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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
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.
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?
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.
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.
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
