Adjoint model: Difference between revisions
From Glossary of Meteorology
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|Meaning= | |Meaning=A [[model]] composed of adjoint equations that maps a sensitivity [[gradient]] [[vector]], '''∇'''<sub>''x''</sub>''J''(''t''<sub>0</sub>) = 𝗟<sup>''T''</sup>'''∇'''<sub>''x''</sub>''J''(''t''<sub>1</sub>) , from a forecast time, ''t''<sub>1</sub>, to an earlier time, ''t''<sub>0</sub>, which can be the initial time of a forecast trajectory. | ||
A [[model]] composed of adjoint equations that maps a sensitivity [[gradient]] [[vector]], '''∇'''<sub>''x''</sub>''J''(''t''<sub>0</sub>) = 𝗟<sup>''T''</sup>'''∇'''<sub>''x''</sub>''J''(''t''<sub>1</sub>) , from a forecast time, ''t''<sub>1</sub>, to an earlier time, ''t''<sub>0</sub>, which can be the initial time of a forecast trajectory. | |Explanation=''J'' is some [[scalar]] measure of the forecast, 𝗟<sup>''T''</sup> is a [[linear]] adjoint [[operator]], and '''x''' is the model state vector. An adjoint model can provide a first-order (tangent linear) approximation to [[sensitivity]] in a [[nonlinear]] model. <br/>''See'' [[adjoint equation]], [[adjoint sensitivity]], [[tangent linear equation]]. | ||
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Latest revision as of 20:59, 13 January 2024
A model composed of adjoint equations that maps a sensitivity gradient vector, ∇xJ(t0) = 𝗟T∇xJ(t1) , from a forecast time, t1, to an earlier time, t0, which can be the initial time of a forecast trajectory.
J is some scalar measure of the forecast, 𝗟T is a linear adjoint operator, and x is the model state vector. An adjoint model can provide a first-order (tangent linear) approximation to sensitivity in a nonlinear model.
See adjoint equation, adjoint sensitivity, tangent linear equation.
