Transcript Importance of Photochemical Processes in the Sea

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 Dx in a
homogeneous water column (r = constant)
• The sea level at Sta. B is higher than at
Sta. A by a small distance Dz
• Hydrostatic relationship holds
• Note, Dz/Dx is very small (typically ~ 1:106)
Horizontal Pressure Force
Pressure Gradients
@ Sta A seafloor
ph(A) = r g z
@ Sta B seafloor
ph(B) = r g (z + Dz)
Dp = ph(B) - ph(A) = r g (z + Dz) - r g z
Dp = r g Dz
HPF  Dp/Dx = r g Dz/Dx = r g tanq
or HPF per unit mass = g tanq [m s-2]
Horizontal Pressure Force
Geostrophy
• What balance HPF?
• Coriolis!!!!
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 = 2W sinf u = f u
HPF = g tanq
• Geostrophic relationship:
u = (g/f) tanq
• Know f (= 2W sinf) & tanq, calculate u
f = Coriolis parameter (= 2W sinf)
Estimating tanq
• 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 Dz/Dx (or tanq) & ugeo
• Later, we’ll talk about traditional method
Satellite Altimetry
Satellite Altimetry
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
The Geoid
Groundtracks
• 10 day repeat
orbit
• Alongtrack 1 km
resolution
• Cross-track 300 km
resolution
Validation
• Two sites
– Corsica
– Harvest
• RMS ~ 2.5 cm
Mapped SSH
• SSH is optimally
interpolated
• Cross-shelf SSH
DSSH ~20 cm
over ~500 km
• tanq = Dz/Dx
~ 0.2 / 5x105 or
~ 4 x 10-7
Geostrophic Relationship
• Balance:
Coriolis force = fu
HPF = g tanq
• Geostrophic relationship:
u = (g/f) tanq
• Know f (= 2W sinf) & tanq, calculate u
Calculating Currents
• Know tanq = 4x10-7
• Need f (= 2W sinf)
– f = ~37oN
– f = 2 (7.29x10-5 s-1) sin(37o) = 8.8x10-5 s-1
• u = (g/f) tanq
= (9.8 m s-2 / 8.8x10-5 s-1) (4x10-7)
= 0.045 m/s = 4.5 cm/s !!
Mapped SSH
• u = 4.5 cm/s
• Direction is along
D’s in SSH
• The California
Current
Geostrophy
• Geostrophy describes balance between
horizontal pressure & Coriolis forces
• Geostrophic relationship can be used to
diagnose currents - u = (g/f) tanq
• 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) tanq
• Showed how satellite altimeters can be
used to estimate surface currents
• What if density changes??
Our Simple Case
Here, r, tanq & u are = constant WRT depth
Barotropic Conditions
• A current where u  f(z) is referred to as
a barotropic current
• Holds for r = constant or when isobars &
isopycnals coincide
• Thought to contribute some, but not
much, large scale kinetic energy
Barotropic Conditions
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 = r 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 Conditions
Baroclinic vs. Barotropic
• Barotropic conditions
– Isobar depths are parallel to sea surface
– tanq = constant WRT depth
– By necessity, changes will be small
• Baroclinic conditions
– Isobars & isopycnals can diverge
– Density can vary enabling u = f(z)
Baroclinic vs. Barotropic
Baroclinic vs. Barotropic
Baroclinic Flow
• Density differences drive HPF’s -> u(z)
• Hydrostatics says ph = r g D
• Changes in the mean r above an isobaric
surface will drive changes in D (=Dz)
• Changes in D (over distance Dx) gives
tanq 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 tanq
• Will hold for each depth
• Geostrophic relationship:
u(z) = (g/f) (tanq(z))
Example as a f(z)
rA  rB
Goal:
q1 or Dz1
Example as a f(z)
• Define pref - “level of no motion” = po
• Know p1@A = p1@B
-> rA g hA = rB g hB
• Dz = hB - hA =
= hB - rB hB / rA
= hB ( 1 - rB / rA )
Example as a f(z)
u = (g/f) (Dz/Dx)
= (g/f) hB ( 1 - rB / rA ) / L
If rA > rB
(1 - rB/rA) (& u) > 0
If rA < rB
(1 - rB/rA) (& u) < 0
Density D’s drive u
Example as a f(z)
• Two stations 50 km apart along 45oN
• rA(500/1000 db) = 1028.20 kg m-3
rB(500/1000 db) = 1028.10 kg m-3
• What is Dz, tanq & u at 500 m??
Example as a f(z)
• Dz = hB - hA = hB ( 1 - rB / rA )
• Assume average distance (hA) ~ 500 m
• Dz = (500 m) (1 - 1028.10/1028.20)
= 0.0486 m = 4.86 cm
• tanq = Dz / L = (0.0486 m)/(50x103 m)
= 9.73x10-7
Example as a f(z)
• u(z) = (g/f) (tanq(z))
• f = 2 W sinf = 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 - rB / rA ) / 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
Level of No Motion
• Level of no motion assumption misses
the barotropic part of u(z)
Example of an Eddy in
Southern Ocean
30 km
http://gyre.umeoce.maine.edu/physicalocean/Tomczak/IntExerc/advanced4/index.html
So Ocean Example
So Ocean Example
Remember ph = r g h
Dz = hA - hB
= hB (1 - rA / rB)
Start @ 2500 db & work
upwards in layers
Often specific volume, a, or
its anomaly, d, are used
So Ocean Example
• u(z) = (g/f) tan q(z)
• Adjust level of known motion
Dynamic Height
• Hydrostatics give us ph = r g D
• Given isobars & average r, D represents
the dynamic height
• Let r(0/1000 db) = 1028.30 kg m-3
• D(0/1000 db) = ph / (g r(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
Dynamic Height
• Dynamic height anomaly, DD(0/1500db)
Dynamic Height
Surface Currents from Hydrography
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
Surface Currents from Altimetry
Dynamic Height
• California Cooperative
Fisheries Investigations
(CalCoFI)
• Understand ocean
processes in pelagic
fisheries
• Started in 1947
Dynamic Height
• January 2000 - CalCoFI Cruise 0001
Dynamic Height
• DD(0/500db)
• Shows CA Current
• Recirculation in the
SoCal Bight
Geostrophy
• Barotropic vs. baroclinic flow
• Flow is along lines of constant dynamic
height (light on the right)
• Baroclinic portion can be diagnosed from CTD
surveys
• Quantifies the circulation of upper layers of
the ocean