Published In

Monthly Weather Review

Document Type

Article

Publication Date

4-1-2006

Subjects

Ocean circulation -- Mathematical models, Atmospheric physics, Hydrologic models -- Data processing

Abstract

Assimilating hydrographic observations into a planetary geostrophic model is posed as a problem in control theory. The cost functional is the sum of weighted model and data residuals. Model errors are assumed to be spatially correlated, and hydrographic station data are assimilated directly. Searches in state space and data space, for minimizing the cost functional, are compared to a direct matrix inversion algorithm in the data space. State-space methods seek the minimizer of the cost functional by performing a preconditioned search in an N-dimensional space of state or control variables, where N is approximately 650 000 in the present calculations. Data-space methods solve the Euler?Lagrange equations for the extremum of the cost functional by working in an M-dimensional dual space, where M is the number of measurements. The following four solvers are compared: (i) an iterative state-space solver, with a naive diagonal matrix preconditioner; (ii) an iterative state-space solver, with a sophisticated preconditioner based on the inverse of the model?s dynamical operators; (iii) an iterative data-space solver, with no preconditioning; and (iv) a direct, M ? M matrix inversion, data-space solver. The best solver is the iterative data-space solver, (iii), which is approximately 10 times faster than the sophisticated preconditioned state-space solver, (ii), and 100 times faster than the direct data-space solver, (iv).

Description

This is the publisher's final PDF. © Copyright 2006 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyrights@ametsoc.org.

DOI

10.1175/MWR3124.1

Persistent Identifier

http://archives.pdx.edu/ds/psu/8380

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