Title

A Complementary Error Model for Finite Difference Linear Barotropic Ocean Model

Author

Farnaz Zand

Date of Award

2006

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computing

First Advisor

A. Louise Perkins

Advisor Department

Computing

Abstract

We construct an error model of a finite difference linear barotropic ocean model. We discuss how this error model could be used to augment numerical simulations on a given grid providing a more comprehensive interpretation of the model results. Our method of constructing error models works for systems of partial differential equations numerically approximated with finite differences. We transform the truncated portions of fully-dimensional Taylor Series term expansions to frequency space. The transformation replaces the higher order, unknown and unmodelled partial derivatives in physical space with harmonic components in frequency space whose impact can be exactly understood within the approximation space associated with a given numerical grid. The construction of the error model requires the transform of the function itself, which may be estimated from data sources. Alternatively a test function may be used. The technique works whenever a Taylor Series representation of a function is available (We note that the Taylor Series remainder term may also be used to produce an error bound, but that it is not grid specific.) We present an error model for the linear barotropic ocean model developed at the Naval Research Laboratory.