SENSITIVITY OF FORECAST ERRORS TO INITIAL CONDITIONS WITH A QUASI-INVERSE LINEAR METHOD

A quasi-inverse linear method has been developed to study the sensitiv ity of forecast errors to initial conditions for the National Centers for Environmental Prediction's (NCEP) global spectral model. The inver se is approximated by running the tangent linear model (TLM) of the no nlinear forecast model with a negative time step, but reversing the si gn of friction and diffusion terms, in order to avoid the computationa l instability that would be associated with these terms if they were r un backward. As usually done using the adjoint model integrations, the quasi-inverse TLM is started at the time of the verified forecast err or and integrated backward to the corresponding initial time. First, a numerical experiment shows that this quasi-inverse linear estimation is able to trace back the differences between two perturbed forecasts from the NCEP ensemble forecasting system and recover with good accura cy the known difference between the two forecasts at the initial time. This result shows that both the linear estimation and the quasi-inver se linear estimation are quite close to the nonlinear evolution of the perturbation in the nonlinear forecast model, suggesting that it shou ld be possible to apply the method to the study of the sensitivity of forecast errors to initial conditions. The authors then calculate the perturbation field at the initial time (estimate the initial error) by tracing back a 1-day forecast error using the TLM quasi-inverse estim ation. As could be expected from the previous experiment, when the est imated error is subtracted from the original analysis, the new initial conditions lead to an almost perfect 1-day forecast. The forecasts be yond the first day are also considerably improved, indicating that the initial conditions have indeed been improved. In the remainder of the paper, this quasi-inverse linear method is compared with the adjoint sensitivity method (Rabier et al., Pu et al.) for medium-range weather forecasting. The authors find that both methods are able to trace bac k the forecast error to perturbations that improve the initial conditi ons. However, the forecast improvement obtained by the quasi-inverse l inear method is considerably better than that obtained with a single a djoint iteration and similar to the one obtained using five iterations of the adjoint method, even though each adjoint iteration requires at least twice the computer resources of the quasi inverse TLM estimatio n. Whereas the adjoint forecast sensitivities are closely related to s ingular vectors, the quasi-inverse linear perturbations are associated with the bred (Lyapunov) vectors used for ensemble forecasting at NCE P (Toth and Kalnay). The features of the two types of perturbations ar e also compared in this study. Finally, the possibility of the use of the sensitivity perturbation to improve future forecast skill is discu ssed, and preliminary experiments encourage further testing of this ra ther inexpensive method for possible operational use. The model used i n this study is the NCEP operational global spectral model at a resolu tion of T62/L28. The corresponding TLM, and its adjoint, are based on an adiabatic version of the model but include both horizontal and vert ical diffusion.