论文标题
分数布朗尼动作及其多重分析分析应用于Parana河流
Fractional Brownian Motions and their multifractal analysis applied to Parana river flow
论文作者
论文摘要
从确定Hurst系数开始，许多不同的分析技术已用于分析来自不同河流的长期时间序列数据。我们总结了分形，多重折叠和分数布朗运动（FBM）的概念，并将某些此类技术应用于阿根廷Corrientes的Parana河的日常流流数据，已有106年的历史。在确定了整个数据集的HURST系数（H = 0.76）之后，我们分析了四个季节的每个季节的数据，并绘制相应的FBM图及其多型光谱（MFS）。其中三个季节相似，但是FBM和MFS的秋季都大不相同。基于MFS结果，我们提出了许多用于测量流流变化的指标，并确定三个相似季节的指数值。这些指数基于多重谱光谱的重要参数。光谱的几何形状以及索引都表明冬季是最稳定的季节。这与季节流数据的框图相反，季节性流流数据显示冬季最大变化。因此，这些指数提供了对河流流稳定性的见解，而不是从基本统计分析中检测到的，也没有与之矛盾。
A number of different analysis techniques have been used to analyze long-term time series data from different rivers, starting with the determination of the Hurst coefficient. We summarize the concept of fractals, multifractals and Fractional Brownian Motion (FBM), and apply some such techniques to daily stream flow data from the Parana River recorded at Corrientes, Argentina, for 106 years. After determining the Hurst coefficient for the entire data set (H = 0.76), we analyze the data for each of four seasons and draw the corresponding FBM graphs and their multifractal spectra (MFS). Three of the seasons are similar, but autumn is very different for both FBM and MFS. Based on the MFS results, we propose a number of indices for measuring variations in stream flow, and determine the values of the indices for the three similar seasons. The indices are based on important parameters of the multifractal spectra. The geometry of the spectra as well as the indices all indicate that Winter is the most stable season. This is in contrast to the Boxplot of seasonal stream flow data where Winter shows the largest variation. Thus, these indices provide insight into river flow stability, not detected in, and indeed contradictory to, that from basic statistical analysis.
