Observation Adjoint Sensitivity and the Adaptive Observation-Targeting Problem

摘要

This research introduces the adjoint of the data assimilation system, which together with the classical adjoint sensitivity problem, represents the two fundamental components of the complete forecast adjoint sensitivity problem. This adjoint of the data assimilation system is then used to investigate the sensitivity of the forecast aspect J to the observations and background for idealized analysis problems, and finally a real-data case using the NAVDAS adjoint for a situation with unusually large 72-h forecast errors over the western United States during February 1999. The observation sensitivity is largest when the observations are relatively isolated, assumed to be more accurate than the background, and the analysis sensitivity gradients are large in amplitude and have a spatial scale similar to the background error covariances. The observation sensitivity is considerably weaker for small-scale analysis sensitivity gradients. The large observation sensitivities suggest that adaptive observations near large-scale analysis sensitivity gradients have a greater potential to change the forecast aspect than observations near small- scale analysis sensitivity gradients. Therefore, targeting decisions based on the adjoint of the data assimilation system may be significantly different from targeting decisions based solely on the analysis sensitivity gradients. These results emphasize the importance of accounting for the data assimilation procedures in the adaptive observation-targeting problem.