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OCR for page 85
Common Interests in Geodetic and Oceanographic Research
Victor Zlotnicki
- Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California
INTRODUCTION
The oceanographic community is planning comprehensive and ambitious
studies of the circulation of the oceans on a global scale and in the
key tropical region where such events as the E1 Nino/Southern
Oscillation (ENSO) are more evident. The ocean is the key component of
the climate system that temporarily stores heat and transports energy to
different regions, hence these oceanographic studies are part of the
World Climate Research Programme (WCRP, 1983~. The World Ocean
Circulation Experiment (WOCE) plans to provide during the 1990's ''...the
first comprehensive, global survey of the physical properties of the
oceans...to establish the first global baseline for the long-term
behaviour of the ocean, and to test computer models of the ocean
circulation, vitally needed to understand global climate dynamics and to
predict decadal climate change" (U.S. Science Steering Committee for
WOCE, 1986~. The Tropical Oceans-Global Atmosphere (TOGA) experiment is
aimed at determining the extent to which the coupled tropical ocean-
global atmosphere system is predictable on time scales from months to
years, to learn whether the system can be modelled accurately enough to
allow prediction, and to design an observational program that would
allow operational prediction (WCRP, 1985~.
Both WOCE and TOGA include as a key element measurements of sea
level using In-situ and satellite systems and such measurements
effectively require precision in position and gravity field knowledge
that are current geodetic research. These areas of common interest are
reviewed to understand the accuracy of the relevant geodetic quantities
that would significantly help oceanographic research. The influence of
ocean currents and changes in the volume of ice on Earth rotation
provides other links between current oceanographic and geodetic
research, but these will not be discussed here.
GEOID AT FIXED TIME Us TIME AVERAGED CIRCULATION
Oceanographers know the difference between the mean sea surface and
the geoid to approximately 20 to 30 cm from 100 years of hydrographic
data; however, due to data coverage, such a calculation is very accurate
and has resolution of about 100 km in the North Atlantic and within 1000
km of the continents in the N. Pacific, is adequate and has resolution
of a few hundred km in the central Pacific and the coastal areas of the
85
OCR for page 86
86
southern ocean, and is fairly inaccurate and has resolution worse than
1000 km over most of the southern oceans (see Levitus, 1982, pp. 118-
1191. Oceanographers can measure the difference between sea surface and
geoid to +10 cm (Roemmich and Wunsch, 1982) using additional in-situ
measurements. While such measurements are of limited coverage due to
the slow speed of ships (relative to the quasi-synoptic coverage of an
altimetric satellite), they provide essential information about the deep
ocean layers, whose motion can be quite different, even opposite, to the
surface motion defined by the difference between altimetric and geoidal
height.
To improve on the oceanographic capabilities, the combined error of
altimetric sea surface minus geoid heights should not exceed about 10 cm
rms over all wavelengths larger than that implied by the Rossby radius
of deformation. The radius of deformation (e.g., Gill, 1982) is the
smallest length scale over which exact geostrophic balances can occur.
The radius associated with the first baroclinic mode, about 10-30 km
(Gill 1982, sec. 7.5) at mid-latitudes, implies a shortest wavelength
between 63 and 189 km (the wavelengths increase towards the equator).
Features whose size is comparable to the radius of deformation often are
close to geostrophy but shift in position, such as the Gulf Stream axis,
or drift, like eddies, so they can be measured as altimetric variability
without using a geoid model. However, the extent to which such features
remain in a fixed position in the oceans, perhaps tied to bathymetric
features, and require a geoid model to be measured, is not clearly
known. At wavelengths much larger than the minimum, let us say greater
than 1000 km, geostrophy is approximated to a closer degree, and the
error in the difference (altimetric sea surface - geoid) should be much
lower than 10 cm, ideally of the order of 1 cm.
A more accurate gravity field model at wavelengths of 400 km and
longer, as the Geopotential Research Mission's goal is, would help in
quantifying permanent sea surface topography in two ways: (1) by
reducing the error in the geoid that is subtracted from the corrected
altimetric measurement, and (2) by reducing the error in the corrected
altimetric measurement, whose largest error source is the uncertainty in
the satellite height above the reference ellipsoid, dominated by
imprecise modelling of the gravity field (Stewart et al., 1986, p. 7~.
GEODETIC REFERENCE FRAMES AND THE POSITION OF TIDE STATIONS AND
ALTIMETRIC SATELLITES
Several studies of global sea level trends (especially Barnett,
1983) show that sea level records since the beginning of the century
contain a component coherent across various places on the earth: a
trend of apparent rising global sea level at a rate of 15 cm/century.
The interpretation of this result is complicated by the effect on this
signal of inaccurately known continental uplift or subsidence, unknown
geoid changes, and by the difficulties of precision levelling across
whole continents or from a continental margin to a mid-ocean island.
The first need, therefore, is to differentiate sea level motion from
land motion and from geoid change at wavelengths greater than about 4000
km, over one decade, with accuracy of about 1 cm.
OCR for page 87
87
Since both tide gauges and altimeters measure sea level, the former
providing excellent time coverage, the latter excellent space coverage,
it is essential to have sea level stations and altimetric satellites in
the same reference system-at any time. If different reference frames
must be used, it is essential to know their relative positions, at all
times, to an accuracy better than that required for sea level
measurements. This allows not only calibration of altimetric
measurements from one satellite, but also comparison of the results of
different satellite missions carried out at different times.
The U.S. Science Steering Committee for WOCE (1986) suggested taking
advantage of GPS and VLBI developments that promise to allow the
position of tide stations to be known at the 1 cm order of magnitude in
the vertical relative to a geocentric reference frame. Diamante et
al., (198J) have argued that the installation on the order of 100 well
distributed and calibrated tide stations, accurately positioned with
differential GPS measurements relative to a network of VLBI stations,
plus another 150 less accurately positioned tide stations, would provide
absolute sea level accurately enough for tropical studies (e.g., Wyrtki,
1984) and global sea level studies.
The reference frame implicit in the previous paragraph is different
from that used to track altimetric satellites, a fact that could cause
errors when tide gauges are used to calibrate satellite altimeters
(e.g., Wunsch, 1986~. As pointed out by Mather et al. (1979),
observations to either extra-galactic sources (as in VLBI) or to earth-
orbiting satellites (laser ranging or range-rate measurements) are
sensitive to the instantaneous rotation vector of the earth relative to
the observing station. In addition, the satellite observations are
sensitive to the instantaneous position of the earth's centre of mass
('geocentre') because it is the focus of any ellipse that osculates the
orbit. At present, altimetric satellites are positioned with respect to
a geocentric reference system known in a time averaged sense, because
the coordinates of the observing stations are constrained by the
observations to many satellites over many years. A global network of
VLBI stations (to which the tide stations are proposed to be tied)
defines a different reference frame, both because of its insensitivity
to the earth's center of mass and because of different averaging times
over which the reference frames are implicitly defined (see Mather et
al., 1979, for estimates of the rates of change in coordinates). Hence,
it is important that not only the position of tide stations, but also
the relative positions of the two reference frames be measured with
sufficient accuracy and frequency to allow decadal and secular studies
of sea level change with both tide gauges and altimeters.
TIME V^YING MEW SEA SURFACE vs TIME V~YING GEOID
Let us assume that accurately positioned tide gauges detect a tilt
of l cm across an ocean basin over a period of a few years. Does it
reflect a subtle change in ocean circulation or an equally subtle change
in the geoid?
OCR for page 88
88
Wagner and McAdoo (1986) modelled a variety of possible changes in
the geoid due to the mass redistr~butions in the "solid" earth
associated with post-glac~al rebound, ablation of continental glaciers,
large earthquakes and steady-state plate tectonics. They find plausible
rates of change in geoid height of the order of 0.1 cm/yr at wavelengths
greater than 4000 km, a number of the same order of magnitude as the
coherent component of tide records usually associated with sea level
rise. Rubincam (1984) and Yoder et al. (1983) actually measured, albeit
indirectly, the decrease in the J2 coefficient of the earth's gravity
field between 1976 and 1981, based on the measured acceleration of the
ascending node of the LAGEOS satellite. Rubincam's (1984) value of
(-8.2 + 1.8) 10-~9 s~i is equivalent to a geoid change of 0.016 cm/yr x
(3 sin2 ~ - 1), where ~ is geographic latitude.
Even though any such tilts in mean sea surface would be interpreted
in conjunction with other oceanographic data, it is highly desirable to
avoid ambiguities by a long-term program of gravity monitoring. Any
such geoid changes may also cause changes in the position of the
geocentre, which affects the reference system from which altimetric
satellites are observed and ultimately, the accuracy of altimetric
observations of the ocean. Mather et al. (1979) point out that a
network of 25 stations measuring absolute gravity to + 10 microGal can
detect geocentre motion of at least 1 cm/yr after 10 years. We also
know that changes in the second harmonic of the earth's gravity field
can be measured from changes in the orbit of the LAGEOS satellite. The
elements seem to be available for a long-term program to monitor changes
in the longest wavelengths of the gravity field that would distinguish
these from changes in ocean circulation.
ACKNOWLEDGEMENTS
Discussions with Professors Carl Wunsch, Richard Rapp and Byron
Tapley were very helpful. The research described in this paper was
performed at the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration.
OCR for page 89
89
REFERENCES
Barnett, T. P., Recent Changes in Sea Level and Their Possible Causes,
Climatic Change, 5, 15-38, 1983.
Diamante, J. M., T. E. Pyle, W. E. Carter, and W. Scherer, Global Change
and the Measurement of Absolute Sea Level, Prog. Oceanography, 18,
1-21, 1987.
Gill A. E., Atmosphere-Ocean Dynamics, Academic Press, 662 pp., 1982.
Levitus S., Climatological Atlas of the World Ocean, NOAA Prof. Paper
13, National Oceanic and Atmospheric Administration, U.S. Dept. of
Commerce, (available from the author at Geophys. Fluid Dyn. Lab.,
P.O. Box 308, Princeton, NJ 08540), 1982.
Mather, R. S., C. Rizos, R. Coleman, and E. G. Masters, Geodetic
Reference Systems for Crustal Motion Studies, Tectonophysics, 52,
15-37, 1979.
Roemmi ch D . and C . Wuns ch, On C omb ining S ate 11 i te Al t ime try wi th
HYdrographic Data, J. Mar. Res. 40, 605-619, 1982.
Rubincam, D. P., Postglacial Rebound Observed by LAGEOS and the
Effective Viscosity of the Lower Mantle, J. Geophys. Res., 89, 1077-
1087, 1984 .
Stewart, R., L. -L. Fu, and M. Lefebvre , Science Opportunities from the
Topex/Poseidon Mission National Aeronautics and Space
Adminstratior~, JPL Publ . 86-18 (available from Topex Proj ect, Jet
Propulsion Lab ., Pasadena, CA 91109), 1986 .
U. S . Science Steering Committee for WOCE, Status Report on U. S . WOCE
Planning U. S. WOCE Planning Report Number 3, 229 pp., U. S. Planning
Office for WOCE, College Station, TX, 1986.
Wagner, C. A. and D. C. McAdoo, Time Variations in the Earth's Gravity
Field Detectable with Geopotential Research Mission Intersatellite
Tracking J. Geophys. Res. 91 8373-8386 1986.
, , ,
WCRP-Joint Scientific Committee and Committee on Climatic Changes and
the Ocean, Large-Scale Oceanographic Experiments in the World
Climate Research Programme, WCRP Publication Series No 1, 121 pp.,
Intergovernmental Oceanographic Commission (UNESCO), Paris, France,
1983.
WCRP-Toga Scientific Steering Group, Scientific Plan for the Tropical
Ocean and Global Atmosphere Programme WCRP Publication Series No.
?
3, 147 pp., Intergovernmental Oceanographic Commission (UNESCO),
Paris, France, 1985.
OCR for page 90
go
Wyrtki, K., The Slope of Sea Level Along the Equator During the
1982/1983 E1 Nino, J . Geophys . Res ., 89, 10419 - 10424, 1984.
Wunsch, C ., Calibrating an Altimeter: How Many Tide Gauges - is Enough?,
J . AtInosph. and Oceanic Technology, 3, 746 - 754, 1986.
Yoder, C. F.
and B. D.
Harmonic
, J. G. Williams, J. O. Dickey, B. E. Schutz, R. J. Eanes
Tapley, Secular Variation of Earth's Gravitational
Coeffi Hi ant from T.A(~.F.n.~ and Nnn_Ti A=1 Ammm1 magi ^~ ~¢
Earth Rotation, Nature, 303, 757-762, 1983
Representative terms from entire chapter:
gravity field
