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    Finite Difference of Adjoint or Adjoint of Finite Difference?

    Source: Monthly Weather Review:;1997:;volume( 125 ):;issue: 012::page 3373
    Author:
    Sirkes, Ziv
    ,
    Tziperman, Eli
    DOI: 10.1175/1520-0493(1997)125<3373:FDOAOA>2.0.CO;2
    Publisher: American Meteorological Society
    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 tf, 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 ti, 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.
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      Finite Difference of Adjoint or Adjoint of Finite Difference?

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4203991
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    contributor authorSirkes, Ziv
    contributor authorTziperman, Eli
    date accessioned2017-06-09T16:11:42Z
    date available2017-06-09T16:11:42Z
    date copyright1997/12/01
    date issued1997
    identifier issn0027-0644
    identifier otherams-63032.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4203991
    description abstractAdjoint 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 tf, 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 ti, 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.
    publisherAmerican Meteorological Society
    titleFinite Difference of Adjoint or Adjoint of Finite Difference?
    typeJournal Paper
    journal volume125
    journal issue12
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1997)125<3373:FDOAOA>2.0.CO;2
    journal fristpage3373
    journal lastpage3378
    treeMonthly Weather Review:;1997:;volume( 125 ):;issue: 012
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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