Application of a probabilistic method for estimating the flood distribution of the Rhône at Beaucaire, based on a continuous discharge series from 1816 to 2020 and a collection of historical floods from 1500 to 1815. Development of a propagation chain for the different sources of uncertainty. Evaluation of the impact of uncertainties related to the inclusion of a perception threshold on historical floods and the starting date of the historical period.

The statistical estimation of flood risk generally consists of estimating the parameters of a distribution based on streamflow time series. This exercise is affected by substantial uncertainties that come from the accuracy of the available data, but also from the limited length of the records. The main objective of this thesis is to develop a flood frequency analysis method that makes the most of continuous or sporadic historical data with a complete and homogeneous consideration of the various sources of uncertainty.

The method is applied to the exceptionally rich case study of the Rhône River at Beaucaire, France (95 590 km²), with continuous stage records over more than 200 years and a comprehensive dataset on hydroclimatic events from the XIIIth century. A continuous streamflow series with uncertainties from 1816 to 2020 was established. The hydrometric uncertainty was propagated to the design flood estimates, and the contribution of both hydrometric and sampling uncertainties to the total uncertainty was quantified. Tests showed that the total uncertainty decreases significantly when the length of the series increases from 20 to 100 years. Beyond 100 years, the total uncertainty remains constant because the sampling uncertainty decrease is offset by the hydrometric uncertainty increase.

To reduce the sampling uncertainty, the dataset was expanded by using sporadic historical flood data, prior to the hydrometric records. An original feature of this method is the inclusion of the perception threshold and the length of the historical period as parameters of the probabilistic model, using a Bayesian approach. The model was tested on the subsampled 1816-2020 streamflow series, for which the perception threshold and historical period length are known. The imperfect knowledge of the perception threshold resulted in a much greater uncertainty than the imperfect knowledge of the length of the historical period. The model was then applied to the full dataset with historical floods since the XVIth century. The design flood uncertainty was smaller than using the continuous 1816-2020 streamflow time serie only, even when the perception threshold and the length of the historical period are considered uncertain. Nevertheless, this application suggests that the historical data are probably incomplete, which complicates the use of these results. Beyond the specific case of Beaucaire, it would be interesting to apply this method to watersheds for which the climatic context and the nature of the historical data are different. Moreover, the long series reconstructed in Beaucaire could also be used to study the hydroclimatic variability of the Rhône River.

Funding

50% INRAE, 30 % CNR, 20 % H20

For more information

Lucas M. 2023. Comment valoriser les données anciennes pour l’analyse fréquentielle des crues : application au Rhône à Beaucaire de 1500 à 2020. Thèse de Doctorat, Univ. Lyon, 3 Juillet 2023, 159 p.

Cite the thesis

Mathieu Lucas. Comment valoriser les données anciennes pour l’analyse fréquentielle des crues : application au Rhône à Beaucaire de 1500 à 2020. Statistiques [math.ST]. Université Claude Bernard - Lyon I, 2023. Français. ⟨NNT : 2023LYO10114⟩. ⟨tel-04390159⟩

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