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

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 β_PS  ≈  0.39 and an equivalent power-spectral 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 palaeofloods cluster in time as they are Weibull distributed with a 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 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 POT_{FGN + 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.