Assimilation of future ocean-current measurements from satellites

Over the coming years space agencies plan to launch satellite instruments that can measure the ocean surface current velocity. Ingesting such measurements into ocean models using data assimilation has the potential to increase accuracy of forecasts of the ocean itself, and of the atmosphere through coupled modelling. In order to achieve this, it is necessary to build an assimilation system that treats the rotational and divergent parts of the velocity separately, since then the errors in these two components can be assumed to be approximately uncorrelated. This is commonly done in atmospheric forecasting systems, where the wind is decomposed into the streamfunction and velocity potential within the assimilation scheme. However, the presence of coastlines in ocean models makes this much harder to do for the ocean. The decomposition of the currents into their rotational and divergent parts requires the solution of an elliptic equation, a problem that is ill-posed in the presence of coastal boundary conditions. Methods to overcome this problem have been proposed in the literature with different assumptions, but none have been implemented within ocean data assimilation systems. In this project we will investigate the following questions:

- How can ocean velocity fields be decomposed into their rotational and divergent parts in a way that is numerically stable?
- Does this decomposition lead to fields whose errors are uncorrelated? Are there better decompositions to use, e.g. based on potential vorticity?
- How can such decompositions be used to assimilate future ocean current measurements?