{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:41:27Z","timestamp":1760139687039,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,23]],"date-time":"2022-04-23T00:00:00Z","timestamp":1650672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Watershed climatic diversity poses a hard problem when it comes to finding suitable models to estimate inter-annual rainfall runoff (IARR). In this work, a hybrid model (dubbed MR-CART) is proposed, based on a combination of MR (multiple regression) and CART (classification and regression tree) machine-learning methods, applied to an IARR predicted data series obtained from a set of non-parametric and empirical water balance models in five climatic floors of northern Algeria between 1960 and 2020. A comparative analysis showed that the Yang, Sharif, and Zhang\u2019s models were reliable for estimating input data of the hybrid model in all climatic classes. In addition, Schreiber\u2019s model was more efficient in very humid, humid, and semi-humid areas. A set of performance and distribution statistical tests were applied to the estimated IARR data series to show the reliability and dynamicity of each model in all study areas. The results showed that our hybrid model provided the best performance and data distribution, where the R2Adj and p-values obtained in each case were between (0.793, 0.989), and (0.773, 0.939), respectively. The MR model showed good data distribution compared to the CART method, where p-values obtained by signtest and WSR test were (0.773, 0.705), and (0.326, 0.335), respectively.<\/jats:p>","DOI":"10.3390\/s22093241","type":"journal-article","created":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T00:45:21Z","timestamp":1650761121000},"page":"3241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Hybrid Water Balance Machine Learning Model to Estimate Inter-Annual Rainfall-Runoff"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1731-0489","authenticated-orcid":false,"given":"Amir","family":"Aieb","sequence":"first","affiliation":[{"name":"Laboratory of Biomathematics, Biophysics, Biochemistry, and Scientometric (BBBS), Bejaia University, Bejaia 06000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2773-4421","authenticated-orcid":false,"given":"Antonio","family":"Liotta","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2801-1919","authenticated-orcid":false,"given":"Ismahen","family":"Kadri","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering and Hydraulics, 8 May 1945 Guelma University, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5356-6890","authenticated-orcid":false,"given":"Khodir","family":"Madani","sequence":"additional","affiliation":[{"name":"Laboratory of Biomathematics, Biophysics, Biochemistry, and Scientometric (BBBS), Bejaia University, Bejaia 06000, Algeria"},{"name":"Research Center of Agro-Food Technologies (CRTAA), Bejaia 06000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.gloplacha.2010.03.003","article-title":"Hydrological response of Mediterranean headwaters to climate oscillations and land-cover changes: The mountains of Duero River basin (Central Spain)","volume":"72","year":"2010","journal-title":"Glob. 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