Sensitivity Analysis Using an Adjoint of the PSU-NCAR Mesoseale Model

An adjoint of the Pennsylvania State University-National Center for Atmospheric Research (PSU-NCAR) Mesoscale Model has been developed for use in sensitivity analysis following Cacuci. Sensitivity analysis is defined as the determination of the potential impact on some quantitative measure of a forecast aspect due to arbitrary perturbations of the model dynamic fields at earlier times. Input to the adjoint operator is the gradient of the forecast-aspect measure with respect to the model fields at the verification time, and output is the corresponding gradients defined at earlier times. The adjoint is exactly determined from a tangent linear model, which is itself an approximation to the dry nonlinear model. This approximation is shown to be accurate even when evaluated with regard to the moist nonlinear model for periods up to 36 h, although this accuracy is necessarily case and perturbation dependent. The mathematics describing the scheme are applied to the model in its spatially and temporally discrete form, which greatly simplifies the scheme's presentation. Examples of adjoint fields for three forecast aspects and two synoptic cases are shown, and their meanings and implications are discussed. They are valuable for determinations of forecast dependencies on data, predictability, and the relationships between consecutive synoptic conditions. The uses of the adjoint model therefore have much greater scope than only variational analysis and parameter filling.