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Paläozeanographische Modellierung

Paläozeanographische Modellierung. André Paul Email: apaul@marum.de Raum: GEO 5510, Tel.: 218 65450. “The feature, which runs parallel to the contour of zero wind stress curl some 5 - 10 degrees north of it , is called the Subtropical Front .” (Tomczak and Godfrey, 1994).

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Paläozeanographische Modellierung

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  1. Paläozeanographische Modellierung André Paul Email: apaul@marum.de Raum: GEO 5510, Tel.: 218 65450

  2. “The feature, which runs parallel to the contour of zero wind stress curl some 5 - 10 degrees north of it, is called the Subtropical Front.” (Tomczak and Godfrey, 1994)

  3. Tomczak and Godfrey (1994), after Sverdrup et al. (1942)‏

  4. Tomczak and Godfrey (1994)‏

  5. Speer et al. (2000)‏

  6. What is a model? Models are smallerthan reality (finite number of processes, reduced size of “phase space”) simplerthan reality (description of processes is idealized) closed,whereas reality is open (infinite number of external, unpredictable forcing factors is reduced to a few specified factors) (Hans von Storch)‏

  7. Basics of numerical models State variables Fundamental equations Parameterization Discretization Numerical solution

  8. State variables Many variables can be thought of as a “concentration“ or “property per unit volume“. Fluxes then have dimensions of “property per unit time and area”.

  9. Examples of state variables Ocean Temperature Salinity Pressure Current velocity Atmosphere Temperature Density Humidity Cloud water content Pressure Wind velocity

  10. Fundamental equations Conservation of momentum (horizontal) velocity (winds, currents)‏ Conservation of mass (“principle of continuity”)‏ vertical velocity, humidity, salinity Conservation of energy (“first law of thermodynamics”)‏ temperature Equation of state density (air, sea water)‏

  11. Parameterization in climate models Sub-gridscale processes, or processes that cannot be derived from „first principles“, must be parameterized e.g. thundercloud formation, soil moisture transfer in the atmosphere, eddies and convection in the ocean

  12. Beispiele für Parametrisierungen in CLISIM: Ost-West-Druckgradient (als proportional zum Nord-Süd-Druckgradienten angenommen)‏ Wärmezufuhr an der Meeresoberfläche (als proportional zur Abweichung von einer Referenztemperatur oder “restoring temperature” angenommen)‏

  13. Discretization To find a numerical solution to the fundamental equations on a digital computer, they must be discretized in space and time.

  14. Most common in ocean models: “Finite difference” method in time “Finite difference” or “finite volume” method in space

  15. Discretization in space for a three-dimensional ocean model [Figure 3-30 from Ruddiman (2001)]

  16. In CLISIM gibt es verschiedene “versetzte” oder “gestaffelte Gitter” für Temperatur und Salzgehalt (“tracer”  “T-Gitterzellen”) horizontale Geschwindigkeit (an den nördlichen und südlichen Grenzflächen der T-Gitterzellen definiert) und vertikale Geschwindigkeit (am Boden der T-Gitterzellen definiert).

  17. In CLISIM ist der Zeitschritt t so gewählt, dass 40 Zeitschritte einem Modelljahr entsprechen.

  18. Numerical solution Must be implemented as computer code (mostly in Fortran) Must satisfy stability criteria

  19. Numerical solution Example of stability criterion for many explicit time-stepping schemes: Courant-Friedrich-Levy (CFL) criterion “No transport faster than one grid cell per timestep”  Puts severe constraint on time step and determines duration of model simulation

  20. Initialization with T and S Calculation of density field Wind stress at sea surface Calculation of new velocities T and S at sea surface (or heat and fresh- water fluxes) Calculation of new T and S fields Model output No Run completed? Yes End of run Flow diagram for an ocean model

  21. Zonally-averaged ocean circulation models Based on zonally-averaged primitive equations Solved in zonally-averaged ocean basins (only latitude and depth are resolved)‏

  22. Zonally-averaged ocean circulation models: geometry No longitudinal resolution within basins! Wright and Stocker (1991, 1995)‏

  23. Atlantic Pacific Salinity Overturning Zonally-averaged ocean circulation models : example output Stocker and Wright (1995)‏

  24. Stromfunktion der Meridionalzirkulation im Atlantischen Ozean: Massenfluss in der Deckschicht vom Südatantischen Ozean in den Nordatlantischen Ozean wird durch eine Gegenströmung in der Tiefe kompensiert

  25. Vertical-meridional streamfunction:A measure of the meridional overturning circulation • Vertical-meridional streamfunction:A measure of the meridional overturning circulation • Common unit of  is a Sverdrup with 1 Sv = 106 m3 s-1. • Streamlines are lines of constant  values. • Rule: Volume transport between any two streamlines = difference between corresponding streamfunction values, where: volume transport = velocity × cross-sectional area

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