{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T12:45:06Z","timestamp":1781613906241,"version":"3.54.5"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T00:00:00Z","timestamp":1577318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, sample entropy, two-dimensional entropy and fuzzy entropy are introduced into hydrology research to investigate the spatial distribution and dynamic change in streamflow complexity. The results indicate that the complexity of the streamflow has spatial differences in the Weihe River watershed, exhibiting an increasing tendency along the Weihe mainstream, except at the Linjiacun station, which may be attributed to the elevated anthropogenic influence. Employing sliding entropies, the variation points of the streamflow time series at the Weijiabu station were identified in 1968, 1993 and 2003, and those at the Linjiacun station, Xianyang station and Huaxian station occurred in 1971, 1993 and 2003. In the verification of the above points, the minimum value of t-test is 3.7514, and that of Brown\u2013Forsythe is 7.0307, far exceeding the significance level of 95%. Also, the cumulative anomaly can detect two variation points. The t-test, Brown\u2013Forsythe test and cumulative anomaly test strengthen the conclusion regarding the availability of entropies for identifying the streamflow variability. The results lead us to conclude that four entropies have good application effects in the complexity analysis of the streamflow time series. Moreover, two-dimensional entropy and fuzzy entropy, which have been rarely used in hydrology research before, demonstrate better continuity and relative consistency, are more suitable for short and noisy hydrologic time series and more effectively identify the streamflow complexity. The results could be very useful in identifying variation points in the streamflow time series.<\/jats:p>","DOI":"10.3390\/e22010038","type":"journal-article","created":{"date-parts":[[2019,12,27]],"date-time":"2019-12-27T05:37:08Z","timestamp":1577425028000},"page":"38","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Analysis of Streamflow Complexity Based on Entropies in the Weihe River Basin, China"],"prefix":"10.3390","volume":"22","author":[{"given":"Weijie","family":"Ma","sequence":"first","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forest University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Kang","sequence":"additional","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forest University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1746-5288","authenticated-orcid":false,"given":"Songbai","family":"Song","sequence":"additional","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forest University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.physa.2019.03.041","article-title":"Analysis of daily streamflow complexity by Kolmogorov measures and Lyapunov exponent","volume":"525","author":"Singh","year":"2019","journal-title":"Physica A"},{"key":"ref_2","first-page":"76","article-title":"A statistical measure of complexity in hydrological systems","volume":"29","author":"Feng","year":"1998","journal-title":"J. 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