global energy spectrum of the ocean’s surface geostrophic circulation \cite{Storer2022} using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales ($>1000 $km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100–500 km) have a root-mean-square (rms) velocity of $\sim15 $cm/s, which increases to $\sim30$–40 cm/s locally in the Gulf Stream and Kuroshio and to $\sim16$–28 cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that $\approx25$–50\% of total geostrophic energy is at scales smaller than 100 km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean component show that most of its energy (up to $70\%$) resides in stationary mesoscales ($<500 $km), highlighting the preponderance of ‘standing’ small-scale structures in the global ocean. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at $\approx200$ km and $\approx2$–3 weeks.

A document by Henri Drake. Click on the document to view its contents.

Using a recently developed 1/12th degree regional ocean model, we establish a link between U.S. East Coast sea level variability and offshore upper-ocean heat content change. This link manifests as a cross-shore mass redistribution driven by an offshore thermosteric sea level response to subsurface warming or cooling. Approximately 50\% of simulated monthly to inter-annual coastal sea level variance south of Cape Hatteras can be statistically accounted for by this mechanism, realized as a function of regional ocean hypsometry, gyre scale warming, and the depth-dependence of density change. This response to offshore warming explains the non-stationarity of U.S. East coast sea level covariance, specifically observed and modeled behavior after $\sim$ 2010. Since approximately 2010, elevated rates of sea level rise south of Cape Hatteras can be partly explained as the result of shore-ward mass redistribution due to offshore sub-surface warming within the North Atlantic subtropical gyre. These results reveal a mechanism that connects local coastal sea level to a broader region and identifies the influence of regional heat content changes on coastal sea level. This analysis presents a framework for identifying new regions that may be susceptible to enhanced sea level rise due to ocean warming and helps bridge the gap between quantifying large scale change and anticipating local coastal impacts like flooding and storm surge.

Understanding advective-diffusive dispersal of trace substances in environmental fluids like the global ocean is a ubiquitous challenge in geophysics. Since the turn of the millennium, substantial progress has been made in the theory, implementation in models, and application of such tracers in oceanography. For the first time, this progress is reviewed here in a synthetic way. We focus on tracer techniques in ocean models, including naturally-occurring and hypothetical tracers that diagnose timescale information, and we emphasize the connection to the Green's function that solves the advection-diffusion equation. Implementation of these techniques in ocean models is explained in an accessible way. We present example applications of these techniques to questions concerning ocean circulation, transport of biogeochemicals, and paleooceanography, including future opportunities.

Two coupled climate models, differing primarily in horizontal resolution and treatment of mesoscale eddies, were used to assess the impact of perturbations in wind stress and Antarctic ice sheet (AIS) melting on the Southern Ocean meridional overturning circulation (SO MOC), which plays an important role in global climate regulation. The largest impact is found in the SO MOC lower limb, associated with the formation of Antarctic Bottom Water (AABW), which in both models is enhanced by wind and weakened by AIS meltwater perturbations. Even though both models under the AIS melting perturbation show similar AABW transport reductions of 4-5 Sv (50-60%), the volume deflation of AABW south of 30˚S is four times greater in the higher resolution simulation (-20 vs -5 Sv). Water mass transformation (WMT) analysis reveals that surface-forced dense water formation on the Antarctic shelf is absent in the higher resolution and reduced by half in the lower resolution model in response to the increased AIS melting. However, the decline of the AABW volume (and its inter-model difference) far exceeds the surface-forced WMT changes alone, which indicates that the divergent model responses arise from interactions between changes in surface forcing and interior mixing processes. This model divergence demonstrates an important source of uncertainty in climate modeling, and indicates that accurate shelf processes together with scenarios accounting for AIS melting are necessary for robust projections of the deep ocean’s response to anthropogenic forcing and role as the largest sink in Earth’s energy budget.

A submesoscale-permitting global ocean model is used to study the upper ocean turbulence. Submesoscale processes peak in winter and, consequently, geostrophic kinetic energy (KE) spectra tend to be relatively shallow in winter (∼k-2) with steeper spectra in summer (∼k-3). This seasonal transition from steep to shallow power-law in the KE spectra indicates a transition from quasi-geostrophic (QG) turbulence in summer to pronounced surface-QG-like turbulence in winter. It is shown that this transition in KE spectral scaling has two phases. In the first phase (late autumn), KE spectra show a presence of two spectral regimes: ∼k-3 scaling in mesoscales (100-300 km) and ∼k-2 scaling in submesoscales (<50 km), indicating the coexistence of QG, surface-QG, and frontal dynamics. In the second phase (late winter), mixed-layer instabilities convert available potential energy into KE, which cascades upscale leading to flattening of the KE spectra at larger scales, and k-2 power-law develops in mesoscales too.

Numerical mixing, defined here as the physically spurious diffusion of tracers due to the numerical discretization of advection, is known to contribute to biases in ocean circulation models. However, quantifying numerical mixing is non-trivial, with most studies utilizing specifically targeted experiments in idealized settings. Here, we present a precise, online water-mass transformation-based method for quantifying numerical mixing that can be applied to any conserved variable in global general circulation models. Furthermore, the method can be applied within individual fluid columns to provide a spatially-resolved metric. We apply the method to a suite of global ocean-sea ice model simulations with differing grid spacings and sub-grid scale parameterizations. In all configurations numerical mixing drives across-isotherm heat transport of comparable magnitude to that associated with explicitly-parameterized mixing. Numerical mixing is prominent at warm temperatures in the tropical thermocline, where it is sensitive to the vertical diffusivity and resolution. At colder temperatures, numerical mixing is sensitive to the presence of explicit neutral diffusion, suggesting that much of the numerical mixing in these regions acts as a proxy for neutral diffusion when it is explicitly absent. Comparison of equivalent (with respect to vertical resolution and explicit mixing parameters) $1/4^\circ$ and $1/10^\circ$ horizontal resolution configurations shows only a modest enhancement in numerical mixing at $1/4^\circ$. Our results provide a detailed view of numerical mixing in ocean models and pave the way for future improvements in numerical methods.

We apply a coarse-grained decomposition of the ocean’s surface geostrophic flow derived from satellite and numerical model products. In the extra-tropics we find that roughly 60\% of the global surface geostrophic kinetic energy is at scales between 100 km and 500 km, peaking at ~300 km. Our analysis also reveals a clear seasonality in the kinetic energy with a spring peak. We show that traditional mean-fluctuation (or Reynolds) decomposition is unable to robustly disentangle length-scales since the time mean flow consists of a significant contribution (greater than 50%) from scales <500 km. By coarse-graining in both space and time, we find that every length-scale evolves over a wide range of time-scales. Consequently, a running time-average of any duration reduces the energy content of all length-scales, including those larger than 1000 km, and is not effective at removing length-scales smaller than 300 km. By contrasting our spatio-temporal analysis of numerical model and satellite products, we show that the AVISO gridded product suppresses temporal variations less than 10 days for all length-scales, especially between 100 km and 500 km.