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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 11
Hydrol. Earth Syst. Sci., 21, 5547–5581, 2017
https://doi.org/10.5194/hess-21-5547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 21, 5547–5581, 2017
https://doi.org/10.5194/hess-21-5547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 14 Nov 2017

Research article | 14 Nov 2017

Analysis and modelling of a 9.3 kyr palaeoflood record: correlations, clustering, and cycles

Annette Witt1, Bruce D. Malamud2, Clara Mangili3,a, and Achim Brauer3 Annette Witt et al.
  • 1Max Planck Institute for Dynamics and Self-Organisation, Göttingen, Germany
  • 2Department of Geography, King's College London, London, UK
  • 3GFZ German Research Centre for Geosciences, Potsdam, Germany
  • anow at: Section of Earth and Environmental Sciences, University of Geneva, Geneva, Switzerland

Abstract. In this paper, we present a unique 9.5 m palaeo-lacustrine record of 771 palaeofloods which occurred over a period of 9.3 kyr in the Piànico–Sèllere Basin (southern Alps) during an interglacial period in the Pleistocene (sometime from 780 to 393 ka) and analyse its correlation, clustering, and cyclicity properties. We first examine correlations, by applying power-spectral analysis and detrended fluctuation analysis (DFA) to a time series of the number of floods per decade, and find weak long-range persistence: a power-spectral exponent βPS  ≈  0.39 and an equivalent power-spectral exponent from DFA, βDFA ≈  0.25. We then examine clustering using the one-point probability distribution of the inter-flood intervals and find that the palaeofloods cluster in time as they are Weibull distributed with a shape parameter kW =  0.78. We then examine cyclicity in the time series of number of palaeofloods per year, and find a period of about 2030 years. Using these characterizations of the correlation, clustering, and cyclicity in the original palaeoflood time series, we create a model consisting of the superposition of a fractional Gaussian noise (FGN) with a 2030-year periodic component and then peaks over threshold (POT) applied. We use this POTFGN + Period model to create 2 600 000 synthetic realizations of the same length as our original palaeoflood time series, but with varying intensity of periodicity and persistence, and find optimized model parameters that are congruent with our original palaeoflood series. We create long realizations of our optimized palaeoflood model, and find a high temporal variability of the flood frequency, which can take values of between 0 and > 30 floods century−1. Finally, we show the practical utility of our optimized model realizations to calculate the uncertainty of the forecasted number of floods per century with the number of floods in the preceding century. A key finding of our paper is that neither fractional noise behaviour nor cyclicity is sufficient to model frequency fluctuations of our large and continuous palaeoflood record, but rather a model based on both fractional noise superimposed with a long-range periodicity is necessary.

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Here we present a unique 9.5 m palaeo-lacustrine record of 771 palaeofloods which occurred over a period of 10 000 years in the Piànico–Sèllere basin (southern Alps) during an interglacial period in the Pleistocene (sometime between 400 000 and 800 000 years ago). We analyse the palaeoflood series correlation, clustering, and cyclicity properties, finding a long-range cyclicity with a period of about 2030 years superimposed onto a fractional noise.
Here we present a unique 9.5 m palaeo-lacustrine record of 771 palaeofloods which occurred over...
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