Chapter 11
The Marine Geoid and Satellite Altimetry
Walter H.F. Smith
11.1 Introduction
If the tides and currents in the ocean and atmosphere ceased their motion, so that
the fluid parts of the Earth came to rest on the solid parts, with all parts rotating
together uniformly as a rigid body, then hydrostatic equilibrium would require that
the ocean-atmosphere interface (that is, sea level) must lie on a surface of constant
potential energy of the Earth’s gravity field. (Gravity in this sense is what is experienced by an observer rotating with the Earth, so that it includes the effects of a
uniform rigid body rotation added to the Newtonian gravitational attraction.) This
equipotential surface, the hydrostatic equilibrium shape for sea level in the absence
of tides, currents and winds, is called the marine geoid.
Satellite altimeters measure the instantaneous sea surface height above a reference Earth ellipsoid. This height is the sum of the geoid height plus the dynamic
topography associated with the ocean’s flows and responses to tidal and atmospheric
forcings. If the geoid height can be removed from the altimetric observations, then
the residual height can be directly interpreted in terms of ocean dynamics. Until
recently, however, geoid heights were not known with sufficient accuracy to be used
directly in this way.
In some altimetric applications to ocean dynamics, it is the horizontal gradient of the dynamic height, that is, the dynamic slope, that is most relevant. In the
geostrophic approximation, e.g., the dynamic slope is related to the surface current
velocity through the Coriolis parameter; at mid-latitudes, a 1 m/s current produces a
dynamic slope of ∼10 μrad (1 μrad is 1 mm change in height per 1 km of horizontal
distance). If a geoid model is to be used to obtain the dynamic ocean signal, one
must consider not only errors in geoid height, but also in geoid slope. The geoid
slope is coupled to gravity anomalies via Laplace’s equation. Therefore one can use
gravity anomaly data to verify the accuracy of a geoid slope model.
W.H.F. Smith (B)
Laboratory for Satellite Altimetry, National Oceanic and Atmospheric Administration, Silver
Spring, MD 20910, USA
e-mail: Walter.HF.Smith@noaa.gov
181
V. Barale et al. (eds.), Oceanography from Space,
DOI 10.1007/978-90-481-8681-5_11, C
All Rights Reserved
The Marine Geoid and Satellite Altimetry
Walter H.F. Smith
11.1 Introduction
If the tides and currents in the ocean and atmosphere ceased their motion, so that
the fluid parts of the Earth came to rest on the solid parts, with all parts rotating
together uniformly as a rigid body, then hydrostatic equilibrium would require that
the ocean-atmosphere interface (that is, sea level) must lie on a surface of constant
potential energy of the Earth’s gravity field. (Gravity in this sense is what is experienced by an observer rotating with the Earth, so that it includes the effects of a
uniform rigid body rotation added to the Newtonian gravitational attraction.) This
equipotential surface, the hydrostatic equilibrium shape for sea level in the absence
of tides, currents and winds, is called the marine geoid.
Satellite altimeters measure the instantaneous sea surface height above a reference Earth ellipsoid. This height is the sum of the geoid height plus the dynamic
topography associated with the ocean’s flows and responses to tidal and atmospheric
forcings. If the geoid height can be removed from the altimetric observations, then
the residual height can be directly interpreted in terms of ocean dynamics. Until
recently, however, geoid heights were not known with sufficient accuracy to be used
directly in this way.
In some altimetric applications to ocean dynamics, it is the horizontal gradient of the dynamic height, that is, the dynamic slope, that is most relevant. In the
geostrophic approximation, e.g., the dynamic slope is related to the surface current
velocity through the Coriolis parameter; at mid-latitudes, a 1 m/s current produces a
dynamic slope of ∼10 μrad (1 μrad is 1 mm change in height per 1 km of horizontal
distance). If a geoid model is to be used to obtain the dynamic ocean signal, one
must consider not only errors in geoid height, but also in geoid slope. The geoid
slope is coupled to gravity anomalies via Laplace’s equation. Therefore one can use
gravity anomaly data to verify the accuracy of a geoid slope model.
W.H.F. Smith (B)
Laboratory for Satellite Altimetry, National Oceanic and Atmospheric Administration, Silver
Spring, MD 20910, USA
e-mail: Walter.HF.Smith@noaa.gov
181
V. Barale et al. (eds.), Oceanography from Space,
DOI 10.1007/978-90-481-8681-5_11, C
All Rights Reserved