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.

Sub-Ensemble Coastal Flood Forecasting: A Case Study of Hurricane Sandy

“…consisting of N ensemble members generated by the numerical model M [26]. Let~be an equivalence relation on the set X .…”

“…Another approach to creating larger ensemble sizes was proposed by [26]. In the proposed approach (referred to as the phase-aware extension procedure, hereafter), the wavelet transform of the X 1 (t), .…”

“…As noted by [26], the W k (s, t) do not represent all possible outcomes because one ensemble member can predict the observed phase spectrum correctly, while another ensemble member can predict the observed modulus spectrum correctly. In other words, the set of all N 2 possible outcomes is given by Ω = W µν (s, t) = R µ (s, t)e iϕ ν (s,t) :…”

“…, N . As noted by [26], numerical errors can arise from the computation of inverse wavelet transformations. To correct for such errors, a wavelet error reduction procedure was performed.…”

Statistical hypothesis testing in wavelet analysis: theoretical developments and applications to Indian rainfall

“…More recently, the frequency domain analogs of partial and multiple correlation (Ng and Cha, 2012;Hu and Si, 2016) have been developed in wavelet analysis, making the method an even more powerful exploratory tool for researchers. Given these desirable aspects of wavelet analysis, it is not surprising that wavelet analysis has been applied to a broad range of topics, including climatology (Gallegati, 2018), hydrology (Schaefli et al, 2007;Labat, 2010;Schulte et al, 2017), forecast model verification (Lane, 2007;Liu et al, 2011), ensemble forecasting (Schulte and Georgas, 2018), climate network analysis (Agarwal et al, 2018;Paluš, 2018;Ramana et al, 2013;Sahay and Srivastava, 2014;Elsanabary and Gan, 2004), and biomedicine (Addison, 2005).…”