Examination of the accuracy of a tangent linear model

Abstract

The accuracy of a tangent linear version of a 3-dimensional mesoscale primitive equation model (the PSU/NCAR MM4) is investigated by comparing its results with those produced by identical perturbations introduced in nonlinear forecasts of the original model. Moist physical processes are not considered in this study. For perturbation magnitudes as large as typical current analysis errors, the perturbation tendencies are shown to be very accurately estimated by the tangent linear model (TLM), with greater relative error in a summer case than in a winter one. The evolutions of perturbations in forecasts out to 72 h are also accurately estimated, although the unperturbed lateral boundary conditions that act to sweep perturbations out of the domain are an artificial means of perturbation constraint. It is shown that for many cases it is sufficient to approximate a true TLM by using an infrequent update of the basic state, thereby reducing the amount of stored fields and input required by the TLM software. For perturbations not smaller than one-tenth the size of typical analysis errors, a 30-min update appears sufficient. The TLM accuracy is related to the accuracy of adjoint sensitivity calculations with regard to finite-amplitude perturbations. An example of an adjoint application is shown to have two-digit accuracy for a moderately sized perturbation. All these results indicate that our TLM and corresponding adjoint yield quantitatively accurate results for many important uses.