# Publications by David Marshall

## Locations and mechanisms of ocean ventilation in the high-latitude North Atlantic in an eddy-permitting ocean model

Journal of Climate American Meteorological Society (2020) 1-61

<jats:title>Abstract</jats:title> <jats:p>A substantial fraction of the deep ocean is ventilated in the high-latitude North Atlantic. Consequently, the region plays a crucial role in transient climate change through the uptake of carbon dioxide and heat. However, owing to the Lagrangian nature of the process, many aspects of deep Atlantic Ocean ventilation and its representation in climate simulations remain obscure. We investigate the nature of ventilation in the high latitude North Atlantic in an eddy-permitting numerical ocean circulation model using a comprehensive set of Lagrangian trajectory experiments. Backwards-in-time trajectories from a model-defined ‘North Atlantic DeepWater’ (NADW) reveal the locations of subduction from the surface mixed layer at high spatial resolution. The major fraction of NADW ventilation results from subduction in the Labrador Sea, predominantly within the boundary current (̴ 60% of ventilated NADW volume) and a smaller fraction arising from open ocean deep convection (̴ 25%). Subsurface transformations — due in part to the model’s parameterization of bottom-intensified mixing—facilitate NADWventilation, such that water subducted in the boundary current ventilates all of NADW, not just the lighter density classes. There is a notable absence of ventilation arising from subduction in the Greenland-Iceland-Norwegian Seas, due to the re-entrainment of those waters as they move southward. Taken together, our results emphasize an important distinction between ventilation and dense water formation in terms of the location where each takes place, and their concurrent sensitivities. These features of NADW ventilation are explored to understand how the representation of high-latitude processes impacts properties of the deep ocean in a state-of-the-science numerical simulation.</jats:p>

## Resolving and parameterising the ocean mesoscale in earth system models

Current Climate Change Reports Springer Nature **6** (2020) 137-152

Purpose of ReviewAssessment of the impact of ocean resolution in Earth System models on the mean state, variability, andfuture projections and discussion of prospects for improved parameterisations to represent the ocean mesoscale.Recent FindingsThe majority of centres participating in CMIP6 employ ocean components with resolutions of about 1 degree intheir full Earth System models (eddy-parameterising models). In contrast, there are also models submitted to CMIP6 (both DECKand HighResMIP) that employ ocean components of approximately 1/4 degree and 1/10 degree (eddy-present and eddy-richmodels). Evidence to date suggests that whether the ocean mesoscale is explicitly represented or parameterised affects not onlythe mean state of the ocean but also the climate variability and the future climate response, particularly in terms of the Atlanticmeridional overturning circulation (AMOC) and the Southern Ocean. Recent developments in scale-aware parameterisations ofthe mesoscale are being developed and will be included in future Earth System models.SummaryAlthough the choice of ocean resolution in Earth System models will always be limited by computational consider-ations, for the foreseeable future, this choice is likely to affect projections of climate variability and change as well as otheraspects of the Earth System. Future Earth System models will be able to choose increased ocean resolution and/or improvedparameterisation of processes to capture physical processes with greater fidelity.

## Ertel potential vorticity versus Bernoulli potential on approximately neutral surfaces in the Antarctic Circumpolar Current

Journal of Physical Oceanography American Meteorological Society (2020) 1-79

<jats:title>Abstract</jats:title> <jats:p>We investigate the relationship between Ertel potential vorticity, Q, and Bernoulli potential, B, on orthobaric density surfaces in the Antarctic Circumpolar Current (ACC), using the Southern Ocean State Estimate. Similar to the extratropical atmospheres of Earth and Mars, Q and B correlate in the ACC in a function-like manner with modest scatter. Below the near-surface, the underlying function relating Q and B appears to be nearly linear. Nondimensionalizing its slope yields “Ma”, a “Mach” number for long Rossby waves, the ratio of the local flow speed to the intrinsic long Rossby wave speed. We empirically estimate the latter using established and novel techniques that yield qualitatively consistent results. Previous work related “Ma” to the degree of homogeneity of Q and to Arnol’d’s shear stability criteria. Estimates of “Ma” for the whole ACC are notably positive, implying inhomogeneous Q, on all circumpolar buoyancy surfaces studied. Upper layers generally exhibit “Ma” slightly less than unity, suggesting that shear instability may operate within these layers. Deep layers exhibit “Ma” greater than unity, implying stability. On surfaces shallower than 1000 m just north of the ACC, the Q versus B slope varies strongly on sub-annual and interannual time-scales, but “Ma” hovers near unity. We also study spatial variability: the ACC is speckled with hundreds of small-scale features with “Ma” near unity, whereas away from the ACC “Ma” is more commonly negative or above unity, both corresponding to stability. Maps of the time-mean “Ma” show stable regions occupy most of the Southern Ocean, except for several topographically controlled hotspots where “Ma” is always near unity.</jats:p>

## Random Movement of Mesoscale Eddies in the Global Ocean

Journal of Physical Oceanography American Meteorological Society **50** (2020) 2341-2357

<jats:title>Abstract</jats:title> <jats:p>In this study we track and analyze eddy movement in the global ocean using 20 years of altimeter data and show that, in addition to the well-known westward propagation and slight polarity-based meridional deflections, mesoscale eddies also move randomly in all directions at all latitudes as a result of eddy–eddy interaction. The speed of this random eddy movement decreases with latitude and equals the baroclinic Rossby wave speed at about 25° of latitude. The tracked eddies are on average isotropic at mid- and high latitudes, but become noticeably more elongated in the zonal direction at low latitudes. Our analyses suggest a critical latitude of approximately 25° that separates the global ocean into a low-latitude anisotropic wavelike regime and a high-latitude isotropic turbulence regime. One important consequence of random eddy movement is that it results in lateral diffusion of eddy energy. The associated eddy energy diffusivity, estimated using two different methods, is found to be a function of latitude. The zonal-mean eddy energy diffusivity varies from over 1500 m2 s−1 at low latitudes to around 500 m2 s−1 at high latitudes, but significantly larger values are found in the eddy energy hotspots at all latitudes, in excess of 5000 m2 s−1. Results from this study have important implications for recently developed energetically consistent mesoscale eddy parameterization schemes which require solving the eddy energy budget.</jats:p>

## Sensitivity of deep ocean mixing to local internal tide breaking and mixing efficiency

Geophysical Research Letters Wiley (2019)

There have been recent advancements in the quantification of parameters describing the proportion of internal tide energy being dissipated locally and the “efficiency” of diapycnal mixing, that is, the ratio of the diapycnal mixing rate to the kinetic energy dissipation rate. We show that oceanic tidal mixing is nontrivially sensitive to the covariation of these parameters. Varying these parameters one at a time can lead to significant errors in the patterns of diapycnal mixing‐driven upwelling and downwelling and to the over and under estimation of mixing in such a way that the net rate of globally integrated deep circulation appears reasonable. However, the local rates of upwelling and downwelling in the deep ocean are significantly different when both parameters are allowed to covary and be spatially variable. These findings have important implications for the representation of oceanic heat, carbon, nutrients, and other tracer budgets in general circulation models.

## AMOC sensitivity to surface buoyancy fluxes: the role of air-sea feedback mechanisms

Climate Dynamics Springer **53** (2019) 4521-4537

We interrogate the sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) to surface heat and freshwater fluxes over the Subpolar Gyre in an ocean general circulation model and its adjoint. Surface heat loss out of the Subpolar Gyre in the winter strengthens the AMOC at a lead time of approximately 6 months. However, the same surface heat flux anomaly in the summer leads to a delayed AMOC weakening that emerges at a lag of 8 months. Under a summer surface cooling perturbation, the AMOC progressively weakens up to a lag of approximately 80 months, and then the negative overturning anomaly persists for years. Compared with the sensitivity to surface heat fluxes, seasonality in the AMOC sensitivity to surface freshwater fluxes is less pronounced, and there is no sign reversal between the response to summer and winter perturbations. We explain the mechanisms behind the large seasonal differences in the AMOC sensitivity to surface heat fluxes and highlight the role of evaporation. Heat flux anomalies over the Subpolar Gyre trigger changes in the rate of evaporation and hence affect the salinity of the mixed layer. Surface cooling gives rise to freshening in the following months, whereas warming leads to salinification. Persistent buoyancy changes due to salinity responses counteract the impact of heat fluxes to a varying extent depending on the seasonal mixed layer depth. On the other hand, air-sea feedback mechanisms exert a positive feedback on the AMOC response to surface freshwater flux perturbations both in the summer and in the winter months.

## A geometric interpretation of Southern Ocean eddy form stress

Journal of Physical Oceanography American Meteorological Society **49** (2019) 2553-2570

An interpretation of eddy form stress via the geometry described by the Eliassen-Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape and orientation with respect to the mean-flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent-McWilliams eddy transfer coefficient which depends on eddy energy and a non-dimensional geometric parameter α, bounded in magnitude by unity. α expresses the efficiency by which eddies exchange energy with baroclinic mean-flow via along-gradient eddy buoyancy flux - a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean-flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. α is subject to pronounced vertical structure and is maximum at ∼ 3 km depth where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.

## Recent contributions of theory to our understanding of the Atlantic Meridional Overturning Circulation

Journal of Geophysical Research: Oceans American Geophysical Union **124** (2019) 5376-5399

Revolutionary observational arrays, together with a new generation of ocean and climate models, have provided new and intriguing insights into the Atlantic Meridional Overturning Circulation (AMOC) over the last two decades. Theoretical models have also changed our view of the AMOC, providing a dynamical framework for understanding the new observations and the results of complex models. In this paper we review recent advances in conceptual understanding of the processes maintaining the AMOC. We discuss recent theoretical models that address issues such as the interplay between surface buoyancy and wind forcing, the extent to which the AMOC is adiabatic, the importance of mesoscale eddies, the interaction between the middepth North Atlantic Deep Water cell and the abyssal Antarctic Bottom Water cell, the role of basin geometry and bathymetry, and the importance of a three‐dimensional multiple‐basin perspective. We review new paradigms for deep water formation in the high‐latitude North Atlantic and the impact of diapycnal mixing on vertical motion in the ocean interior. And we discuss advances in our understanding of the AMOC's stability and its scaling with large‐scale meridional density gradients. Along with reviewing theories for the mean AMOC, we consider models of AMOC variability and discuss what we have learned from theory about the detection and meridional propagation of AMOC anomalies. Simple theoretical models remain a vital and powerful tool for articulating our understanding of the AMOC and identifying the processes that are most critical to represent accurately in the next generation of numerical ocean and climate models.

## A sea change in our view of overturning in the subpolar North Atlantic

Science American Association for the Advancement of Science **363** (2019) 516-521

To provide an observational basis for the Intergovernmental Panel on Climate Change projections of a slowing Atlantic meridional overturning circulation (MOC) in the 21st century, the Overturning in the Subpolar North Atlantic Program (OSNAP) observing system was launched in the summer of 2014. The first 21-month record reveals a highly variable overturning circulation responsible for the majority of the heat and freshwater transport across the OSNAP line. In a departure from the prevailing view that changes in deep water formation in the Labrador Sea dominate MOC variability, these results suggest that the conversion of warm, salty, shallow Atlantic waters into colder, fresher, deep waters that move southward in the Irminger and Iceland basins is largely responsible for overturning and its variability in the subpolar basin.

## Impacts of Atmospheric Reanalysis Uncertainty on Atlantic Overturning Estimates at 25°N

Journal of Climate American Meteorological Society **31** (2018) 8719-8744

<jats:p> Atmospheric reanalyses are commonly used to force numerical ocean models, but despite large discrepancies reported between different products, the impact of reanalysis uncertainty on the simulated ocean state is rarely assessed. In this study, the impact of uncertainty in surface fluxes of buoyancy and momentum on the modeled Atlantic meridional overturning at 25°N is quantified for the period January 1994–December 2011. By using an ocean-only climate model and its adjoint, the space and time origins of overturning uncertainty resulting from air–sea flux uncertainty are fully explored. Uncertainty in overturning induced by prior air–sea flux uncertainty can exceed 4 Sv (where 1 Sv ≡ 10<jats:sup>6</jats:sup> m<jats:sup>3</jats:sup> s<jats:sup>−1</jats:sup>) within 15 yr, at times exceeding the amplitude of the ensemble-mean overturning anomaly. A key result is that, on average, uncertainty in the overturning at 25°N is dominated by uncertainty in the zonal wind at lags of up to 6.5 yr and by uncertainty in surface heat fluxes thereafter, with winter heat flux uncertainty over the Labrador Sea appearing to play a critically important role. </jats:p>

## Implementation of a geometrically informed and energetically constrained mesoscale eddy parameterization in an ocean circulation model

Journal of Physical Oceanography American Meteorological Society **48** (2018) 2363-2382

The global stratification and circulation, and their sensitivities to changes in forcing, depend crucially on the representation of the mesoscale eddy field in a numerical ocean circulation model. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies — termed GEOMETRIC — is proposed and implemented in three-dimensional channel and sector models. The GEOMETRIC framework closes eddy buoyancy fluxes according to the standard Gent–McWilliams scheme, but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, provided through a prognostic eddy energy budget evolving with the mean state. It is found that coarse resolution models employing GEOMETRIC display broad agreement in the sensitivity of the circumpolar transport, meridional overturning circulation and depth-integrated eddy energy pattern to surface wind stress as compared with analogous reference calculations at eddy permitting resolutions. Notably, eddy saturation — the insensitivity of the time-mean circumpolar transport to changes in wind forcing — is found in the coarse resolution sector model. In contrast, differences in the sensitivity of the depth-integrated eddy energy are found in model calculations in the channel experiments that vary the eddy energy dissipation, attributed to the simple prognostic eddy energy equation employed. Further improvements to the GEOMETRIC framework require a shift in focus from how to close for eddy buoyancy fluxes to the representation of eddy energetics.

## Implications of eddy cancellation on nutrient distribution within subtropical gyres

Journal of Geophysical Research: Oceans John Wiley and Sons, Inc. **123** (2018) 6720-6735

The role of mesoscale eddies within the nutrient budget of subtropical gyres remains poorly understood and poorly constrained. We explore a new mechanism by which mesoscale eddies may contribute to these nutrient budgets, namely eddy cancellation. Eddy cancellation describes the rectified effect of mesoscale eddies acting to oppose the Eulerian‐mean Ekman pumping. We present an idealized axisymmetric two‐layer model of a nutrient in a wind‐driven gyre and explore the sensitivity of this model to variations in its parameter values. We find that the residual Ekman pumping velocity has a substantial impact on nutrient concentration, as does mode water thickness. These results suggest the response to both residual Ekman pumping and mode water thickness is non‐monotonic: for small values of these parameters the nutrient concentration decreases as the parameter increases. However, beyond a critical value, further increases in Ekman pumping or mode water thickness increase nutrient concentration throughout our highly idealized model. A thin mode water layer promotes vertical diffusion of nutrients from the abyss, while a thicker mode water layer increases productivity by reducing the parametrized particulate flux through the thermocline. The impact of mode water thickness is modulated by the residual Ekman pumping velocity: strong Ekman pumping suppresses the influence of mode water thickness on nutrient concentrations. We use satellite and in‐situ measurements to assess the influence of mode water thickness on primary productivity, and find a statistically significant relationship; thicker mode water correlates with higher productivity. This result is consistent with a small residual Ekman pumping velocity.

## Eddy-mixing entropy and its maximization in forced-dissipative geostrophic turbulence

Journal of Statistical Mechanics: Theory and Experiment
IOP Publishing **2018** (2018) 073206

An equilibrium, or maximum entropy, statistical mechanics theory can be derived for ideal, unforced and inviscid, geophysical flows. However, for all geophysical flows which occur in nature,forcing and dissipation play a major role. Here, a study of eddy-mixing entropy in a forced dissipative barotropic ocean model is presented. We heuristically investigate the temporal evolution of eddy-mixing entropy, as defined for the equilibrium theory, in a strongly forced and dissipative system. It is shown that the eddy-mixing entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability; formation of large scale structures; and steady state fluctuations. The fact that the eddy-mixing entropy behaves in a dynamically balanced way is not a priori clear and provides a novel means of quantifying turbulent disorder in geophysical flows. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance of entropy and statistical mechanics in the study of geostrophic turbulence.

## Atlantic-Pacific asymmetry in deep-water formation

Annual Review of Earth and Planetary Sciences Annual Reviews **46** (2018) 327-352

While the Atlantic Ocean is ventilated by high-latitude deep water formation and exhibits a pole-to-pole overturning circulation, the Pacific Ocean does not. This asymmetric global overturning pattern has persisted for the past 2–3 million years, with evidence for different ventilation modes in the deeper past. In the current climate, the Atlantic-Pacific asymmetry occurs because the Atlantic is more saline, enabling deep convection. To what extent the salinity contrast between the two basins is dominated by atmospheric processes (larger net evaporation over the Atlantic) or oceanic processes (salinity transport into the Atlantic) remains an outstanding question. Numerical simulations have provided support for both mechanisms; observations of the present climate support a strong role for atmospheric processes as well as some modulation by oceanic processes. A major avenue for future work is the quantification of the various processes at play to identify which mechanisms are primary in different climate states.

## Submesoscale Instabilities in Mesoscale Eddies

JOURNAL OF PHYSICAL OCEANOGRAPHY **47** (2017) 3061-3085

## A Model of the Ocean Overturning Circulation with Two Closed Basins and a Reentrant Channel

JOURNAL OF PHYSICAL OCEANOGRAPHY **47** (2017) 2887-2906

## Characterising the chaotic nature of ocean ventilation

Journal of Geophysical Research: Oceans American Geophysical Union **122** (2017) 7577-7594

Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterise the chaotic nature of ventilation pathways according to a nondimensional ‘filamentation number', which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces — implying highly chaotic ventilation pathways — and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior.

## Relative strength of the Antarctic Circumpolar Current and Atlantic Meridional Overturning Circulation

Tellus A: Dynamic Meteorology and Oceanography Taylor and Francis **69** (2017) 1338884-1338884

<p>A simple relationship, based on thermal wind balance, is derived that relates the relative strength of the Antarctic Circumpolar Current (ACC) and Atlantic Meridional Overturning Circulation (AMOC) to the ratios of three depth scales: the e-folding depth of the global stratification, the depth of maximum overturning streamfunction and the maximum depth of the ACC. For realistic values of these depth scales, the relationship predicts a factor 8 &pm; 4 difference in the volume transports of the ACC and AMOC, consistent with the observation-based ratio of 8 &pm; 2.</p>

## The statistical nature of turbulent barotropic ocean jets

Ocean Modelling Elsevier **113** (2017) 34-49

Jets are an important element of the global ocean circulation. Since these jets are turbulent, it is important that they are characterized using a statistical framework. A high resolution barotropic channel ocean model is used to study jet statistics over a wide range of forcing and dissipation parameters. The first four moments of the potential vorticity distribution on contours of time-averaged streamfunction are considered: mean, standard deviation, skewness and kurtosis. A self-similar response to forcing is found in the mean and standard deviation for eastward barotropic jets which exhibit strong mixing barriers; this self-similarity is related to the global potential enstrophy of the flow. The skewness and kurtosis give a behaviour which is characteristic of mixing barriers, revealing a bi/trimodal statistical distribution of potential vorticity with homogenized potential vorticity on each side of the barrier. The mixing barrier can be described by a simple statistical model. This behaviour is shown to be lost in westward jets due to an asymmetry in the formation of zonal mixing barriers. Moreover, when the statistical analysis is performed on eastward jets in a streamfunction following frame of reference, the distribution becomes monomodal. In this way we can distinguish between the statistics due to wave-like meandering of the jet and the statistics due to the more diffusive eddies. The statistical signature of mixing barriers can be seen in more realistic representations of the Southern Ocean and is shown to be an useful diagnostic tool for identifying strong jets on isopycnal surfaces. The statistical consequences of the presence, and absence, of mixing barriers are likely to be valuable for the development of stochastic representations of eddies and their dynamics in ocean models.

## Emergent eddy saturation from an energy constrained eddy parameterisation

Ocean Modelling Elsevier **112** (2017) 125-138

The large-scale features of the global ocean circulation and the sensitivity of these features with respect to forcing changes are critically dependent upon the influence of the mesoscale eddy field. One such feature, observed in numerical simulations whereby the mesoscale eddy field is at least partially resolved, is the phenomenon of eddy saturation, where the time-mean circumpolar transport of the Antarctic Circumpolar Current displays relative insensitivity to wind forcing changes. Coarse-resolution models employing the Gent–McWilliams parameterisation with a constant Gent–McWilliams eddy transfer coefficient seem unable to reproduce this phenomenon. In this article, an idealised model for a wind-forced, zonally symmetric flow in a channel is used to investigate the sensitivity of the circumpolar transport to changes in wind forcing under different eddy closures. It is shown that, when coupled to a simple parameterised eddy energy budget, the Gent–McWilliams eddy transfer coefficient of the form described in Marshall et al. (2012) [ A framework for parameterizing eddy potential vorticity fluxes , J. Phys. Oceanogr., vol. 42, 539–557], which includes a linear eddy energy dependence, produces eddy saturation as an emergent property.