1. 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 OGCM Configuration

3. OSCAR Currents

4. Equations of Motion

5. Spherical Co-ordinate System r=radius of the earth =latitude =longitude

6. Equations in Spherical Co-ordinates

7. Modular Ocean Model Hydrostatic Thin shell Boussinesq Sub-grid scale processes are represented by eddy mixing coefficients

8. 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=-H At z= Griffies, 2001, MOM4 guide

10. Equation for free surface For a Boussinesq ocean: Assume volume sources/sinks only at the surface lead to balance of volume per unit area within a ocean column 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) Kinematic surface and bottom boundary conditions At z=-H At z= = volume per unit time per unit horizontal area of freshwater crossing the sea surface = depth integrated horizontal velocity field Water column thickness: D = H +

11. Closed Lateral boundaries : no slip, no normal flow Open lateral boundaries : sponge Surface dynamic boundary conditions for momentum and freshwater Bottom drag

12. Surface heat and fresh water fluxes

13. Forcing

14. Smagorinsky viscosity Viscosity depends on flow, nonlinear Viscosity due to unresolved scales are proportional to (deformation rates X △ 2 ) km is the largest resolvable wave number How do you choose ? Deformation rate: Viscosity: Let Then for R < 2 Tracers, Veronis effect, background viscosity Grid Reynolds No. should be < 2 Griffies, S. M.: Fundamentals of Ocean Climate Models, Princeton University Press, Princeton, USA, 518+xxxiv pages, 2004.

15. J. Kurian, Ph. D. Thesis, 2007, IISc

16. Vertical Mixing Schemes PP KPP MY

17. Horizontal Grid Size Rossby radius = c m /f Equatorail Rossby radius =( c m /) 1/2 Eqn. 14.83 m m Horizontal grid spacing should resolve the Rossby Radius

18. Model Domain

19. Vertical Grid

20. 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

21. River Runoff

22. Spin-up

23. Sigma – coordinates (Princeton Ocean Model) Mellor, 2002

24. ROMS Non-linear stretching of the vertical coordinates depending on local water depth Haidvogel et al., 2000

27. Chassignet et al., 2000