Ensemble-based sensitivity analysis

An important problem in predictability concerns the sensitivity of forecasts to initial condition errors as measured by a cost function. Determining such sensitivity is useful for observing network design (e.g. targeted observations) and for understanding the dynamics of weather systems. Adjoint sensitivity analysis provides a solution to this problem by linearizing around a control solution trajectory and integrating an adjoint model backward in time. Here we explore an alternative approach using an ensemble of analyses and forecasts from an ensemble Kalman filter. The method is attractive because it implicitly accounts for analysis errors, which the adjoint technique does not, and because it does not require an adjoint model.

After discussing the general theory of ensemble sensitivity, the technique will be illustrated using analyses and 24-hour forecasts of sensible weather (e.g., sea-level pressure, wind speed, and precipitation) over western Washington state. These data are drawn from a pseudo-operational real-time ensemble Kalman filter running at the University of Washington. Results for "climatological" sensitivities (for the entire data record) will be presented and used to find locations for adding new observation stations. Case studies will also be presented that demonstrate how the assimilation of observations in sensitive regions leads to changes in the subsequent forecast.