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DYNAMICAL OCEANOGRAPHY
(4.5) Altimetry
Using a satellite, one can determine the height of the sea-surface η with respect
to a reference surface (the geoid).
a. Describe how a seamount at the bottom of an ocean basin (through its
influence on the local gravity field) affects the position of the sea surface.
b. How accurate can the geoid currently be determined (search the world wide
web)?
c. Use the hydrostatic balance to show that
p = p 0 +
h
−z
gρ dz
′
where z is the depth and p 0 is a constant pressure at the sea surface (z = h).
Take now a horizontal plane z = −z 0 below the sea surface and assume that
the density ρ of the water is constant in the layer above this plane.
d. Assume that inertia is not important in the flow and that the flow is steady.
Derive from the equations (4.30) that the surface velocities are given by
u = −
g
f
∂h
∂y
; v =
g
f
∂h
∂x
DYNAMICAL OCEANOGRAPHY
(4.5) Altimetry
Using a satellite, one can determine the height of the sea-surface η with respect
to a reference surface (the geoid).
a. Describe how a seamount at the bottom of an ocean basin (through its
influence on the local gravity field) affects the position of the sea surface.
b. How accurate can the geoid currently be determined (search the world wide
web)?
c. Use the hydrostatic balance to show that
p = p 0 +
h
−z
gρ dz
′
where z is the depth and p 0 is a constant pressure at the sea surface (z = h).
Take now a horizontal plane z = −z 0 below the sea surface and assume that
the density ρ of the water is constant in the layer above this plane.
d. Assume that inertia is not important in the flow and that the flow is steady.
Derive from the equations (4.30) that the surface velocities are given by
u = −
g
f
∂h
∂y
; v =
g
f
∂h
∂x