On the Approximation of Precision Matrices for Wide-Swath Altimetry
New observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variations have to be weighted against other types of ass...
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MDPI AG
2024-12-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/16/23/4562 |
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| author | Max Yaremchuk Christopher Beattie Gleb Panteleev |
| author_facet | Max Yaremchuk Christopher Beattie Gleb Panteleev |
| author_sort | Max Yaremchuk |
| collection | DOAJ |
| description | New observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variations have to be weighted against other types of assimilated data using information on their precision, as represented by the inverse of the SSH error covariance matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">R</mi></semantics></math></inline-formula>. The latter can be well approximated by a block-circulant (BC) structure and, therefore, allows numerically efficient implementation in operational data assimilation (DA) systems. In this note, we extend the technique of approximating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">R</mi></semantics></math></inline-formula> for wide-swath altimeters by including the uncertainties associated with the state of the atmosphere. It is shown that such an extension keeps the BC approximation error within acceptable (±10%) bounds in a wide range of environmental conditions and could be beneficial for improving the accuracy of SSH retrievals from wide-swath altimeter observations. |
| format | Article |
| id | doaj-art-0dabe7229ad544ca81498360588d234c |
| institution | Kabale University |
| issn | 2072-4292 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj-art-0dabe7229ad544ca81498360588d234c2024-12-13T16:31:16ZengMDPI AGRemote Sensing2072-42922024-12-011623456210.3390/rs16234562On the Approximation of Precision Matrices for Wide-Swath AltimetryMax Yaremchuk0Christopher Beattie1Gleb Panteleev2US Naval Research Laboratory, Stennis Space Center, MS 39522, USADepartment of Mathematics, Virginia Tech, Blacksburg, VA 24061, USAUS Naval Research Laboratory, Stennis Space Center, MS 39522, USANew observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variations have to be weighted against other types of assimilated data using information on their precision, as represented by the inverse of the SSH error covariance matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">R</mi></semantics></math></inline-formula>. The latter can be well approximated by a block-circulant (BC) structure and, therefore, allows numerically efficient implementation in operational data assimilation (DA) systems. In this note, we extend the technique of approximating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">R</mi></semantics></math></inline-formula> for wide-swath altimeters by including the uncertainties associated with the state of the atmosphere. It is shown that such an extension keeps the BC approximation error within acceptable (±10%) bounds in a wide range of environmental conditions and could be beneficial for improving the accuracy of SSH retrievals from wide-swath altimeter observations.https://www.mdpi.com/2072-4292/16/23/4562swath altimetryerror covariancedata assimilation |
| spellingShingle | Max Yaremchuk Christopher Beattie Gleb Panteleev On the Approximation of Precision Matrices for Wide-Swath Altimetry Remote Sensing swath altimetry error covariance data assimilation |
| title | On the Approximation of Precision Matrices for Wide-Swath Altimetry |
| title_full | On the Approximation of Precision Matrices for Wide-Swath Altimetry |
| title_fullStr | On the Approximation of Precision Matrices for Wide-Swath Altimetry |
| title_full_unstemmed | On the Approximation of Precision Matrices for Wide-Swath Altimetry |
| title_short | On the Approximation of Precision Matrices for Wide-Swath Altimetry |
| title_sort | on the approximation of precision matrices for wide swath altimetry |
| topic | swath altimetry error covariance data assimilation |
| url | https://www.mdpi.com/2072-4292/16/23/4562 |
| work_keys_str_mv | AT maxyaremchuk ontheapproximationofprecisionmatricesforwideswathaltimetry AT christopherbeattie ontheapproximationofprecisionmatricesforwideswathaltimetry AT glebpanteleev ontheapproximationofprecisionmatricesforwideswathaltimetry |