{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T14:48:38Z","timestamp":1774363718912,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad de Buenos Aires","award":["UBACYT-20020190200305BA"],"award-info":[{"award-number":["UBACYT-20020190200305BA"]}]},{"name":"Universidad de Buenos Aires","award":["UBACYT-20020220400162BA"],"award-info":[{"award-number":["UBACYT-20020220400162BA"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen\u2013Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyret\u00e1 dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.<\/jats:p>","DOI":"10.3390\/e26010056","type":"journal-article","created":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T04:38:51Z","timestamp":1704775131000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0649-7332","authenticated-orcid":false,"given":"Micaela","family":"Suriano","sequence":"first","affiliation":[{"name":"Departamento de Hidr\u00e1ulica, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, Av. Las Heras 2214, Buenos Aires C1127AAR, Argentina"},{"name":"Laboratorio de Redes y Sistemas M\u00f3viles, Departamento de Electr\u00f3nica, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, Buenos Aires C1063ACV, Argentina"}]},{"given":"Leonidas Facundo","family":"Caram","sequence":"additional","affiliation":[{"name":"Laboratorio de Redes y Sistemas M\u00f3viles, Departamento de Electr\u00f3nica, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, Buenos Aires C1063ACV, Argentina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1288-2528","authenticated-orcid":false,"given":"Osvaldo Anibal","family":"Rosso","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica (IFLP), Universidad Nacional de La Plata, CONICET, La Plata B1900AJJ, Argentina"},{"name":"Instituto de F\u00edsica, Universidade Federal de Alagoas (UFAL), Macei\u00f3 57072-970, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6532","DOI":"10.1002\/2015WR016958","article-title":"Complexity and organization in hydrology: A personal view","volume":"51","author":"Bras","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1029\/90RG02615","article-title":"Hydrologic science: A distinct geoscience","volume":"29","author":"Eagleson","year":"1991","journal-title":"Rev. Geophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2695","DOI":"10.1007\/s11269-014-0637-8","article-title":"Hydrological Modeling of Large river Basins: How Much is Enough?","volume":"28","author":"Johnston","year":"2014","journal-title":"Water Resour. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4119","DOI":"10.5194\/hess-16-4119-2012","article-title":"Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework","volume":"16","author":"Sivakumar","year":"2012","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1007\/s00477-008-0265-z","article-title":"Nonlinear dynamics and chaos in hydrologic systems: Latest developments and a look forward","volume":"23","author":"Sivakumar","year":"2009","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/S0022-1694(04)00421-4","article-title":"On the Need for Catchment Classification","volume":"299","author":"McDonnell","year":"2004","journal-title":"J. Hydrol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/15715124.2019.1628033","article-title":"Catchment classification in a transboundary river using runoff and sub-basin characteristics","volume":"18","author":"Salami","year":"2020","journal-title":"Int. J. River Basin Manag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0022-1694(87)90138-7","article-title":"Looking for hydrologic laws","volume":"96","author":"Dooge","year":"1986","journal-title":"J. Hydrol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s00477-007-0161-y","article-title":"Multi-scale entropy analysis of Mississippi River flow","volume":"22","author":"Li","year":"2008","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1061\/(ASCE)HE.1943-5584.0000392","article-title":"Flow-Complexity Analysis of the Upper Reaches of the Yangtze River, China","volume":"16","author":"Huang","year":"2011","journal-title":"J. Hydrol. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.physa.2005.11.053","article-title":"Generalized statistical complexity measures: Geometrical and analytical properties","volume":"369","author":"Plastino","year":"2006","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"154102","DOI":"10.1103\/PhysRevLett.99.154102","article-title":"Distinguishing Noise from Chaos","volume":"99","author":"Rosso","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation Entropy: A Natural Complexity Measure for Time Series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1140\/epjst\/e2013-01858-3","article-title":"Ordinal pattern and statistical complexity analysis of daily stream flow time series","volume":"222","author":"Lange","year":"2013","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1007\/s00477-013-0825-8","article-title":"Complexity\u2013entropy analysis of daily stream flow time series in the continental United States","volume":"28","author":"Serinaldi","year":"2014","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1016\/j.jhydrol.2016.07.034","article-title":"Investigating anthropically induced effects in streamflow dynamics by using permutation entropy and statistical complexity analysis: A case study","volume":"540","author":"Stosic","year":"2016","journal-title":"J. Hydrol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"023115","DOI":"10.1063\/5.0135352","article-title":"Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis","volume":"33","author":"Stosic","year":"2023","journal-title":"Chaos"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1007\/s00477-016-1315-6","article-title":"Complexity as a streamflow metric of hydrologic alteration","volume":"31","author":"Jovanovic","year":"2017","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.physa.2003.11.005","article-title":"Intensive entropic non-triviality measure","volume":"334","author":"Lamberti","year":"2004","journal-title":"Physica A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1038\/s42005-021-00696-z","article-title":"Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series","volume":"4","author":"Zanin","year":"2021","journal-title":"Commun. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"066116","DOI":"10.1103\/PhysRevE.63.066116","article-title":"Tendency towards maximum complexity in a nonequilibrium isolated system","volume":"63","author":"Calbet","year":"2001","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.4279\/pip.070006","article-title":"Noise versus chaos in a causal Fisher-Shannon plane","volume":"7","author":"Rosso","year":"2015","journal-title":"Pap. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1098\/rsta.1922.0009","article-title":"On the mathematical foundations of theoretical statistics","volume":"222","author":"Fisher","year":"1922","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Frieden, B. (2004). Science from Fisher Information: A Unification, Cambridge University Press.","DOI":"10.1017\/CBO9780511616907"},{"key":"ref_26","unstructured":"Bohner, M. (2009). Proceedings of the 14th International Conference on Difference Equations and Applications, Instanbul, Turkey, 21\u201325 July 2008, Ugur\u2013Bah\u00e7e\u015fehir University Publishing Company. Difference Equations and Applications."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"063110","DOI":"10.1063\/5.0049901","article-title":"ordpy: A Python package for data analysis with permutation entropy and ordinal network methods","volume":"31","author":"Pessa","year":"2021","journal-title":"Chaos"},{"key":"ref_28","first-page":"707","article-title":"On generating power law noise","volume":"300","author":"Timmer","year":"1995","journal-title":"Astron. Astrophys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D Graphics Environment","volume":"9","author":"Hunter","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.21105\/joss.03021","article-title":"Seaborn: Statistical data visualization","volume":"6","author":"Waskom","year":"2021","journal-title":"J. Open Source Softw."},{"key":"ref_31","unstructured":"Jordahl, K., Van den Bossche, J., Fleischmann, M., Wasserman, J., McBride, J., Gerard, J., Fleischmann, M., Tratner, J., Perry, M., and Farmer, C. (2020). Geopandas\/Geopandas: v0.8.1 (Version v0.8.1), Zenodo."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kantelhardt, J.W., Koscielny-Bunde, E., Rybski, D., Braun, P., Bunde, A., and Havlin, S. (2006). Long-term persistence and multifractality of precipitation and river runoff records. J. Geophys. Res. Atmos., 111.","DOI":"10.1029\/2005JD005881"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"W12529","DOI":"10.1029\/2009WR009000","article-title":"River flow fluctuation analysis: Effect of watershed area","volume":"46","author":"Hirpa","year":"2010","journal-title":"Water Resour. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"W01202","DOI":"10.1029\/2006WR005721","article-title":"Long memory of rivers from spatial aggregation","volume":"43","author":"Mudelsee","year":"2007","journal-title":"Water Resour. Res."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/1\/56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:42:40Z","timestamp":1760103760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/1\/56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,9]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["e26010056"],"URL":"https:\/\/doi.org\/10.3390\/e26010056","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,9]]}}}