{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T18:31:09Z","timestamp":1763663469353,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T00:00:00Z","timestamp":1464048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1413454","DMS-0940249"],"award-info":[{"award-number":["DMS-1413454","DMS-0940249"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The \u201cpolar data gap\u201d is a region around the North Pole where satellite orbit inclination and instrument swath for SMMR and SSM\/I-SSMIS satellites preclude retrieval of sea ice concentrations. Data providers make the irregularly shaped data gap round by centering a circular \u201cpole hole mask\u201d over the North Pole. The area within the pole hole mask has conventionally been assumed to be ice-covered for the purpose of sea ice extent calculations, but recent conditions around the perimeter of the mask indicate that this assumption may already be invalid. Here we propose an objective, partial differential equation based model for estimating sea ice concentrations within the area of the pole hole mask. In particular, the sea ice concentration field is assumed to satisfy Laplace\u2019s equation with boundary conditions determined by observed sea ice concentrations on the perimeter of the gap region. This type of idealization in the concentration field has already proved to be quite useful in establishing an objective method for measuring the \u201cwidth\u201d of the marginal ice zone\u2014a highly irregular, annular-shaped region of the ice pack that interacts with the ocean, and typically surrounds the inner core of most densely packed sea ice. Realistic spatial heterogeneity in the idealized concentration field is achieved by adding a spatially autocorrelated stochastic field with temporally varying standard deviation derived from the variability of observations around the mask. To test the model, we examined composite annual cycles of observation-model agreement for three circular regions adjacent to the pole hole mask. The composite annual cycle of observation-model correlation ranged from approximately 0.6 to 0.7, and sea ice concentration mean absolute deviations were of order     10  \u2212 2      or smaller. The model thus provides a computationally simple approach to solving the increasingly important problem of how to fill the polar data gap. Moreover, this approach based on solving an elliptic partial differential equation with given boundary conditions has sufficient generality to also provide more sophisticated models which could potentially be more accurate than the Laplace equation version. Such generalizations and potential validation opportunities are discussed.<\/jats:p>","DOI":"10.3390\/rs8060442","type":"journal-article","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T21:53:40Z","timestamp":1464126820000},"page":"442","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Filling the Polar Data Gap in Sea Ice Concentration Fields Using Partial Differential Equations"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5866-4377","authenticated-orcid":false,"given":"Courtenay","family":"Strong","sequence":"first","affiliation":[{"name":"Department of Atmospheric Sciences, University of Utah, 135 S 1460 E, Rm 819, Salt Lake City, UT 84112-0102, USA"}]},{"given":"Kenneth","family":"Golden","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Utah, 155 S 1400 E, RM 233, Salt Lake City, UT 84112-0090, USA"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"881","DOI":"10.5194\/tc-6-881-2012","article-title":"Arctic sea ice variability and trends, 1979\u20132010","volume":"6","author":"Cavalieri","year":"2012","journal-title":"Cryosphere"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"18","DOI":"10.3189\/2015AoG69A909","article-title":"Comparing and contrasting the behavior of Arctic and Antarctic sea ice over the 35 year period 1979\u20132013","volume":"56","author":"Simmonds","year":"2015","journal-title":"Ann. Glaciol."},{"key":"ref_3","unstructured":"Cavalieri, D., Parkinson, C., Gloersen, P., and Zwally, H.J. (1996). Sea Ice Concentrations from Nimbus-7 SMMR and DMSP SSM\/I Passive Microwave Data, National Snow and Ice Data Center."},{"key":"ref_4","unstructured":"Meier, W., Fetterer, F., Savoie, M., Mallory, S., Duerr, R., and Stroeve, J. (2011). NOAA\/NSIDC Climate Data Record of Passive Microwave Sea Ice Concentration, National Snow and Ice Data Center."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1029\/JC091iC01p00975","article-title":"Characteristics of arctic winter sea ice from satellite multispectral microwave observations","volume":"91","author":"Comiso","year":"1986","journal-title":"J. Geophys. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5355","DOI":"10.1029\/JD089iD04p05355","article-title":"Determination of sea ice parameters with the NIMBUS 7 SMMR","volume":"89","author":"Cavalieri","year":"1984","journal-title":"J. Geophys. 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Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/6\/442\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:24:24Z","timestamp":1760210664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/6\/442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,24]]},"references-count":15,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2016,6]]}},"alternative-id":["rs8060442"],"URL":"https:\/\/doi.org\/10.3390\/rs8060442","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2016,5,24]]}}}