Gu Hating, Cheng Weiping, Chen Hao, Liu Li, Xie Jingkai, Xu Yue-Ping
Institute of Water Science and Engineering, Zhejiang University, Hangzhou, 310058, China.
School of Earth Sciences and Engineering, Hohai University, Nanjing, 211100, Jiangsu, China.
Sci Rep. 2025 Apr 24;15(1):14305. doi: 10.1038/s41598-025-98191-w.
Hydrological processes, as part of a natural system, are highly complex and chaotic. By analyzing long time series of streamflow data from ~ 4800 hydrologic stations, it is interesting to find out that probability density functions in second order difference (SOD) of the streamflow data are fat-tailed and bell-shaped curves, and their cumulative distribution functions (CDFs) follow an S-shaped curve (S-curve). We found that t-distribution is a good approximation for S-curve, which uses the degree of freedom (DF) to control the tail thickness. We also found that DF of more than 80% of stations are gathered in the range between 5 and 8. Analysis of the S-curves in seven large river basins indicated that the S-curves can vary with time and space, which is regarded as a good indicator for identifying natural and anthropogenic changes. This study provides a symmetrical, identical and concise probability distribution to describe global streamflow under changing environment.
水文过程作为自然系统的一部分，高度复杂且具有混沌性。通过分析约4800个水文站的长时间序列径流数据，有趣地发现径流数据二阶差分（SOD）中的概率密度函数是肥尾和钟形曲线，其累积分布函数（CDF）呈S形曲线（S曲线）。我们发现t分布是S曲线的良好近似，它使用自由度（DF）来控制尾部厚度。我们还发现超过80%的站点的自由度聚集在5到8的范围内。对七个大流域的S曲线分析表明，S曲线会随时间和空间变化，这被视为识别自然和人为变化的良好指标。本研究提供了一种对称、一致且简洁的概率分布，以描述变化环境下的全球径流。
