{"id":917,"date":"2000-09-06T04:54:48","date_gmt":"2000-09-06T08:54:48","guid":{"rendered":"http:\/\/mseas.net16.net\/?p=917"},"modified":"2021-08-16T21:32:21","modified_gmt":"2021-08-17T01:32:21","slug":"on-the-mapping-of-multivariate-geophysical-fields-error-and-variability-subspace-estimates","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=917","title":{"rendered":"On the mapping of multivariate geophysical fields: error and variability subspace estimates"},"content":{"rendered":"A basis is outlined for the first-guess spatial mapping of three-dimensional multivariate and multiscale\r\ngeophysical fields and their dominant errors. The a priori error statistics are characterized by covariance matrices\r\nand the mapping obtained by solving a minimum-error-variance estimation problem. The size of the problem is\r\nreduced efficiently by focusing on the error subspace, here the dominant eigendecomposition of the a priori error\r\ncovariance. The first estimate of this a priori error subspace is constructed in two parts. For the &#8220;observed&#8221; portions\r\nof the subspace, the covariance of the a priori missing variability is directly specified and eigendecomposed.\r\nFor the &#8220;non-observed&#8221; portions, an ensemble of adjustment dynamical integrations is utilized, building the nonobserved\r\ncovariances in statistical accord with the observed ones. This error subspace construction is exemplified\r\nand studied in a Middle Atlantic Bight simulation and in the eastern Mediterranean. Its use allows an accurate,\r\nglobal, multiscale and multivariate, three-dimensional analysis of primitive-equation fields and their errors, in real\r\ntime. The a posteriori error covariance is computed and indicates complex data-variability influences. The error\r\nand variability subspaces obtained can also confirm or reveal the features of dominant variability, such as the\r\nIerapetra Eddy in the Levantine basin.","protected":false},"excerpt":{"rendered":"<p>A basis is outlined for the first-guess spatial mapping of three-dimensional multivariate and multiscale geophysical fields and their dominant errors. The a priori error statistics are characterized by covariance matrices and the mapping obtained by solving a minimum-error-variance estimation problem. The size of the problem is reduced efficiently by focusing on the error subspace, here [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,182,33,34,5,62,64],"tags":[],"class_list":["post-917","post","type-post","status-publish","format-standard","hentry","category-uncertainty-quantification-and-reduced-order-modeling","category-learning-and-data-assimilation","category-uncertainty-quantification-and-predictions","category-data-assimilation","category-publications","category-papers-in-refereed-journals-data-assimilation","category-papers-in-refereed-journals-uncertainty-quantification-and-predictions"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=917"}],"version-history":[{"count":4,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/917\/revisions"}],"predecessor-version":[{"id":5736,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/917\/revisions\/5736"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}