Abstract This study presents a new approach for complex networks-based analysis of temporal streamflow dynamics. The novelty comes in the form of using nonlinear dynamic concepts to construct the temporal streamflow network. The approach involves three steps. First, the single-variable streamflow time series is represented in a multi-dimensional phase space using delay embedding, i.e. phase space reconstruction. Next, this reconstructed phase space is treated as a network , with the reconstructed vectors (instead of the streamflow values themselves) serving as the nodes and the connections between them serving as the links . Finally, the strength of each node in the network is determined using a distance metric. The approach is employed independently to monthly streamflow time series observed over a period of 53 years (January 1950–December 2002) from each of 639 stations in the contiguous United States. For each time series, different delay time values for phase space reconstruction are considered and the optimum embedding dimension is determined using the false nearest neighbor (FNN) method. The results indicate the usefulness of the phase space reconstruction-based network construction for examining the temporal connections in streamflow. The distribution of the strengths of nodes for any streamflow network is used to identify the type of the underlying network. The average node strength of each of the 639 streamflow networks are also interpreted: (1) to identify similarities and differences between the stations; (2) to explain the role of catchment and flow properties (drainage area, elevation, and flow mean) on network strength; and (3) to assess the influence of time (i.e. month of the year) on network strength.

中文翻译：

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时间流分析：非线性动力学与复杂网络的耦合

摘要 本研究提出了一种基于复杂网络的时间流动力学分析的新方法。新颖之处在于使用非线性动态概念来构建时间流网络。该方法包括三个步骤。首先，使用延迟嵌入在多维相空间中表示单变量流时间序列，即相空间重构。接下来，这个重建的相空间被视为一个网络，重建的向量（而不是流值本身）作为节点，它们之间的连接作为链接。最后，使用距离度量确定网络中每个节点的强度。该方法独立用于在 53 年期间（1950 年 1 月至 2002 年 12 月）从美国本土 639 个站点中的每个站点观测到的月流量时间序列。对于每个时间序列，考虑相空间重构的不同延迟时间值，并使用假最近邻 (FNN) 方法确定最佳嵌入维度。结果表明基于相空间重构的网络构建对于检查流中的时间连接是有用的。任何流网络的节点强度分布用于识别底层网络的类型。还解释了 639 个水流网络中每一个的平均节点强度： (1) 识别站点之间的异同；(2) 解释流域和流量特性（排水面积、高程和流量平均值）对网络强度的作用；(3) 评估时间（即一年中的月份）对网络强度的影响。