Satellite Oceanography for Ocean Forecasting
29
bottom pressure changes, but density changes, if not compensated over the water
column, can also induce bottom pressure changes. This shows that the dynamic
topography is an integral of density (steric height - baroclinic part), with a contribution from bottom pressure. It is really a measurement representative of the total
water column (although it is directly related to surf ace geostrophic current). This is
why satellite altimetry is so useful for constraining the 3D ocean circulation.
Numerical applications
Influence of latitude on sea level slope and ocean current
The Coriolis parameter fis equal to 20 sin <1> (O is the angular rotation of the
earth, <1> is latitude). This gives f '" 10- 4 s-1 (at 45°N/S) and f '" 10- 5 s-1 (at 5°N/S).
From equation l' (and 2'), a slope of 1 meter over 100 km will give a current of 1
rn/s at 45°N/S. A slope of 10 cm over 100 km only will give the same current speed
at 5°N/S.
Influence of temperature gradient on dynamic topography
If we assume a reference level at 1000 m and no salinity influence, the dynamic
topography change measured by altimetry for a track crossing the Gulf Stream (or
a ring) with a temperature gradient of 10°C over 100 - 200 km and over a depth of
1000 m will be:
TJ = TJs = - f 1000 P' / Po dz => il TJs = il TJ = 1000 ilp / Po = 1000 a il T '" 1.5 m
with a = -11 P ap/aT (thermal expansion coefficient) equal to 1 - 2 10- 4 s-1
Equatorial regions
At the equator, the Coriolis parameter fis equal to zero. This means we can no
longer assume geostrophy or use dynamic topography to infer the oceanic circulation. It stiU reflects, of course, the change in density field (e.g. thermocline depth or
heat content variations). In particular, the sea level variations (TJ) in the equatorial
regions are closely related to the variations of the depth of the thermocline (H) ( TJ
'" -ilp I Po H, where ~p is the density difference between the deep and surface layers). In practice, geostrophy works up to about ± 2 degrees (although the estimation
is more sensitive to noise). A relationship between zonal current and dynamic
topography has been proposed, however, by Picaut et al. (1990) ("equatorial geostrophy"). This relationship is derived as foUows:
fu = - oTJ/ay (geostrophy)
af /ay u + f auldy = -g a 2 TJ/ai
At the equator ~ u = -g a 2 TJ/ai.
This relationship is valid at low frequencies but the estimation is very sensitive to
noise (because ofthe second derivative). It has been shown to provide good results
with altimetry (compared to currentmeter data) but altimeter data need to be filtered both in space and time.
29
bottom pressure changes, but density changes, if not compensated over the water
column, can also induce bottom pressure changes. This shows that the dynamic
topography is an integral of density (steric height - baroclinic part), with a contribution from bottom pressure. It is really a measurement representative of the total
water column (although it is directly related to surf ace geostrophic current). This is
why satellite altimetry is so useful for constraining the 3D ocean circulation.
Numerical applications
Influence of latitude on sea level slope and ocean current
The Coriolis parameter fis equal to 20 sin <1> (O is the angular rotation of the
earth, <1> is latitude). This gives f '" 10- 4 s-1 (at 45°N/S) and f '" 10- 5 s-1 (at 5°N/S).
From equation l' (and 2'), a slope of 1 meter over 100 km will give a current of 1
rn/s at 45°N/S. A slope of 10 cm over 100 km only will give the same current speed
at 5°N/S.
Influence of temperature gradient on dynamic topography
If we assume a reference level at 1000 m and no salinity influence, the dynamic
topography change measured by altimetry for a track crossing the Gulf Stream (or
a ring) with a temperature gradient of 10°C over 100 - 200 km and over a depth of
1000 m will be:
TJ = TJs = - f 1000 P' / Po dz => il TJs = il TJ = 1000 ilp / Po = 1000 a il T '" 1.5 m
with a = -11 P ap/aT (thermal expansion coefficient) equal to 1 - 2 10- 4 s-1
Equatorial regions
At the equator, the Coriolis parameter fis equal to zero. This means we can no
longer assume geostrophy or use dynamic topography to infer the oceanic circulation. It stiU reflects, of course, the change in density field (e.g. thermocline depth or
heat content variations). In particular, the sea level variations (TJ) in the equatorial
regions are closely related to the variations of the depth of the thermocline (H) ( TJ
'" -ilp I Po H, where ~p is the density difference between the deep and surface layers). In practice, geostrophy works up to about ± 2 degrees (although the estimation
is more sensitive to noise). A relationship between zonal current and dynamic
topography has been proposed, however, by Picaut et al. (1990) ("equatorial geostrophy"). This relationship is derived as foUows:
fu = - oTJ/ay (geostrophy)
af /ay u + f auldy = -g a 2 TJ/ai
At the equator ~ u = -g a 2 TJ/ai.
This relationship is valid at low frequencies but the estimation is very sensitive to
noise (because ofthe second derivative). It has been shown to provide good results
with altimetry (compared to currentmeter data) but altimeter data need to be filtered both in space and time.