Preprints
https://doi.org/10.5194/hess-2024-50
https://doi.org/10.5194/hess-2024-50
04 Mar 2024
 | 04 Mar 2024
Status: a revised version of this preprint is currently under review for the journal HESS.

A more comprehensive uncertainty framework for historical flood frequency analysis: a 500-year long case study

Mathieu Lucas, Michel Lang, Benjamin Renard, and Jérôme Le Coz

Abstract. The value of historical data for flood frequency analysis has been acknowledged and studied for a long time. A specific statistical framework must be used to comply with the censored nature of historical data. Indeed, it is assumed that all floods having exceeded a given perception threshold were recorded as written testimonies or flood marks. Conversely, all years without a flood record in the historical period are assumed to have a maximum discharge below the perception threshold. This paper proposes a Binomial model which explicitly recognizes the uncertain nature of both the perception threshold and the starting date of the historical period. This model is applied to a case study for the Rhône River at Beaucaire, France, where a long (1816–2020) systematic series of annual maximum discharges is available along with a collection of 13 historical floods from documentary evidences over three centuries (1500–1815). Results indicate that the inclusion of historical floods reduces the uncertainty of 100- or 1000-year flood quantiles, even when only the number of perception threshold exceedances is known. However, ignoring the uncertainty around the perception threshold leads to a noticeable underestimation of flood quantiles uncertainty. A qualitatively similar conclusion is found when ignoring the uncertainty around the historical period length. However, its impact on flood quantiles uncertainty appears to be much smaller than that of the perception threshold.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Mathieu Lucas, Michel Lang, Benjamin Renard, and Jérôme Le Coz

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2024-50', Neil Macdonald, 27 Mar 2024
    • AC2: 'Reply on RC1', Michel Lang, 07 May 2024
  • RC2: 'Comment on hess-2024-50', Helen Hooker, 25 Apr 2024
    • AC1: 'Reply on RC2', Michel Lang, 07 May 2024
Mathieu Lucas, Michel Lang, Benjamin Renard, and Jérôme Le Coz
Mathieu Lucas, Michel Lang, Benjamin Renard, and Jérôme Le Coz

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Short summary
This paper proposes Binomial models for the inclusion of historical data into flood frequency analysis, which recognize the uncertain nature of the perception threshold and the starting date of the historical period. The procedure is applied to a long systematic series 1816–2020 and 13 historical floods over 1500–1815 (Rhône River, Beaucaire, France). Inclusion of historical floods reduces the uncertainty flood quantiles, even when only the number of perception threshold exceedances is known.