GOOS is an international programme for a permanent global framework of observations, modelling and analysis of ocean variables which are needed to support operational services around the world. The EuroGOOS strategy has two streams: the first is to improve the quality of marine information in European home waters, and the second is to collaborate with similar organisations in other continents to create a new global ocean observing and modelling system that will provide the open ocean forecasts needed to achieve the best possible performance by local marine information services everywhere. The EuroGOOS strategy envisages our national agencies making a major contribution to that challenging task of globalizing ocean forecasting. The conference also provided an opportunity to take stock of the state of marine science and technology in Europe relevant to the EuroGOOS strategy, and the state of information services and customer needs.
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
GOOS is an international programme for a permanent global framework of observations, modelling and analysis of ocean variables which are needed to support operational services around the world. The EuroGOOS strategy has two streams: the first is to improve the quality of marine information in European home waters, and the second is to collaborate with similar organisations in other continents to create a new global ocean observing and modelling system that will provide the open ocean forecasts needed to achieve the best possible performance by local marine information services everywhere. The EuroGOOS strategy envisages our national agencies making a major contribution to that challenging task of globalizing ocean forecasting. The conference also provided an opportunity to take stock of the state of marine science and technology in Europe relevant to the EuroGOOS strategy, and the state of information services and customer needs.
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