{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:39:24Z","timestamp":1766137164738,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41771365"],"award-info":[{"award-number":["41771365"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Parameterization schemes (bulk formulae) are widely used to estimate all-sky surface downward longwave radiation (SDLR) due to the simple, readily available inputs and acceptable accuracy from local to regional scales. Seven widely used bulk formulae are evaluated using the ground measurements collected from 44 globally distributed flux measurement sites of five networks. The Bayesian model averaging (BMA) method is introduced to integrate multiple bulk formulae to obtain an estimate of cloudy-sky SDLR for the first time. The second multiple linear regression model of Carmona et al. (2014) performs the best, with BIAS, RMSE, and R2 of zero, 20.13 W\u00b7m\u22122 and 0.87, respectively. The BMA method can achieve balanced results that are close to the accuracy of the second multiple linear regression model of Carmona et al. (2014) and better than the average accuracy of seven bulk formulae, with BIAS, RMSE, and R2 of \u22121.08 W\u00b7m\u22122, 21.99 W\u00b7m\u22122 and 0.87, respectively. In addition, the bulk formula of Crawford and Duchon (1999) is preferred if there is insufficient data to calibrate the bulk formulae because it does not need local calibration and has an acceptable accuracy, with BIAS, RMSE, and R2 of 0.96 W\u00b7m\u22122, 26.58 W\u00b7m\u22122 and 0.82, respectively. The effects of climate type, land cover type, and surface elevation are also investigated to fully assess the applicability of each bulk formula and BMA. In general, there is no cloudy-sky bulk parametrization scheme that can be successfully applied everywhere.<\/jats:p>","DOI":"10.3390\/rs11050528","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T11:19:50Z","timestamp":1551784790000},"page":"528","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["A Comparative Study of Bulk Parameterization Schemes for Estimating Cloudy-Sky Surface Downward Longwave Radiation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7620-4507","authenticated-orcid":false,"given":"Jie","family":"Cheng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Faculty of Geographical Science, Beijing Normal University; Beijing 100875, China"},{"name":"Institute of Remote Sensing Science and Engineering, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"}]},{"given":"Feng","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Faculty of Geographical Science, Beijing Normal University; Beijing 100875, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3980-5933","authenticated-orcid":false,"given":"Yamin","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Faculty of Geographical Science, Beijing Normal University; Beijing 100875, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1109\/JSTARS.2010.2048556","article-title":"Review of estimation of land surface radiation and energy budgets from ground measurements, remote sensing and model simulation","volume":"3","author":"Liang","year":"2010","journal-title":"IEEE J. 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