Inversion Algorithm for Civil Flood Defense Optimization: Application to Two-Dimensional Numerical Model of the Garonne River in France

Yann Richet,Vito Bacchi

doi:10.3389/fenvs.2019.00160

Abstract

The objective of this study is to investigate inversion-approach for optimization of flood defense in a inundated area. This is a new methodology in this engineering field which consists in definition of a criterion (as for instance the water level in a given location must be lower than a given value) and analysis of all uncertain controlled parameters (i.e. flood defense geometry, location, and so on) combinations allowing to not exceed safety objective for all possible uncontrolled parameters combination (i.e. flow hydrograph parameters) representing natural phenomenon. In order to estimate this safety set, we will use a transient meta-modelling approach, which reduces widely number of model evaluations required. This algorithm relies on a kriging surrogate built from few model evaluations, sequentially fulfilled with new numerical model evaluations as long as remaining uncertainty of whole safety set remains too high. Also known as Stepwise Uncertainty Reduction, this algorithm is embedded in Funz engine in charge of bridging numerical model and any design of experiments algorithm. We applied this algorithm to a real bi-dimensional numerical model of Garonne River. Especially, we focused our attention on water depth at a given area when considering influence of a simplified flood defense during a flooding event. In order to simplify problem, we only analyze two parameters describing slab and dyke elevations of flood defense system. The results will be analyzed in terms of safety control inside operating range of river. It appears that once properly evaluated, this constrained zone gives highly valuable data for a fully risk informed management of area to protect.

Highlights

It is well-known that the world’s major lowland rivers are protected against flooding by embankments or other flood defenses (Ciullo et al, 2019)
Another good example is the optimization model introduced by van Dantzig (1956) for the embankment height, which was further developed by other authors, as reported by Eijgenraam et al (2016)
This method consists in defining a “safety criterion” and the analysis of suitable design parameters that ensure the safety objective for all the possible combinations of uncertain input parameters describing the natural phenomenon to be met. To estimate this safety set, a standard surrogate approach will be used (Jones et al, 1998), which significantly reduces the number of model evaluations needed. This algorithm relies on a kriging surrogate built from a few model evaluations, sequentially enriched with new numerical model evaluations as long as the remaining uncertainty of the entire safety set remains too high (Chevalier, 2013)

Summary

Introduction

It is well-known that the world’s major lowland rivers (the Rhine, the Po, the Elbe River, and the Loire River) are protected against flooding by embankments or other flood defenses (Ciullo et al, 2019). The embankments and so-called primary flood defenses such as flood walls and dams (Kind, 2014) are aimed primarily at reducing the likelihood of flooding in the protected area, and Inversion-Optimization Against Garonne Flooding historically they have been the most commonly-adopted flood risk reduction measure (Ciullo et al, 2019) The design of these flood protection measures is of major importance society-wide, and can have a considerable impact on the economic and demographic development of the alluvial plains (White, 1945). Another good example is the optimization model introduced by van Dantzig (1956) for the embankment height, which was further developed by other authors, as reported by Eijgenraam et al (2016)

Objectives

Methods

Conclusion