Adjoint model: Difference between revisions

Revision as of 16:17, 7 November 2023

A model composed of adjoint equations that maps a sensitivity gradient vector, ∇_xJ(t₀) = 𝗟^T∇_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, 𝗟^T 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.

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+{{Term
+|Display title=adjoint model
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+A [[model]] composed of adjoint equations that maps a sensitivity [[gradient]] [[vector]],  '''&nabla;'''<sub>''x''</sub>''J''(''t''<sub>0</sub>) = &#x1D5DF;<sup>''T''</sup>'''&nabla;'''<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.<br/> ''J'' is some [[scalar]] measure of the forecast, &#x1D5DF;<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]].
-  <div class="term">
+}}
-== adjoint model ==
+}}
-  </div>
-<div class="definition"><div class="short_definition">A [[model]] composed of adjoint equations that maps a sensitivity [[gradient]] [[vector]],  '''&nabla;'''<sub>''x''</sub>''J''(''t''<sub>0</sub>) = &#x1D5DF;<sup>''T''</sup>'''&nabla;'''<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.</div><br/> <div class="paragraph">''J'' is some [[scalar]] measure of the forecast, &#x1D5DF;<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]].</div><br/> </div>
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