114
performed at spatial geographic grid nodes and propagated through the grid at predetermined time steps. Griffies and Treguier (2013) estimate a grid size on the order
of 10
27
nodes for the world ocean at the millimeter scale, and around 10
10
time steps
for a millennial simulation at 1 s resolution. Limitations in computational capacity
thus necessitate constraint of spatial and temporal resolution. For global ocean models, spatial resolution on the horizontal is for historical reasons related to fractions
of degrees of latitude that ranged from very coarse 2° resolution to the now common
1/12° resolution (equivalent to about 9.3 km). Nevertheless, as computational
capacity increases, ultra-high resolution global implementations are now possible
as is the case of NASA JPL’s 1 km resolution sea surface temperature product
(https://ourocean.jpl.nasa.gov/SST/. Accessed August 5 2017). Operational models
are updated at periods of minutes to hours.
6.2 Physical Models for Operational Ocean Observing
6.2.1 Ocean General Circulation Models for Operational
Ocean Observing
Ocean general circulation models (OGCM) constitute digital representations of
ocean hydrodynamics at the global scale making use of the equations of fluid
dynamics. Atmospheric forcing (pressure, wind); buoyancy differentials caused by
solar heating, freezing, and melting; rain and runoff; and, in extreme, tectonic movements impart acceleration to fluid parcels setting up horizontal and vertical currents.
Subsequent displacement and mixing of these water parcels is constrained by equations describing the conservation of mass, momentum, and thermal energy (the socalled primitive equations), by turbulence and by boundary interactions with the
atmosphere, cryosphere, and ocean bottom. Since seawater density is parameterized
to temperature, salinity, and pressure through the equation of state of seawater (IOC
et al. 2010), a mass balance equation for salinity is incorporated. Modeled on a
rotating earth, such representations incorporate planetary vorticity through the
Coriolis parameter. A free surface, referred to as the height (H), is permitted at the
air-sea interface (distinct from bathymetric depth (h) relative to the reference geoid)
which allows modeling of the surface displacements associated to tides, eddies,
waves, wave and wind-driven run-up, tsunamis, and other phenomena. Atmospheric
forcing may be derived from global climatologies but is today more commonly
derived from atmospheric general circulation models with and without assimilation
schemes to incorporate meteorological or satellite wind observations. Various truncation schemes are applied to reduce computational demand such as the hydrostatic
approximation that assumes hydrostatic equilibrium throughout the water column
and the Boussinesq approximation which assumes constant density throughout the
water column to simplify computation of horizontal momentum.
Ocean general circulation models are implemented on three-dimensional (3-D)
spatial geographic computational grids. Models are thus categorized as to how spatial discretization is achieved for nodes upon which solution approximations to
6 Numerical Models for Operational Ocean Observing
performed at spatial geographic grid nodes and propagated through the grid at predetermined time steps. Griffies and Treguier (2013) estimate a grid size on the order
of 10
27
nodes for the world ocean at the millimeter scale, and around 10
10
time steps
for a millennial simulation at 1 s resolution. Limitations in computational capacity
thus necessitate constraint of spatial and temporal resolution. For global ocean models, spatial resolution on the horizontal is for historical reasons related to fractions
of degrees of latitude that ranged from very coarse 2° resolution to the now common
1/12° resolution (equivalent to about 9.3 km). Nevertheless, as computational
capacity increases, ultra-high resolution global implementations are now possible
as is the case of NASA JPL’s 1 km resolution sea surface temperature product
(https://ourocean.jpl.nasa.gov/SST/. Accessed August 5 2017). Operational models
are updated at periods of minutes to hours.
6.2 Physical Models for Operational Ocean Observing
6.2.1 Ocean General Circulation Models for Operational
Ocean Observing
Ocean general circulation models (OGCM) constitute digital representations of
ocean hydrodynamics at the global scale making use of the equations of fluid
dynamics. Atmospheric forcing (pressure, wind); buoyancy differentials caused by
solar heating, freezing, and melting; rain and runoff; and, in extreme, tectonic movements impart acceleration to fluid parcels setting up horizontal and vertical currents.
Subsequent displacement and mixing of these water parcels is constrained by equations describing the conservation of mass, momentum, and thermal energy (the socalled primitive equations), by turbulence and by boundary interactions with the
atmosphere, cryosphere, and ocean bottom. Since seawater density is parameterized
to temperature, salinity, and pressure through the equation of state of seawater (IOC
et al. 2010), a mass balance equation for salinity is incorporated. Modeled on a
rotating earth, such representations incorporate planetary vorticity through the
Coriolis parameter. A free surface, referred to as the height (H), is permitted at the
air-sea interface (distinct from bathymetric depth (h) relative to the reference geoid)
which allows modeling of the surface displacements associated to tides, eddies,
waves, wave and wind-driven run-up, tsunamis, and other phenomena. Atmospheric
forcing may be derived from global climatologies but is today more commonly
derived from atmospheric general circulation models with and without assimilation
schemes to incorporate meteorological or satellite wind observations. Various truncation schemes are applied to reduce computational demand such as the hydrostatic
approximation that assumes hydrostatic equilibrium throughout the water column
and the Boussinesq approximation which assumes constant density throughout the
water column to simplify computation of horizontal momentum.
Ocean general circulation models are implemented on three-dimensional (3-D)
spatial geographic computational grids. Models are thus categorized as to how spatial discretization is achieved for nodes upon which solution approximations to
6 Numerical Models for Operational Ocean Observing