Theory and practice of phase‐aware ensemble forecasting

Abstract

Skilfully forecasting the intensity of flood events with advanced lead times is necessary for the issuing of flood warnings that subsequently provide adequate time for evacuations and infrastructural preparations. The ensemble mean is often used for deterministic guidance, but it is numerically demonstrated that the presence of large timing differences among ensemble members generates ensemble skewness that renders the ensemble mean an underestimate of the magnitude of an event. We show that one can associate to an ensemble forecast a complementary phase‐aware ensemble forecast whose corresponding statistics are unaffected by timing differences among ensemble members. Corresponding to a phase‐aware ensemble forecast is a phase‐aware mean that remedies the magnitude underestimation problem of the ensemble mean. Uncertainty around the phase‐aware mean is captured by phase‐aware spread, which quantifies the spread of the magnitude of an event. We show that the uncertainty envelope associated with the phase‐aware spread better preserves the structure of the individual ensemble member trajectories. The new methods were applied to storm surge reforecasts for Hurricanes Irene and Sandy at 13 stations located around the New York City metropolitan area. Consistent with theory, the phase‐aware mean was found to be a better representation of storm surge magnitude than the ensemble mean. The phase‐aware uncertainty envelopes around the phase‐aware means were also found to depict the uncertainty of event magnitudes better than traditional uncertainty envelopes. The storm surge applications suggest that such methods should be incorporated into ensemble forecasting frameworks in which timing uncertainty is present, and thus a Matlab toolbox implementing the new methodology has been developed.