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Hans Burchard Leibniz Institute for Baltic Sea Research Warnemünde

How to make a three-dimensional numerical model that works for lakes and estuaries? . Hans Burchard Leibniz Institute for Baltic Sea Research Warnemünde hans.burchard@io-warnemuende.de. Essential problem in ocean models :.

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Hans Burchard Leibniz Institute for Baltic Sea Research Warnemünde

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  1. How to make a three-dimensional numerical model that works for lakes and estuaries? Hans Burchard Leibniz Institute for Baltic Sea Research Warnemünde hans.burchard@io-warnemuende.de

  2. Essential problem in oceanmodels: Tomove a continuouspropertythrough a fixedgridwithoutchangingits form. Example: solid bodyrotation: Resultof a high-order linear scheme: newartificialmaximaandminima.

  3. Twostrategiesforsolutions: Non-linear limiterschemes. Vertically adaptive coordinates. + a numericalmixinganalysistoquantifythenumericalmixing.

  4. Principleof non-linear schemes: combinetheadvantages oftwo linear schemes in a non-linear way. Usemonotonicityfromthediffusive first-order upstreamand the 2nd orderofaccuracyfromthe non-diffusive Lax-Wendroffscheme.

  5. Whatismixing ? Salinityequation (no horizontal mixing): Salinityvarianceequation: ? Mixing isdissipationoftracervariance.

  6. Principleofnumericalmixingdiagnostics: First-order upstream (FOU) fors: 1D advectionequationforS: 1D advectionequationfors2: FOU forsisequivalenttoFOU fors²withvariancedecay: numericaldiffusivity Salinitygradientsquared See Maqueda Morales and Holloway (2006)

  7. Transport pathways in the Baltic Sea Reissmann et al. (2009)

  8. Sigma coordinateproblem Inflows Pressuregradientproblemofsigmacoordinates

  9. Geopotential coordinateproblem Inflows Inflowapproximationproblemof geopotential coordinates Additionally, bothcoordinatetypessharetheproblemofnumericalmixing.

  10. Adaptive vertical grids in GETM Horizontal direction z hor. filteringof layer heights Vertical zooming of layer interfaces towards: a) Stratification b) Shear c) surface/ bottom hor. filteringof vertical position Lagrangiantendency Vertical direction isopycnaltendency Solution of a verticaldiffusionequation forthecoordinateposition bottom Burchard & Beckers (2004); Hofmeister, Burchard & Beckers (2010)

  11. www.getm.eu

  12. The philosophybehind GETM GETM is a coastalandshelfsea (andlake?) hydrodynamic model. GETM is a Public Domain Community Model. GETM isreleasedunderthe Gnu Public Licence. GETM is Open Source. GETM has a modular structure (open forextentions). GETM has an international developerandusercommunity. GETM started in 1997 andhasbeensteadilydevelopedsincethen.

  13. The physics & numericsofthe GETM core • GETM • isbased on the 3D shallowwaterequations • hasbeenextendedtorepresent non-hydrostaticpressure • isusingGOTMasturbulenceclosure model • isusingbulkformulaetocalculatesurfacefluxes • is a finite volume (i.e., conservative) model • usesCartesian, sphericalorcurvilinear horizontal coordinates • usesgeneralverticalcoordinates (including adaptive) • useshigh-resolution TVD advectionschemes • isbased on explicit modesplitting • isfullyparalellisedusing MPI anddomaindecomposition • workswithnetCDFinputandoutput

  14. Baltic slice with adaptive verticalcoordinates Fixed coordinates Adaptive coordinates Numericalmixing Physicalmixing Numericalmixing Physicalmixing Hofmeister, Burchard & Beckers (2010)

  15. Adaptive verticalcoordinates alongtransect in 600 m Western Baltic Sea model Gräwe et al. (in prep.)

  16. Adaptive coordinates in Bornholm Sea

  17. 1 nm Baltic Sea model with adaptive coordinates - refinement partially towards isopycnal coordinates - reduced numerical mixing - reduced pressure gradient errors - still allowing flow along the bottom Observations November 2003 salinity Feistel et al., 2004 temperature km Hofmeister, Beckers & Burchard (2011)

  18. Channelled gravity current in Bornholm Channel sigma-coordinates - stronger stratification with adaptive coordinates- larger core of g.c. - salinity transport increased by 25% - interface jet along the coordinates adaptive coordinates Hofmeister, Beckers & Burchard (2011)

  19. Gotland Sea time series • 3d baroclinic simulation • 50 adaptive layers vs. 50 sigma layers num. : turb. mixing 80% : 20% num. : turb. mixing 50% : 50% Hofmeister, Beckers & Burchard (2011)

  20. Multi-scale applications Structured models Unstructured models Gräwe et al. (in prep.) de Bauwere et al. (2009)

  21. Does this model also work for lakes? Yes, but you have to resolve the slopes which are generally steeper in lakes than in the shelf sea. Example: seiches in Lake Alpnach:

  22. Study ofboundarymixing (Lake Alpnach, Switzerland) Becherer & Umlauf (2011)

  23. Simulation Lake Alpnacher(Switzerland) Becherer & Umlauf (2011)

  24. Take home: Itis a demandingnumericaltasktoobtainefficientandaccurate discretisationsfortheadvectionterms. Massconservationcanbeobtainedby finite-volume schemes, but varianceconservationwouldonlywork in Lagrangean (particletracking) models. Vertically adaptive coordinatesareoneefficientmethodtoreduce numericalvariancedecay due toadvectionschemes. Question: Whatisthe 3D type ofmodelforthefuture? Will in 20 years still structuredandunstructuredmodelsco-exist, or will oneortheotheror a thirdmethodrule out theothers?

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