Creation of a Geostrophic Velocity Cross Section Matrix

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Creation of a Geostrophic Velocity Cross Section
Matrix

• A Happy Meal Thesis by
• LT Roland Clark
• 16 March 2005
• Operational Oceanography

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Geostrophic Theory

• Geostrophic balance requires that the coriolis
  force balance the horizontal pressure gradient.
• Assumes
• flow has no acceleration
• horizontal velocities are much larger than
  vertical
• only external force is gravity
• friction is small

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Geostrophic Theory

• The equations can be written
• With further manipulation
• Using Boussinesq approximation
• If homogenous and r and g are constant, the
  horizontal pressure gradient is homogenous

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Geostrophic Theory

• If the ocean is stratified, the horizontal
  pressure gradient has two terms
• One due to slope at z 0
• One due to horizontal r differences
• We can determine geostrophic currents in the
  ocean using S,TP
• The geopotential F is
• The horizontal pressure gradient can be found by
• Finding the slope of the constant pressure
  surface
• Find the change in pressure on a surface of
  constant geopotential

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Geostrophic Theory

• In oceanography, we find the slope of the
  constant-pressure surfaces by
• Find the difference in geopotential b/w 2
  surfaces at stations A and B
• Find the slope of the upper pressure surface
  relative to lower
• Find the geostrophic current at the upper surface
  relative to lower (shear)
• Integrate the shear from some depth where
  currents are known
• Assume a level of no motion
• Use surface currents from satellite altimetry

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Geostrophic Theory

• Recipe for geostrophic velocity
• Find vertical pressure gradient as a function of
  specific volume a a(s,t,p)
• Differentiate wrt dx
• Find the specific volume anomaly
• Find the geopotential anomaly

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Geostrophic Theory

• Now consider the geopotential anomaly b/w 2
  pressure surfaces at station A and B distance L
  apart
• Because the standard geopotential distance is the
  same at A and B, the geostrophic velocity at the
  upper surface is
• Remember warmer, lighter water is to the right
  looking downstream in the northern hemisphere

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Point Sur Cruises 2005

• 80 total CTD casts
• Approx 40 each cruise
• Identical stations
• Sampled approx 96 hours apart

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Point Sur Cruises 2005

• 11 cross-sections
• Zonal
• Meridional
• Geostrophic velocity cross sections (rel. to
  sfc.) for each leg

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2
3
4
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Fun with MATLAB

• DESCRIPTION
• Asks the user for the station numbers of
  CTD stations
• INPUT
• Input min and max CTD station numbers
  upon request
• OUTPUT
• VEL geostrophic velocity RELATIVE to the
  sea surface.
• dim(m,nstations-1)
• REFERENCE S. Pond G.Pickard 2nd Edition
  1986
• Introductory Dynamical Oceanogrpahy
• Pergamon Press Sydney. ISBN
  0-08-028728-X
• Equation 8.9A p73 Pond Pickard
• CALLS monterey.coastline
• CALLER project.m
• CALLEE sw_gpan.m (inputs T,S,P)
• WHICH CALLS sw_svan.m
• WHICH CALLS sw_dens.m
• WHICH CALLS sw_dens0.m
• WHICH CALLS sw_smow.m

files from Phil Morgan available _at_ SEA-MAT
http//woodshole.er.usgs.gov/operations/sea-mat/
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Frustration with MATLAB

• Challenging to combine lines of CTDs of different
  depths
• Had to renumber a few the stations
• Data points were taken UP and DOWN the cast

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1
Cruise One
Cruise Two
ZONAL LEGS
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3
4
5
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Cruise One Line 3Temp Profile
Images\Cruise 2\line5.jpg
California undercurrent?
Station Number
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Cruise One Line 3Salinity Profile
Station Number
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MERIDIONAL LEGS
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Cruise Two
Cruise One
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Santa Cruz County Rivers
http//ca.water.usgs.gov/archive/waterdata/99/sant
acruz.gif
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Cruise One Line 11Temp Profile
Station Number
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Cruise One Line 11Salinity Profile
Station Number
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Aqua 20050210.2055ZTrue Color
http//www.nrlmry.navy.mil/nexsat_pages/nexsat_hom
e.html
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Aqua 20050210.2055ZBluGrnBlu
R/V Point Sur
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From the log book CTD 27 36-57.24
122-38.36 784.0 2007-2041 (UTC) Arrive MLML
_at_ 0120Z on 3 February 2005. (Dropping off very
sick student.)
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Conclusions

• Geostrophic theory works!
• There actually is something to gain from dropping
  6 dozen CTDs in the water.
• Having this type of information in real time
  would be beneficial.

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References

• National Geophysical Data Center.
  NGDC-bathymetry, topography, relief. 10 Mar,
  2005 2005. Internet on-line. Available from
  lthttp//www.ngdc.noaa.gov/mgg/bathymetry/relief.ht
  mlgt. 10 Mar, 2005, 2005.
• Naval Research Lab Monterey. NextSat, NRL/NPOESS
  next-generation weather satellite demonstration
  project. Mar 10, 2005 2005. Internet on-line.
  Available from lthttp//www.nrlmry.navy.mil/nexsat_
  pages/nexsat_home.htmlgt. Mar 10, 2005, 2005.
• Pond, Stephen, George L. Pickard. 1983.
  Introductory dynamical oceanography. 329.
• Stewart, Robert. Introduction to physical
  oceanography. 10 January, 2005 2005. Internet
  on-line. Available from lthttp//oceanworld.tamu.ed
  u/resources/ocng_textbook/contents.htmlgt. 10
  March, 2005, 2005.