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Spurious multiple equilibria introduced by convective adjustment
► Convective adjustment leads to additional multiple equilibria in ocean models. ► Multiple equilibria due to convective adjustment represent a numerical artifact. ► Convective adjustment cannot be used to capture convective feedback. The application of bifurcation analysis to ocean climate models i...
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| Published in: | Ocean modelling (Oxford) 2011, Vol.38 (1), p.126-137 |
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| Language: | English |
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| container_title | Ocean modelling (Oxford) |
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| creator | den Toom, Matthijs Dijkstra, Henk A. Wubs, Fred W. |
| description | ► Convective adjustment leads to additional multiple equilibria in ocean models. ► Multiple equilibria due to convective adjustment represent a numerical artifact. ► Convective adjustment cannot be used to capture convective feedback.
The application of bifurcation analysis to ocean climate models is substantially hampered by difficulties associated with the use of convective adjustment, i.e. a parameterisation of convection in which the vertical diffusion of heat and salt is greatly enhanced whenever the water column becomes statically unstable. When tracking steady solutions of these models in parameter space, problems arise due to the occurrence of a multitude of saddle-node bifurcations, each of which is related to a minor reorganisation of convection. In this paper, we analyse the origin of the multiple steady states in detail using a one-dimensional column model. By analytical evaluation of the eigenvalue problem conditions are formulated under which bifurcations may occur. Using numerical continuation methods a regime of multistability is identified and it is shown that the number of coexisting steady states increases with increasing resolution, while the extent of parameter space in which they occur decreases. A comparison of the numerical results to corresponding analytical solutions reveals that the multiple equilibria are inherent to the discretisation and hence artificial. Apparently, successful application of convective adjustment requires knowledge of subgrid-scale tracer fields. Two alternative convective adjustment schemes are proposed that (partially) overcome these problems. Results from a fully implicit model based on the two-dimensional primitive equations indicate that the physically relevant phenomena due to the nonlinear character of large-scale oceanic flow, notably the bifurcations related to the salt advection feedback, are preserved under the alternative formulations. |
| doi_str_mv | 10.1016/j.ocemod.2011.02.009 |
| format | article |
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The application of bifurcation analysis to ocean climate models is substantially hampered by difficulties associated with the use of convective adjustment, i.e. a parameterisation of convection in which the vertical diffusion of heat and salt is greatly enhanced whenever the water column becomes statically unstable. When tracking steady solutions of these models in parameter space, problems arise due to the occurrence of a multitude of saddle-node bifurcations, each of which is related to a minor reorganisation of convection. In this paper, we analyse the origin of the multiple steady states in detail using a one-dimensional column model. By analytical evaluation of the eigenvalue problem conditions are formulated under which bifurcations may occur. Using numerical continuation methods a regime of multistability is identified and it is shown that the number of coexisting steady states increases with increasing resolution, while the extent of parameter space in which they occur decreases. A comparison of the numerical results to corresponding analytical solutions reveals that the multiple equilibria are inherent to the discretisation and hence artificial. Apparently, successful application of convective adjustment requires knowledge of subgrid-scale tracer fields. Two alternative convective adjustment schemes are proposed that (partially) overcome these problems. Results from a fully implicit model based on the two-dimensional primitive equations indicate that the physically relevant phenomena due to the nonlinear character of large-scale oceanic flow, notably the bifurcations related to the salt advection feedback, are preserved under the alternative formulations.</description><identifier>ISSN: 1463-5003</identifier><identifier>EISSN: 1463-5011</identifier><identifier>DOI: 10.1016/j.ocemod.2011.02.009</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Bifurcation analysis ; Bifurcations ; Convection ; Convection modes ; Eigenvalues ; Feedback ; Marine ; Mathematical analysis ; Mathematical models ; Oceans ; Parameterisation ; Steady state</subject><ispartof>Ocean modelling (Oxford), 2011, Vol.38 (1), p.126-137</ispartof><rights>2011 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-af8ebda58459a16e79150d60abfe7695a6822b724044e741b3231b49f8e914443</citedby><cites>FETCH-LOGICAL-c384t-af8ebda58459a16e79150d60abfe7695a6822b724044e741b3231b49f8e914443</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,783,787,4031,27935,27936,27937</link.rule.ids></links><search><creatorcontrib>den Toom, Matthijs</creatorcontrib><creatorcontrib>Dijkstra, Henk A.</creatorcontrib><creatorcontrib>Wubs, Fred W.</creatorcontrib><title>Spurious multiple equilibria introduced by convective adjustment</title><title>Ocean modelling (Oxford)</title><description>► Convective adjustment leads to additional multiple equilibria in ocean models. ► Multiple equilibria due to convective adjustment represent a numerical artifact. ► Convective adjustment cannot be used to capture convective feedback.
The application of bifurcation analysis to ocean climate models is substantially hampered by difficulties associated with the use of convective adjustment, i.e. a parameterisation of convection in which the vertical diffusion of heat and salt is greatly enhanced whenever the water column becomes statically unstable. When tracking steady solutions of these models in parameter space, problems arise due to the occurrence of a multitude of saddle-node bifurcations, each of which is related to a minor reorganisation of convection. In this paper, we analyse the origin of the multiple steady states in detail using a one-dimensional column model. By analytical evaluation of the eigenvalue problem conditions are formulated under which bifurcations may occur. Using numerical continuation methods a regime of multistability is identified and it is shown that the number of coexisting steady states increases with increasing resolution, while the extent of parameter space in which they occur decreases. A comparison of the numerical results to corresponding analytical solutions reveals that the multiple equilibria are inherent to the discretisation and hence artificial. Apparently, successful application of convective adjustment requires knowledge of subgrid-scale tracer fields. Two alternative convective adjustment schemes are proposed that (partially) overcome these problems. Results from a fully implicit model based on the two-dimensional primitive equations indicate that the physically relevant phenomena due to the nonlinear character of large-scale oceanic flow, notably the bifurcations related to the salt advection feedback, are preserved under the alternative formulations.</description><subject>Bifurcation analysis</subject><subject>Bifurcations</subject><subject>Convection</subject><subject>Convection modes</subject><subject>Eigenvalues</subject><subject>Feedback</subject><subject>Marine</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Oceans</subject><subject>Parameterisation</subject><subject>Steady state</subject><issn>1463-5003</issn><issn>1463-5011</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOI7-AxfduWrNq6-NKIMvGHChrkOS3kJK23SStDD_3gwVl67u5XLO4Z4PoVuCM4JJcd9lVsNgm4xiQjJMM4zrM7QhvGBpHk_nfztml-jK-w5jUhKWb9Dj5zQ7Y2efDHMfzNRDAofZ9EY5IxMzBmebWUOTqGOi7biADmaBRDbd7MMAY7hGF63sPdz8zi36fnn-2r2l-4_X993TPtWs4iGVbQWqkXnF81qSAsqa5LgpsFQtlEWdy6KiVJWUY86h5EQxyojidbTVhHPOtuhuzZ2cPczggxiM19D3coT4vqjKgtK8qsuo5KtSO-u9g1ZMzgzSHQXB4sRLdGLlJU68BKYi8oq2h9UGscViwAmvDYyxu3GxtWis-T_gB0kvdc0</recordid><startdate>2011</startdate><enddate>2011</enddate><creator>den Toom, Matthijs</creator><creator>Dijkstra, Henk A.</creator><creator>Wubs, Fred W.</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2011</creationdate><title>Spurious multiple equilibria introduced by convective adjustment</title><author>den Toom, Matthijs ; Dijkstra, Henk A. ; Wubs, Fred W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-af8ebda58459a16e79150d60abfe7695a6822b724044e741b3231b49f8e914443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Bifurcation analysis</topic><topic>Bifurcations</topic><topic>Convection</topic><topic>Convection modes</topic><topic>Eigenvalues</topic><topic>Feedback</topic><topic>Marine</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Oceans</topic><topic>Parameterisation</topic><topic>Steady state</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>den Toom, Matthijs</creatorcontrib><creatorcontrib>Dijkstra, Henk A.</creatorcontrib><creatorcontrib>Wubs, Fred W.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Ocean modelling (Oxford)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>den Toom, Matthijs</au><au>Dijkstra, Henk A.</au><au>Wubs, Fred W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spurious multiple equilibria introduced by convective adjustment</atitle><jtitle>Ocean modelling (Oxford)</jtitle><date>2011</date><risdate>2011</risdate><volume>38</volume><issue>1</issue><spage>126</spage><epage>137</epage><pages>126-137</pages><issn>1463-5003</issn><eissn>1463-5011</eissn><abstract>► Convective adjustment leads to additional multiple equilibria in ocean models. ► Multiple equilibria due to convective adjustment represent a numerical artifact. ► Convective adjustment cannot be used to capture convective feedback.
The application of bifurcation analysis to ocean climate models is substantially hampered by difficulties associated with the use of convective adjustment, i.e. a parameterisation of convection in which the vertical diffusion of heat and salt is greatly enhanced whenever the water column becomes statically unstable. When tracking steady solutions of these models in parameter space, problems arise due to the occurrence of a multitude of saddle-node bifurcations, each of which is related to a minor reorganisation of convection. In this paper, we analyse the origin of the multiple steady states in detail using a one-dimensional column model. By analytical evaluation of the eigenvalue problem conditions are formulated under which bifurcations may occur. Using numerical continuation methods a regime of multistability is identified and it is shown that the number of coexisting steady states increases with increasing resolution, while the extent of parameter space in which they occur decreases. A comparison of the numerical results to corresponding analytical solutions reveals that the multiple equilibria are inherent to the discretisation and hence artificial. Apparently, successful application of convective adjustment requires knowledge of subgrid-scale tracer fields. Two alternative convective adjustment schemes are proposed that (partially) overcome these problems. Results from a fully implicit model based on the two-dimensional primitive equations indicate that the physically relevant phenomena due to the nonlinear character of large-scale oceanic flow, notably the bifurcations related to the salt advection feedback, are preserved under the alternative formulations.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.ocemod.2011.02.009</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Bifurcation analysis Bifurcations Convection Convection modes Eigenvalues Feedback Marine Mathematical analysis Mathematical models Oceans Parameterisation Steady state |
| title | Spurious multiple equilibria introduced by convective adjustment |
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