Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing

Upwelling of global deep waters to the sea surface in the Southern Ocean closes the global overturning circulation and is fundamentally important for oceanic uptake of carbon and heat, nutrient resupply for sustaining oceanic biological production, and the melt rate of ice shelves. However, the exact pathways and role of topography in Southern Ocean upwelling remain largely unknown. Here we show detailed upwelling pathways in three dimensions, using hydrographic observations and particle tracking in high-resolution models. The analysis reveals that the northern-sourced deep waters enter the Antarctic Circumpolar Current via southward flow along the boundaries of the three ocean basins, before spiraling southeastward and upward through the Antarctic Circumpolar Current. Upwelling is greatly enhanced at five major topographic features, associated with vigorous mesoscale eddy activity. Deep water reaches the upper ocean predominantly south of the Antarctic Circumpolar Current, with a spatially nonuniform distribution. The timescale for half of the deep water to upwell from 30° S to the mixed layer is ~60–90 years.

Retrospectively comparing future model projections to observations provides a robust and independent test of model skill. Here we analyze the performance of climate models published between 1970 and 2007 in projecting future global mean surface temperature (GMST) changes. Models are compared to observations based on both the change in GMST over time and the change in GMST over the change in external forcing. The latter approach accounts for mismatches in model forcings, a potential source of error in model projections independent of the accuracy of model physics. We find that climate models published over the past five decades were skillful in predicting subsequent GMST changes, with most models examined showing warming consistent with observations, particularly when mismatches between model‐projected and observationally estimated forcings were taken into account.

Small-scale turbulent mixing drives the upwelling of deep water masses in the abyssal ocean as part of the global overturning circulation¹. However, the processes leading to mixing and the pathways through which this upwelling occurs remain insufficiently understood. Recent observational and theoretical work^2–5 has suggested that deep-water upwelling may occur along the ocean’s sloping seafloor; however, evidence has, so far, been indirect. Here we show vigorous near-bottom upwelling across isopycnals at a rate of the order of 100 metres per day, coupled with adiabatic exchange of near-boundary and interior fluid. These observations were made using a dye released close to the seafloor within a sloping submarine canyon, and they provide direct evidence of strong, bottom-focused diapycnal upwelling in the deep ocean. This supports previous suggestions that mixing at topographic features, such as canyons, leads to globally significant upwelling^3,6–8. The upwelling rates observed were approximately 10,000 times higher than the global average value required for approximately 30 × 10⁶ m³ s⁻¹ of net upwelling globally⁹.

The emerging view of the abyssal circulation is that it is associated with bottom-enhanced mixing, which results in downwelling in the stratified ocean interior and upwelling in a bottom boundary layer along the insulating and sloping seafloor. In the limit of slowly varying vertical stratification and topography, however, boundary layer theory predicts that these upslope and downslope flows largely compensate, such that net water mass transformations along the slope are vanishingly small. Using a planetary geostrophic circulation model that resolves both the boundary layer dynamics and the large-scale overturning in an idealized basin with bottom-enhanced mixing along a midocean ridge, we show that vertical variations in stratification become sufficiently large at equilibrium to reduce the degree of compensation along the midocean ridge flanks. The resulting large net transformations are similar to estimates for the abyssal ocean and span the vertical extent of the ridge. These results suggest that boundary flows generated by mixing play a crucial role in setting the global ocean stratification and overturning circulation, requiring a revision of abyssal ocean theories.

The physical circulation of the Southern Ocean sets the surface concentration and thus air‐sea exchange of . However, we have a limited understanding of the three‐dimensional circulation that brings deep carbon‐rich waters to the surface. Here, we introduce and analyze a novel high‐resolution ocean model simulation with active biogeochemistry and online Lagrangian particle tracking. We focus our attention on a subset of particles with high dissolved inorganic carbon (DIC) that originate below 1,000 m and eventually upwell into the near‐surface layer (upper 200 m). We find that 71% of the DIC‐enriched water upwelling across 1,000 m is concentrated near topographic features, which occupy just 33% of the Antarctic Circumpolar Current. Once particles upwell to the near‐surface layer, they exhibit relatively uniform levels and DIC decorrelation timescales, regardless of their origin. Our results show that Southern Ocean bathymetry plays a key role in delivering carbon‐rich waters to the surface.