Adaptive importance sampling for efficient probabilistic storm surge estimation

Abstract

During landfalling tropical storms, probabilistic predictions of the storm surge constitute important products for guiding emergency response decisions. The probabilistic formulation for these predictions is established by considering historical forecast errors for the intensity, size, cross- and along-track variability of the National Hurricane Center (NHC) advisories. These errors quantify ultimately uncertainties in storm features, serving as input to a numerical model for predicting storm surge, while propagation of these uncertainties provides the desired statistical products. This probabilistic estimation is repeated whenever the NHC updates the storm advisory. Monte Carlo (MC) simulation is considered for facilitating the uncertainty propagation in this paper, and in order to improve computational efficiency, the implementation of adaptive importance sampling (IS) across the storm advisories is introduced, using simulation results from the current advisory to select the optimal IS density to use for the next advisory. The requirement to estimate the storm surge across a large geographic domain, leading to the definition of a large number of quantities of interests (QoIs), poses a significant challenge, since these quantities typically represent competing IS choices. Principal component analysis (PCA) is utilized for dimensionality reduction to establish a compromising solution with a reduced computational burden. An adaptive selection of the IS characteristics is discussed, utilizing an efficient estimation of the anticipated IS accuracy, and a defensive IS scheme is introduced to guarantee robustness.