The time-averaged circulation of the north Pacific Ocean : an analysis based on inverse methods Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/9019s572w

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  • The time-averaged velocity field in the North Pacific was estimated in two sets of inverse calculations. The planetary geostrophic equations were the basis for dynamical models of the flow in each case. The inverse estimates of the circulation were obtained by minimizing a positive-definite cost function, which measured the inconsistency of the model's predictions against a set of observations comprised of a large, high-quality hydrographic data set, and surface fluxes of heat, fresh water, and momentum. In the first part of this work, four solution methods for the generalized inverse of a linear planetary geostrophic model of the North Pacific are compared. A conjugate gradient solver applied to the equation for the generalized inverse, expressed in terms of a representer expansion, was the most computationally efficient solution method. The other methods, in order of decreasing efficiency, were, a conjugate gradient descent solver (preconditioned with the inverse of the model operators), a direct solver for the representer coefficients, and a second conjugate gradient descent solver (preconditioned so that the diagonal elements of the cost Redacted for Privacy function Hessian were unity). All but the last method were successful at minimizing the penalty function. Inverse estimates of the circulation based on the linear planetary geostrophic model were stable to perturbations in the data, and insensitive to assumptions regarding the model forcing and boundary condition uncertainties. A large calculation, which involved approximately 18,000 observations and 60,000 state variables, indicated that the linear model is remarkably consistent with the observations. The second part of this work describes an attempt to use a nonlinear planetary geostrophic model (which included realistic bottom topography, lateral momentum mixing, out-cropping layers, and air-sea fluxes of heat, freshwater, and momentum) to assimilate the same hydrographic data set as above. Because of the nonlinearity in the model, descent methods (rather than a representer-based method) were used to solve the inverse problem. The nonlinearity of the model and the poor conditioning of the cost function Hessian confounded the minimization process. A solver for the tangent-linearization of the planetary geostrophic system should be used as a preconditioner if calculations of this type are attempted in the future.
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