Adaptive formulation for probabilistic storm surge predictions through sharing of numerical simulation results across storm advisories

As a tropical storm/cyclone approaches landfall, real-time probabilistic predictions for the anticipated surge provide valuable information for emergency preparedness/response decisions. These probabilistic predictions are made through an uncertainty quantification process that involves: (i) generating a sufficiently large ensemble of storm scenarios based on the nominal storm advisory and the anticipated forecast errors; (ii) performing high-fidelity numerical simulations to obtain surge predictions for each storm scenario; and (iii) estimating surge statistics of interest by assembling the simulation results. This process is repeated whenever the nominal storm advisory is updated. The number of storm scenarios utilized in the analysis directly impacts the statistical accuracy of the probabilistic predictions; a larger ensemble improves accuracy but requires greater computational resources to provide predictions with the desired expediency to guide real-time decisions. This paper revisits two recently proposed Monte-Carlo (MC) frameworks that aim to improve accuracy without increasing the computational burden: adaptive importance sampling (AIS) and adaptive multi-fidelity Monte Carlo (AMFMC). The foundational concept behind them is similar: share numerical simulation results across the probabilistic predictions performed for different storm advisories to accelerate the MC estimation. This is achieved differently for each approach, through adaptive development of an importance sampling proposal density (for AIS) or a surrogate model (for AMFMC). Here, a direct comparison between these frameworks is established, focusing on the mechanisms for the information sharing and the challenges encountered in tuning the algorithm adaptive characteristics to provide probabilistic estimates across a large number of quantities of interest (QoIs), corresponding to the surge predictions for different locations within the coastal region of interest. As this large number results in conflicting choices for the adaptive characteristics, a compromise solution needs to be promoted. The efficacy of the two frameworks is examined in detail in this setting, comparing the accuracy of idealized implementations (adaptive decisions independently made for each QoI) to the accuracy of practical implementations (single, compromise decision within the MC implementation). The study also showcases the importance of information sharing across storm advisories in real-time probabilistic storm