FOAM
401
The limited area models use the Flow Relaxation Scheme (FRS) (Davies
1983, McDonald 1997) as boundary conditions for all prognostic variables
(including temperature, salinity and horizontal velocity components). This
relaxes the model fields in the inner model towards those in the outer model
over a relaxation zone typically 4-8 gridpoints wide, the strength of the
relaxation increasing as the outer edge of the inner model is approached.
(When FOAM transitions to a free-surface we will transition to Flather
conditions for the external modes.) Most of the limited area models use a
rotated latitude-longitude grid to achieve for given resolution the largest
minimum grid-spacing 'x . This allows a longer time-step to be used. At
present resolutions it has been found that the maximum model timestep 't
is limited by the CFL criterion 2(c u)'t 'x in which is the speed of
fastest internal waves (about 3 m/s),
is the fastest advecting velocity in
the model and the factor of 2 arises from the use of the leapfrog scheme.
c
u
The prognostic equation for horizontal momentum is similar to that in the
Bryan-Cox code except that the advection of momentum uses the Webb
(1995) scheme and a simple quadratic bottom friction with
D
is
used to crudely parametrise tidal mixing. To increase the timestep that can
be used the Coriolis term is calculated semi-implicitly in coarser resolution
configurations, and the pressure gradient is averaged across timesteps in
higher resolution configurations (Brown & Campana 1978). A combination
of harmonic and biharmonic viscosities is used to damp gridscale noise and
westward migrating eddies. The choice of parameters has a significant
impact on the model simulation (Chassignet & Garraffo 2001). The
barotropic flow is represented by a streamfunction using the rigid-lid
approximation (see Storkey 2004 for details).
C
0.00125
The prognostic equation for tracers presently uses a form of third-order
upwind advection similar to Holland et al. (1998). A combination of a less
diffusive advection scheme and the thickness diffusion scheme of Gent &
McWilliams (1990) is being trialled as an alternative. The Griffies et al.
(1998) formulation of isopycnal diffusion is employed.
The formulation of vertical mixing is explained by Gordon et al. (2000)
and Storkey (2004). Momentum and tracers are mixed using the Pacanowski
& Philander (1981) scheme and a simplified form of the Large et al. (1994)
scheme. In addition tracers are mixed using a mixed-layer energetics scheme
based on Kraus & Turner (1967) and Davis et al. (1981). Convective
adjustment of tracers is performed by applying the Roussenov scheme
(Roether et al 1994) followed by the Rahmstorf (1993) scheme.
The thermodynamic component of the sea-ice model uses the zero-layer
model of Semtner (1976) and Hibler’s (1979) formulation for leads
processes. The dynamic component is based on Bryan et al. (1975): the ice
concentration is advected using the top-level ocean currents and smoothed
using Laplacian diffusion. The EVP formulation of Hunke & Dukowicz
.
401
The limited area models use the Flow Relaxation Scheme (FRS) (Davies
1983, McDonald 1997) as boundary conditions for all prognostic variables
(including temperature, salinity and horizontal velocity components). This
relaxes the model fields in the inner model towards those in the outer model
over a relaxation zone typically 4-8 gridpoints wide, the strength of the
relaxation increasing as the outer edge of the inner model is approached.
(When FOAM transitions to a free-surface we will transition to Flather
conditions for the external modes.) Most of the limited area models use a
rotated latitude-longitude grid to achieve for given resolution the largest
minimum grid-spacing 'x . This allows a longer time-step to be used. At
present resolutions it has been found that the maximum model timestep 't
is limited by the CFL criterion 2(c u)'t 'x in which is the speed of
fastest internal waves (about 3 m/s),
is the fastest advecting velocity in
the model and the factor of 2 arises from the use of the leapfrog scheme.
c
u
The prognostic equation for horizontal momentum is similar to that in the
Bryan-Cox code except that the advection of momentum uses the Webb
(1995) scheme and a simple quadratic bottom friction with
D
is
used to crudely parametrise tidal mixing. To increase the timestep that can
be used the Coriolis term is calculated semi-implicitly in coarser resolution
configurations, and the pressure gradient is averaged across timesteps in
higher resolution configurations (Brown & Campana 1978). A combination
of harmonic and biharmonic viscosities is used to damp gridscale noise and
westward migrating eddies. The choice of parameters has a significant
impact on the model simulation (Chassignet & Garraffo 2001). The
barotropic flow is represented by a streamfunction using the rigid-lid
approximation (see Storkey 2004 for details).
C
0.00125
The prognostic equation for tracers presently uses a form of third-order
upwind advection similar to Holland et al. (1998). A combination of a less
diffusive advection scheme and the thickness diffusion scheme of Gent &
McWilliams (1990) is being trialled as an alternative. The Griffies et al.
(1998) formulation of isopycnal diffusion is employed.
The formulation of vertical mixing is explained by Gordon et al. (2000)
and Storkey (2004). Momentum and tracers are mixed using the Pacanowski
& Philander (1981) scheme and a simplified form of the Large et al. (1994)
scheme. In addition tracers are mixed using a mixed-layer energetics scheme
based on Kraus & Turner (1967) and Davis et al. (1981). Convective
adjustment of tracers is performed by applying the Roussenov scheme
(Roether et al 1994) followed by the Rahmstorf (1993) scheme.
The thermodynamic component of the sea-ice model uses the zero-layer
model of Semtner (1976) and Hibler’s (1979) formulation for leads
processes. The dynamic component is based on Bryan et al. (1975): the ice
concentration is advected using the top-level ocean currents and smoothed
using Laplacian diffusion. The EVP formulation of Hunke & Dukowicz
.