Adjoint sensitivity

From Glossary of Meteorology

adjoint sensitivity

A gradient, xJ, 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 productx, xJ), where δx is a perturbation vector and xJ is an adjoint sensitivity vector, provides δJ, a first-order (tangent linear) approximation to the difference, ΔJ, between an unperturbed nonlinear forecast and a nonlinear forecast with control variables perturbed by δx.
See adjoint model, tangent linear equation, tangent linear approximation.