Basis Functions for Data Assimilation and Modeling of the Gulf Stream
NAVAL OCEANOGRAPHIC AND ATMOSPHERIC RESEARCH LAB STENNIS SPACE CENTER MS
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The Gulf Stream model in use by NOARL is based upon the 2-layer, primitive equations in spherical coordinates. The finite-difference implementation is eddy-resolving, but the 18-degree grid generates over 100,000 variables - too many to be directly applied to inverse techniques. Since most data assimulation schemes employ linearizations about a first-guess solution, it makes sense to extend this procedure by reducing the number of state variables as much as possible. This is done by using the statistical properties of the region of phase space sampled by the base trajectory. Empirical orthogonal functions EOFs are used to estimate the Karhunen-Loeve transformation of coordinates which compresses the local state-space information. These EOFs are used in the implementation of a local, nonlinear spectral model, having only several hundred degrees of freedom. The evolved fields of both numerical models are compared, and applications to data assimilation are discussed. One of these schemes, dynamic data inversion, is new and is real impetus for our developing this basis functions approach.
- Physical and Dynamic Oceanography