116
that the analysis output estimate minimizes the cost function (J). Thus the numerical
estimate is smoothly and repeatedly nudged toward the observation. Optimal interpolation (OI) methods minimize cost function based on the inverse error co- variance
matrix. Assimilation is complicated due to the limited number of observations in
time and space and poor synopticity except in special cases such as satellite sea
surface observations or HF radar. For these data-rich cases, analysis may be limited
to known variability hotspots dispensing with analysis of low variability regions to
optimize use of computational resources.
6.2.2 Coastal Ocean Hydrodynamic Models
Coastal users of hydrodynamic models, by and large, require finer-scale detail than
that provided by OCGMs to explicitly model shallow water dynamics along convoluted coasts. Regional coastal ocean circulation models, at the most fundamental
level, seek to resolve variations in sea level, currents, temperature, and salinity
which variables encompass the bulk of physical variability of the coastal ocean.
Such regional-scale models are commonly embedded or nested within an appropriate OGCM which provides the boundary conditions for the smaller, finer scale
model. For a coastal model in an orthogonal framework, one open boundary (e.g.,
for an inner bay) can be specified. Oftentimes three open boundaries are specified
encompassing an ocean domain along a single coastline. For an island or archipelago, the entire area may be within the nested model domain and thus four boundaries are specified. Exchange of mass, thermal energy, salt, and momentum across
these boundaries (including free surface displacements) must be assimilated from
the larger domain model. Enhanced viscosity and diffusivity sponges can be parameterized to a certain distance into and out from the nested model in order to dampen
transfer across the boundaries (Edwards et al. 2015).
Regional hydrodynamic models now abound. Models based on structured grids
such as ROMS in US coastal waters and NEMO in European waters are used extensively in regional implementations for operational coastal ocean modeling.
Nevertheless, in recent years, finite element and finite volume methods that allow the
use of unstructured topology representations, such as triangulation grids, have
gained favor. These methods greatly facilitate construction of dense computational
meshes along convoluted coastlines gradually transitioning to a sparser offshore
mesh thus avoiding the large discretization errors incurred when applying structured
grids. Examples of such models are the Finite Volume Community Ocean Model –
FVCOM (Chen et al. 2003, 2006, 2007), the SELFE model (semi-implicit EulerianLagrangian finite-element model for cross-scale ocean circulation) (Zhang and
Baptista 2008), and the ADvanced CIRCulation Model – ADCIRC (see Xie et al.
2016 and references therein). ADCIRC features a versatile 2-D (nonstratified) version used extensively for inundation modeling (e.g., Xie et al. 2016). A detail of
an unstructured grid developed for ADCIRC implementation in the CariCOOS
region is shown in Fig. 6.1.
6 Numerical Models for Operational Ocean Observing
that the analysis output estimate minimizes the cost function (J). Thus the numerical
estimate is smoothly and repeatedly nudged toward the observation. Optimal interpolation (OI) methods minimize cost function based on the inverse error co- variance
matrix. Assimilation is complicated due to the limited number of observations in
time and space and poor synopticity except in special cases such as satellite sea
surface observations or HF radar. For these data-rich cases, analysis may be limited
to known variability hotspots dispensing with analysis of low variability regions to
optimize use of computational resources.
6.2.2 Coastal Ocean Hydrodynamic Models
Coastal users of hydrodynamic models, by and large, require finer-scale detail than
that provided by OCGMs to explicitly model shallow water dynamics along convoluted coasts. Regional coastal ocean circulation models, at the most fundamental
level, seek to resolve variations in sea level, currents, temperature, and salinity
which variables encompass the bulk of physical variability of the coastal ocean.
Such regional-scale models are commonly embedded or nested within an appropriate OGCM which provides the boundary conditions for the smaller, finer scale
model. For a coastal model in an orthogonal framework, one open boundary (e.g.,
for an inner bay) can be specified. Oftentimes three open boundaries are specified
encompassing an ocean domain along a single coastline. For an island or archipelago, the entire area may be within the nested model domain and thus four boundaries are specified. Exchange of mass, thermal energy, salt, and momentum across
these boundaries (including free surface displacements) must be assimilated from
the larger domain model. Enhanced viscosity and diffusivity sponges can be parameterized to a certain distance into and out from the nested model in order to dampen
transfer across the boundaries (Edwards et al. 2015).
Regional hydrodynamic models now abound. Models based on structured grids
such as ROMS in US coastal waters and NEMO in European waters are used extensively in regional implementations for operational coastal ocean modeling.
Nevertheless, in recent years, finite element and finite volume methods that allow the
use of unstructured topology representations, such as triangulation grids, have
gained favor. These methods greatly facilitate construction of dense computational
meshes along convoluted coastlines gradually transitioning to a sparser offshore
mesh thus avoiding the large discretization errors incurred when applying structured
grids. Examples of such models are the Finite Volume Community Ocean Model –
FVCOM (Chen et al. 2003, 2006, 2007), the SELFE model (semi-implicit EulerianLagrangian finite-element model for cross-scale ocean circulation) (Zhang and
Baptista 2008), and the ADvanced CIRCulation Model – ADCIRC (see Xie et al.
2016 and references therein). ADCIRC features a versatile 2-D (nonstratified) version used extensively for inundation modeling (e.g., Xie et al. 2016). A detail of
an unstructured grid developed for ADCIRC implementation in the CariCOOS
region is shown in Fig. 6.1.
6 Numerical Models for Operational Ocean Observing