{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T00:53:47Z","timestamp":1781657627092,"version":"3.54.5"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T00:00:00Z","timestamp":1548979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Key Research and Development Program of China","award":["2016YFC0401306"],"award-info":[{"award-number":["2016YFC0401306"]}]},{"name":"The National Natural Science Fund in China","award":["51879222"],"award-info":[{"award-number":["51879222"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Streamflow forecasting is vital for reservoir operation, flood control, power generation, river ecological restoration, irrigation and navigation. Although monthly streamflow time series are statistic, they also exhibit seasonal and periodic patterns. Using maximum Burg entropy, maximum configurational entropy and minimum relative entropy, the forecasting models for monthly streamflow series were constructed for five hydrological stations in northwest China. The evaluation criteria of average relative error (RE), root mean square error (RMSE), correlation coefficient (R) and determination coefficient (DC) were selected as performance metrics. Results indicated that the RESA model had the highest forecasting accuracy, followed by the CESA model. However, the BESA model had the highest forecasting accuracy in a low-flow period, and the prediction accuracies of RESA and CESA models in the flood season were relatively higher. In future research, these entropy spectral analysis methods can further be applied to other rivers to verify the applicability in the forecasting of monthly streamflow in China.<\/jats:p>","DOI":"10.3390\/e21020132","type":"journal-article","created":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T03:08:05Z","timestamp":1548990485000},"page":"132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Application of Entropy Spectral Method for Streamflow Forecasting in Northwest China"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8218-8910","authenticated-orcid":false,"given":"Gengxi","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Northwest A&amp;F University, Yangling 712100, China"},{"name":"Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&amp;F University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenghong","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Northwest A&amp;F University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoling","family":"Su","sequence":"additional","affiliation":[{"name":"College of Water Resources and Architectural Engineering, Northwest A&amp;F University, Yangling 712100, China"},{"name":"Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&amp;F University, Yangling 712100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olusola O.","family":"Ayantobo","sequence":"additional","affiliation":[{"name":"Department of Water Resources Management and Agricultural-Meteorology, Federal University of Agriculture, PMB 2240, Abeokuta 110282, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, Z., Ju, J., Su, X., Singh, V., and Zhang, G. (2017). Comparison of Two Entropy Spectral Analysis Methods for Streamflow Forecasting in Northwest China. Entropy, 19.","DOI":"10.3390\/e19110597"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jhydrol.2014.11.065","article-title":"Configurational entropy theory for streamflow forecasting","volume":"521","author":"Cui","year":"2015","journal-title":"J. Hydrol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.physa.2015.08.060","article-title":"Maximum entropy spectral analysis for streamflow forecasting","volume":"442","author":"Cui","year":"2016","journal-title":"Phys. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1007\/s00477-016-1281-z","article-title":"Minimum relative entropy theory for streamflow forecasting with frequency as a random variable","volume":"30","author":"Cui","year":"2016","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s00477-016-1306-7","article-title":"Application of minimum relative entropy theory for streamflow forecasting","volume":"31","author":"Cui","year":"2017","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_6","unstructured":"Burg, J.P. (1975). Maximum Entropy Spectral Analysis. [Ph.D. Thesis, Stanford University]."},{"key":"ref_7","first-page":"36","article-title":"Application of time series free regreession model in dynamic simulation and prediction of groundwater in irrigation area","volume":"1","author":"Huo","year":"1990","journal-title":"Geotech. Investig. Surv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF00872477","article-title":"A real-time flood forecasting model based on maximum-entropy spectral analysis: I. Development","volume":"7","author":"Krstanovic","year":"1993","journal-title":"Water Resour. Manag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1364\/JOSA.62.000511","article-title":"Restoring with maximum likelihood and maximum Entropy","volume":"62","author":"Frieden","year":"1972","journal-title":"J. Opt. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1038\/272686a0","article-title":"Image reconstruction from incomplete and noisy data","volume":"272","author":"Gull","year":"1978","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0165-1684(92)90055-2","article-title":"Finite length cepstrum modelling\u2014A simple spectrum estimation technique","volume":"26","author":"Nadeu","year":"1992","journal-title":"Signal Proc."},{"key":"ref_12","unstructured":"Shore, J.E. (1979). Minimum Cross-Entropy Spectral Analysis."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1109\/TASSP.1981.1163539","article-title":"Minimum cross-entropy spectral-analysis","volume":"29","author":"Shore","year":"1981","journal-title":"IEEE Trans. Acoust. Speech"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1109\/TASSP.1985.1164605","article-title":"A general method of minimum cross-entropy spectral estimation","volume":"33","author":"Tzannes","year":"1985","journal-title":"IEEE Trans. Acoust. Speech"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s004770050024","article-title":"Minimum relative entropy and probabilistic inversion in groundwater hydrology","volume":"12","author":"Woodbury","year":"1998","journal-title":"Stoch. Hydrol. Hydraul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s40710-015-0080-8","article-title":"Entropy Theory for Streamflow Forecasting","volume":"2","author":"Singh","year":"2015","journal-title":"Environ. Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1964.tb00553.x","article-title":"An analysis of transformations","volume":"26","author":"Box","year":"1964","journal-title":"J. R. Stat. Soc. B"},{"key":"ref_18","unstructured":"Burg, J.P. (1967, January 31). Maximum entropy spectral analysis. Proceedings of the 37th Meeting of Society Exploration Geophysics, Oklahoma City, OK, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1111\/j.1752-1688.1986.tb00762.x","article-title":"A comparison of transformation methods for flood frequency analysis","volume":"22","author":"Jam","year":"1986","journal-title":"J. Am. Water Resour."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:30:06Z","timestamp":1760185806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,1]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020132"],"URL":"https:\/\/doi.org\/10.3390\/e21020132","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,1]]}}}