# Adjoint model

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## adjoint model

A model composed of adjoint equations that maps a sensitivity gradient vector,

**∇**_{x}*J*(*t*_{0}) = 𝗟^{T}**∇**_{x}*J*(*t*_{1}) , from a forecast time,*t*_{1}, to an earlier time,*t*_{0}, 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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