Implementation and optimisation of geostrophic eddy parameterisations in ocean circulation models

The global ocean is populated by a vigorous and dynamic eddy field. This eddy field has a significant impact on the wider structure of the ocean circulation, but it is computationally extremely expensive to resolve directly. While recent simulations have allowed for direct eddy resolving calculations to be performed, equilibrated eddy resolving calculations are unlikely to become routine at any point in the near future. There therefore remains an urgent need for eddy parameterisation schemes, which aim to capture the aggregated effects of the eddy field in coarse resolution numerical models.

The development of ocean eddy closures remains a formidable challenge. However, one can apply fundamental principles in order to rule out eddy closures which lead to unphysical behaviour. For example, the eddies require energy in order to mix ocean properties, and must observe the principle of conservation of momentum. A somewhat more subtle property is that ocean eddies must, on average, mix out gradients in the fluid potential vorticity. Eddy parameterisations which fail to observe these constraints can be ruled out as a possible solution for the underlying eddy dynamics.

A particularly important challenge for ocean eddy parameterisations is the accurate reproduction of ocean sensitivities to forcing changes. These responses have implications for the long term ocean response to climate change. Recent studies indicate that the Southern Ocean may exhibit reduced responses to wind forcing changes when the influence of the eddies is well sufficiently resolved. Coarse resolution models, which parameterise the eddies and do not resolve them directly, often give wildly incorrect predictions for the ocean responses.

This study proposes the implementation of a suite of new and existing ocean eddy parameterisations. The parameterisations are to be implemented in a simplified context (in a "quasi-geostrophic" model), and then in a full ocean circulation model. This research has three key novel aspects. First, optimisation techniques will be employed in order to assess the performance of the closures in the simplified quasi-geostrophic case. These techniques can be used to identify the best possible configuration of a given eddy parameterisation scheme, enabling the best-case performance of the scheme to be rigorously identified. This will provide a robust comparison of a broad range of possible approaches for eddy parameterisation. Secondly, the research aims to impose the three physical principles, imposed by energetic constraints, momentum conservation, and the need to mix potential vorticity, simultaneously. Thirdly, the research will investigate the performance of a broad range of parameterisations in determining the ocean sensitivity to wind forcing changes.

Particularly important questions to be addressed are: How important are the fundamental physical constraints in controlling the ocean eddy dynamics? Can the restoration of these constraints in ocean eddy parameterisation schemes lead to improved coarse resolution simulations?

This project primarily involves the practical application of abstract theory in order to implement and study new geostrophic ocean eddy parameterisations. The primary impacts will be within the academic community.

However, ocean circulation models form an essential component of complex models used to study and predict the impact of future climate change. The representation of ocean eddies in these models can have a significant influence upon the resulting model predictions. A successful conclusion of the research has the potential to generate significant impacts on the ways in which ocean eddies are modelled. Such advancements would be of benefit to climate modellers in general, and to modellers at the Hadley centre in particular.

While the theoretical background of the research is somewhat esoteric in nature, the wider implications of the research itself are not. The response of the ocean circulation to forcing changes forms an important ingredient in our understanding of the wider climate system. Outreach activities will be undertaken to communicate the links between the new research and its wider implications.

This research also involves the application of recent developments in automated code generation, specifically including the application of automated adjoining and optimisation technologies. This research provides an opportunity for interdisciplinary communication, enabling novel applications of the new automated code generation technologies to the fields of physical oceanography and ocean modelling. The research additionally has the potential to raise awareness of the technical and performance demands of ocean models within the automated code generation community, thereby ensuring its continued relevance for future applications in oceanographic research.

The impact of the research will be increased via:
- Publication of articles in high quality international journals.
- Presentation of key results at international conferences.
- Attendance at smaller specialised meetings within the United Kingdom.
- Active engagement with developers of automated code generation software.
- The regular maintenance of an online blog, and active participation in social media.
- The online distribution of model figures and videos.
- The attraction of mathematics students to NERC related science activities in general, and to oceanographic research in particular.