The Variability of Adjoint Sensitivity with Respect to Model Physics and Basic-State Trajectory

Adjoint sensitivity fields have generally been viewed deterministically in the atmospheric science literature. However, uncertainty exists in the components of the adjoint model, such as the physics and the basic-state trajectories used to calculate the sensitivity fields. In this paper, the variability of adjoint sensitivity fields is examined for two collections of trajectories, each valid over a single time window: one supplied by three global operational models, and the other from a regional, operational ensemble Kalman filter system. Adjoint sensitivities are also compared using a dry adjoint and dry basic state, a moist adjoint and moist basic state, and a moist basic state and dry adjoint. The goal of these latter experiments is to explore the differences in mesoscale sensitivity fields with and without moisture, and to examine how sensitivities degrade when adjoint models utilize simplified physics. In all cases, 24-h sensitivities are produced with a low-level pressure response function over the coastal lowlands of the Pacific Northwest. Furthermore, this study examines these adjoint sensitivities at higher resolution than in previous studies. It is found that adjoint sensitivity can vary significantly in structure, magnitude, and location when different, but equally likely, basic-state trajectories are considered. Since the predicted response function shows large variance when using different basic-state trajectories, adjoint sensitivity should be viewed probabilistically. It is also found that the inclusion of moisture in both the forward and adjoint model produces significantly different sensitivity fields from the fully dry run. Furthermore, a large degradation occurs when removing moisture from the adjoint model but retaining moisture in the basic state, causing sensitivity fields to resemble that of a fully dry adjoint integration. This suggests that simplified physics relative to the forward nonlinear physics may produce significant differences from the desired “true” sensitivity field. The implications of these results for modern applications of adjoint models are discussed.