An entropy approach for the optimization of cross-section spacing for river modelling

Abstract

An accurate definition of river geometry is essential to implement one-dimensional (1D) hydraulic models and, in particular, appropriate spacing between cross-sections is key for capturing a river's hydraulic behaviour. This work explores the potential of an entropy-based approach, as a complementary method to existing guidelines, to determine the optimal number of cross-sections to support 1D hydraulic modelling. To this end, given a redundant collection of existing cross-sections, a location subset is selected minimizing total correlation (as a measure of redundancy) and maximizing joint entropy (as a measure of information content). The problem is posed as a multiobjective optimization problem and solved using a genetic algorithm: the Non-dominated Sorting Genetic Algorithm (NSGA)-II. The proposed method is applied to a river reach of the Po River (Italy) and compared to standard guidelines for 1D hydraulic modelling. Cross-sections selected through the proposed methodology were found to provide an accurate description of the flood water profile, while optimizing computational efficiency.Key words cross-sections; heuristic entropy; hydraulic modelling; one-dimensional flow; network optimization; genetic algorithm; NGSA-II Une approche fondée sur l'entropie pour l'optimisation de l'espacement entre sections en travers pour la modélisation en riviére Résumé Une définition précise de la géométrie de la riviére est essentielle pour mettre en oeuvre des modéles hydrauliques unidimensionnels (1D). L'espacement approprié entre les sections en travers de la riviére est un élément clé pour reproduire son comportement hydraulique. Ce travail a pour objectif de fournir une méthode se basant sur l'entropie, complémentaire des guides existants et permettant de fournir des informations supplémentaires pour l'optimisation des modéles hydrauliques 1D et la gestion des jeux de données sur les sections en travers. Plus spécifiquement, sur la base d'une collecte redondante de sites de sections en travers existantes, un sous-ensemble de sites est sélectionné en minimisant la corrélation totale (comme mesure de redondance) et en maximisant l'entropie conjointe (comme mesure du contenu en information). Le probléme est posé sous la forme d'une optimisation multi-objectif, résolue en utilisant un algorithme génétique (NSGA-II). Nous appliquons la méthode proposée aux données de sections en travers sur le Po, en Italie, et nous la comparons aux méthodes existantes en utilisant un modéle hydraulique 1D. Les jeux de sections en travers sélectionnées par la méthodologie proposée fournissent une description précise du profil des eaux en crue, tout en optimisant l'efficacité de calcul.Mots clefs sections en travers ; entropie heuristique ; modélisation hydraulique ; flux unidimensionnel ; optimisation de réseau, algorithme génétique ; NGSA-II 126

Can assimilation of crowdsourced data in hydrological modelling improve flood prediction?

“…In particular, there is a limit in the number of CSD for which satisfactory model improvements can be achieved and for which additional CSD become redundant. This asymptotic behaviour, when extra information is added, has also been observed using other metrics by Krstanovic and Singh (1992), Ridolfi et al (2014), Alfonso et al (2013), among others. From Fig.…”

Improving Flood Prediction Assimilating Uncertain Crowdsourced Data into Hydrological and Hydraulic Models

“…This means that the additional CS observations do not add information useful for improving the model performance. This asymptotic behavior when extra information is added has also been observed using other metrics by Krstanovic and Singh (1992), Ridolfi et al (2014), Alfonso et al (2013), among others. In all flood events, similar trends of the NSE are found.…”

Ensemble Entropy for Monitoring Network Design

“…Although the approach described so far has been applied in different studies (see e.g., [29][30][31]34]), the estimation of the Information Theory quantities presented in Section 2.1 is sensitive to different assumptions in the calculation of probabilities. An example is the histogram bin size used to estimate probabilities via frequency methods.…”