Earth Planets Space, 51, 159–168, 1999 Precise determination of geoid height and free-air gravity anomaly at Syowa Station, Antarctica Kazuo Shibuya, Koichiro Doi, and Shigeru Aoki Center for Antarctic Environment Monitoring, National Institute of Polar Research, Kaga 1-9-10, Itabashi-ku, Tokyo 173-8515, Japan (Received July 1, 1998; Revised December 14, 1998; Accepted December 15, 1998) From the International Terrestrial Reference Frame 1994 (ITRF94) coordinates of the Doppler Orbitography Radiopositioning Integrated by Satellites (DORIS) beacon marker at Syowa Station (69.0◦S, 39.6◦E), Antarctica, we derived the ellipsoidal height of the Scientific Committee on Antarctic Research (SCAR) Global Positioning System (GPS) point as 42.240 m on the World Geodetic System 1984 (WGS84) associated ellipsoid of a tide free Earth at the epoch of 1993.0. Because the SCAR GPS reference mark was 21.165 m above the local mean sea level at the epoch of 1993.0, and because the sea surface topography is estimated as −1.29 m, the ground data of geoid height can be estimated as 22.37 m on the WGS84 ellipsoid. As for error estimate of the above value, 20–30 cm formal error can be assigned including 3 cm error from the DORIS determination, 1 cm error from the local geodetic tie, and the dominant 20–30 cm error from uncertain modeling of sea surface topography, etc. The EGM96 geoid model gives the synthetic geoid height of 22.10 m at Syowa Station; the discrepancy of 27 cm from the observed value is within the 36 cm cumulative (to the degree 360) rms (root-mean-square) error of the model. We retried similar determination at Breid Bay (70.2◦S, 23.8◦E) and made a tie to the inland outcropped Seal Rock; the obtained value of 21.4 m has an overall error of 1.8 m. These ground data can be used as test data for generating higher- order (n, m ≥ 360) geopotential models. With the establishment of the International Absolute Gravity Basestation Network (IAGBN) standard value at Syowa Station and gravimetric connection to the Seal Rock, ground data of free-air gravity anomalies of 0.05 mgal accuracy at Syowa Station and 1 mgal accuracy at Seal Rock were obtained. These gravity ground data will also serve as test data for adjusting the satellite- and/or shipborne-derived gravity anomaly maps in the region concerned. 1. Introduction ephemeris NNSS (Navy Navigation Satellite System) po- Determination of an accurate geoid model in the Antarc- sitioning result and make the tie to the inland Seal Rock tic region is important to study global geodynamics of the No. 25-01 geodetic mark in East Dronning Maud Land. With atmosphere/ocean and solid-earth interaction. Before GPS these accurate geoid height data and the estimated elevation (Global Positioning System) development, only satellite above sea level, the gravity measurements were re-analyzed Doppler positioning was practically applicable in the to obtain free-air gravity anomalies after adjustment to the In- marginal sea ice zone of Antarctica to obtain the ground data ternational Absolute Gravity Basestation Network (IAGBN; of geoid height. The attained accuracy was 4 m, restricted Boedecker and Fritzer, 1986) Syowa Station standard value. by the uncertainty of broadcast ephemeris positioning (e.g. the obtained value of 16.8 m at Breid Bay (70.2◦S, 23.8◦E); Shibuya et al., 1991). Today, combined use of GPS and other 2. DORIS Determined Coordinates of the Beacon space geodetic techniques enables us to estimate rather pre- Marker at Syowa Station cise geoid height in Antarctica, and we present a result of Figure 1 illustrates Syowa Station which is located on East 20–30 cm accuracy ground data obtained at Syowa Station Ongul Island of L¨utzow-Holm Bay, Antarctica. There are (69.0◦S, 39.6◦E). four reference marks by different space geodetic techniques, The most convenient positioning in the Antarctic region, namely satellite Doppler point A which is identical to the that is, GPS positioning is based on the WGS84 (World classic astronomical station, DORIS (Doppler Orbitography Geodetic System 1984; Defense Mapping Agency, 1987) by Radiopositioning Integrated by Satellites) beacon point geocentric coordinate system. Since the WGS84 reference D, SCAR (Scientific Committee on Antarctic Research) GPS frame usually applies the ellipsoid with the semi-major campaign point G which is identical to the classic geodetic axis a = 6378137.0 m and the flattening factor 1/f = control point No. 23-16, and the VLBI (Very Long Base- 298.2572235630, we hereafter call the associated ellipsoid line Interferometry) reference point R at the 11 m S/X band as the WGS84 ellipsoid and place the final result on it. We paraboloid antenna. All these four reference marks are in also re-determine ground data at Breid Bay with a precise bedrock area. According to Boucher et al. (1996; Table T7), ITRF94 (International Terrestrial Reference Frame 1994) coordinates Copy rightc The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; of the DORIS beacon marker (Photo 1) at the epoch of 1993.0 The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. were obtained as 159 160 K. SHIBUYA et al.: PRECISE DETERMINATION OF GEOID HEIGHT AND FREE-AIR GRAVITY ANOMALY Fig. 1. Syowa Station is located on East Ongul Island of Lutzow-Holm¨ Bay, Antarctica (left). There are four reference marks by different space geodetic techniques around the main facilities (right). All the four reference marks are in bedrock area. As for explanation of the abbreviated marks and facilities, see text. that Eq. (1) is given in the tide free system (C. Boucher, 1997; personal communication). −→ Kanao et al. (1995) estimated the offset vector DG as −→ DG = (−316.322 m, 62.323 m, −73.692 m) (2) by combined use of two-frequency GPS relative position- ing and classic geodetic surveying within an overall error of 1 cm. Thus the DORIS-determined ITRF94 coordinates of the SCAR GPS point were estimated as XG,DORIS = 1766498.873 − 316.322 = 1766182.551 m, YG,DORIS = 1460274.430 + 62.323 = 1460336.753 m, (3) ZG,DORIS =−5932211.730 − 73.692 =−5932285.422 m. 3. WGS84 Coordinates of the SCAR GPS Point in a Tide Free System It is well known that the WGS84 coordinate system has a slight inconsistency against the ITRF coordinate system (e.g. Abusali et al., 1995), and we apply a summary of seven parameter transformations by Tobita (1997) to convert Eq. (3) into the WGS84 coordinate values: X 0.078 −8 Photo 1. DORIS beacon pier installed near the Earth Science Laboratory Y = −0.505 + (1.0 − 1.01 × 10 ) (ESL; see Fig. 1) of Syowa Station. Z −0.253 WGS84 1 δω −δψ X · −δω 1 δε Y , (4) δψ −δε 1 Z ITRF94 XD = 1766498.873 m, YD = 1460274.430 m, (1) where δω =−3.394 × 10−8, δψ = 1.454 × 10−9 and Z =−5932211.730 m, D δε =−8.872 × 10−8 are given as the rotational parame- with an uncertainty of 3 cm for each coordinate. It is noted ters. It is noted that δω in the original formula of McCarthy K. SHIBUYA et al.: PRECISE DETERMINATION OF GEOID HEIGHT AND FREE-AIR GRAVITY ANOMALY 161 Fig. 2. Sea surface topography around Syowa Station in the region bounded by (0◦–60◦E, 60◦S–75◦S) after the degree 20 expansion model as part of the EGM96 geoid modeling (Lemoine et al., 1997). Contour interval is 10 cm. Calculated based on the information from the NIMA (National Imagery and Mapping Agency) web site. (1992) has opposite sign. Application of Eq. (4) to Eq. (3) 1992), Odamaki et al. (1991) indicate apparent sea level fall and subsequent transformation into the WGS84 geodetic co- with a rate of 1.0 cm/year. From Eqs. (5) and (5), we estimate ordinates results in hNo. 23-16 = dh + hBM1040 + (apparent rise) φ = ◦ . ,λ= ◦ . , G 69 00 24 600 S G 39 35 06 152 E ∼ 18.816 m + 2.338 m + 0.01 m = 21.16 m (6) (4 ) HG = 42.240 m at the epoch of 1993.0. at the epoch of 1993.0. The uncertainty of the seven param- eters in Eq. (4) may introduce about 2 cm uncertainty into 5. Obtained Ground Data of Geoid Height at Syowa Station the ellipsoidal height HG of Eq. (4 ). It is noted that local mean sea level is not identical to the global geoid surface, and sea surface topography has 4. Reduction to the Local Mean Sea Level to be corrected for in order to estimate the geoidal undula- In East Ongul Island, there is a leveling route in the form tion. For example, Rapp et al. (1991) modeled the sea sur- of a closed loop from the bench mark BM1040 at the tide face topography ζ for the global ocean using the GEOSAT gauge station of Syowa Station (Fig. 1), which passes through data. An improved sea surface topography expanded to de- the No. 23-16 geodetic mark, that is, the SCAR GPS point. gree and order 20 is now available from the information at Several Japanese Antarctic Research Expeditions (JARE-23, the web site http://cddis.gsfc.nasa.gov/egm96/general info/ -33 and -37) repeated a first-order leveling survey within the readme.sst egm96 topex ers1, and Fig. 2 illustrates the cal- closure error of 3 mm, and the height difference between the culated 0.1 m model contours around Lutzow-Holm¨ Bay. We bench mark BM1040 and the SCAR GPS point, h, at the obtain ζ at Syowa Station as epoch of 1992.0 was obtained as ζSYO =−1.29 m.