Adaptive Multi-fidelity Monte Carlo for real-time probabilistic storm surge predictions

Real-time, probabilistic predictions of the expected storm surge represent an important information source for guiding emergency response decisions during landfalling tropical storms. The uncertainty quantification in these predictions is accomplished as follows: an ensemble of sample storm scenarios is generated based on the nominal storm advisory and a probabilistic description of the corresponding forecast errors; subsequently high-fidelity numerical simulations are performed to predict the surge for each of these scenarios; the simulation results are finally leveraged to estimate the statistics of interest. This process is repeated whenever a new storm advisory is issued. The need to establish predictions in real-time, to support emergency planning decisions, creates incentives for high computational efficiency for this probabilistic estimation. This paper investigates an adaptive Multi-Fidelity Monte Carlo (MFMC) framework for achieving such an objective. As a lower-fidelity model within the MFMC setup, a surrogate model is adaptively developed based on high-fidelity numerical simulations from the current or past storm advisories, achieving information sharing across them. MFMC leverages the correlation between the high- and low-fidelity models to establish unbiased predictions with high statistical accuracy, significantly improving abilities to provide timely and informative estimates. To facilitate the development of the low-fidelity model using only a small number of high-fidelity numerical simulations, a combination of physics-based and data-driven dimensionality reduction techniques are introduced for the input and the output, respectively, of the surrogate model. To accommodate the use of high-fidelity simulations from the current advisory in the surrogate model calibration, the MFMC implementation is established using leave-one-out surrogate model predictions. Finally, the challenge of establishing MFMC predictions for a large number of quantities of interest (QoIs), corresponding to the surge at different geographic locations, is discussed. These QoIs may advocate conflicting decisions for the optimal MFMC implementation, and an efficient search for a compromise solution is introduced. The efficiency of the proposed MFMC framework is showcased by considering its application to different historical storms.