A Technical Description of the NRL Adjoint Modeling System

This report describes the tangent linear model TLM, and the accompanying adjoint model, for the Navy Operational Global Atmospheric Prediction System NOGAPS spectral forecast model. Details are given for the linearization of the model equations, the development of the matrix transpose operators that constitute the adjoint model, and a discussion of the self-adjoint properties of the spherical harmonic transforms, unique to spectral models such as NOGAPS. A powerful application of the TLM and adjoint models, the calculation of singular vectors about a basic state trajectory forecast of the non-linear NOGAPS model, is also described. Some illustrative examples of singular vector and adjoint model calculations are given. Full model codes are available by request from the author.