Comparing Adjoint and Ensemble Sensitivity Analysis with Applications to Observation Targeting

The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. We show that ensemble sensitivity is proportional to the projection of the analysis-error covariance onto the adjoint sensitivity field. Furthermore, the ensemble sensitivity approach proposed here involves a small calculation that is easy to implement. Ensemble and adjoint-based sensitivity fields are compared for a representative wintertime flow pattern near the West Coast of North America for a 90-member ensemble of independent initial conditions derived from an ensemble Kalman filter. The forecast metric is taken for simplicity to be the 24-hr forecast of sea-level pressure at a single point in western Washington state. Results show that adjoint and ensemble sensitivities are very different in terms of location, scale, and magnitude. Adjoint sensitivity fields reveal mesoscale lower-tropospheric structures that tilt strongly upshear, whereas ensemble sensitivity fields emphasize synoptic-scale features that tilt modestly throughout the troposphere and are associated with significant weather features at the initial time. Optimal locations for targeting can easily be determined from ensemble sensitivity, and results indicate that the primary targeting locations are located away from regions of greatest adjoint and ensemble sensitivity. We show that this method of targeting is similar to previous ensemble-based methods that estimate forecast-error variance reduction, but easily allows for the application of statistical confidence measures to deal with sampling error.