Layered ocean models

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Layered ocean models
N layers in the vertical, primitive equations for
continuity and momentum are intergrated over each
layer to obtain expressions for, thickness and
velocity in each layer. Hydrostatic approximation
is needed, layers of equal density
The n-th layer contains the topography and its
thickness is H- sum of all other layers
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Layered ocean models
Entrainment for layer-thicknesses h(ma) and
h(mi) Omega is the n-th interface global mixing
correction scale factor
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Layered ocean models
Problems thinning of layers, entrain fluid into
the thinning layer from below to thicken it. Such
entrainment has to be balanced by global
detrainment from entraining layer into detraining
layer in order to keep density in layer constant,
difficulties also with thermodynamics
Layered ocean models gt reduced gravity models
Deepest layer is infinitely deep and no motion,
similar equations to that of N-layer models,
except that
No barotropic mode
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Isopycnal ocean models
Similar to layer models, do not prevent
thinning/vanishing of layers and surfacing of
isopycnals, realistics bottom topography and
complex equation of state, are now fully
dynamical/thermodynamical
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Air-sea fluxes and coupling
Ce depends on wind-speed
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Air-sea fluxes and coupling
Net heat flux
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ATMOSPHERIC MODELS
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Performance of atmospheric models
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Model structure
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Governing Equations for AGCMs
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Spectral Galerkin apparoach
m,l are wavebymbers, 2 x m is the number of knots
in zonal and l-m is the number of knots in
meridional direction
Example shallow water eq.
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Numerical Methods in AGCMs

• Spectral transform method Use a spherical
  harmonic basis for horizontal expansion of scalar
  fields

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Spectral Transform Method

• Advantages
• Analytic representation of derivatives improves
  numerical accuracy.
• Semi-implicit time differencing implemented
  easily.
• Absence of pole problem.

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Spectral Transform Method

• Disadvantages
• Representation of topography (smoothness, Gibbs
  ripples).
• Computational overhead at high resolution.
• Less intuitive mapping onto scalable computer
  architecture.

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Spectral Truncation Methods
R Rhomboidal T Triangular B Both
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Spectral Truncation Methods
R Rhomboidal T Triangular B Both
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Spectral Truncation Methods
R Rhomboidal T Triangular B Both
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Spectral Truncation Methods
Typically prognostic equations for vorticity and
the divergence of the velocity potential,
temperature, water vapor and cloud water
vapor mixing ration and log surface pressure are
solved Nonlinear terms and
paramterizations are evaluated on a Gaussian grid
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Equations used in ECHAM3
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Governing Equations for AGCMs