Interpreting adjoint and ensemble sensitivity toward the development of optimal observation targeting strategies

Two general methods, adjoint or singular vector methods, and ensemble-based methods, have been previously investigated to identify locations where observations would have a significant positive impact on a numerical weather model forecast. In this paper, we perform a basic comparison of targeting regions chosen to reduce the expected variance of a chosen forecast response function within an ensemble Kalman filter (EnKF) based on both an adjoint method and an ensemble method. Ensemble sensitivity is defined by linear regressions of a chosen forecast response function onto the model initial-time state variables, and is used to calculate variance reduction fields to provide targeting guidance for the ensemble-based method. Adjoint sensitivity is used to provide targeting guidance for the adjoint-based method. 90 ensemble forecasts are considered over a 24-hour forecast period, and the response function is chosen to represent the sea-level pressure at a single point in the Pacific Northwest United States. Targeting by ensemble guidance is shown to be a function of ensemble sensitivity and both the initial-time model state and observation variance. We find that large areas of variance reduction exist away from regions of large ensemble sensitivity, adjoint sensitivity, and the initial-time variance of the model state. For hypothetical aircraft observations, ensemble guidance is superior to adjoint guidance for 850 hPa temperature observations in a single case. This advantage increases as the number of flight tracks increases. In all cases, as more flight tracks are considered, diminishing returns on response function variance reduction are realized. Implications of these results for the development of targeting strategies are discussed.