A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 361

15.2 The Model

NCOM is described in the literature ( Martin 2000 ; Barron et al. 2006 ). The
description of the model equations given in the appendix is only repeated in order
to exhibit the nonlinear terms in the model equations, as they directly affect the
development of the linearized and adjoint models associated with NCOM. NCOM
is a free surface model based on the primitive equations and employs the hydrostatic,
Boussinesq and incompressible approximations. The model is discretized using
finite differences on an Arakawa C-grid in the spatial dimensions. The equations are
solved in three dimensions for momentum (both zonal and meridional components
of velocity), temperature and salinity, and two dimensions for the free-surface mode:
surface elevation and barotropic velocities.
The leapfrog scheme is used for time stepping in conjunction with an Asselin
filter to avoid time splitting. All terms are treated explicitly in time except for
the solution for the free surface and vertical diffusion. In the solution for the
free surface, the surface pressure gradient terms in the depth-averaged momentum
equations and the divergence terms in the depth-averaged continuity equation are
evenly split between the old and new time levels to minimize the damping of surface
waves. The model equations discretized with finite differences in flux-conservative
form are given in the appendix.
The model domain used for this experiment contains the Monterey Bay, California
region. This location is favorable for ocean modeling due to its strong land/sea breeze
circulation patterns, complex coastline with steep topography, and the existence of
frequent local upwelling and relaxation events ( Shulman et al. 2002 ). The domain
covers latitudes 123:2 ı West with a

horizontal resolution of 2 km and 41 layers in the vertical. The model was initialized
on 01 August, 2003 and ran for one month to 01 September, 2003. The initial condi-
tions were obtained from downscaling the operational

35:6 ı - 37:49 ı 121:38 ı -

North and longitudes

1=8 ı resolution global NCOM
to an intermediate model with horizontal resolution of 6 km, and then via a 3-to-1
nesting ratio to the 2 km model. Horizontal viscosities and diffusivities are computed
using either the grid-cell Reynolds number (Re) or the Smagorinsky schemes, both
of which tend to decrease as resolution is increased. The grid-cell Re scheme sets
the mixing coefficient K to maintain a grid cell Re number below a specified value,

e.g. if Re D u dx K D u dx

decreases
proportionally. A similar computation is performed for the Smagorinsky scheme.
Surface boundary conditions (e.g. wind stress, IR radiation flux, etc.) are
provided by the atmospheric mesoscale model COAMPS ( Hodur 1997 ), which is
run at the same horizontal resolution as the ocean model, with forcings archived
every 12 h at the synoptic times of 0000 and 1200 UTC. Open boundary conditions
use a combination of radiative models and prescribed values provided by the
1=8 ı Global NCOM (GNCOM). Different radiative options are used at the open
boundaries depending on the model state variables: a modified Orlanski radiative
model is used for the tracer fields (temperature and salinity), an advective model for
the zonal velocity (u), a zero gradient condition for the meridional velocity (v) as
well as the barotropic velocities, and the Flather boundary condition for elevation.

=K D 30 ,then =30 . Hence, as dx decreases, K