SMILES Modelling

The SMILES project is unique in that it is a synthesis of two distinct yet closely related branches of physical oceanography. The principal component of the SMILES research will involve the collection of observational data from a research cruise to the Subantarctic Front Region downstream of the Drake Passage. The data collected in this part of the study will be used to inform the initialisation of a set of numerical models which are designed to test and evaluate present theories of mode water formation under the influence of submesoscale instabilities. The models will therefore be used to support and help facilitate understanding of the observational data, and may open up new avenues of research which will persist long after the end of the SMILES field campaign.

Ocean Models

Ocean models are particularly useful for studying regions where observational data is sparse or difficult to collect. The waters of and the around the Subantactic Front comprise such a region, where a combination of weather, strong currents, remoteness, and the resulting operational costs make collecting oceanographic data highly challenging. A primary advantage of numerical modelling is that it largely avoids many of these difficulties by simulating the fluid flow on a supercomputer. Assuming that the governing equations the models solve are physically justified (which, to the best of our knowledge, they are), one may obtain a broader, more comprehensive view of the fluid motion at locations where the field observations were unable to reach.

Ocean models, in and of themselves, are a representation of how we believe the real ocean to behave. They are based on fundamental conservation laws (of momentum, mass, and energy) that are associated with the coordinate invariance of the physical system (that is, the physical laws governing fluid motion are the same at all points in space and time). Given a set of governing equations for each of these conservation laws, one may calculate the forces experienced by fluid parcels and the resulting fluid motion can be simulated. The cumulative result of these calculations is a discretised physical representation of the fluid state at the future time. The same process is then repeated by calculating the forces on the new fluid state, and subsequent “time-stepping” yields an evolving solution that allows us to study ocean behaviour far into the future.

Models are intrinsically limited by how well the physical processes are represented in the governing equations, and by how many computational resources are available to perform the calculations. These two limitations are often closely linked together. A conventional approach to ocean modelling is to create a spatial grid and to solve the fluid equations at each point on the grid at discrete points in time. The size of the grid and the size of the “time-step” one may take is often limited by computational resources, which may refer to the available time on large computing clusters, man-hours dedicated to the processing of model results, or numerical capability of the model being used. In turn, these limitations manifest in the accuracy of the model solution, as a finer-scale grid reveals richer dynamics via the resolution of smaller turbulent scales.

Ocean models inherently contain a great deal of uncertainty associated with the (lack of) resolution of fine-scale turbulent structures, dynamically-important boundary conditions such as wind and waves, and the representation of processes for which our physical understanding is limited (such as breaking waves). The observational data often acts as a sort of “truth”, by which one may compare the model solution to the observed fields to better understand both. Therefore, ocean models should be considered a complimentary source of knowledge and a research tool, not a complete solution to open research problems.

An advantage of the SMILES modelling study is that it will be limited in scope to the region corresponding to the track of the research cruise. Regional models such as these benefit from a smaller overall domain size and thus may dedicate more of the computational load toward resolving small-scale turbulence. As the goal of the project is to study submesoscale instability, which at the latitude of the Subantarctic Front can imply eddy sizes of O(1 km) or even less, such high resolution is a necessity. Preliminary, pre-cruise modelling efforts have utilised a model grid resolution of 500 m, which already yields massively more complex eddying scales than the coarser model which serves as the initial condition.

The modelling aspect of SMILES is a collaborative effort combining the expertise of scientists at the University of Cambridge, Plymouth University, and British Antarctic Survey. Post-cruise, publication-quality models will be run on the UK’s national supercomputer, Archer, and will benefit from a substantial allocation of computer time. A minimum of four high-resolution (O(500 m)) models will be run using surface forcing parameters gleaned from the cruise. These models will be used to study the vertical transport and mixed layer depth coincident

with strong frontal gradients, which are associated with the strain fields from larger mesoscale eddies. Passive tracers will also be initialised to study the vertical transport properties associated with these same frontal gradients, which is representative of the transport of atmospheric gases that are fluxed into the oceanic mixed layer. Finally, the high-resolution model will allow for testing of a new class of turbulence parameterizations that must be developed to capture these small dynamics on larger, coarser grids.

An early version of these models has already been tested successfully using a preliminary allocation on Archer. The modelling approach uses a quasi-idealised domain which covers the latitudes from 56* S to 60* S and longitudes from 55* W to 65* W. The domain uses bathymetry and forcing fields obtained from the Southern Ocean State Estimate (SOSE). The initial state, including velocity and density profiles, are also read from SOSE beginning on April 1, 2010. The native SOSE resolution is approximately 18 km in the meridional and 10 km in the zonal directions, so the initial fields are interpolated down to 500 m resolution. Open boundary conditions are used on the north and south sides of the box, and are relaxed to the “climatological” SOSE state with a relaxation timescale of 1 hour. To avoid using open boundary conditions on the upstream, zonal sides of the box, all fields are duplicated, mirrored in the zonal direction, and “stitched” together on the eastern side of the box (see schematic below). The meridional geostrophic velocities are also reversed in sign in this box to accommodate the zonal reversal in density gradient.

The model is integrated with a time step of 15 seconds, and is used to simulate the time period from April 15 (approximately equivalent to the cruise start date in 2015) to May 31, 2010. The surface forcing is updated with a frequency of 2 hours, and is linearly interpolated in time to allow the oceanic flow to smoothly respond without the risk of being spuriously forced. The K-Profile parameterisation (Large et al., 1994) is employed to handle potential convectively unstable regions that may develop due to strong heat loss to the atmosphere.

Full 3D model output is collected at 4-hourly intervals. MATLAB postprocessing scripts are employed to diagnose and extract dynamically important variables, such as relative vorticity. The movie embedded below shows the relative vorticity field from one subregion of the model. Areas of high, cyclonic relative vorticity are apparent around the margins of submesoscale fronts; further investigation of these locations will be the principle objective of this research.