P. N. Vinayachandran Centre for Atmospheric and Oceanic Sciences (CAOS) Indian Institute of Science (IISc) Bangalore Summer School on Dynamics of North Indian Ocean June-July 2010 OGCM Configuration

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

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 +

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

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 ) 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.

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

Vertical Mixing Schemes PP KPP MY

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

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