{"id":910,"date":"1999-09-06T04:47:41","date_gmt":"1999-09-06T08:47:41","guid":{"rendered":"http:\/\/mseas.net16.net\/?p=910"},"modified":"2021-08-16T21:38:31","modified_gmt":"2021-08-17T01:38:31","slug":"data-assimilation-via-error-subspace-statistical-estimation","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=910","title":{"rendered":"Data assimilation via Error Subspace Statistical Estimation. Part I: Theory and schemes"},"content":{"rendered":"A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean-atmosphere\r\nmodels. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After\r\nstating the present goals and describing some of the existing schemes, the constraints and issues particular to\r\nocean-atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the\r\ngoals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and\r\nmodels. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales\r\nand processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is\r\ndefined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and\r\nenergetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is\r\ncharacterized by error singular vectors and values, or in other words, the error principal components and\r\ncoefficients.\r\nSchemes for filtering and smoothing via ESSE are derived. The data-forecast melding minimizes variance in\r\nthe error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is\r\nbased on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures\r\nare made. The theoretical and practical advantages of ESSE are discussed. The concepts introduced by the\r\nsubspace approach are as useful as the practical benefits. The formalism forms a theoretical basis for the\r\nintercomparison of reduced dimension assimilation methods and for the validation of specific assumptions for\r\ntailored applications. The subspace approach is useful for a wide range of purposes, including nonlinear field\r\nand error forecasting, predictability and stability studies, objective analyses, data-driven simulations, model\r\nimprovements, adaptive sampling, and parameter estimation.","protected":false},"excerpt":{"rendered":"<p>A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean-atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean-atmosphere data assimilation are emphasized. An [&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-910","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\/910","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=910"}],"version-history":[{"count":5,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/910\/revisions"}],"predecessor-version":[{"id":5740,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/910\/revisions\/5740"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}