Global sensitivity analysis with 2d hydraulic codes: applied protocol and practical tool

TL;DR

This paper introduces a protocol and a coupled computational tool for performing global sensitivity analysis on 2D hydraulic models, specifically using the 2D shallow water equations, to quantify the influence of input uncertainties on flood simulations.

Contribution

It develops a practical, automated GSA protocol and a coupled tool (Prométhée-FullSWOF 2D) for efficient uncertainty quantification in 2D hydraulic modeling.

Findings

Successfully computed Sobol indices maps for flood modeling.

Enabled large-scale simulations with up to 17.9 million points.

Demonstrated the tool's applicability on urban flood scenarios.

Abstract

Global Sensitivity Analysis (GSA) methods are useful tools to rank input parameters uncertainties regarding their impact on result variability. In practice, such type of approach is still at an exploratory level for studies relying on 2D Shallow Water Equations (SWE) codes as GSA requires specific tools and deals with important computational capacity. The aim of this paper is to provide both a protocol and a tool to carry out a GSA for 2D hydraulic modelling applications. A coupled tool between Prom{\'e}th{\'e}e (a parametric computation environment) and FullSWOF 2D (a code relying on 2D SWE) has been set up: Prom{\'e}th{\'e}e-FullSWOF 2D (P-FS). The main steps of our protocol are: i) to identify the 2D hydraulic code input parameters of interest and to assign them a probability density function, ii) to propagate uncertainties within the model, and iii) to rank the effects of each input parameter on the output of interest. For our study case, simulations of a river flood event were run with uncertainties introduced through three parameters using P-FS tool. Tests were performed on regular computational mesh, spatially discretizing an urban area, using up to 17.9 million of computational points. P-FS tool has been installed on a cluster for computation. Method and P-FS tool successfully allow the computation of Sobol indices maps. Keywords Uncertainty, flood hazard modelling, global sensitivity analysis, 2D shallow water equation, Sobol index. Analyse globale de sensibilit{\'e} en mod{\'e}lisation hydrauliqu{\`e} a surface libre 2D : application d'un protocole et d{\'e}veloppement d'outils op{\'e}rationnels -- Les m{\'e}thodes d'analyse de sensibilit{\'e} permettent de contr{\^o}ler la robustesse des r{\'e}sultats de mod{\'e}lisation ainsi que d'identifier le degr{\'e} d'influence des param etres d' entr{\'e}e sur le r{\'e}sultat en sortie d'un mod ele. Le processus complet constitue une analyse globale de sensibilit{\'e} (GSA). Ce type d'approche pr{\'e}sente un grand int{\'e}r{\^e}t pour analyser les incer-titudes de r{\'e}sultats de mod{\'e}lisation , mais est toujours a un stade exploratoire dans les etudes appliqu{\'e}es mettant en jeu des codes bas{\'e}s sur la r{\'e}solution bidimensionnelle des equations de Saint-Venant. En effet, l' impl{\'e}mentation d'une GSA est d{\'e}licate car elle