Callum J. Shakespeare

As the ocean tide flows over the rough seafloor, it induces topographic stresses that feed back on the strength of the tide. Here, we examine how these topographic stresses change as the dynamical regime transitions from barotropic to baroclinic with increasing stratification and/or decreasing topographic length scale, thereby bridging between previous work which studied one or other regime in isolation. Our investigation is conducted using linear theory validated by comparison with a suite of over 100 fully nonlinear numerical simulations. For superinertial tidal flows across an isolated ridge, it is shown that the topographic stress rapidly transitions from out of phase with the tidal flow to in phase with the tidal flow at ridge widths of 1–2 times the baroclinic mode-1 wavelength. This change in stress is associated with a switch from topographically confined perturbation flows in the barotropic regime to radiating waves in the baroclinic regime. The transition becomes more complicated in the presence of multiple ridges due to the interference of the waves generated at each. These interactions lead to significant changes in both the magnitude and phase of the topographic stress as compared to the sum of the contributions from two isolated ridges. Further, particular combinations of ridges—so-called “invisible topographies”—lead to exactly zero stress and, therefore, have no effect on the barotropic tide. These results have implications for improving models of ocean tides and tidally driven mixing.

Ocean tides are a major energy reservoir in Earth's climate system, yet global tide models systematically fail to reproduce observed tidal energetics. This limitation arises because existing models do not adequately represent how tide‐generated internal waves in the deep ocean regulate ocean tide energy, accounting only for their initial generation and neglecting the wave stresses associated with their subsequent propagation. These wave stresses can be out of phase with the tidal flow and substantially modify tidal amplitudes. Here we explicitly represent these wave stresses in a global tide model and assess their impact on the energetics of global tides. We show that including these wave stresses is essential for reproducing observed tidal energetics and enables energetically consistent simulations even at coarse spatial resolution. These results highlight a previously missing physical process in tide models and facilitate more accurate and efficient modeling of global ocean tides.

Coupled general circulation models (GCMs) ubiquitously predict polar-amplified surface warming in response to increasing carbon dioxide (CO ₂ ) concentrations but with significant variation in the magnitude of polar temperature rises. Here, we develop a simplified model of climate change over the global ocean to better understand the fundamental physics underpinning polar amplification and untangle the role of ocean dynamics in modulating its strength. Our model is composed of a forcing-feedback formulation for the surface energy balance coupled to the ocean circulation, with the atmosphere slaved to the ocean. Our results suggest that polar-amplified warming is a fundamental property of any climate where the poles are colder than the equator, due largely to the variation of the (negative) evaporative and (positive) longwave feedbacks with temperature. The evaporative feedback weakens more rapidly than the longwave feedback as temperature decreases, leading to larger temperature changes at the poles than at the equator. In our model, the polar oceans are highly sensitive to feedbacks associated with ocean dynamics, which we decompose into circulation and mixing. We find that the amplification of warming in both the Southern Ocean and the Arctic Ocean is most sensitive to the strength of the Atlantic meridional overturning circulation at centennial time scales and near-surface mixing at decadal time scales. There is also significant sensitivity of Southern Ocean temperature changes to the strength of the abyssal overturning, as well as the deep diapycnal mixing. As such, our results suggest that the differing representation of ocean dynamics in GCMs may partly explain their significant variation in the meridional structure of warming under CO ₂ forcing. Significance Statement: This work untangles the role of surface heating and ocean heat transport in driving enhanced surface warming over the polar oceans as the amount of atmospheric greenhouse gases increases. We show that polar-amplified warming can occur due to the differences in local surface heating at the colder poles compared to the warmer regions nearer the equator, without any changes in circulation or atmospheric structure. The ocean influences the amount and speed of this warming with stronger circulation and mixing generally resulting in reduced polar warming. However, this result can vary depending on the time and pole of interest. Our work may help explain the reasons behind the large variation in polar-amplified warming projected by climate models for the coming century.

Tides can modify sea surface height by several meters, yet their representation in models remains imperfect, largely owing to errors in simulating tidal energy loss. In the open ocean, barotropic tides lose energy to internal tides; this process is typically parameterized using a wave drag scaled by a scaling factor greater than one to compensate for processes not captured by the parameterization. Here, we implement a novel wave drag parameterization consistent with linear internal tide theory in MOM6 and run a global, barotropic, ‐tide‐only model to examine the sensitivity of modeled tides to resolution. We apply physics‐based, spatially varying tuning to explore the role of missing dissipative processes in simulating tides. Decreasing grid spacing from 100 to 4 km reduces the global tidal elevation error from 10.21 to 4.37 cm and improves the simulated dissipation. Modeled tidal solutions converge at 4–8 km resolution, with the scaling factor converging to ∼6. The scaling factor remaining larger than one suggests that linear internal tide generation alone cannot explain all open‐ocean dissipation. Correcting linear theory for supercritical topography and applying spatially varying tuning reduce tidal elevation error by a further 0.41 cm, but lead to larger regional disagreement in dissipation compared with observations. These results suggest that barotropic tide models should be run with grid spacing of 8 km or less, and that minimizing global tidal elevation error may not, by itself, be a sufficient tuning criterion, as it does not always guarantee an improved distribution of tidal energy loss.

Tides can modify sea surface height by several meters, yet their representation in models remains imperfect, largely owing to errors in simulating tidal energy loss. In the open ocean, barotropic tides lose energy to internal tides; this process is typically parameterized using a wave drag scaled by a scaling factor greater than one to compensate for processes not captured by the parameterization. Here, we implement a novel wave drag parameterization consistent with linear internal tide theory in MOM6 and run a global, barotropic, M ₂ -tide-only model to examine the sensitivity of modelled tides to resolution. We apply physics-based, spatially varying tuning to explore the role of missing dissipative processes in simulating M ₂ tides. Decreasing grid spacing from 100 km to 4 km reduces the global tidal elevation error from 10.21 cm to 4.37 cm and improves the simulated dissipation. Modelled tidal solutions converge at 4–8 km resolution, with the scaling factor converging to ∼6. The scaling factor remaining larger than one suggests that linear internal tide generation alone cannot explain all open-ocean dissipation. Correcting linear theory for supercritical topography and applying spatially varying tuning reduce tidal elevation error by a further 0.41 cm, but lead to larger regional disagreement in dissipation compared with observations. These results suggest that barotropic tide models should be run with grid spacing of 8 km or less, and that minimising global tidal elevation error may not, by itself, be a sufficient tuning criterion, as it does not always guarantee an improved distribution of tidal energy loss.

Polar ice sheets are losing mass as a result of ocean‐driven melting processes and thus affecting global climate and sea level. Understanding the relevant dynamics and interactions at the ice‐ocean interface is crucial to developing more accurate sea‐level rise projections, but key ocean processes have not yet been considered in detail. In particular, although the potential impact of internal waves on the melting of ice has been hypothesized, no physical validation studies have yet been conducted. This study provides the first direct laboratory measurements of the interaction of internal waves with a pure‐ice interface. The laboratory experiments involve exposing vertical ice slabs to a salt stratification in the presence of an internal wave field generated by a remote wavemaker. Our results indicate that, relative to unforced environments, melting rates can be enhanced by up to in the vicinity of an incident wave beam, with high wave velocities generally equating to higher melting rates. These novel results, which invoke explanation by a hypothetical laminar Stokes boundary layer mechanism, suggest the need for melting parameterizations in ice‐ocean models to be modified to include information about the internal wave climate.

Whenever oceanic currents flow over rough topography, there is an associated stress that acts to modify the flow. In the deep ocean, this stress is predominantly a form drag due to pressure differentials across topography, caused by the formation of internal waves and other baroclinic motions: processes that act on such small scales most global ocean models cannot resolve. Despite the need to incorporate this stress into ocean models, existing parameterizations are limited in their applicability. For instance, most parameterizations are only suitable for small-scale topography and are either for periodic or steady flows but rarely a combination thereof. Here, we summarize some of the most widely used parameterizations and evaluate the accuracy of a carefully selected subset using hundreds of idealized two-dimensional and three-dimensional simulations spanning a wide parameter space. We focus on the case of an isolated Gaussian hill as an idealized representation of a seamount. In cases where the parameterizations prove to be inaccurate, we use our data to suggest improved formulations. Our results thus provide a starting point for a comprehensive parameterization of topographic stresses in ocean models where fine-scale topography is unresolved. Significance Statement: As the ocean flows over topographic features, it experiences a force. Such topography includes undersea mountains that are too small to be accurately described by global ocean and climate models. These forces shape the ocean structure considerably and affect large-scale ocean circulation features, like the Atlantic meridional overturning circulation. Because there is no hope to accurately include these small-scale effects in climate projections, we need expressions (a.k.a. parameterizations) for the collective force they exert on the ocean. Here, we evaluate existing parameterizations for the force created when an oceanic current flows over an underwater hill by comparing them to the output of small-scale, high-resolution ocean simulations. Compared to previous studies, we cover a much wider range of cases. This allows us to see where existing parameterizations break down and also suggests improvements to these parameterizations, taking us closer to the goal of developing a general and widely applicable mathematical description of this phenomenon.

Barotropic tide models are single-layer, shallow water models forced by an oscillatory body force at the tidal frequency. They are widely used in a variety of applications at increasingly high spatial resolutions to take advantage of new high-resolution bathymetric datasets. Here, we investigate the impact of the small-scale roughness present in such bathymetry on the solutions obtained by these models. It is shown that rough topography induces a form stress that scales with the depth variance relative to the mean depth and is out of phase with the tidal flow. As such, this force extracts no energy from the tide but can significantly damp or amplify tidal elevations depending on the resonant properties of the basin. Due to these effects, barotropic tidal models only converge with increasing resolution once the variance of the topography is fully represented. These results have important implications for improving the accuracy of barotropic tide models.

Understanding the processes that drive nutrient transport across Southern Ocean (SO) fronts is critical for accurately modeling global biogeochemical cycles. In this study, we examine the role of mesoscale processes in cross frontal nitrate transport in the SO. Using a novel decomposition method for tracer advection, we spatially decompose velocity and nitrate concentration fields from global ocean models into mesoscale and larger‐scale components. Our analysis reveals two key ways in which mesoscale features influence cross frontal nutrient transport. First, mesoscale flows modify large‐scale circulation, leading to differences in large‐scale nitrate fluxes in mesoscale resolving models compared to coarser resolution models. Second, mesoscale flows and enhanced nitrate gradients directly drive additional nutrient fluxes that are absent in coarse‐resolution models. The importance of these effects varies with region and depth with small‐scale velocity features dominating nutrient transport near rough bottom topography, and mesoscale nitrate structures being crucial for capturing transient, eddy driven transport in the upper water column. These findings highlight the significance of mesoscale processes in cross frontal nutrient fluxes, especially at depth, and underscore the need for improved parameterizations of mesoscale processes in lower resolution models to better simulate cross frontal nitrate transport.