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

We developed a new version of the Alfred Wegener Institute Climate Model (AWI-CM3), which has higher skills in representing the observed climatology and better computational efficiency than its predecessors. Its ocean component FESOM2 (Finite-volumE Sea ice–Ocean Model) has the multi-resolution functionality typical of unstructured-mesh models while still featuring a scalability and efficiency similar to regular-grid models. The atmospheric component OpenIFS (CY43R3) enables the use of the latest developments in the numerical-weather-prediction community in climate sciences. In this paper we describe the coupling of the model components and evaluate the model performance on a variable-resolution (25–125 km) ocean mesh and a 61 km atmosphere grid, which serves as a reference and starting point for other ongoing research activities with AWI-CM3. This includes the exploration of high and variable resolution and the development of a full Earth system model as well as the creation of a new sea ice prediction system. At this early development stage and with the given coarse to medium resolutions, the model already features above-CMIP6-average skills (where CMIP6 denotes Coupled Model Intercomparison Project phase 6) in representing the climatology and competitive model throughput. Finally we identify remaining biases and suggest further improvements to be made to the model.

Three different trajectory schemes for oceanic and atmospheric general circulation models are compared in two different experiments. The theories of the trajectory schemes are presented showing the differential equations they solve and why they are mass conserving. One scheme assumes that the velocity fields are stationary for set intervals of time between saved model outputs and solves the trajectory path from a differential equation only as a function of space, i.e. stepwise stationary. The second scheme is a special case of the stepwise-stationary scheme, where velocities are assumed constant between general circulation model (GCM) outputs; it uses hence a fixed GCM time step. The third scheme uses a continuous linear interpolation of the fields in time and solves the trajectory path from a differential equation as a function of both space and time, i.e. a time-dependent scheme. The trajectory schemes are tested offline, i.e. using the already integrated and stored velocity fields from a GCM. The first comparison of the schemes uses trajectories calculated using the velocity fields from a high-resolution ocean general circulation model in the Agulhas region. The second comparison uses trajectories calculated using the wind fields from an atmospheric reanalysis. The study shows that using the time-dependent scheme over the stepwise-stationary scheme greatly improves accuracy with only a small increase in computational time. It is also found that with decreasing time steps the stepwise-stationary scheme becomes increasingly more accurate but at increased computational cost. The time-dependent scheme is therefore preferred over the stepwise-stationary scheme. However, when averaging over large ensembles of trajectories, the two schemes are comparable, as intrinsic variability dominates over numerical errors. The fixed GCM time step scheme is found to be less accurate than the stepwise-stationary scheme, even when considering averages over large ensembles.

The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated. Here, we quantify the kinetic energy budget in a suite of realistic global ocean models, with varying horizontal resolution and horizontal viscosity. We show that eddy-permitting ocean models have weaker kinetic energy cascades than eddy-resolving models due to discrepancies in the effect of wind forcing, horizontal viscosity, potential to kinetic energy conversion, and nonlinear interactions on the kinetic energy (KE) budget. However, the change in eddy kinetic energy between the eddy-permitting and the eddy-resolving model is not enough to noticeably change the scale where the inverse cascade arrests or the Rhines scale. In addition, we show that the mechanism by which baroclinic flows organise into barotropic flows is weaker at lower resolution, resulting in a more baroclinic flow. Hence, the horizontal resolution impacts the vertical structure of the simulated flow. Our results suggest that the effect of mesoscale eddies can be parameterised by enhancing the potential to kinetic energy conversion, i.e., the horizontal pressure gradients, or enhancing the inverse cascade of kinetic energy.

We examine the sensitivity of the Weddell and Ross seas to vertical mixing and surface freshwater forcing using an ocean–sea ice model. The high latitude Southern Ocean is very weakly stratified, with a winter salinity difference across the pycnocline of only ∼0.2 PSU. We find that insufficient vertical mixing, freshwater supply from the Antarctic Ice Sheet, or initial sea ice causes a high salinity bias in the mixed layer which erodes the stratification and causes excessive deep convection. This leads to vertical homogenisation of the Weddell and Ross seas, opening of polynyas in the sea ice and unrealistic spin-up of the subpolar gyres and Antarctic Circumpolar Current. The model freshwater budget shows that a ∼30% error in any component can destratify the ocean in about a decade. We find that freshwater forcing in the model should be sufficient along the Antarctic coastline to balance a salinity bias caused by dense coastal water that is unable to sink to the deep ocean. We also show that a low initial sea ice area introduces a salinity bias in the marginal ice zone. We demonstrate that vertical mixing, freshwater forcing and initial sea ice conditions need to be constrained simultaneously to reproduce the Southern Ocean hydrography, circulation and sea ice in a model. As an example, insufficient vertical mixing will cause excessive convection in the Weddell and Ross seas even in the presence of large surface freshwater forcing and initial sea ice cover