Introduction
Some studies have been carried out in regard to the recent growth or shrinkage of the Greenland and the Antarctic ice sheets on the basis of the measurements of the ice flow. Reference Federer, Federer, von Sury, Philberth and de QuervainFederer and others (1970) obtained a mass deficit amounting to 0.1 m a–1 (corrected later to 0.077 ma–1: Reference Federer, Sury and NyeFederer and Sury, 1976) during the ten years from 1959 to 1968 at Jarl-Joset Station on the Greenland ice sheet. Using their data, Reference NyeNye (1975) discussed the resultant lowering of the ice-sheet surface. Meanwhile, it was suggested that the West Antarctic ice sheet is currently thinning (Reference HughesHughes, 1973; Reference WeertmanWeertman, 1976; Reference ThomasThomas, 1976) and is slightly thinning or stable (Reference WhillansWhillans, 1973, Reference Whillans1976, Reference Whillans1977). Reference ThomasThomas (1976) estimated that the Ross Ice Shelf is growing thicker by almost 1 m a–1 in the vicinity of its grounding line. More detailed information is much sought on the flow of the Antarctic ice sheet in the study of such dynamical problems. Direct measurements of the flow have, however, been very few, and have only been made intensively in limited regions near the coast or on the ice shelf.
A study on ice-sheet flow was one of the main subjects of the Japanese Glaciological Research Program (Reference Shimizu and IshidaShimizu, 1978) conducted from 1969–75 over the ice sheet of Mizuho Plateau, East Antarctica. For this study, during a period from 24 November to 30 December 1969, the traverse party of the 10th Japanese Antarctic Research Expedition (JARE-10) set up (first survey) a triangulation chain over a distance of 250 km in the inland region of Mizuho Plateau (Reference Naruse, Naruse, Yoshimura, Shimizu and IshidaNaruse and others, 1972). The second survey was carried out four years later during a period from 20 December 1973 to 16 January 1974 by JARE-14 (Reference Naruse and NaruseNaruse, 1975[b]). The triangulation chain composed of 164 stations stretched along the parallel of latitude 72° S., between A001 at the south-east end of the Yamato Mountains and A164 at long. 43° E. (see Fig. 1). The surface elevation of the ice sheet increased gradually along the chain from 2250 m near A001 to 2600 m near A164, so the chain was approximately parallel to a surface contour line. Obtained from the two surveys were horizontal and vertical components of surface velocities at 140 points and also various parameters of surface strains in 140 triangles of the chain. Some of these results were published in other articles (Reference Naruse and IshidaNaruse, 1978; Reference Naruse, Shimizu and IshidaNaruse and Shimizu, 1978; Reference Mae and NaruseMae and Naruse, 1978) with some discussions on the general flow and strain patterns and the dynamical features of the ice sheet in Mizuho Plateau. Measurements were also made along the chain of the surface slope (Reference Naruse and NaruseNaruse, 1975[b]), ice thickness (Reference Shimizu, Shimizu, Naruse, Omoto, Yoshimura and IshidaShimizu and others, 1972; Reference Naruse, Yokoyama and NaruseNaruse and Yokoyama, 1975), gravity (Reference Yoshida, Yoshimura and IshidaYoshida and Yoshimura, 1972; Reference Abe and NaruseAbe, 1975), and net accumulation (Reference Yokoyama and NaruseYokoyama, 1975).
Fig. 1. Distribution of horizontal vectors of ice flow (m a–1) at every 5’ in longitude along the triangulation chain in Mizuho Plateau. Surface contours of the ice sheet are marked for every 200 m.
The present paper reports chiefly a thinning phenomenon of the ice sheet deduced from the measurements of the vertical component of the surface flow velocity in Mizuho Plateau. The method of triangulation survey and some results from it are also briefly described.
Outline of the Survey of A Triangulation Chain and Distribution of Horizontal Flow Vectors
The datum point of a triangulation chain, A001, was selected upon a nunatak at lat. 71° 47’ 28” S. and long. 36° 12’ 12” E., which belongs to the Yamato Mountains. Positions and elevations of all the triangulation stations were determined relative to their values at the datum point. The adopted elevation of this point was 2254 m obtained by the barometric method.
The triangulation chain was composed of 164 stations. Each station was marked by a metal pole 3 m long or a bamboo stake 2.5 m long, which were used also as snow stakes. Both the first and the second survey of the chain were conducted principally by angle measurements with Wild T2 theodolites. Measurements were made of the horizontal angles of the three interior angles of all the constituent triangles, and the vertical angles from each station to four neighbouring stations. With the aim of correcting the accumulation of errors, the distance was measured with a radiowave distance meter (Cubic DM-20) and an azimuth was observed by shooting the sun for one side of every 10 to 15 triangles.
The geodetic coordinates and their mean-square errors (standard errors) were obtained at all the triangulation stations in 1969 and 1973–74 respectively, from the calculations by applying the least-squares method to a number of observation equations based on measured angles, azimuths, and distances. Then, the horizontal vector of ice movement was determined at each station from the difference between two geodetic positions. The surface elevations of the stations were obtained in 1969 and 1973–74 respectively, by the measured values of vertical angles and the calculated distances from the above geodetic coordinates of the neighbouring two stations. Possible errors resulting from refraction due to the vertical gradient of air temperature and also from the curvature of the Earth can be counterbalanced, because measurements of vertical angles were carried out twice from both the stations in opposite directions and these were averaged. The “submergence or emergence velocity” Vz was, then, calculated on the basis of the above two surface elevations, as described in the following section.
The results obtained for the three components of the surface velocity (namely the magnitude of the horizontal velocity V h, the azimuth α of V h and the submergence or emergence velocity Vz ) are shown in Table I, with calculated root-mean-square errors every ten stations along the chain. Since the surface flow is almost in a direction from south to north, the error in horizontal velocity was strongly controlled by the error involved in latitude, and not by the error in longitude. The absolute value of error in V h showed a gradual increase from the datum point towards the end of the chain (A164); the relative error reached a minimum value of 3% at the middle part of the chain and 3 to 10% in other parts. Errors in azimuth are given as large values at places where the horizontal velocity is small. Relative errors in the submergence (emergence) velocity were considerably larger in the region from A003 to around A060 where the submergence (emergence) velocity was very small, while in the region eastward from A060 relative errors showed rather small values around 25%.
Table I. Three Components Of Surface Velocity Of Ice Flow and Their Root-Mean-Square Errors at Every Ten Stations Of a Triangulation Chain
α: clockwise from the north point
Vz : positive sign, submergence velocity; negative sign, emergence velocity
The distribution of horizontal flow vectors (m a–1) across the triangulation chain every 5′ in longitude are shown by the thin arrows in Figure 1. It is clear that the flow is converging into the Shirase Glacier. Remarkable features noted of the horizontal flow along the parallel of latitude 72° S. in Mizuho Plateau are as follows:
The flow velocity had very small values less than 2 m a–1 and the flow direction was north-westward in the vicinity of the Yamato Mountains, namely the region to the west of long. 36° 35′ E. The small value is considered to be caused by the effect of many nunataks lying down-stream. The direction of the flow was different on either side of long. 37° E. To the west of the boundary, the flow had a westward component, while to the east of it, the flow had an eastward component. The macro-scale surface contours of the ice sheet showed a ridge there (Reference Shimizu, Shimizu, Yoshimura, Naruse, Yokoyama and IshidaShimizu and others, 1978[b]). It must follow, therefore, that the ice divide exists near long. 37° E. between the drainage of the Shirase Glacier and the drainage at its west side. The velocity increased gradually with the increase of distance from the datum point, that is from west to east. It was more than 20 m a–1 in the region around long. 39° E. The velocity then decreased slightly and reached 13.6 m a–1 at A164 which was located at the east end of the triangulation chain. The direction of the flow shifted gradually from northward to westward in the eastern part of the chain, and finally it was north-north-west at A164.
Thinning Rate Of the Ice Sheet Along the Chain
The submergence or emergence velocity Vz of the surface flow can be obtained from
where 
is the vertical velocity component of the top of a marker stake, V
h is the horizontal velocity and θ is the surface slope (positive sign) along the flow direction. As the value of 
is taken positive downward, a positive value of Vz
indicates a submergence velocity and a negative value indicates an emergence velocity. The quantity, Vz — A, gives the rate of change of the surface elevation per year, where A is annual net accumulation in snow depth (positive value of A shows accumulation; negative value ablation). We call the quantity, Vz — A, the thinning-rate of the ice sheet.
Figure 2 shows the submergence (emergence) velocity Vz (m a–1) at the surface, the thinning rate VZ — A (m a–1), and the surface and the bedrock profiles along the chain plotted against the longitude from 36° 10′ E., the south-cast end of the Yamato Mountains, to long. 43° 10′ E. Annual net accumulation A was obtained by averaging over four years from the measurements of snow stakes. The variations of Vz and Vz — A were slightly smoothed by using the running mean over three stations. The following results are characteristic in Figure 2:
Fig. 2. Variations in submergence (emergence) velocity vz (m a–1), thinning-rate Vz — A (m a–1), and profiles of the ice sheet and bedrock surfaces along the triangulation chain in 72° S. in MizullO Plateau. Positive Vz indicates submergence velocity; negative vz emergence velocity. Running mean over three stations was applied to Vz and Vz — A. The bedrock profile was obtained from the results of radio echo-soundings and gravity measurements as well.
(1) Negative velocities which signify emergence flow of ice were obtained in the limited regions around long. 36° 30′ E. and 38° E. The annual net accumulation was negative (mean value, —0.05 m a–1) in the former region near the Yamato Mountains, which represents ablation due mainly to sublimation of the exposed surface ice. A large number of meteorites were found (Reference Yoshida, Yoshimura and IshidaYoshida and others, 1971; Reference Shiraishi, Shiraishi, Naruse and KusunokiShiraishi and others, 1976; Reference Yanai, Nagata and IshidaYanai, 1978; Reference Matsumoto and NagataMatsumoto, 1978) in this region which, therefore, was named the Meteorite Ice Field. The bedrock profile is marked by the great rise there.
(2) In most parts except the above regions, positive Vz indicative of submergence flow was observed. The value of Vz increased suddenly near long. 39° E. where the horizontal velocity was close to the maximum value (see Fig. 1), and then it decreased gradually from long. 42° E. eastward. The value of Vz reached 1 m a–1 in the region between long. 40° E. and 42° E., where the mean-square errors of Vz were from ±0.25 m a–1 to ±0.30 m a–1, as shown in Table 1.
(3) The amount of net accumulation A showed remarkable variations from place to place. Observation of the surface topography revealed a strong correlation between A and surface reliefs. Namely, the net accumulation was large in the depressed terrain (mean value, 0.47 m a–1), small in the mounded terrain (mean value, 0.09 m a–1), and average in the whole area is 0.20 m a–1 in thickness of snow. Assuming the average density of the surface snow as 450 kg m–3 [Reference Naruse and ShimizuNaruse, 1975[a]; Reference Watanabe and ShimizuWatanabe, 1975), the annual net accumulation was 90 kg m–2 a–1 in the region along the chain except near the Yamato Mountains.
(4) The value of Vz — A was close to 0 m a–1 in the region from long. 39° E. westward; while in the region eastward, it was a large value showing a considerable thinning-rate of about 0.7 m a−1.
Concluding Remarks
Results of the present study indicated that the average submergence velocity was 0.9±0.25 m a–1 in the region from long. 39° E. to 43° E. along lat. 72° S. Submergence flow is considered to have resulted from densification in the upper snow layer and also from outflow of ice from a vertical column with unit cross-sectional area through the thickness of the ice sheet. The rate of surface lowering due to densification of snow was estimated as about 0.1 to 0.2 m a–1 from the calculations of the equation on the non-Newtonian densification of snow derived by Reference Bader and KingeryBader (1963).
The distribution of Vz — A shows that the supply of snow on the ice-sheet surface was insufficient to maintain a stable condition of the ice sheet in the region to the east of long. 39° E. It is concluded that the ice sheet was shrinking along a part of the chain during this observation period, as estimated using a similar method in the West Antarctic ice sheet (Reference HughesHughes, 1973; Reference WhillansWhillans, 1973; Reference ThomasThomas, 1976). However, surface lowering was not necessarily taking place over the entire area of Mizuho Plateau. As for the entire ice in the drainage basin of the Shirase Glacier in Mizuho Plateau, Reference Shimizu and IshidaShimizu and others (1978[a]) discussed the mass budget. The following estimates were made from the measurements in 1969–75: the drainage area: 20 × 1010 m2; the stored ice: 32 × 1016 kg (Reference Shimizu and IshidaShimizu and others, 1978[b]); the total accumulation rate: (13±8) × 1012 kg a−1 (Reference Yamada, Watanabe and IshidaYamada and Watanabe, 1978); the annual discharge of ice through the Shirase Glacier: (7.4±1.9) × 1012kg a–1 (Reference Nakawo [i.e. Nakao], Nakawo, Ageta, Yoshimura and IshidaNakawo and others, 1978). Then, we obtained the mass budget of (6±8)×1012 kg a–1 by subtracting the discharge from the total accumulation, since the latter included the estimated amounts of melting at the coastal region and of the drifting snow. The mean value indicated a reasonably large positive budget. Therefore, it remains possible that the observed intense thinning of the ice sheet in the region from long. 39° E. to 43° E. along the parallel of latitude 72° S. might be a rather local or recent occurrence. To elucidate the causes and mechanisms of the instability of the ice sheet, more knowledge is urgently called for especially as to the flow-rates along a flow line and also along a vertical direction, together with the thermal regime of the ice sheet, in East Antarctica.
Acknowledgements
The author is deeply indebted to many members of the wintering parties of the 10th and the 14th Japanese Antarctic Research Expedition led by Dr K. Kusunoki and Dr T. Hirasawa respectively, for generous support in the field. Special thanks are due to Mr H. Ando, Drs M. Yoshida, K. Omoto, Messrs Y. Ageta, S. Kobayashi, Y. Abe, K. Yokoyama, and K. Shiraishi for their co-operation with him in carrying out triangulation surveys. He also expresses his gratitude to Dr S. Mae of the National Institute of Polar Research, and Dr G. Wakahama and Dr T. Ishida of the Institute of Low Temperature Science, Hokkaido University for their useful comments on this paper.
Discussion
I. M. Whillans: IS it possible that the surface lowering could be due to more rapid firn densification now than in the recent past?
R. Naruse: I think not. The thinning rate h in Reference MaeMae (1979) excluded the amount of the surface lowering due to the densification of the upper firn layers. I calculated the densification-rate by using the equation of non-Newtonian densification of snow derived by H. Bader. The amount of the surface lowering obtained was 0.1 to 0.2 m a–1. But it is an approximate value because the data of the density profile used were those at Mizuho Station, which was located 150–200 km from the surveyed region of the triangulation chain.
T.J. Hughes: A good companion study to your transverse strain network would be construction of a strain network along your central flow line. Do you plan to do that?
Naruse: We think that a strain network study along the central flow line is important, and we want to carry out such a study in the future.
