Flood hazard assessment of the Rhône River revisited with reconstructed discharges from lake sediments

doi:10.1016/j.gloplacha.2018.09.010

Global and Planetary Change

Volume 172, January 2019, Pages 114-123

https://doi.org/10.1016/j.gloplacha.2018.09.010 Get rights and content

Abstract

Accurate flood hazard assessments are crucial for adequate flood hazard mapping and hydraulic infrastructure design. The choice of an acceptable and cost-effective solution for such assessments depends upon the estimation of quantiles for different characteristics of floods, usually maximum discharges. However, gauge series usually have a limited time length and, thereby, quantile estimates associated to high return periods are subject to large uncertainties. To overcome this limitation, reconstructed flood series from historical, botanical or geological archives can be incorporated. In this study, we propose a novel approach that i) combines classic series of observations with paleodischarges (of the Rhône River) reconstructed from open lake sediments (Lake Bourget, Northwestern Alps, France) and ii) propagates uncertainties related to the reconstruction method during the estimation of extreme quantiles.

A Bayesian approach is adopted in order to properly treat the non-systematic nature of the reconstructed flow data, as well as the uncertainties related to the reconstruction method. While this methodology has already been applied to reconstruct maximum discharges from historical documents, tree rings or fluvial sediments, similar applications need to be tested today on open lake sediments as they are one of the only archives that provide long and continuous paleoflood series. Reconstructed sediment volumes being subject to measurement errors, we evaluate and account for this uncertainty, along with the uncertainty related to the reconstruction method, the parametric uncertainty, and the rating-curve errors for systematic gauged flows by propagating these uncertainties through the modeling chain. Reconstructed maximum discharges appear to largely overcome values of observations, reaching values of approximately 2,600, 4,200, 2,450 and 2,500 m³/s in 1689, 1711, 1733 and 1737 respectively, which correspond to historically-known catastrophic floods. Extreme quantiles are estimated using direct measurements of maximum discharges (1853-2004) only and then combined to the sedimentary information (1650-2013). The comparison of the resulting estimates demonstrates the added value of the sedimentary information. In particular, the four historical catastrophic floods are very unlikely if only direct observations are considered for quantile estimations.

Introduction

Flood events are among the most usual causes of natural disasters, affecting more people worldwide than any natural hazards and resulting in important damage to infrastructures [estimated cost around 50 billion USD per year on average, (CRED, 2015), (Benfield, 2016). These societal impacts are partly due to a growing exposure of people and assets in flood-prone areas [e.g. (Kundzewicz et al., 2014)] and emphasize the need for more accurate flood hazard assessments. Such assessments could then be deployed to improve flood hazard mapping and hydraulic infrastructure (e.g. embankments, dam spillways) design, permitting the sustainable development of societies living along rivers. The choice of an acceptable and cost-effective solution for the flood hazard assessment depends upon the estimation of quantiles for different characteristics of floods, usually maximum discharges, based on Flood Frequency Analysis, aka FFA (Hamed & Rao, 1999). However, series of observed floods have a limited time length (often 10 to 100 years), and quantile estimates associated with high return periods (usually 100 for hazard mapping, 1000 for dam spillway and 10000-year return period for hazardous flooding in nuclear plants) are subject to large uncertainties. Different approaches have been proposed to reinforce the estimation of these quantiles, and reduce the associated uncertainties. For example, regionalization methods combine information gathered around the study area (Burn, 1990; Gaume et al., 2010; Renard, 2011). Alternatively, many studies aim at collecting and assessing indirect flow measurements:

1.
Historical data: Historical records can be of various form and usually refer to documentary sources [reports, diaries, chronicles, memoirs; (Naulet et al., 2005), (Machado et al., 2015)], flood stage/crest measurements (Neppel et al., 2010; Parkes & Demeritt, 2016) or both (Payrastre et al., 2011; Ruiz-Bellet et al., 2015).
2.
Paleofloods: Past maximum flood discharges can also be reconstructed using botanical analyses like trees [e.g. (Ballesteros Cánovas et al., 2017)] or geological evidence like fluvial sediments (Lam et al., 2017; O’Connor et al., 1994; Thorndycraft et al., 2005; Wilhelm et al., 2018).

Recently, (Jenny et al., 2014) have shown that paleoflood discharges can also be reconstructed from lake sediment sequences. When the Rhône River waters entering the Lake Bourget (Nortwestern Alps, France) exceed a threshold of approximately 1500 m³/s, large amounts of sediment are transported and deposited in the lake basin. These flood sediment volumes appear positively correlated to the maximum discharges of the eleven greatest Rhône River floods of the last 150 years. The flood sediment volumes trace back to AD 1650 in the Lake Bourget sediment sequence provided. Flood sediment volumes thus provide a reasonable proxy of flood magnitude for the events of the last 360 years (Jenny et al., 2014). This long series of reconstructed paleofloods from lake sediments motivate the application of FFA to the combined dataset of direct observations and paleoflood information. Assuming that all large floods (i.e. exceeding a threshold of approximately 1500 m³/s) are consistently recorded by the lake sediment deposits, the continuity of this paleoflood series presents a great advantage compared to historical or other geological flood data. This study completes the dataset provided by (Jenny et al., 2014), assesses the uncertainties associated with this novel method of maximum discharge reconstruction and presents an application of FFA to this new dataset on a major European river that has numerous critical infrastructures along its length.

The effect of the different sources of uncertainty (estimation of sediment volumes, reconstruction of flood maximum discharges using sediment volumes, parameter uncertainty, the uncertainty of direct flow measurements) is properly taken into account using a Bayesian approach. Bayesian approaches are particularly relevant for FFA with different sources of information (Kuczera, 1999; O’Connell et al., 2002; Reis & Stedinger, 2005). They provide a rigorous framework for the treatment of non-systematic (i.e. floods exceeding a certain threshold) and imperfect information (Lam et al., 2017; Neppel et al., 2010; Payrastre et al., 2011; Reis & Stedinger, 2005). In particular, Bayesian methods are particularly relevant for the treatment of the different sources of uncertainty (Toonen et al., 2016). In our case, sediment volumes are subject to measurement errors. We evaluate and account for this uncertainty, along with the uncertainty related to the reconstruction method, the parametric uncertainty, and the rating-curve errors for systematic gauged flows by propagating these uncertainties through the modeling chain.

We first describe the data and the study area in Section 2. The method applied to reconstruct the paleofloods is then detailed in Section 3. Section 4 presents the Bayesian FFA, including the explicit treatment of measurement errors. In Section 5, this methodology is first applied to direct measurements of maximum discharges (1853-2004) only, and then combined with the sedimentary information (1650-2013).

Section snippets

Data and study area

The narrow Lake Bourget (18 km long, 2.8 km wide, 147 m deep) is located in the foothills (231.5 m asl) of the northwestern French Alps (Fig. 1A). Lake Bourget waters usually come from two small rivers (Leysse and Sierroz Rivers), which then flow to the Rhône River by the Savière channel (Fig. 1B). However, during severe flooding of the Rhône River, the water current of the Savière channel is reversed and waters of the Rhône River enter Lake Bourget (Fig. 1c). During such flood events, Lake

Estimation of the sediment volumes

The volumes of the flood sediment deposits are estimated using interpolations of deposit thicknesses measured in each core ${\tilde{d}}_{i, c}$ , where i = 1, …, n_S = 31 is the event number and c = 1, …, n_C = 23 is the core number. The notation $\tilde{.}$ indicates that this quantity corresponds to a direct measurement. For each deposit thickness, the precision of the measurement is approximately 1 mm.

To interpolate these deposit thicknesses and provide sediment volumes, many methods are available. (Jenny et al., 2014

Extreme value distribution

Extreme Value Theory (Coles, 2001) indicates that, under some conditions, the Generalized Extreme Value distribution (or GEV) is a suitable model for block maxima. This limiting distribution is adequate when maxima are applied on very large blocks. Concerning flood frequency analysis, a year is generally accepted as a reasonable block size and annual maxima can be assumed to follow a GEV distribution. For a discharge q, its cumulative distribution function (cdf) is: $F (q| Θ_{FFA}) = (\begin{array}{c} exp \{- {(1 + ξ (\frac{q - μ}{σ}))}^{- 1 / ξ}\} & if ξ \neq 0 \\ exp \end{array}$

Results and discussion

Fig. 5 shows the time series of all floods (reconstructed and observed). 22 flood events have been reconstructed from the sediment volumes prior to 1850 and complement the time series of observed annual maximum discharges for the period from 1853 to 2000.

The reconstruction of these past flood discharges relies on the extrapolation of the relationship observed over the last 150 years between peak discharges and volumes of flood sediments transported by the Rhone River and deposited in Lake

Conclusion

This study presents a flood frequency analysis combining, for the first time, classic series of observations and maximum discharges reconstructed from open lake sediment analysis in order to reduce uncertainties of quantile estimations. Incorporating the paleoflood data in a FFA presents a great advantage since open lake sediments systematically record large floods, which is not the case for historical (e.g. for time series greater than 1000 years, for which historical archives are sparse) or

Acknowledgements

We thank the two anonymous reviewers for their constructive comments and useful suggestions. We would like to express our special thanks to Lothar Schulte and Daniel Schillereff who accepted to serve as guest editors for these special issue, in particular Daniel Schillereff who also proofread the final version of this paper.

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Research ArticleFlood hazard assessment of the Rhône River revisited with reconstructed discharges from lake sediments

Abstract

Introduction

Section snippets

Data and study area

Estimation of the sediment volumes

Extreme value distribution

Results and discussion

Conclusion

Acknowledgements

Quater. Sci. Rev.

J. Hydrol.

J. Hydrol.

J. Hydrol.

J. Hydrol.

J. Hydrol.

J. Hydrol.

Water Security

Annual Global Climate and Catastrophe Report

Le Rhône, du Léman à Lyon

Evaluation of regional flood frequency analysis with a region of influence approach

Water Resour. Res.

Les inondations en France depuis le Vie siècle jusqu’à nos jours

Rhone River flood deposits in Lake Le Bourget: a proxy for Holocene environmental changes in the NW Alps, France

Boreas

An Introduction to Statistical Modeling of Extreme Values

Human Cost of Natural Disasters: A Global Perspective

Bayesian Data Analysis

Flood Frequency Analysis

Research Article
Flood hazard assessment of the Rhône River revisited with reconstructed discharges from lake sediments