paläozeanographische modellierung andré paul email: [email protected] raum: geo 5510, tel.: 218 65450
TRANSCRIPT
Paläozeanographische Modellierung
André Paul
Email: [email protected]
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)
Tomczak and Godfrey (1994), after Sverdrup et al. (1942)
Tomczak and Godfrey (1994)
Speer et al. (2000)
What is a model?
Models are• smaller than reality
(finite number of processes, reduced size of “phase space”)
• simpler than 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)
Basics of numerical models
1. State variables
2. Fundamental equations
3. Parameterization
4. Discretization
5. Numerical solution
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”.
Examples of state variables
• Ocean
– Temperature
– Salinity
– Pressure
– Current velocity
• Atmosphere
– Temperature
– Density
– Humidity
– Cloud water content
– Pressure
– Wind velocity
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 statedensity (air, sea water)
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
• 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)
To find a numerical solution to the fundamental equations on a digital
computer, they must be discretized in space and time.
Discretization
Most common in ocean models:
• “Finite difference” method in time
• “Finite difference” or “finite volume”
method in space
[Figure 3-30 from Ruddiman (2001)]
Discretization in space for a three-dimensional ocean model
• 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).
• In CLISIM ist der Zeitschritt t so gewählt, dass 40 Zeitschritte einem Modelljahr entsprechen.
Numerical solution
• Must be implemented as computer code
(mostly in Fortran)
• Must satisfy stability criteria
Numerical solution
u
xt
“No transport faster than one grid cell per timestep”
Example of stability criterion for many explicit time-stepping schemes: Courant-Friedrich-Levy (CFL) criterion
Puts severe constraint on time step and determines duration of model simulation
Initialization with T and S
Calculation of density field
Calculation of new velocities
Calculation of new T and S fields
Run completed?
End of run
T and S at sea surface(or heat and fresh-
water fluxes)
Wind stress at sea surface
No
Yes
Model output
Flow diagram for an ocean model
Zonally-averaged ocean circulation models
• Based on zonally-averaged primitive
equations
• Solved in zonally-averaged ocean basins
(only latitude and depth are resolved)
Wright and Stocker (1991, 1995)
Zonally-averaged ocean circulation models: geometry
No longitudinal resolution within
basins!
Stocker and Wright (1995)
Zonally-averaged ocean circulation models : example output
Pacific Atlantic
Salinity
Overturning
• 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
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