Why do we need models?

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 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 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 conversation 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 full 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 every point 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 universally acceptable 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.