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.

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