Exploring the sensitivity of probabilistic surge estimates to forecast errors

Statistical predictions of storm surge are critical for guiding evacuation and emergency response/preparedness decisions during landfalling storms. The probabilistic characteristics of these predictions are formulated by utilizing historical forecast errors to quantify relevant uncertainties in the National Hurricane Center advisories. This ultimately leads to the description of probability distributions quantifying the deviation from the nominal advisory for four different storm features: intensity, size, cross-track variability and along-track variability. Propagation of the uncertainty in these four storm features, serving as input to a numerical model for calculating storm surge, leads to the definition of the statistical surge estimates. This work investigates the application of variance-based global sensitivity analysis (GSA), quantified through the estimation of Sobol' indices, to explore the importance of the forecast errors in the peak storm surge predictions. This GSA can assist in better understanding the impact of the different forecast errors for typical storms, and can also offer important insights for a specific storm, regarding the characteristics that influence the probabilistic surge predictions across its different advisories, as the storm comes closer to landfall. An efficient GSA implementation is presented here to address two key challenges of the specific problem: (i) the need to perform the GSA for a multi-dimensional output, corresponding to the surge for multiple locations within the geographic domain of interest that will be affected by a specific storm, and (ii) the restriction to use only a small number of hydrodynamic numerical simulations, since the associated computational burden of such simulations is significant. For addressing these challenges, dimensionality reduction through Principal Component Analysis (PCA) and a probability-based estimation of the variance of conditional expectations are combined to provide the necessary efficiency in the proposed GSA framework. The development of aggregated importance indices across the entire geographic domain is also discussed, incorporating the importance of the surge for each separate location (within this domain) using a variance-based weighting. This formulation is compared with an alternative, computationally efficient, definition of the aggregated importance, based on the readily available PCA information. A demonstration of this framework’s utility considering different historical storms (using National Weather Service advisories and forecast errors for past events) is provided, establishing comparisons across them and across multiple advisories for each storm.