Primitive equation models

1
Primitive equation models
These are the most sophisticated type of ocean
circulation model, including more of the physics
than the analysis systems and shallow water
equation models we have discussed previously.
While their increased complexity makes them
applicable to a broader class of applications,
and should result in more accurate solutions, it
can also be more difficult to diagnose their
behavior and to understand how various model
choices affect the results.
2
Fixed Vertical Coordinates

• POM
• SWAFS
• POP
• NCOM

Lagrangian Vertical Coordinate

• NLOM

Hybrid Vertical Coordinate

• HYCOM

3
POMPrinceton Ocean Model

• The first set of models we will examine are based
  on the Princeton Ocean Model, which was developed
  in the late 1970s by Blumberg and Mellor (of
  Princeton University), with subsequent
  contri-butions by other people. It is a very
  widely used model, both for research and
  operationally.

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POMhttp//www.aos.princeton.edu/WWWPUBLIC/htdocs.
pom/
POM is a sigma coordinate, free surface,
primitive equation ocean model, which includes a
turbulence sub-model. The model has been used for
modeling of estuaries, coastal regions and open
oceans.
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Physics

• It contains an imbedded second moment turbulence
  closure sub-model to provide vertical mixing
  coefficients. The turbulence model does a
  reasonable job simulating mixed layer dynamics,
  although there have been indications that
  calculated mixed layer depths are a bit too
  shallow (Mellor, 1998).
• Complete thermodynamics have been implemented.
  (Mellor, 1998)
• The model has a free surface.

6
Grid and Coordinate System

• It is a ? coordinate model (vertical coordinate
  is scaled on the water column depth). The ?
  coordinate system is probably a necessary
  attribute in dealing with significant
  topographical variability such as that
  encountered in estuaries or over continental
  shelf breaks and slopes. Together with the
  turbulence sub-model, the model produces
  realistic bottom boundary layers. (Mellor, 1998)
• Significant errors in the pressure gradient terms
  can result when sigma coordinate models with
  insufficient horizontal resolution are used with
  very steep topography.
• The horizontal grid uses curvilinear orthogonal
  coordinates and an "Arakawa C" differencing
  scheme. (Mellor, 1998)

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Time Step

• The model has a free surface and a split time
  step. The external mode portion of the model is
  2D and uses a short time step based on the CFL
  condition and the external wave speed. The
  internal mode is three-dimensional and uses a
  long time step based on the CFL condition and the
  internal wave speed. (Mellor, 1998)
• The calculation of the 3D (internal) variables is
  separated into a vertical diffusion time step and
  an advection plus horizontal diffusion time step.
  The former is implicit (to accommodate small
  vertical spacing near the surface and bottom)
  whereas the latter is explicit. (Mellor, 1998)

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Boundary Conditions

• A number of different conditions may be
  implemented along the open boundaries for the
  external mode.
• Sea surface elevation
• Depth-integrated flow
• Radiation conditions
• There are also numerous options for the open
  boundary conditions on the internal mode.
• Radiation conditions
• Advection of T and S
• Specified inflow

9
Forcing

• Wind stress
• Heat flux
• River inflow
• Tides

10
Output

• 3D fields of velocity, T, and S
• SSH

11
References

• http//www.aos.princeton.edu/WWWPUBLIC/htdocs.pom/
  
• Mellor, G.L., Users Guide for a
  Three-Dimensional, Primitive Equation, Numerical
  Ocean Model, Program in Atmospheric and Oceanic
  Sciences, Princeton University, Princeton, NJ,
  1998.

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MODAS/POMMODAS Relocatable POM Model

• Primary contacts Dan Fox (NRLSSC) Martin Booda
  (NAVO) Germana Peggion (USM)
• A relocatable version of the Princeton Ocean
  Model which takes advantage of MODAS for model
  initialization and data assimilation has been
  developed at NRLSSC. This model has been run
  operationally for a number of domains. It is
  likely that in the future, NCOM rather than POM,
  will be used for this purpose.

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MODAS/POM http//www7320.nrlssc.navy.mil/modas/po
m.html

• Provide short-term (2-day) forecast
• User-friendly interface
• Relocatable from deep to shallow, from open sea
  to inlets
• Portability (toward PC)
• Primary clients NAVO and Navy operational units

Courtesy of Germana Peggion
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Domain

• Fine resolution domains may be nested inside
  coarser resolution domains.
• Domains in recent use include Yellow Sea,
  Arabian Gulf, Southeastern US, Strait of
  Gibraltar, Taiwan Strait
• Establishment of new domains requires care in
  picking boundary locations and specifying other
  parameters.
• The number of domains in use is being reduced
  over time with the expectation that a new
  relocatable POM version, and eventually NCOM,
  will be used in the future.

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Spatial Resolution

• User specifies the resolution in MODAS
• Current domains have resolution anywhere from 0.5
  km to over 20 km
• Default configuration has 25 ? levels in the
  vertical
• User may specify up to 100 ? levels, and how they
  are distributed in the water column (as a
  percentage of depth).

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Initialization

• This version of POM can be initialized in
  various ways using the information from the MODAS
  analysis.
• Cold start MODAS T and S grids, but not
  geostrophic currents, are used.
• Diagnostic mode POM is run for 1-2 days, holding
  initial MODAS T and S fields constant so the
  dynamic model develops its own currents
  consistent with the user-supplied density field.
• Warm start MODAS-estimated geostrophic currents
  (default), or currents extracted from a larger
  domain numerical ocean model, are used.
• (Fox et al. 2002a)

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• Presently, all but one POM domains running at
  NAVO use the North Pacific Ocean Nowcast/Forecast
  System for initialization.
• The area around Cadiz, Spain uses the daily MODAS
  analysis for initialization.

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NPACNFS consists of a data assimilative dynamic
ocean model based on POM, with 1/4o horizontal
resolution and 26 sigma levels in the vertical,
the MODAS 3D ocean temperature/salinity analysis,
and a real-time data stream from NRL/NAVO
satellite data fusion center and NOGAPS from
FNMOC.
An example of regional finer resolution POM
models initialized from a coarser resolution
basin scale POM, North Pacific Nowcast/Forecast
follows.
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The North Pacific Ocean Nowcast/Forecast System
(NPACNFS) is an automated real-time ocean
prediction system for the North Pacific Ocean. It
produces daily nowcast/forecast sea level
variation, 3D current, temperature and salinity
for the North Pacific Ocean.
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(No Transcript)
21
From Harding et al.s 2001 GRC poster
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Boundary Conditions

• Radiation-like open boundary condition requiring
  reference velocities.
• Reference velocity values are held constant
  during the forecast.
• MODAS T and S are used to calculate baroclinic
  geostrophic reference velocity.
• Barotropic reference velocity (transport) is
  derived from MODAS or a numerical ocean model.
• Tidal heights (the same solutions from the
  Grenoble tidal model as are used in PCTides and
  ADCIRC) applied at open boundaries every
  baroclinic mode time step
• (Fox et al. 2002a)

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Forcing

• NOGAPS or COAMPSTM winds
• Tidal forcing may be included as a boundary
  condition. Product Info should indicate whether
  or not tidal forcing has been included.

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Location Strait of Gibralter Type Princeton
Ocean Model Description Currents Surface Series
(U) POC NAVO - Princeton Ocean Model
Library Custodian COMM 228-688-5176
DSN 828-5176 or E-mail Us Update
Cycle 24 hour(s) Typical File Size 35(K)
Level-of-Confidence This product is
unvalidated and fully beyond the control of NMOC
to ensure the quality of the underlying data
and/or availability of product. Current
File Statistics i.cadvelpom000_0000.gif
Size 48 (Kbytes) Last Update
19-Jul-1250 CDT (U) ii.cadvelpom024_000
0.gif Size 51 (Kbytes) Last Update
19-Jul-1250 CDT (U) iii.cadvelpom048_000
0.gif Size 56 (Kbytes) Last Update
19-Jul-1250 CDT (U) Additional
Information i.Product reflects geostrophic
influence on model. (U) ii.Product reflects
wind-driven influence on model. (U) iii.Product
reflects tidal influence on model. (U)
iv.Product does NOT reflect Sea Surface Height
influence on model. (U)
Location Taiwan Strait Type Princeton Ocean
Model Description Currents over Temperature
Surface Series (U)  POC NAVO - Princeton Ocean
Model Library Custodian COMM 228-688-5176
DSN 828-5176 or E-mail Us Update
Cycle 24 hour(s) Typical File Size 73(K)
Level-of-Confidence This product is
unvalidated and fully beyond the control of NMOC
to ensure the quality of the underlying data
and/or availability of product. Current
File Statistics i.taivelsstpom024_0000.
gif Size 99 (Kbytes) Last Update
19-Jul-1306 CDT (U) ii.taivelsstpom048_
0000.gif Size 95 (Kbytes) Last Update
19-Jul-1306 CDT (U) Additional
Information i.Product reflects
geostrophic influence on model. (U)
ii.Product reflects wind-driven influence on
model. (U) iii.Product does NOT reflect
tidal influence on model. (U)
25
Data Assimilation

• Data assimilation is through MODAS, so in areas
  where MODAS doesnt use satellite SSH, that wont
  be in relocatable POM either.
• No new data is assimilated during the forecast.

26
Implementation

• Relocatable POM is included in the full MODAS2.1
  version (at NRLSSC) and MODAS-Heavy (at NAVO).
  Presently it is not implemented at any of the
  METOC regional centers.

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Output

• Nowcast, and 24 and 48 hr forecasts
• Velocity, T, MLD, critical depth, deep and
  shallow sound channel axes, depth excess
• Depths for which V and T are shown vary by domain
• Graphical format
• Animations (of the same 3 pictures as in series)
  available for some domains
• No byte-encoded or wavelet compressed SV fields
• Some fields for some domains output for REACTs
  (viewed with ArcExplorer)
• Above is as of 7/19/02

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Example Implementation

• Updates once per day.
• 24 and 48 h forecasts.
• Currents, and currents over temperature, at
  surface and selected subsurface layers are
  displayed.
• Critical depth, shallow sound channel axis, deep
  sound channel axis, depth excess, mixed layer
  depth, sonic layer depth, and sea surface
  temperature are output.
• Products may be output in graphical, ArcView (for
  REACTS), EOF-compacted, NetCDF or other formats

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POM
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(No Transcript)
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Velocity scale arrow is same as in image above
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Taiwan Strait
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Gulf of Cadiz
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POM SST and Sfc. Currents Relative to Satellite
SST
Arabian Gulf Gulf of Oman
Courtesy of John Harding, NRL-SSC
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References
http//www7320.nrlssc.navy.mil/modas/ Fox, D.N.,
C.N. Barron, M.R. Carnes, M. Booda, G. Peggion,
and J. Gurley, The Modular Ocean Data
Assimilation System, Oceanography, 15 (1), 22-28,
2002a.