发表机构
University of Novi Sad; University at Albany, State University of New York; Texas A&M University; Geographical Institute "Jovan Cvijić" SASA; Peoples' Friendship University of Russia (RUDN University)（诺维萨德大学; 纽约州立大学奥尔巴尼分校; 德克萨斯农工大学; SASA乔万·茨维伊奇地理研究所; 俄罗斯人民友谊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于序数模式熵的状态转移信息空间，以K_t-K_q平面刻画动力学机制，应用于美国河流径流数据，揭示尺度依赖的组织规律。
AI 中文摘要
刻画时间序列中的动力学组织需要区分可达状态的多样性与时间转移中的不确定性。本文基于序数模式导出的两个归一化熵度量，引入了一个状态转移信息空间：K_q量化序数状态多样性，K_t量化转移不确定性。二者的联合K_t-K_q表示提供了一个二维框架，在该框架中可以考察动力学机制及其时间演化。理论性质确立了有界关系0 ≤ K_t ≤ K_q ≤ 1，而典型时间序列识别出从有序动力学到接近最大随机性的不同经验域。滑动窗口分析进一步表明，系统可以在K_t-K_q平面上呈现时间轨迹，而非停留在固定动力学状态。应用于美国河流的1,879个月自然径流记录表明，河流动力学占据有序与高度无序机制之间的一个独特中间区域。此外，随着流域面积的增加，河流位置系统性地向更高的K_t和K_q移动，揭示了径流动力学的尺度依赖组织。因此，该框架提供了一种紧凑的手段，用于比较时间序列系统中的状态多样性、转移不确定性及其时间与空间组织。
英文摘要
Characterizing dynamical organization in time series requires distinguishing the diversity of accessible states from uncertainty in their temporal transitions. Here we introduce a state-transition information space based on two normalized entropy measures derived from ordinal patterns: K_q, quantifying ordinal-state diversity, and K_t, quantifying transition uncertainty. Their joint K_t-K_q representation provides a two-dimensional framework in which dynamical regimes and their temporal evolution can be examined. Theoretical properties establish the bounded relation 0 <= K_t <= K_q <= 1, while canonical time series identify distinct empirical domains ranging from ordered dynamics to near-maximal randomness. Sliding-window analysis further shows that systems can exhibit temporal trajectories through the K_t-K_q plane rather than remaining at a fixed dynamical state. Application to 1,879 monthly naturalized streamflow records from the U.S. rivers shows that river dynamics occupy a distinct intermediate region between ordered and highly disordered regimes. Moreover, river positions shift systematically toward higher K_t and K_q with increasing drainage area, revealing scale-dependent organization of streamflow dynamics. The framework therefore provides a compact means of comparing state diversity, transition uncertainty, and their temporal and spatial organization across time-series systems.
Comments30 pages, 3 figures, 4 tables
