OGCM Configuration
P. N. Vinayachandran
Centre for Atmospheric and Oceanic Sciences (CAOS)
Indian Institute of Science (IISc)
Bangalore 560 012
vinay@caos.iisc.ernet.in
Summer School on
Dynamics of North Indian Ocean
June-July 2010
OSCAR Currents
Equations of Motion
Spherical Co-ordinate System
r=radius of the earth
=latitude
=longitude
Equations in Spherical Co-ordinates
Modular Ocean Model
Hydrostatic
Thin shell
Boussinesq
Sub-grid scale processes are represented by eddy mixing coefficients
Water column thickness: D = H + 
H(x,y) = Ocean depth; = (x,y,t) is the sea surface deviation from rest (z=0)
Kinematic surface and bottome boundary conditions
At z=
At z=-H
Griffies, 2001, MOM4 guide
Equation for free surface
Ocean surface is affected by three processes:
1. Convergence of vertically integrated momentum
2. Mass entering through the ocean surface
3. Water column dialations due to changes in vertically inegrated density field (steric effects)
Water column thickness: D = H + 
For a Boussinesq ocean: Assume volume sources/sinks only at the surface lead to
balance of volume per unit area within a ocean column
Kinematic surface and bottom boundary conditions
At z=
At z=-H
= volume per unit time per unit horizontal area of freshwater crossing the sea surface
= depth integrated horizontal velocity field
Surface dynamic boundary conditions for momentum and freshwater
Bottom drag
Closed Lateral boundaries : no slip, no normal flow
Open lateral boundaries : sponge
Surface heat and fresh water fluxes
Forcing
Smagorinsky viscosity
Viscosity depends on flow, nonlinear
Viscosity due to unresolved scales are proportional to (deformation rates X 2)
Viscosity:
Deformation rate:
km is the largest resolvable wave number
How do you choose ?
Grid Reynolds No. should be < 2
Let
Then for R < 2
Tracers, Veronis effect, background viscosity
Griffies, S. M.: Fundamentals of Ocean Climate Models, Princeton University Press, Princeton, USA, 518+xxxiv pages, 2004.
J. Kurian, Ph. D. Thesis, 2007, IISc
Vertical Mixing Schemes
PP
KPP
MY
Horizontal Grid Size
Horizontal grid spacing should resolve the Rossby Radius
Rossby radius = cm/f
Equatorail Rossby radius =( cm/)1/2
Eqn. 14.83
m
m
Model Domain
Vertical Grid
Topography
ETOPO5, ETOPO2 & modified
Minimum depth of the ocean is 30m. Cells are deepened
Isolated ocean points are converted to land
Palk strait is closed, Red Sea and Persian Gulf are connected to the Arabian Sea,
widened to allow 2 grid points
River Runoff
Spin-up
Sigma – coordinates
(Princeton Ocean Model)
Mellor, 2002
ROMS
Non-linear stretching of the vertical coordinates depending on local water depth
Haidvogel et al., 2000
Chassignet et al., 2000