{"id":815,"date":"2010-09-06T03:01:31","date_gmt":"2010-09-06T07:01:31","guid":{"rendered":"http:\/\/mseas.net16.net\/?p=815"},"modified":"2021-07-30T16:44:10","modified_gmt":"2021-07-30T20:44:10","slug":"multiscale-two-way-embedding-schemes-for-free-surface-primitive-equations-in-the-multidisciplinary-simulation-estimation-and-assimilation-system-2","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=815","title":{"rendered":"Multiscale two-way embedding schemes for free-surface primitive-equations in the Multidisciplinary Simulation, Estimation and Assimilation System"},"content":{"rendered":"We derive conservative time-dependent\r\nstructured discretizations and two-way embedded\r\n(nested) schemes for multiscale ocean dynamics\r\ngoverned by primitive equations (PEs) with a nonlinear\r\nfree surface. Our multiscale goal is to resolve tidalto-\r\nmesoscale processes and interactions over large\r\nmultiresolution telescoping domains with complex\r\ngeometries including shallow seas with strong tides,\r\nsteep shelfbreaks, and deep ocean interactions. We\r\nfirst provide an implicit time-stepping algorithm for\r\nthe nonlinear free-surface PEs and then derive a\r\nconsistent time-dependent spatial discretization with\r\na generalized vertical grid. This leads to a novel timedependent\r\nfinite volume formulation for structured\r\ngrids on spherical or Cartesian coordinates, second\r\norder in time and space, which preserves mass and\r\ntracers in the presence of a time-varying free surface.\r\nWe then introduce the concept of two-way nesting,\r\nimplicit in space and time, which exchanges all of the\r\nupdated fields values across grids, as soon as they become available. A class of such powerful nesting\r\nschemes applicable to telescoping grids of PE models\r\nwith a nonlinear free surface is derived. The schemes\r\nmainly differ in the fine-to-coarse scale transfers and\r\nin the interpolations and numerical filtering, specifically\r\nfor the barotropic velocity and surface pressure\r\ncomponents of the two-way exchanges. Our scheme\r\ncomparisons show that for nesting with free surfaces,\r\nthe most accurate scheme has the strongest implicit\r\ncouplings among grids. We complete a theoretical\r\ntruncation error analysis to confirm and mathematically\r\nexplain findings. Results of our discretizations and\r\ntwo-way nesting are presented in realistic multiscale\r\nsimulations with data assimilation for the middle\r\nAtlantic Bight shelfbreak region off the east coast of\r\nthe USA, the Philippine archipelago, and the Taiwan-Kuroshio region. Multiscale modeling with two-way\r\nnesting enables an easy use of different sub-gridscale\r\nparameterizations in each nested domain. The new\r\ndevelopments drastically enhance the predictive capability\r\nand robustness of our predictions, both qualitatively\r\nand quantitatively. Without them, our multiscale\r\nmultiprocess simulations either were not possible or\r\ndid not match ocean data.","protected":false},"excerpt":{"rendered":"<p>We derive conservative time-dependent structured discretizations and two-way embedded (nested) schemes for multiscale ocean dynamics governed by primitive equations (PEs) with a nonlinear free surface. Our multiscale goal is to resolve tidalto- mesoscale processes and interactions over large multiresolution telescoping domains with complex geometries including shallow seas with strong tides, steep shelfbreaks, and deep ocean [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32,28,5,54],"tags":[],"class_list":["post-815","post","type-post","status-publish","format-standard","hentry","category-numerical-ocean-modeling","category-multiscale-ocean-modeling","category-publications","category-papers-in-refereed-journals-multiscale-ocean-modeling"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/815","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=815"}],"version-history":[{"count":5,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/815\/revisions"}],"predecessor-version":[{"id":2508,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/815\/revisions\/2508"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}