{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T16:47:10Z","timestamp":1792255630936,"version":"4.4.0"},"reference-count":36,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T00:00:00Z","timestamp":1765497600000},"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>Real-time, reliable forecasting of water quality (WQ) is a critical component of sustainable environmental management. A key challenge, however, is modeling time-varying uncertainty (heteroscedasticity), particularly during disruptive events like storms where predictability decreases dramatically. Standard probabilistic models often fail in these high-stakes scenarios, producing forecasts that are either too conservative during calm periods or dangerously overconfident during volatile events. This paper introduces the Gated Hybrid\u2013Mixture Density Network (GH-MDN), an architecture explicitly designed for adaptive uncertainty estimation. Its core innovation is a dedicated gating network that learns to adaptively modulate the prediction interval width in response to a domain-relevant, event-precursor signal. We evaluate the GH-MDN on both synthetic and real-world WQ datasets using a rigorous cross-validation protocol. The results demonstrate that our gated model provides robust calibration and trustworthy adaptive coverage; specifically, it successfully widens prediction intervals to capture extreme events where standard benchmarks fail. We further show that common aggregate metrics such as CRPS can mask over-confident behavior during rare events, underscoring the need for evaluation approaches that prioritize calibration. This science-informed approach to modeling heteroscedasticity prioritizes reliable risk coverage over aggregate error minimization, marking a critical step towards the development of more trustworthy environmental forecasting systems.<\/jats:p>","DOI":"10.3390\/s25247560","type":"journal-article","created":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T14:04:40Z","timestamp":1765548280000},"page":"7560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Reliable and Adaptive Probabilistic Forecasting for Event-Driven Water-Quality Time Series Using a Gated Hybrid\u2013Mixture Density Network"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1993-1074","authenticated-orcid":false,"given":"Nadir","family":"Ehmimed","sequence":"first","affiliation":[{"name":"Information System and Software Engineering (SIGL) Laboratory, National School of Applied Sciences of Tetouan, Abdelmalek Essaadi University, Tetouan 93000, Morocco"},{"name":"Department of Engineering Sciences and Technology (INDI), Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7256-329X","authenticated-orcid":false,"given":"Mohamed Yassin","family":"Chkouri","sequence":"additional","affiliation":[{"name":"Information System and Software Engineering (SIGL) Laboratory, National School of Applied Sciences of Tetouan, Abdelmalek Essaadi University, Tetouan 93000, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8891-180X","authenticated-orcid":false,"given":"Abdellah","family":"Touhafi","sequence":"additional","affiliation":[{"name":"Department of Engineering Sciences and Technology (INDI), Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.envsoft.2014.09.013","article-title":"Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions","volume":"62","author":"Maier","year":"2014","journal-title":"Environ. 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