Abstract
Abstract. The identification of recurrences at various timescales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method.
Highlights
One of the main challenges of society is to understand and manage natural disasters, such as earthquakes, tsunamis, and floods, which often lead to big loss of economic assets and even lives
We propose a distance measure for recurrencebased analysis of extreme event time series
The occurrence of recurring events of a real-world time series due to changes in seasonal patterns by replacing the linear dependency of the cost of shifting events by a nonlinear dependency using the logistic function. This is a substantial improvement over the previous definition of the edit distance as used for the TACTS algorithm proposed by Ozken et al (2015) as the optimization of 0 is based on the temporal delay between events, which is of physical relevance to the study of extreme events and can be chosen according to the phenomenon being studied
Summary
One of the main challenges of society is to understand and manage natural disasters, such as earthquakes, tsunamis, and floods, which often lead to big loss of economic assets and even lives. There are powerful techniques based on phase space reconstruction of a wide range of nonlinear dynamical processes, they are not directly applicable to event-like time series Extreme events such as flood, earthquakes, or solar flares are known to have long-term correlations (Jentsch et al, 2006). Capturing the correlations of extreme events using such methods is difficult as the phase space reconstruction and the Euclidean distance for measuring the distances of states are not suitable for event-like time series because, by definition, extreme events are small in number and are separated by large temporal gaps. The proposed extension allows us to consider the shifting parameter of the edit distance metric in terms of a temporal delay which can be physically interpreted as a tolerance introduced to deal with the quasi-periodic nature of a real-world extreme event time series. By using the random shuffle surrogate method, we show that there is a significant serial dependency in the flood events
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