Document Type

Article

Publication Date

12-1-1997

Department

Marine Science

Abstract

Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time t(f), averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the sensitivity to initial conditions as function of the initial time t(i), may be obtained directly and most efficiently from the adjoint model solution. There are two approaches to formulating an adjoint of a given model. In the first (''finite difference of adjoint''), one derives the continuous adjoint equations from the linearized continuous forward model equations and then formulates the finite-difference implementation of the continuous adjoint equations. In the second (''adjoint of finite difference''), one derives the finite-difference adjoint equations directly from the finite difference of the forward model. It is shown here that the time-dependent sensitivity obtained by using the second approach may result in a very strong nonphysical behavior such as a large-amplitude two-time-step leapfrog computational mode, which may prevent the solution from being used for time-dependent sensitivity studies. This is an especially relevant problem now, as this second approach is the one used by automatic adjoint compilers that are becoming widely used. The two approaches are analyzed in detail using both a simple model and the adjoint of a primitive equations ocean general circulation model. It is emphasized that both approaches are valid as long as they are used for obtaining the gradient or sensitivity at a single time, as needed in data assimilation, for example. Criteria are presented for the choice of the appropriate adjoint formulation for a given problem.

Comments

© Copyright 1997 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 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website 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. All AMS journals and monograph publications are registered with the Copyright Clearance Center (http://www.copyright.com). Questions about permission to use materials for which AMS holds the copyright can also be directed to the AMS Permissions Officer at permissions@ametsoc.org. Additional details are provided in the AMS Copyright Policy statement, available on the AMS website (http://www.ametsoc.org/CopyrightInformation).

Publisher Version

Publication Title

Monthly Weather Review

Volume

125

Issue

12

First Page

3373

Last Page

3378

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