### Generalized Inversion of Geophysical Fluid Dynamics

Andrew Bennett

Oregon State University

Regressing linear models against data is such standard practice in experimental
science, that the formulae are preprogrammed into pocket calculators. This methodology
has been late in application to Geophysical Fluid Dynamics (GFD), owing the
nonlinearity and the enormous complexity of the models in general. Exact solutions
of numerical approximations to phenomenological models have instead been simply
compared with observations, leading invariably to unsatisfactory results owing
almost certainly to the parameterization of unresolved processes rather than
errors in the observations. Thus, modelers were really little the wiser for
having the extremely expensive data, which are often collected with considerable
hardship to the observer.

Picard iteration, functional analysis of the optimization problem, and advances
in computing have now facilitated formal testing of GFD models as in all other
scientific disciplines. Examples ranging from global ocean tides to typhoons
to El Nino will be presented.

Provided a model survives its regression test, the analysis of conditioning
of the optimization problem allows assessment of the efficiency of the observing
system. Modular software is now expediting the application of rigorous but standard
testing practice to varieties of GFD models.

Return
to the Program