EXAMINATION OF THE ACCURACY OF A TANGENT LINEAR-MODEL

The accuracy of a tangent linear version of a 3-dimensional mesoscale primitive equation model (the PSU/NCAR MM4) is investigated by compari ng its results with those produced by identical perturbations introduc ed in nonlinear forecasts of the original model. Moist physical proces ses are not considered in this study. For perturbation magnitudes as l arge as typical current analysis errors, the perturbation tendencies a re shown to be very accurately estimated by the tangent linear model ( TLM), with greater relative error in a summer case than in a winter on e. The evolutions of perturbations in forecasts out to 72 h are also a ccurately estimated, although the unperturbed lateral boundary conditi ons that act to sweep perturbations out of the domain are an artificia l 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 appear s sufficient. The TLM accuracy is related to the accuracy of adjoint s ensitivity calculations with regard to finite-amplitude perturbations. An example of an adjoint application is shown to have two-digit accur acy for a moderately sized perturbation. All these results indicate th at our TLM and corresponding adjoint yield quantitatively accurate res ults for many important uses.