# Adjoint sensitivity

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## adjoint sensitivity

A gradient,

**∇**_{x}*J*, of some scalar measure of a forecast,*J*, with respect to the vector of model control variables,**x**, that can include initial conditions, boundary conditions, and parameters.The inner product (δ

**x**,**∇**_{x}*J*), where δ**x**is a perturbation vector and**∇**_{x}*J*is an adjoint sensitivity vector, provides δ*J*, a first-order (tangent linear) approximation to the difference, Δ*J*, between an unperturbed nonlinear forecast and a nonlinear forecast with control variables perturbed by δ**x**.*See*adjoint model, tangent linear equation, tangent linear approximation.

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