{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:12Z","timestamp":1760241552873,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,2]],"date-time":"2018-05-02T00:00:00Z","timestamp":1525219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PML and University of Exeter Research Collaboration Fund"},{"name":"PML Research Programme"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Uncertainty estimation is crucial to establishing confidence in any data analysis, and this is especially true for Essential Climate Variables, including ocean colour. Methods for deriving uncertainty vary greatly across data types, so a generic statistics-based approach applicable to multiple data types is an advantage to simplify the use and understanding of uncertainty data. Progress towards rigorous uncertainty analysis of ocean colour has been slow, in part because of the complexity of ocean colour processing. Here, we present a general approach to uncertainty characterisation, using a database of satellite-in situ matchups to generate a statistical model of satellite uncertainty as a function of its contributing variables. With an example NASA MODIS-Aqua chlorophyll-a matchups database mostly covering the north Atlantic, we demonstrate a model that explains 67% of the squared error in log(chlorophyll-a) as a potentially correctable bias, with the remaining uncertainty being characterised as standard deviation and standard error at each pixel. The method is quite general, depending only on the existence of a suitable database of matchups or reference values, and can be applied to other sensors and data types such as other satellite observed Essential Climate Variables, empirical algorithms derived from in situ data, or even model data.<\/jats:p>","DOI":"10.3390\/rs10050695","type":"journal-article","created":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T03:20:27Z","timestamp":1525317627000},"page":"695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Statistical Modeling Framework for Characterising Uncertainty in Large Datasets: Application to Ocean Colour"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7518-8683","authenticated-orcid":false,"given":"Peter E.","family":"Land","sequence":"first","affiliation":[{"name":"Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH, UK"}]},{"given":"Trevor C.","family":"Bailey","sequence":"additional","affiliation":[{"name":"17 The Glebe, Thorverton, Exeter EX55LS, UK"}]},{"given":"Malcolm","family":"Taberner","sequence":"additional","affiliation":[{"name":"EUMETSAT, Eumetsat-Allee 1, 64295 Darmstadt, Germany"}]},{"given":"Silvia","family":"Pardo","sequence":"additional","affiliation":[{"name":"Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH, UK"}]},{"given":"Shubha","family":"Sathyendranath","sequence":"additional","affiliation":[{"name":"Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH, UK"}]},{"given":"Kayvan","family":"Nejabati Zenouz","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, 5605 JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7153-928X","authenticated-orcid":false,"given":"Vicki","family":"Brammall","sequence":"additional","affiliation":[{"name":"Centrica, Millstream, Maidenhead Road, Windsor SL4 5GD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8018-123X","authenticated-orcid":false,"given":"Jamie D.","family":"Shutler","sequence":"additional","affiliation":[{"name":"College of Life and Environmental Sciences, University of Exeter, Penryn TR10 9FE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9132-9511","authenticated-orcid":false,"given":"Graham D.","family":"Quartly","sequence":"additional","affiliation":[{"name":"Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH, UK"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,2]]},"reference":[{"key":"ref_1","unstructured":"Global Climate Observing System (GCOS) (2011). Systematic Observation Requirements for Satellite-Based Products for Climate 2011 Update, WMO GCOS Report 154, World Meteorological Organization (WMO)."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24937","DOI":"10.1029\/98JC02160","article-title":"Ocean color chlorophyll algorithms for SeaWiFS","volume":"103","author":"Maritorena","year":"1998","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_3","unstructured":"(2018, February 20). Level 2 Ocean Color Flags, Available online: https:\/\/oceancolor.gsfc.nasa.gov\/atbd\/ocl2flags\/."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0034-4257(00)00206-6","article-title":"How precise are SeaWiFS ocean color estimates? Implications of digitization-noise errors","volume":"76","author":"Hu","year":"2001","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6045","DOI":"10.1364\/AO.51.006045","article-title":"Dynamic range and sensitivity requirements of satellite ocean color sensors: Learning from the past","volume":"51","author":"Hu","year":"2012","journal-title":"Appl. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2424","DOI":"10.1016\/j.rse.2009.07.016","article-title":"A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product","volume":"113","author":"Moore","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_7","unstructured":"Joint Committee for Guides in Metrology (2008). Evaluation of Measurement Data\u2014Guide to the Expression of Uncertainty in Measurement, Joint Committee for Guides in Metrology."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Merchant, C.J., Paul, F., Popp, T., Ablain, M., Bontemps, S., Defourny, P., Hollmann, R., Lavergne, T., Laeng, A., and de Leeuw, G. (2017). Uncertainty information in climate data records from Earth observation. Earth Syst. Sci. Data Discuss.","DOI":"10.5194\/essd-2017-16"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Stasinopoulos, D.M., and Rigby, R.A. (2008). Generalized Additive Models for Location Scale and Shape (GAMLSS) in R. J. Stat. Softw., 23.","DOI":"10.18637\/jss.v023.i07"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-4076(81)90071-3","article-title":"Likelihood of a model and information criteria","volume":"16","author":"Akaike","year":"1981","journal-title":"J. Econom."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1080\/01621459.1975.10479865","article-title":"The predictive sample reuse method with applications","volume":"70","author":"Geisser","year":"1975","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_12","unstructured":"(2018, February 13). MODIS-Aqua Reprocessing 2012, Available online: https:\/\/oceancolor.gsfc.nasa.gov\/reprocessing\/r2012\/aqua\/."},{"key":"ref_13","unstructured":"O\u2019Reilly, J.E., Maritorena, S., Siegel, D.A., O\u2019Brien, M.C., Toole, D., Mitchell, B.G., Kahru, M., Chavez, F.P., Strutton, P., and Cota, G.F. (2000). Ocean color chlorophyll a algorithms for SeaWiFS, OC2, and OC4: Version 4. SeaWiFS Postlaunch Calibration and Validation Analyses Part 3, NASA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1109\/36.701082","article-title":"MODIS land data storage, gridding, and compositing methodology: Level 2 grid","volume":"36","author":"Wolfe","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","unstructured":"International Ocean-Colour Coordinating Group (2000). Remote Sensing of Ocean Colour in Coastal, and Other Optically-Complex, Waters, IOCCG."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7887","DOI":"10.1364\/AO.36.007887","article-title":"Remote sensing of ocean color: Assessment of water-leaving radiance bidirectional effects on atmospheric diffuse transmittance","volume":"36","author":"Yang","year":"1997","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4790","DOI":"10.1364\/AO.40.004790","article-title":"Correction of sun glint contamination on the SeaWiFS ocean and atmosphere products","volume":"40","author":"Wang","year":"2001","journal-title":"Appl. Opt."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7754","DOI":"10.1364\/AO.33.007754","article-title":"Influence of oceanic whitecaps on atmospheric correction of ocean-color sensors","volume":"33","author":"Gordon","year":"1994","journal-title":"Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1364\/AO.33.000443","article-title":"Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm","volume":"33","author":"Gordon","year":"1994","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3196","DOI":"10.1109\/TGRS.2006.876293","article-title":"Cloud masking for ocean color data processing in the coastal regions","volume":"44","author":"Wang","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1109\/TGRS.2009.2024307","article-title":"On-orbit calibration and performance of Aqua MODIS reflective solar bands","volume":"48","author":"Xiong","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1093\/plankt\/17.6.1245","article-title":"An estimate of global primary production in the ocean from satellite radiometer data","volume":"17","author":"Longhurst","year":"1995","journal-title":"J. Plankton Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"13237","DOI":"10.1029\/95JC00458","article-title":"The lognormal distribution as a model for bio-optical variability in the sea","volume":"100","author":"Campbell","year":"1995","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_24","unstructured":"(2018, February 26). SeaDAS, Available online: https:\/\/seadas.gsfc.nasa.gov."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1111\/brv.12221","article-title":"Long-term temporal and spatial trends in eutrophication status of the Baltic Sea","volume":"92","author":"Andersen","year":"2017","journal-title":"Biol. Rev."},{"key":"ref_26","unstructured":"Brewin, R.J.W., Sathyendranath, S., M\u00fceller, D., Brockmann, C., Deschamps, P.Y., Devred, E., Doerffer, R., Fomferra, N., Franz, B., and Grant, M. (2012). The ocean colour climate change initiative: A round-robin comparison of in-water bio-optical algorithms. Remote Sens. Environ."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lee, K., Tong, L.T., Millero, F.J., Sabine, C.L., Dickson, A.G., Goyet, C., Park, G.H., Wanninkhof, R., Feely, R.A., and Key, R.M. (2006). Global relationships of total alkalinity with salinity and temperature in surface waters of the world\u2019s oceans. Geophys. Res. Lett., 33.","DOI":"10.1029\/2006GL027207"},{"key":"ref_28","unstructured":"Antoine, D. (2004). Guide to the Creation and Use of Ocean-Colour, Level-3, Binned Data Products, IOCCG."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/5\/695\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:02:52Z","timestamp":1760194972000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/5\/695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,2]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["rs10050695"],"URL":"https:\/\/doi.org\/10.3390\/rs10050695","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,5,2]]}}}