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

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, for which only floods large enough to induce written records or to trigger flood marks are usually recorded. It is assumed that all floods which 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 had a maximum discharge below the perception threshold. This paper proposes a binomial model that 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 evidence over 3 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 quantile uncertainty. A qualitatively similar conclusion is found when ignoring the uncertainty around the historical period length. However, its impact on flood quantile uncertainty appears to be much smaller than that of the perception threshold.