Tide Models
The Navy sometimes uses the term “tide models” to
designate those numerical ocean models being run
primarily for the purpose of predicting tidal heights
and/or currents. At this time, the tide models used by
the Navy are run in a 2D mode (no variation in the
vertical dimension). By definition these models must
include tidal forcing, but they may also include other
types of forcing, just as other ocean circulation models
used by the Navy may include tidal forcing.
GFMPL TP
• The GFMPL Tide Prediction program is not
an ocean model in the sense of the other
models discussed in this course.
• TP can predict hourly tidal heights at a fixed
number of reference stations by using tidal
constants (amplitude and phase) previously
calculated from measurements made at
those locations.
• Additionally, it can predict tidal heights at a
set of secondary stations, by applying
known corrections to the reference stations.
• Tidal heights may only be forecast at
locations for which historical tidal data are
available (i.e., tide stations provided by
the data base).
• This method does not account for sea level
variations due to changes in atmospheric
pressure, nor those due to wind forcing.
• Tidal currents are not predicted.
ADCIRC
Advanced Circulation model
Primary contacts: Cheryl Ann Blain (NRL-SSC),
Steve Haeger (NAVO)
ADCIRC was developed in the late 1980’s to early
1990’s by Rick Luettich (Univ. of N. Carolina) and
Joannes Westerink (Univ. of Notre Dame) in conjunction
with the Coastal Engineering Research Center (now
called the Engineering Research and Development
Center) of the Army Corps of Engineers. It is currently
used in a 2D mode by NAVO for tidal and surge current
and height predictions in littoral areas, although in the
future, tidal currents may only be shown for those areas
where the currents are dominated by tides. A 3D version,
though still barotropic, is available and a baroclinic
version is under development.
ADCIRC
http://www.marine.unc.edu/C_CATS/adcirc/
http://www.nd.edu/~adcirc/
ADCIRC is a finite element, free surface
barotropic ocean circulation model. NAVO
runs the 2D version with tidal and wind
forcing, for the primary purpose of predicting
sea level height. While sea level is not
strongly influenced by density structure,
currents may be, so tidal current forecasts are
likely to be best where the water is well-mixed
top to bottom.
Physics
•Shallow water equations, including nonlinear terms
The equations have been formulated using
the traditional hydrostatic pressure and
Boussinesq approximations. A quadratic
form of bottom friction is used. Although the
drag coefficient may vary in space, it is
generally specified as constant.
Domain
• Due to the complications in designing and
implementing an efficient and accurate grid, NAVO
runs ADCIRC only in a limited number of domains.
It is technically feasible, but personnel-intensive.
• NRL and others are working to implement an
automated grid generation program so that ADCIRC
can be rapidly relocated to new geographic areas. It
is presently being used in a research, although not an
operational, setting.
• NAVO is currently running ADCIRC for three
geographic regions: the Yellow Sea and Sea of Japan;
the Arabian Gulf and Gulf of Oman; and the western
North Atlantic Ocean including the Caribbean, Gulf
of Mexico and US Eastern Seaboard.
Operational ADCIRC Domains
Grid and Coordinate System
• ADCIRC uses a finite element grid in the
horizontal.
• ADCIRC may be run in either Cartesian or
spherical coordinates. NAVO uses spherical
coordinates.
• Since it is 2D, there is no vertical
coordinate. The velocities are a depthaverage.
Spatial and Temporal Resolution
• One of the advantages of a finite element
grid, is that the spatial resolution is
continuously variable over the domain.
Generally it varies from a few 10’s of meters
to several kilometers.
• The model as implemented at NAVO uses a
time step of 30 seconds.
Yellow Sea and Sea of Japan
THE ADVANTAGES OF FINITE ELEMENTS
South
Korea
Mississippi River Delta
Realistic coastline morphology
Large
domains
with
remote
boundaries
Western
North
Atlantic
Fine-scale
resolution of
inter-tidal
zones
Courtesy of Cheryl Ann Blain
Boundary Conditions
• Open boundaries are in water depths > 1000 m.
• Tidal elevations from the Grenoble tide model (Le
Provost et al. 1994) are applied on the open
boundaries.
• While it is an option in ADCIRC, wetting and drying
along land-sea boundaries is not included in the NAVO
implementation.
• The condition at the land-sea boundary is no normal
flow.
Tidal constituents
Constituent
symbol
M2
S2
N2
K2
2N2
K1
O1
Q1
Name
principal
lunar
principal
solar
elliptical
lunar
luni-solar
2nd order
elliptical
lunar
luni-solar
principal
lunar
elliptical
lunar
Period
Equilibrium tide
(hrs)
amp (m)
12.420601 0.242334
12.000000 0.112841
12.658348 0.046398
11.967235 0.030704
12.905374 0.006131
23.934470 0.141565
25.819342 0.100514
26.868357 0.019256
Forcing
• In addition to the tidal elevations applied on
the open boundaries, astronomical tide
generating forces are applied over the whole
domain.
• Atmospheric pressure and wind stress
forcing from either NOGAPS (the western
North Atlantic Ocean), COAMPSTM (the
Yellow Sea and Sea of Japan) or a
combination of the two (Arabian Gulf and
Gulf of Oman) is used.
Initialization
• The model is started from rest.
• The density is constant and uniform.
• NAVO generally uses a spin-up time of 3
days before results are used.
• A longer spin-up time is desirable. In the
future, this might be accomplished by
changes in the implementation, and/or taking
advantage of a warm start capability after a
long initial spin-up.
Data Assimilation
• No data is assimilated into this model.
Implementation
• Can be executed on all super-computer and
workstation platforms.
• Computationally efficient.
Output
• Tidal heights and currents are output at 30min intervals for a 48-hr forecast.
• The numerical output is post-processed to
produce a graphical format. The graphics
generally do not show the whole domain,
but rather are focused on predetermined
areas of the grid. This may affect how the
results are interpreted.
Following example is from Shatt Al Arab.
NAVO Product Information
• Spatial resolution: variable
• Forcing: 27 km COAMPS_SW_ASIA winds
and atmospheric pressure ; and tidal forcing
• Output available through MVL: sea level
relative to MSL (mean sea level); depthaveraged current speed and direction
• Temporal resolution and forecast duration:
30 min. out to 48 h
• Product update cycle: 12 h
Arabian Gulf
Yellow Sea
References
Blain, C.A., R.H. Preller, and A.P. Rivera, Tidal
prediction using the Advanced Circulation
Model (ADCIRC) and a relocatable PC-based
system, Oceanography, 15 (1), 77-87, 2002.
Luettich, R., and J. Westerink, Users Manual:
ADCIRC, A (Parallel) Advanced Circulation
Model for Oceanic, Coastal and Estuarine
Waters,
http://www.marine.unc.edu/C_CATS/adcirc/,
2000.
PCTides
Primary contacts: Ruth Preller, NRL-SSC
• Over the past 3 years, NRL has developed a
globally relocatable tide/surge prediction
capability, designed for use on or near
continental shelves.
• “The capability is utilized for locations
where neither observations nor a regularly
run operational tide prediction model, such
as ADCIRC, exists.” (Blain et al. 2002).
PCTides
http://www7320.nrlssc.navy.mil/pctides/
• “PCTides is the NRL’s globally relocatable
tide/surge forecast system used for the rapid
prediction of tidal amplitude and phase, as
well as barotropic ocean currents.”
• There are 2D and 3D versions, both based on
the shallow water equations. Normally the
2D version is used.
• “All databases, except for the wind forcing,
are internal to the PCTides system.”
(All quotations in this section are taken from the web site listed
above, unless otherwise noted.)
Physics
• PCTides includes 2 tide/surge models: the Global
Environmental Modeling Services (GEMS) Coastal
Ocean Model (GCOM2D and GCOM3D).
• GCOM2D is a depth-integrated, barotropic
hydrodynamic model. It solves for SSH and mean
current structure (i.e. no vertical variation).
• GCOM3D allows for vertical variations in the
currents. It can be run in either barotropic mode
(no thermal or density variation), or baroclinic
mode (solves for temperature and salinity). The
baroclinic mode is not generally available, and will
not be discussed here.
• A wetting and drying algorithm for simulation of
coastal flooding is included.
Domain
• Selected by the user, using a rubberbanding method through the GUI or by
entering latitude/longitude limits.
• Domains may be nested within one
another to achieve higher spatial
resolution in the inner domain.
Grid and Coordinate System
• The version most commonly used by Navy
METOC is 2D, so has no vertical
coordinate.
• The 3D version uses a z-coordinate system
in the vertical.
• A Cartesian grid is used in the horizontal
plane, with C type finite differencing.
• Grid arrays are constructed such that there
are no more than 40,000 grid points (e.g.
200 x 200). This keeps simulations fast,
while still allowing for large enough regions
with fine enough resolution.
Spatial Resolution
• Selected by the user through the GUI
• Generally from 1 to 10 km
• Bathymetry and open boundary conditions
are automatically interpolated to the domain
and grid selected by the user.
Temporal resolution
• To optimize efficiency, different time steps
are used to solve different aspects of the
equations.
• The continuity equation and gravity wave
and Coriolis terms use the shortest time step.
• The nonlinear advection terms use an
intermediate time step.
• The surface and bottom stress terms are
solved using the longest time step.
Bathymetry
• 2' global bathymetry developed by NRL
from the following bathymetry data bases
Database
Spatial resolution
ETOPO5
5'
DBDBV
DAMEE (North Atlantic)
5' / 2' / 1' / 0.5 '
2.5 '
Gulf of Mexico
CHOI (Yellow Sea)
GTOPO2 (Sandwell)
IBCAO (Arctic)
0.01°
1.0 '
~2.0 '
2.5 km
• This bathymetry provides an improved
coastline and improved matching of
bathymetry data near the coastline.
Boundary Conditions
• Included in PCTides are the Finite Element
Solutions 95.1/2.1 (Shum et al. 1997) from
the Grenoble global tide model (the same as
those used for ADCIRC). These are used to
provide sea surface displacements at the
open boundaries of the ocean model.
• The same 8 tidal constituents as used for
ADCIRC are used for PCTides.
• Atmospheric
barometric
displacement
(change in sea level due to atmospheric
pressure) is also specified at the open
boundaries.
User must make sure there is global tidal data along
all the open boundaries of the chosen domain.
Grenoble Model M2 Tide:
Amplitude and Phase
White areas indicate where there are no tidal
solutions from global tidal model
Forcing
• The model may be driven by astronomical
tidal forcing (through the open boundaries)
and / or surface winds and pressures.
• Winds and pressures may be entered
manually (in which case they are uniform
over the domain), or obtained from
NOGAPS, COAMPSTM, or DAMPS through
MetCast.
Initialization
• All velocities are set to zero initially.
• The initial elevation field is obtained by
interpolating the FES 95.1/2.1 elevation field to the
model grid.
• It is customary to allow about 12 hrs for spin-up of
the model. This allows spurious waves and
boundary forcing to propagate out of the
computational domain.
• The program is set up to automatically start the
simulation 12 hrs before the user-chosen start time
(or the start of the wind file if one is being used).
• With wind forcing, a longer spin-up time (~ 24 hrs)
is used.
Data Assimilation
• Sea level variations from measurements
made at the ~4500 International
Hydrographic Office tidal stations are
included in a PCTides database, and are
used to constrain the solutions by using
a weighted nudging approach described
in Hubbert et al. 2001 (Blain et al.
2002).
Implementation
• Can be run on PCs and UNIX systems.
• “The average PCTides 48 hour forecast
takes anywhere from 3 to 10 minutes of run
time on a 500 MHz PC.” (Blain et al. 2002)
The PCTides System
NRL combined
Bathymetry
Winds/pressures from
NOGAPS, COAMPS,
DAMPS
IHO Coastal Tide
Station Data
Boundary Conditions
FES95.1/.2
2-D Ocean Model
(Barotropic)
Tidal Heights and
Barotropic Ocean Currents
Output
• Results may be output in graphical or text format.
• Time series, with a time step typically of 10-12
min, of sea level and currents are output at userspecified station locations.
• Spatial fields of velocity and sea level are output
at a user-specified time interval (the minimum
interval is 30 min).
• The length of the forecast is determined by the
user, or the length of the wind forecast if one is
being used.
• The sea level deviations output must be added to a
specified reference level (such as mean sea level)
to get actual water depths.
Adapted from Harding et al.’s 2001 GRC poster
Reliability
• Both ADCIRC and PCTides generally
produce sea level predictions that are within
10 cm and 30 minutes of observed values.
• There are some areas of the world, such as
off the U.S. West Coast, where results may
be worse than quoted above due to reduced
accuracy of the boundary conditions from
the global tidal model.
• The following images are from the PCTides
OPTEST.
Chesapeake Bay Region
4.4 km resolution
Chesapeake Station
depth: 8 m
PCTides Evaluation in the Yellow Sea
PCTides currents
were evaluated
against observed
currents from
4 bottom-mounted
current profilers from
Sept. 1-30,1995
Current data were not
assimilated into the
model.
Courtesy of Ruth Preller
PCTides versus measured
currents Sept. 25-30, 1995
Courtesy of Ruth Preller
References
Blaine, C.A., R.H. Preller, and A.P. Rivera, Tidal prediction
using the Advanced Circulation Model (ADCIRC) and a
relocatable PC-based system, Oceanography, 15 (1), 77-87,
2002.
Hubbert, G.D., R.H. Preller, P.G. Posey, and S.N. Carroll,
Software design description for the globally relocateable
Navy time/atmosphere modeling system (PCTides), pp. 97,
Naval Research Laboratory, Stennis Space Center, MS, 2001.
Preller, R.H., P.G. Posey, G.D. Hubbert, S.N. Carroll, and L.
Orsi, User's manual for the globally relocatable Navy
tide/atmosphere modeling system (PCTides), pp. 68, Naval
Research Laboratory, Stennis Space Center, MS, 2001.
Preller, R, P. Posey, G. Dawson, K. Miles, M. Escarra, J.
Ganong (2002) http://www7320.nrlssc.navy.mil/pctides/
Exercise
• Get tidal height prediction for the same
location using ADCIRC, PCTides, and
GFMPL. Go to:
http://www.oc.nps.navy.mil/nom/PCTides/