Subgridscale Representation

Abstract

Among the many aspects of numerical ocean modelling, subgridscale (SGS) pa rameterization is nearly always the ‘black sheep’. It tends to be the last thing a modeller talks about, and then only reluctantly. Why is that? Perhaps it is because most of us went to school in areas like mathematics and physics; we learned that when we are presented with a partial differential equation with boundary and initial conditions, then we are supposed to solve it by a sequence of careful, geometrically precise steps. Or we might be more sophisticated and first ask if a problem is well posed before going after ‘the solution’ regardless. Sometimes, even if we’ve some how caused a problem to be well posed, we still might not have the mathematical power to obtain its solution explicitly, perhaps because of a nonlinearity in the equation. Yet, though we might not obtain the solution exactly, it can often be approximated by perturbation analyses. And if we can’t carry out all the steps by purely analytical means, the computer can carry out numerics. Importantly, in the end we can feel that we have proceeded carefully, as mathematical, physical sorts of scientists should. Until we come to ocean modelling SGS …