Adjoint model
Abstract
An adjoint model is a useful tool for solving data assimilation problems for which the numerical weather prediction (NWP) model serves as a strong constraint. Reviewed is the mathematical definition of an adjoint in ordinary differential equation form, and discussed is its equivalence to the adjoint definition in linear algebra. Provided in sufficient detail are derivations and correctness checks of tangent linear and adjoint models for given nonlinear models. Also demonstrated is the use of the Lagrangian method to derive an analytical adjoint equation having Lagrangian multipliers as adjoint variables for a given linear or nonlinear differential equation. Given are several examples illustrating how tangent linear ...
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