Part A | 3.4
60 Part A Fundamentals
this coarse resolution on modeling extreme waves and
winds. In short, the reanalysis products suffer from poor
resolution of areas of high winds in extratropical storms
and in virtually all parts of tropical storms.
3.4.3 Currents, Surge, and Tides
With the advent of relatively fast and inexpensive computers in the 1970s, numerical models of ocean currents
in shallow water began to proliferate. While the numerical discretization differs, all these models solve
a similar set of differential equations conserving mass
and momentum, which are often referred to as the shallow water equations. Model output includes the time
series of depth-averaged velocity and surface elevation at discrete grid points in the horizontal domain.
This class of model is now routinely used to accurately
simulate astronomical tides and wind-induced currents
and surge in coastal waters where stratification in the
water column is not important, typically in 30 m of
water or less and beyond the influence of substantial
river inflow. Johnsen and Lynch [3.94] provide numerous examples of these so-called two-dimensional (2-D)
models. Several models such as MIKE 21 HD [3.95, 96]
and ADCIRC [3.97] have good user interfaces and can
be successfully applied by users with modest familiarity
with numerical ocean modeling. The accuracy of these
models of course depends on the specifics but assuming
that the bathymetry and the initial and boundary conditions are specified accurately, modeled currents and
surface elevations can achieve a 15% RMS error when
compared to measurements.
A similar story can be told for stratified deeper waters but only for some types of forcing such as winds
and external tides. Some examples are given in [3.94].
An example for hurricane-generated currents is given
by Frolov [3.13], who used a 3-D model to accurately
simulate the ocean response from Katrina and Georges,
both during the initial phase of direct wind forcing and
the subsequent phase of inertial oscillations. It is worth
noting that during the Katrina simulations, a storm
marked by Category 4 winds, Frolov had to cap the surface drag coefficient, as discussed in Sect. 3.2.
Three-dimensional current models can also accurately simulate the longer time and length scales of
quasi-geostrophic currents like the Gulf Stream, provided that they have accurate boundary and initial
conditions, which are typically provided by satellite
altimeters. While these models can achieve less than
20% RMS error on large length scale processes, they
have difficulty simulating processes of approximately
100 km or less [3.98, 99]. That is because these processes often exhibit baroclinic instabilities with small
length and timescales that are undersampled by the
present altimeter array. These limitations can be circumvented to some degree by assimilating fine-scale
measurements from ships, drifters, gliders, etc. [3.99].
A number of models are publicly or commercially
available, but the skill needed to effectively apply these
models is much higher than for the 2-D models, in
large part because the underlying physics of a stratified
ocean (3-D) are far more complex than an unstratified one (2-D). Examples of generally usable 3-D
models include HYCOM [3.100], ROMS [3.101], and
MIKE 3 HD. As in the case of 2-D models, the numerical methods employed by 3-D models differ greatly,
but the better ones are capable of modeling similar realworld situations with equivalent accuracy.
That is the good news. The bad news is that there
are a host of other processes, many of them energetic,
where numerical models yield RMS errors of more than
100%. Published examples are hard to find because
poor matches tend to go unpublished. However, the
authors’ experience suggests models have great difficulty simulating internal (baroclinic) tides and solitons,
turbidity currents, and river outflows. In these cases,
data assimilation is usually impractical because of the
short length and time scales of the characteristic processes. In addition, since these cases are dominated by
small length scales where turbulence and mixing play
an important role, the physics are not well understood.
CFD (Computational Fluid Dynamics) may someday
be a viable tool but not until computer capacity increases substantially.
A number of extensive data sets of ocean currents
have been generated in the last decade and are readily
available over the web. These models assimilate data
from satellite measurements and sometimes buoy and
drifter measurements. Some noteworthy and useful data
sets include:
NOAA’s RTOFS global model [3.102] provides
forecasts up to 7 days. The historical forecasts are not
downloadable at this time, though that may change in
the future (personal communication, Hendrik Tolman,
NCEP, Environmental Modeling Center, 23 Aug 2012).
The model is based on HYCOM and is composed of
curvilinear grid points with variable horizontal sizes
spanning 517 km. It uses 26 hybrid layers/levels in the
vertical.
The HYCOM global model provides forecasts up to
7 days and archives back to 2003, though until 2013 the
archive only saved the modeled fields at midnight. The
model uses a 1=12
ı grid.
NCOM (Navy Coastal Ocean Model) regional models [3.103] provide forecasts up to 4 days. The historical
forecasts are not downloadable at this time, though that
may change in the future. The models use a 1=36
ı
version of the global NCOM model, a version of the
60 Part A Fundamentals
this coarse resolution on modeling extreme waves and
winds. In short, the reanalysis products suffer from poor
resolution of areas of high winds in extratropical storms
and in virtually all parts of tropical storms.
3.4.3 Currents, Surge, and Tides
With the advent of relatively fast and inexpensive computers in the 1970s, numerical models of ocean currents
in shallow water began to proliferate. While the numerical discretization differs, all these models solve
a similar set of differential equations conserving mass
and momentum, which are often referred to as the shallow water equations. Model output includes the time
series of depth-averaged velocity and surface elevation at discrete grid points in the horizontal domain.
This class of model is now routinely used to accurately
simulate astronomical tides and wind-induced currents
and surge in coastal waters where stratification in the
water column is not important, typically in 30 m of
water or less and beyond the influence of substantial
river inflow. Johnsen and Lynch [3.94] provide numerous examples of these so-called two-dimensional (2-D)
models. Several models such as MIKE 21 HD [3.95, 96]
and ADCIRC [3.97] have good user interfaces and can
be successfully applied by users with modest familiarity
with numerical ocean modeling. The accuracy of these
models of course depends on the specifics but assuming
that the bathymetry and the initial and boundary conditions are specified accurately, modeled currents and
surface elevations can achieve a 15% RMS error when
compared to measurements.
A similar story can be told for stratified deeper waters but only for some types of forcing such as winds
and external tides. Some examples are given in [3.94].
An example for hurricane-generated currents is given
by Frolov [3.13], who used a 3-D model to accurately
simulate the ocean response from Katrina and Georges,
both during the initial phase of direct wind forcing and
the subsequent phase of inertial oscillations. It is worth
noting that during the Katrina simulations, a storm
marked by Category 4 winds, Frolov had to cap the surface drag coefficient, as discussed in Sect. 3.2.
Three-dimensional current models can also accurately simulate the longer time and length scales of
quasi-geostrophic currents like the Gulf Stream, provided that they have accurate boundary and initial
conditions, which are typically provided by satellite
altimeters. While these models can achieve less than
20% RMS error on large length scale processes, they
have difficulty simulating processes of approximately
100 km or less [3.98, 99]. That is because these processes often exhibit baroclinic instabilities with small
length and timescales that are undersampled by the
present altimeter array. These limitations can be circumvented to some degree by assimilating fine-scale
measurements from ships, drifters, gliders, etc. [3.99].
A number of models are publicly or commercially
available, but the skill needed to effectively apply these
models is much higher than for the 2-D models, in
large part because the underlying physics of a stratified
ocean (3-D) are far more complex than an unstratified one (2-D). Examples of generally usable 3-D
models include HYCOM [3.100], ROMS [3.101], and
MIKE 3 HD. As in the case of 2-D models, the numerical methods employed by 3-D models differ greatly,
but the better ones are capable of modeling similar realworld situations with equivalent accuracy.
That is the good news. The bad news is that there
are a host of other processes, many of them energetic,
where numerical models yield RMS errors of more than
100%. Published examples are hard to find because
poor matches tend to go unpublished. However, the
authors’ experience suggests models have great difficulty simulating internal (baroclinic) tides and solitons,
turbidity currents, and river outflows. In these cases,
data assimilation is usually impractical because of the
short length and time scales of the characteristic processes. In addition, since these cases are dominated by
small length scales where turbulence and mixing play
an important role, the physics are not well understood.
CFD (Computational Fluid Dynamics) may someday
be a viable tool but not until computer capacity increases substantially.
A number of extensive data sets of ocean currents
have been generated in the last decade and are readily
available over the web. These models assimilate data
from satellite measurements and sometimes buoy and
drifter measurements. Some noteworthy and useful data
sets include:
NOAA’s RTOFS global model [3.102] provides
forecasts up to 7 days. The historical forecasts are not
downloadable at this time, though that may change in
the future (personal communication, Hendrik Tolman,
NCEP, Environmental Modeling Center, 23 Aug 2012).
The model is based on HYCOM and is composed of
curvilinear grid points with variable horizontal sizes
spanning 517 km. It uses 26 hybrid layers/levels in the
vertical.
The HYCOM global model provides forecasts up to
7 days and archives back to 2003, though until 2013 the
archive only saved the modeled fields at midnight. The
model uses a 1=12
ı grid.
NCOM (Navy Coastal Ocean Model) regional models [3.103] provide forecasts up to 4 days. The historical
forecasts are not downloadable at this time, though that
may change in the future. The models use a 1=36
ı
version of the global NCOM model, a version of the