Analysis and Modelling of a 9.3 kyr Palaeoflood Record: Correlations, Clustering and Cycles

In this paper we present a unique 9.5 m palaeo-lacustrine record of 771 palaeofloods which occurred over a period of 10 kyr in the Pianico-Sellere basin (southern Alps) during an interglacial period in the Pleistocene (sometime 400–800 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 year and find weak long-range persistence: power-spectral exponent β PS  ≈ 0.39 and equivalent power-spectra exponent from DFA, β DFA ≈ 0.25. We then examine clustering using the one-point probability distribution of the inter-flood intervals and find that the occurrence of palaeofloods do cluster in time as they are Weibull distributed with shape parameter k W = 0.78. We then examine cyclicity in the time series of number of palaeofloods per year, and find a period of about 2030 yr. 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 yr periodic component and then peaks over threshold (POT) applied. We use this POT (FGN + Period) model to create 2,600,00 synthetic realisations 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 between 0 to > 30 floods century -1 . Finally, we show the practical utility of our optimized model realisations 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, or cyclicity, are 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.