Detrital layer frequency in a 9336 year varved sequence within the Pianico-Sellere Palaeolake (Southern Alps, Italy)

In this paper, we present a unique 9.5 m palaeolacustrine 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 beta-PS approx. 0.39 and an equivalent power-spectral exponent from DFA, beta-DFA approx. 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.

本研究提出了一套独特的9.5米古湖相（palaeolacustrine）记录，该记录涵盖更新世（Pleistocene）间冰期（时间跨度约780~393 ka）内，阿尔卑斯山脉南部皮尼亚尼科-塞莱尔盆地（Piànico-Sèllere Basin）9.3千年（kyr）间发生的771次古洪水（palaeofloods），并对其相关性、聚集性与周期性特征展开分析。首先，我们针对每十年洪水数量的时间序列开展功率谱分析与去趋势波动分析（detrended fluctuation analysis, DFA）以检验相关性，结果发现存在较弱的长程持续性：功率谱指数β-PS约为0.39，而DFA得到的等效功率谱指数β-DFA约为0.25。随后，我们通过洪水平均间隔的单点概率分布检验聚集性特征，发现古洪水在时间上呈现聚集分布，其间隔服从威布尔分布（Weibull distribution），形状参数k_W=0.78。之后，我们针对年古洪水数量的时间序列检验周期性特征，发现其周期约为2030年。基于上述原始古洪水时间序列的相关性、聚集性与周期性特征，我们构建了一种模型：该模型由分形高斯噪声（fractional Gaussian noise, FGN）与2030年周期分量叠加而成，并引入阈值超额（peaks over threshold, POT）模型。我们利用该POTFGN+周期模型，生成了260万条与原始古洪水时间序列长度一致的合成实现序列，并调整周期强度与持续性参数，最终得到与原始古洪水序列特征相符的最优模型参数。我们基于优化后的古洪水模型生成长序列实现结果，发现洪水频率存在显著的时间变异性，其取值范围为0~>30次/百年。最后，我们验证了优化后模型实现序列的实用价值：可基于前一百年的洪水数量，计算未来百年洪水预测数量的不确定性。本研究的核心发现为：仅依靠分形噪声特征或周期性特征，均无法准确模拟这套大规模连续古洪水记录的频率波动；唯有将分形噪声与长程周期分量叠加的模型，方可实现精准模拟。