Precipitation

At Mizuho Station, Reference Kobayashi, Ishikawa and OhataKobayashi and others (1985) obtained from the drift density at 30 m height a value of 140 mm (all values of surface mass balance are given as water equivalent) for the annual precipitation in 1980, where all the drift was assumed to be attributable to precipitation. By the same method, Reference TakahashiTakahashi (1985b) obtained 260 mm as the precipitation in 1982, and 230 mm by attempting to distinguish precipitation from drift flux at 1 m height. We conclude that precipitation was roughly 200 m at Mizuho Station, although it could be within a wide range between 100 and 300 mm.

Fig. 1. Map of East Queen Maud Land, showing surface-elevation contours. A : area for calculation of drifting-snow divergence around the Yamato Mountains, Β : area around Aska Station.

Fig. 2. Sublimation at Mizuho Station in 1982, measured by means of an evaporimeter filled with ice.

Sublimation from the surface

In 1982, the rate of sublimation was measured at Mizuho Station by weighing an evaporimeter filled with ice (Fig. 2). A small amount of sublimation from vapor to ice was predominant in the winter season, from April to the middle of September, whereas a large amount of sublimation from ice to vapor was predominant during the rest of the year. A value of about 50 mm was obtained for the net loss from the surface. Reference Fujii and KusunokiFujii and Kusunoki (1982) obtained a similar result for 1977–78.

Surface mass-balance deficiency

On Mizuho Plateau, the annual net mass balance has been measured since 1968 by means of snow stakes along various traverse routes. Reference Yamada, Okuhira, Yokoyama and WatanabeYamada and others (1978) represented the annual net balance as a function of altitude. According to this understanding, the net balance ranged from 0 to 100 mm at the altitude of Mizuho Station (2230 m a.s.l.).

Reference Narita and MaenoNarita and Maeno (1979) obtained an annual net balance of 70 mm from data on crystal-grain distribution in a snow core.

Around Mizuho Station, therefore, the surface net balance should be less than 100 mm. This is less than the sum of precipitation (about +200 mm) and sublimation (about −50 mm). The deficit can be explained by mass export from the area, caused by the horizontal divergence of drifting snow carried by katabatic winds that are deflected by surface topography. This will be discussed in the following section.

Katabatic wind and surface inclination

Katabatic winds depend on surface slope and inversion intensity (Reference BallBall 1960, Reference AdachiAdachi 1983, Reference SchwerdtfegerSchwerdtfeger 1984, Parish, unpublished). In the two-layer model, the wind speed of the lower layer is determined by balancing the Coriolis force F_c , the friction force F_f and the gradient force of the dense layer on a slope F_g (Fig. 3). If the

Fig. 3. Equilibrium of Coriolis force F_c , friction force F_f and slope gradient force F_g in the two-layer model for katabatic winds.

x-axis is aligned with the direction of maximum slope, the equations of this model are:

where k is the friction coefficient, V is the absolute wind speed, u and v are x- and y-wind components, f is the Coriolis parameter, g is the gravity acceleration, A is the surface slope, Δθ is the inversion intensity (the potential temperature difference of the two layers), and θ is the mean potential temperature of the low layer. Geostrophic winds are neglected as a first approximation in considering the annual mean wind speed. The solutions of these equations are:

where the gradient force F_g is (θ/θ) sin A: the third term on the right-hand side ofEquation (equ.1a).

At Mizuho Station, the annual mean wind speed was 11.1 ms⁻¹ and Β was about 45°. Since A = 4 × 10⁻³ and f = −1.387 × 10⁻⁴ s⁻¹, F_g is given by 2.18 × 10⁻³ m s⁻² and k is 1.25 × 10⁻⁵ m⁻¹ from Equations (2a) and (2b). From these values, the relation between wind velocity V and inclination A is obtained as shown in Figure 4, where V is normalized by the wind speed at Mizuho Station V₀ . The wind-speed data obtained by Reference Inoue, Nishimura and SatowInoue and others (1983) on various slopes on Mizuho Plateau agreed with this relation (Fig. 4).

Fig. 4. Ratio of wind speed to that of Mizuho Station V/V ₀ and deflection angle B as a function of surface inclination, obtained from Equations (2a) and (2b). Solid circles denote the ratio quoted from Inoue and others (1983).

From F _g and the mean annual temperature of −33°C, the inversion intensity Δθ was 13.5 Κ at Mizuho Station. Since Δθ is not as large near sea-level, it should be a function of altitude. When the intensity at sea-level is assumed to be one-third of that at Mizuho Station, the ratio ∆θ/θ is given by

where p = one-third and subscript o represents the value at Mizuho Station. This is based on an assumption that the lapse rate in the upper layer is 0.6°C/100 m and in the lower layer is 1.0°C/100m, as we would expect from 10 m depth snow-temperature observations. As a result, the Δθ of 13.5 Κ at Mizuho Station is reduced to 4.7 Κ at sea-level. From Equations (2a), (2b) and (2c), the katabatic wind speed can be obtained at any place from its surface inclination and altitude.

Drifting-snow divergence at Mizuho Station

At Mizuho Station, Reference TakahashiTakahashi (1985a) obtained a snow-drift transport rate from March 1982 to January 1983 by integrating the drift flux from the surface to a height of 30 m. The relation between the drift transport rate Q (kg m⁻¹d⁻¹) and wind speed V (ms⁻¹) at 1 m height was as follows:

The annual drift transport rate at Mizuho Station Q ₀ was estimated as 3 × 10⁶ kg m⁻¹ a⁻¹. From this value and Equation (equ.3), the transport rate Q of another region with a different wind speed V can be given by

where m is 5.17 and V ₀ is the average wind speed at Mizuho Station, about 11 m s⁻¹.

The horizontal divergence of drifting snow at Mizuho Station was one-dimensionally estimated as follows. If the gradient of the ice-sheet topography changes one-dimensionally, the drifting-snow divergence can be given by the difference in the transport rate at two different places, 1 and 2, along a wind stream line.

where ΔL is the horizontal distance between the two points.

The surface topography around Mizuho Station is convex upward. The surface inclination in the windward region 50 km away from Mizuho Station is about 3 × 10⁻³, and that in the leeward region 50 km away is about 6 × 10⁻³. From the relation between V/V ₀ and A in Figure 4, V/V_n was 0.83 in the windward region and 1.30 in the leeward region. Since ΔL is 100 km, the drifting-snow divergence was obtained as 105 kg m ⁻²a⁻¹ from Equation (equ.5). In other words, annual mass export from the surface was about 100 mm. The annual balance of 70 mm was hence established for precipitation of 140–260 mm, sublimation of 50 mm, and drifting-snow divergence of 100 mm, as illustrated in Figure 5.

Fig. 5. Surface mass-balance model at Mizuho Station.

Equations of two-dimensional divergence

At grid points for calculation as shown in Figure 6, a gradient of surface slope n, defining a descending direction positive, is given by

Fig. 6. Notation of grid points for calculation of the surface gradient n, katabatic wind vector V and snow-drift transport rate Q. Β is the deflection angle between n and V.

where H_i,j is an altitude of the grid point (i,j) and Δx is the distance of a grid point in the x- and y-axis directions. For small inclination, the inclination A is ∣n(= (n_x ² + n_y ²)½). Wind speed V and deflection angle Β are obtained from this A by Equations (4a), (4b) and (4c). Hence the wind speed in a vector V is given by

Similarly to Equation (equ.4), the annual transport rate of drifting snow in a vector is represented by

where Κ is Q₀/V₀ ^m and m is 5.17. The horizontal divergence of drifting snow is, therefore, given as follows:

Thus the drifting-snow divergence at a grid point can be obtained from its altitude and the altitudes of adjacent points.

Drifting-snow divergence and bare ice

Over an area 600 km × 450 km on Mizuho Plateau, the two-dimensional drifting-snow divergence was calculated at a 15 km grid interval. From Equation (equ.7), the annual mean wind speed was obtained at each grid point (Fig. 7).

The horizontal divergence of drifting snow was thus obtained from the wind speed using Equation (equ.9), as shown in Figure 8. Substantial divergence was found on the windward part of the bare ice field around the Yamato Mountains, which indicates a considerable amount of mass export from the surface. If the mass export due to divergence exceeds the precipitation minus sublimation, the net mass balance becomes negative and a bare ice field can be generated. We conclude that the large divergence is the principal cause of the bare ice field. In the leeward area, however, the divergence was small or even negative (deposition), as shown in Figure 8. This will be discussed later.

Fig. 7. Katabatic wind vector at 42 × 28 grid points, with a 15 km grid interval calculated from the topography around the Yamato Mountains. Dark areas denote the bare ice field.

Fig. 8. Horizontal divergence of drifting snow with 200 kg m⁻² isopleth interval, calculated from the wind speed shown in Figure 7. The hatched area defines values above 400 kg m⁻². The isopleth below −1000 kg m⁻² is not shown. Dark areas denote bare ice.

Around the Belgica Mountains, the divergence was large in the windward area despite the fact that no prominent bare ice has been found, except near the mountains. One problem is the inaccuracy of the contour lines. Recent satellite doppler surveys suggested corrections from several tens of meters to 100 m in altitude.

Other factors affecting bare ice fields

The acceleration of wind over the smooth surface of the bare ice should be taken into account. The roughness parameter of bare ice is expected to be smaller than that of a snow surface with sastrugi, dunes and barchans. The lesser roughness should lead to acceleration of the wind and thus divergence of drifting snow.

The low albedo of drifting ice would be another factor. Substantial sublimation has been observed on the bare ice field around the Yamato Mountains. The reason would be the low albedo of bare ice rather than the accelerated wind speed. Once the bare ice has been formed, the low albedo would increase the surface temperature and promote sublimation.

Both these factors have a feed-back effect on the development of a bare ice field. Once bare ice is formed for any reason, the reduced roughness and lowered albedo promote bare-ice formation and the effect extends to leeward, elongating the ice field. Thus the leeward part of a bare ice field can be explained by its lesser roughness and low albedo in addition to unsaturated drifting snow.

Fig. 9. Elongated bare ice fields (dark area) in the lee of Romnaesfjellet and Vesthaugen in the Sør Rondane Mountains.

The orographic effect is a different kind of factor. Owing to turbulence around the mountains, the diffusion coefficient must increase and the stable profile of absolute humidity is broken by mixing of the air mass, which also promotes sublimation. Bare ice fields are commonly found in the lee of mountains. A prominent example can be seen around the Sør Rondane Mountains (Fig. 9). On the leeward side of Romnaesfjellet and Vesthaugen, bare ice fields are elongated to about 50 km.