Comparing ensemble and adjoint 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. It is shown that ensemble sensitivity is proportional to the projection of the analysis-error covariance onto the adjoint-sensitivity field. Furthermore, the ensemblesensitivity 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-h 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, a