192
W.H.F. Smith
The ERM requirement of ground track repeat within ±1 km is a stringent requirement, necessitating maintenance of the orbit’s semi-major axis to about 1 part per
million, for example. Even so, cross-track geoid slopes can introduce apparent variability in sea surface height as the ERM track moves within the ±1 km band. The
movement has the effect of shifting the track east or west as the satellite arrives
early or late to its intended Equator crossing. If the global averages of the geoid
slope components obey:
|∇ 1 N|
2
=
η
2
+
ξ
2
(11.14)
and if the field is isotropic, on average, then each term on the right hand side of
(11.14) is equal in magnitude, and it follows that if the RMS geoid slope is 35
μrad then the RMS east-west component of slope is 35
√
2, or 25 μrad. As the
track moves ±1 km the observed sea surface height will appear to change by 2.5 cm
typically, and much more in areas of strong gravity anomalies such as trenches,
simply due to the east–west slope of the geoid. Thus use of an ERM does not completely eliminate the need for geoid knowledge, and geoid knowledge is perhaps
good enough to make ERMs unnecessary in the future.
Altimetry cannot improve the geoid resolution further without new data collected
along a spatially dense network of ground tracks. The Geosat GM and ERS-1 GM
missions provide a network with a typical spacing of 4 km. To improve upon this will
require a new altimeter with better signal-to-noise (more statistically independent
looks), a long time between exact repeats, and a long mission duration. One may
hope to achieve this with CryoSat-2.
Acknowledgements A. B. Watts and D. T. Sandwell introduced me to this topic. K. M. Marks,
J. L. Lillibridge, and an anonymous reviewer kindly reviewed the manuscript. Any errors are my
own. The manuscript contents are solely the opinions of the author and do not constitute a statement
of policy, decision, or position on behalf of NOAA or the US Government.
References
Backus G, Parker R, Constable C (1996) Foundations of geomagnetism, Cambridge University
Press, New York
Bruns EH (1828) Die figure der erde. Publikation Königl. Preussisch. Geodätisches Institut, P.
Stankiewicz Buchdruckerei, Berlin
Chapman M, Bodine J (1979) Considerations of the indirect effect in marine gravity modelling. J
Geophys Res 84(B8):3889–3892
Ekman M (1989) Impacts of geodynamic phenomena on systems for height and gravity. Bull
Geodesique 63(3):281–296
Goff JA, Smith WHF, Marks KM (2004) The contributions of abyssal hill morphology and noise
to altimetric gravity fabric. Oceanography 17(1):24–37
Haxby WF, Karner GD, LaBrecque JL, Weissel JK (1983) Digital images of combined oceanic
and continental data sets and their use in tectonic studies. Eos Trans AGU 64(52):995–1004
Heiskanen WA, Moritz H (1967) Physical geodesy, W. H. Freeman, San Francisco
Jacobs GA, Barron CN, Rhodes RC (2001) Mesoscale characteristics. J Geophys Res
106(C9):19581–19595
W.H.F. Smith
The ERM requirement of ground track repeat within ±1 km is a stringent requirement, necessitating maintenance of the orbit’s semi-major axis to about 1 part per
million, for example. Even so, cross-track geoid slopes can introduce apparent variability in sea surface height as the ERM track moves within the ±1 km band. The
movement has the effect of shifting the track east or west as the satellite arrives
early or late to its intended Equator crossing. If the global averages of the geoid
slope components obey:
|∇ 1 N|
2
=
η
2
+
ξ
2
(11.14)
and if the field is isotropic, on average, then each term on the right hand side of
(11.14) is equal in magnitude, and it follows that if the RMS geoid slope is 35
μrad then the RMS east-west component of slope is 35
√
2, or 25 μrad. As the
track moves ±1 km the observed sea surface height will appear to change by 2.5 cm
typically, and much more in areas of strong gravity anomalies such as trenches,
simply due to the east–west slope of the geoid. Thus use of an ERM does not completely eliminate the need for geoid knowledge, and geoid knowledge is perhaps
good enough to make ERMs unnecessary in the future.
Altimetry cannot improve the geoid resolution further without new data collected
along a spatially dense network of ground tracks. The Geosat GM and ERS-1 GM
missions provide a network with a typical spacing of 4 km. To improve upon this will
require a new altimeter with better signal-to-noise (more statistically independent
looks), a long time between exact repeats, and a long mission duration. One may
hope to achieve this with CryoSat-2.
Acknowledgements A. B. Watts and D. T. Sandwell introduced me to this topic. K. M. Marks,
J. L. Lillibridge, and an anonymous reviewer kindly reviewed the manuscript. Any errors are my
own. The manuscript contents are solely the opinions of the author and do not constitute a statement
of policy, decision, or position on behalf of NOAA or the US Government.
References
Backus G, Parker R, Constable C (1996) Foundations of geomagnetism, Cambridge University
Press, New York
Bruns EH (1828) Die figure der erde. Publikation Königl. Preussisch. Geodätisches Institut, P.
Stankiewicz Buchdruckerei, Berlin
Chapman M, Bodine J (1979) Considerations of the indirect effect in marine gravity modelling. J
Geophys Res 84(B8):3889–3892
Ekman M (1989) Impacts of geodynamic phenomena on systems for height and gravity. Bull
Geodesique 63(3):281–296
Goff JA, Smith WHF, Marks KM (2004) The contributions of abyssal hill morphology and noise
to altimetric gravity fabric. Oceanography 17(1):24–37
Haxby WF, Karner GD, LaBrecque JL, Weissel JK (1983) Digital images of combined oceanic
and continental data sets and their use in tectonic studies. Eos Trans AGU 64(52):995–1004
Heiskanen WA, Moritz H (1967) Physical geodesy, W. H. Freeman, San Francisco
Jacobs GA, Barron CN, Rhodes RC (2001) Mesoscale characteristics. J Geophys Res
106(C9):19581–19595