{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,16]],"date-time":"2026-08-16T13:08:14Z","timestamp":1786885694452,"version":"build-2736575974"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,11]],"date-time":"2015-05-11T00:00:00Z","timestamp":1431302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Water Resources Agency, Taiwan","award":["MOEAWRA 1010295"],"award-info":[{"award-number":["MOEAWRA 1010295"]}]},{"name":"Water Resources Agency, Taiwan","award":["MOEAWRA 1010216"],"award-info":[{"award-number":["MOEAWRA 1010216"]}]},{"DOI":"10.13039\/501100001868","name":"National Science Council, Taiwan","doi-asserted-by":"publisher","award":["NSC 101-2221-E006-194-MY3"],"award-info":[{"award-number":["NSC 101-2221-E006-194-MY3"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Physical models and grey system models (GSMs) are commonly used to evaluate and predict physical behavior. A physical model avoids the incorrect trend series of a GSM, whereas a GSM avoids the assumptions and uncertainty of a physical model. A technique that combines the results of physical models and GSMs would make prediction more reasonable and reliable. This study proposes a fusion method for combining two trend series, calculated using two one-dimensional models, respectively, that uses a slope criterion and a distance weighting factor in the temporal and spatial domains. The independent one-dimensional evaluations are upgraded to a spatially and temporally connected two-dimensional distribution. The proposed technique was applied to a subsidence problem in Jhuoshuei River Alluvial Fan, Taiwan. The fusion results show dramatic decreases of subsidence quantity and rate compared to those estimated by the GSM. The subsidence behavior estimated using the proposed method is physically reasonable due to a convergent trend of subsidence under the assumption of constant discharge of groundwater. The technique proposed in this study can be used in fields that require a combination of two trend series from physical and nonphysical models.<\/jats:p>","DOI":"10.3390\/e17053035","type":"journal-article","created":{"date-parts":[[2015,5,11]],"date-time":"2015-05-11T10:09:28Z","timestamp":1431338968000},"page":"3035-3052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Dimensional Upgrade Approach for Spatial-Temporal Fusion of Trend Series in Subsidence Evaluation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7616-2343","authenticated-orcid":false,"given":"Shih-Jung","family":"Wang","sequence":"first","affiliation":[{"name":"Georesources Research Center, National Cheng Kung University, Tainan 70101, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,11]]},"reference":[{"key":"ref_1","unstructured":"Bell, F. 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