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

The main characteristics of the new version 1.2 of the three-dimensional Earth system model of intermediate complexity LOVECLIM are briefly described. LOVECLIM 1.2 includes representations of the atmosphere, the ocean and sea ice, the land surface (including vegetation), the ice sheets, the icebergs and the carbon cycle. The atmospheric component is ECBilt2, a T21, 3-level quasi-geostrophic model. The ocean component is CLIO3, which consists of an ocean general circulation model coupled to a comprehensive thermodynamic-dynamic sea-ice model. Its horizontal resolution is of 3° by 3°, and there are 20 levels in the ocean. ECBilt-CLIO is coupled to VECODE, a vegetation model that simulates the dynamics of two main terrestrial plant functional types, trees and grasses, as well as desert. VECODE also simulates the evolution of the carbon cycle over land while the ocean carbon cycle is represented by LOCH, a comprehensive model that takes into account both the solubility and biological pumps. The ice sheet component AGISM is made up of a three-dimensional thermomechanical model of the ice sheet flow, a visco-elastic bedrock model and a model of the mass balance at the ice-atmosphere and ice-ocean interfaces. For both the Greenland and Antarctic ice sheets, calculations are made on a 10 km by 10 km resolution grid with 31 sigma levels. LOVECLIM1.2 reproduces well the major characteristics of the observed climate both for present-day conditions and for key past periods such as the last millennium, the mid-Holocene and the Last Glacial Maximum. However, despite some improvements compared to earlier versions, some biases are still present in the model. The most serious ones are mainly located at low latitudes with an overestimation of the temperature there, a too symmetric distribution of precipitation between the two hemispheres, and an overestimation of precipitation and vegetation cover in the subtropics. In addition, the atmospheric circulation is too weak. The model also tends to underestimate the surface temperature changes (mainly at low latitudes) and to overestimate the ocean heat uptake observed over the last decades.