horizontal pressure gradients pressure changes provide the push that drive ocean currents balance...
TRANSCRIPT
Horizontal Pressure Gradients
• Pressure changes provide the push that drive ocean currents
• Balance between pressure & Coriolis forces gives us geostrophic currents
• Need to know how to diagnose pressure force
• Key is the hydrostatic pressure
Horizontal Pressure Gradients
• Two stations separated a distance x in a homogeneous water column ( = constant)
• The sea level at Sta. B is higher than at Sta. A by a small distance z
• Hydrostatic relationship holds
• Note, z/x is very small (typically ~ 1:106)
Pressure Gradients
@ Sta A seafloor ph(A) = g z
@ Sta B seafloor ph(B) = g (z + z)
p = ph(B) - ph(A) = g (z + z) - g z
p = g z
HPF p/x = g z/x = g tan
or HPF per unit mass = g tan[m s-2]
Geostrophy
• Geostrophy describes balance
between horizontal pressure &
Coriolis forces
• Relationship is used to diagnose
currents
• Holds for most large scale motions
in sea
Geostrophic Relationship
• Balance: Coriolis force = 2 sin u = f u HPF = g tan
• Geostrophic relationship:
u = (g/f) tan
• Know f (= 2 sin) & tan, calculate u
f = Coriolis parameter (= 2 sin)
Estimating tan
• Need to slope of sea surface to get at surface currents
• New technology - satellite altimeters - can do this with high accuracy
• Altimeter estimates of sea level can be
used to get at z/x (or tan) & ugeo
• Later, we’ll talk about traditional method
Satellite Altimetry
• Satellite measures distance between it and ocean surface
• Knowing where it is, sea surface height WRT a reference ellipsoid is determined
• SSHelli made up three important parts
SSHelli = SSHcirc + SSHtides + Geoid
• We want SSHcirc
Modeling Tides
• Tides are now well modeled in
deep water SSHtide =
f(time,location,tidal component)
• Diurnal lunar O1 tide
The Geoid
• The geoid is the surface of constant gravitational acceleration
• Varies in ocean by 100’s m due to differences in rock & ocean depth
• Biggest uncertainty in
determining SSHcirc
Mapped SSH
• SSH is optimally interpolated
• Cross-shelf SSH SSH ~20 cm over ~500 km
• tan = z/x
~ 0.2 / 5x105 or
~ 4 x 10-7
Geostrophic Relationship
• Balance: Coriolis force = fu HPF = g tan
• Geostrophic relationship:
u = (g/f) tan
• Know f (= 2 sin) & tan,
calculate u
Calculating Currents
• Know tan = 4x10-7
• Need f (= 2 sin)
– = ~37oN
– f = 2 (7.29x10-5 s-1) sin(37o) = 8.8x10-
5 s-1
• u = (g/f) tan = (9.8 m s-2 / 8.8x10-5 s-1) (4x10-
7) = 0.045 m/s = 4.5 cm/s !!
Geostrophy
• Geostrophy describes balance between
horizontal pressure & Coriolis forces
• Geostrophic relationship can be used
to diagnose currents - u = (g/f) tan
• Showed how satellite altimeters can
be used to estimate surface currents
• Need to do the old-fashion way next
Geostrophy
• Geostrophy describes balance between
horizontal pressure & Coriolis forces
• Geostrophic relationship can be used
to diagnose currents - u = (g/f) tan
• Showed how satellite altimeters can be
used to estimate surface currents
• What if density changes??
Barotropic Conditions
• A current where u f(z) is
referred to as a barotropic current
• Holds for = constant or when
isobars & isopycnals coincide
• Thought to contribute some, but not
much, large scale kinetic energy
Isobars & Isopycnals
• Isobars are surfaces of constant
pressure
• Isopycnals are surfaces of constant
density
• Hydrostatic pressure is the weight (m*g)
of the water above it per unit area
• Isobars have the same mass above them
Isobars & Isopycnals
• Remember the hydrostatic relationship
ph = g D
• If isopycnals & isobars coincide then
D, the dynamic height, will be the same
• If isopycnals & isobars diverge, values
of D will vary (baroclinic conditions)
Baroclinic vs. Barotropic
• Barotropic conditions
– Isobar depths are parallel to sea surface
– tan = constant WRT depth
– By necessity, changes will be small
• Baroclinic conditions
– Isobars & isopycnals can diverge
– Density can vary enabling u = f(z)
Baroclinic Flow• Density differences drive HPF’s -> u(z)
• Hydrostatics says ph = g D
• Changes in the mean above an isobaric surface will drive changes in D (=z)
• Changes in D (over distance x) gives tan to predict currents
• Density can be used to map currents following the Geostrophic Method
Baroclinic Flow
• Flow is along
isopycnal surfaces
not across
• “Light on the
right”
• u(z) decreases with
depth
Geostrophic Relationship
• Balance: Coriolis force = fu HPF = g tan
• Will hold for each depth
• Geostrophic relationship:
u(z) = (g/f) (tan(z))
Example as a f(z)
• Define pref - “level of no motion” =
po
• Know p1@A = p1@B
-> A g hA = B g hB
• z = hB - hA =
= hB - B hB / A
= hB ( 1 - B / A )
Example as a f(z)
u = (g/f) (z/x)
= (g/f) hB ( 1 - B / A ) / L
If A > B (1 - B/A)
(& u) > 0
If A < B (1 - B/A)
(& u) < 0
Density ’s drive u
Example as a f(z)
• Two stations 50 km apart along
45oN
• A(500/1000 db) = 1028.20 kg m-3
B(500/1000 db) = 1028.10
kg m-3
• What is z, tan & u at 500 m??
Example as a f(z)
• z = hB - hA = hB ( 1 - B / A )
• Assume average distance (hA) ~ 500 m
• z = (500 m) (1 - 1028.10/1028.20)
= 0.0486 m = 4.86 cm
• tan = z / L = (0.0486 m)/(50x103 m)
= 9.73x10-7
Example as a f(z)
• u(z) = (g/f) (tan(z))
• f = 2 sin = 2 (7.29x10-5 s-
1) sin(45o) = 1.03x10-4 s-1
• u = (9.8 m s-2/1.03x10-4 s-1)
(9.73x10-7) = 0.093 m s-1
= 9.3 cm s-1
Geostrophy as a f(z)
• u = (g/f) hB ( 1 - B / A ) / L
• This can be repeated for each level
• Assumes level of no motion
• Calculates only the portion of flow perpendicular to density section
• Calculates only baroclinic portion of flow
Example of an Eddy in Southern Ocean
http://gyre.umeoce.maine.edu/physicalocean/Tomczak/IntExerc/advanced4/index.html
30 km
So Ocean Example
Remember ph = g h
z = hA - hB
= hB (1 - A / B)
Start @ 2500 db & work
upwards in layers
Often specific volume, ,
or its anomaly, , are
used
Dynamic Height
• Hydrostatics give us ph = g D
• Given isobars & average , D represents the dynamic height
• Let (0/1000 db) = 1028.30 kg m-3
• D(0/1000 db) = ph / (g (0/1000
db)) = 1000 db (104 Pa/db)/(9.8 m s-2 *
1028.30 kg m-3) = 992.32 dyn meters
Surface Currents from Hydrography
• Only the baroclinic portion of
the current is sampled
• Need a level of no/known motion
• Need many, many observations
• Can get vertical structure of
currents
Surface Currents from Altimetry
• Satellite altimeters can estimate
the slope of the sea surface
• Both barotropic & baroclinic
portions of current are
determined
• Only surface currents are
determined
Dynamic Height
• California Cooperative Fisheries Investigations (CalCoFI)
• Understand ocean processes in pelagic fisheries
• Started in 1947