Document Type

Article

Publication Date

11-1-2003

Department

Marine Science

Abstract

In many data assimilation applications, adding an error to represent forcing to certain dynamical equations may be physically unrealistic. Four-dimensional variational methods assume either an error in the dynamical equations of motion (weak constraint) or no error (strong constraint). The weak-constraint methodology proposes the errors to represent uncertainties in either forcing of the dynamical equations or parameterizations of dynamics. Dynamical equations that represent conservation of quantities (mass, entropy, momentum, etc.) may be cast in an analytical or control volume flux form containing minimal errors. The largest errors arise in determining the fluxes through control volume surfaces. Application of forcing errors to conservation formulas produces non-physical results (generation or destruction of mass or other properties), whereas application of corrections to the fluxes that contribute to the conservation formulas maintains the physically realistic conservation property while providing an ability to account for uncertainties in flux parameterizations. The results suggest that advanced assimilation systems must not be liberal in applying errors to conservative equations. Rather systems must carefully consider the points at which the errors exist and account for them correctly. Though careful accounting of error sources is certainly not an entirely new idea, this paper provides a focused examination of the problem and examines one possible solution within the 4D variational framework.

Comments

© Copyright 2003 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

131

Issue

11

First Page

2595

Last Page

2607

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