Quantizing rare random maps: application to flooding visualization

TL;DR

This paper introduces a novel method for quantizing rare flooding events using importance sampling and functional PCA to efficiently represent the probability distribution of flood maps, even with costly simulations.

Contribution

It adapts Lloyd's algorithm for rare event quantization by integrating importance sampling and Gaussian process metamodeling to handle expensive hydraulic simulations.

Findings

Validated on a 2D analytical model.

Successfully applied to a real coastal flooding scenario.

Quantified errors from metamodel and importance sampling.

Abstract

Visualization is an essential operation when assessing the risk of rare events such as coastal or river floodings. The goal is to display a few prototype events that best represent the probability law of the observed phenomenon, a task known as quantization. It becomes a challenge when data is expensive to generate and critical events are scarce, like extreme natural hazard. In the case of floodings, each event relies on an expensive-to-evaluate hydraulic simulator which takes as inputs offshore meteo-oceanic conditions and dyke breach parameters to compute the water level map. In this article, Lloyd's algorithm, which classically serves to quantize data, is adapted to the context of rare and costly-to-observe events. Low probability is treated through importance sampling, while Functional Principal Component Analysis combined with a Gaussian process deal with the costly hydraulic simulations. The calculated prototype maps represent the probability distribution of the flooding events in a minimal expected distance sense, and each is associated to a probability mass. The method is first validated using a 2D analytical model and then applied to a real coastal flooding scenario. The two sources of error, the metamodel and the importance sampling, are evaluated to quantify the precision of the method.