The energy balance of the Antarctic ice sheet/atmosphere system appears to be the net result of interactions between the ice active layer and the atmosphere over a certain time period. This energy balance characterizes different amounts of heat and moisture participating in a complex process of glaciation. Recent fragmentary data on the marginal heat exchange are used to derive quantitative estimates of energy processes in the ice/atmosphere system by traditional geographical methods. All balance components were calculated for a closed balance, assuming that:
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(i) The mass of the ice sheet is stable, i.e. iceberg calving is balanced by accumulation Reference Shumskiy and Tolstikov(Shumskiy, 1969);
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(ii) The ice/atmosphere system is in thermal equilibrium, that is the algebraic sum of the heat input and losses should be equal to zero;
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(iii) The mean annual heat exchange through the ice surface should be zero; during cold months the active ice layer loses the same amount of heat as it receives during warm months Reference Rusin(Rusin, 1961; Reference Rubin, Wexler, Wexler, Rubin and CaskeyRubin, 1962).
The moisture balance of the ice surface (mass exchange through the surface), of the atmosphere, and of the ice/atmosphere system can be described by the following expressions (UNESCO, 1978):
where r is the atmospheric precipitation made up of advective precipitation r a and precipitation due to evaporation/condensation, or local precipitation, r E (r = r a + r E), A the solid precipitation accumulated at the ice surface, it balances the iceberg calving, E the evaporation from the surface, q the wind-induced snow-drift from ice onto the ocean, f the melt run-off from the ice surface into the ocean, a the moisture advection to the atmosphere, and c the total atmospheric moisture flux over the ice surface comprised of the transient advective moisture c′ and local moisture discharge c″ (c = c′ + c″), where
Mean annual accumulation over the whole Antarctic ice sheet was calculated from the map constructed by Reference KotlyakovKotlyakov and others (1977), the melt water run-off from the surface of the marginal glaciers was calculated by Reference KlokovKlokov (1979), the value of the wind-driven snow-drift to the ocean was calculated from the results of a few direct measurements of snow-drift made in Antarctica during various expeditions Reference Aver’yanov(Aver’yanov, 1980). The first estimates of the surface evaporation from the whole continental ice sheet were made. The minimum values of direct measurements and calculations for various glaciomorphological zones such as ice shelves, coastal areas, slopes of glaciers with absolute height of 1 000–2 500 m as well as high plateaux were used for these estimations Reference Aver’yanov(Aver’yanov, 1980).
The total moisture advection in the atmosphere was calculated by Drozdov and Grigor’yeva (1963) using the formula
where w is the atmospheric moisture content equal to 2.52 mm (Reference VoskresenskiyVoskresenskiy, 1976), ū the mean speed of effective moisture transfer equal to 8.9 m s−1 (Reference VoskresenskiyVoskresenskiy, 1976), l the linear dimensions of the area equal to √S where S = 13.94 × 106 km2, and N the number of seconds in the period of calculation. The total atmospheric moisture discharge is determined from Equations (2) and (3). The author in his earlier work presented numerical values of the balance components and the scheme of Antarctic moisture turn-over (Reference Aver’yanovAver’yanov, 1979[a]). Mean annual specific values of mass exchange components of the ice surface and of atmospheric moisture exchange together with their thermal equivalents are shown in Table I.
Table I Mean annual values of mass exchange components for the ice sheet surface and those of moisture turnover in the Antarctic atmosphere together with their thermal equivalents (latent heat of water-phase transformations)
The mean annual heat balance of the ice-sheet surface, the atmosphere, and the ice/atmosphere system is expressed by the following expressions. They apply to the whole area of Antarctic glacierization.
where R is the radiation balance of the ice surface, R a the radiation balance of the atmosphere, R s the radiation balance of the ice-atmosphere system, (LE) the latent heat of evaporation, (Lr) the latent heat of precipitation, (La) the latent heat of phase transformations of advective moisture, (Lc) the latent heat of phase transformation of the atmospheric moisture discharge, P the turbulent heat exchange between the ice surface and atmosphere, and (Ad) the heat advection in the atmosphere.
To reduce the heat-balance calculations on the basis of the available solar radiation data the following radiation balance equations are used
where R k is the short-wave radiation absorbed by the surface, I a the short-wave radiation absorbed by the atmosphere, E 0 the effective surface radiation, (E ∞ − E 0) the atmospheric radiation into space, and E ∞ the long-wave radiation into space. It follows that
The absorbed short-wave radiation is calculated from the formula:
where Q is the total radiation coming to the surface, α is the surface albedo, and
where (R k + I a) is the short-wave radiation absorbed by the ice/atmosphere system.
Solar radiation coming to the atmosphere Q s is given by
where α s is the albedo of the ice/atmosphere system.
New maps of the distribution of annual fluxes of total radiation Q and the ice-surface radiation balance R in Antarctica (Reference MarshunovaMarshunova, 1980) together with the long-term surface radiation data from Antarctic stations (Reference Dolgin, Dolgin, Marshunova and PetrovDolgin and others, 1976) were used as initial data for the calculations of the radiation-balance components.
Another important source of information on the heat exchange between the Antarctic ice sheet and the atmosphere is the Nimbus-3 results and the calculations of the solar radiation fluxes and long-wave radiation based on the satellite data (Reference RaschkeRaschke and others, 1973). The results of the calculations are presented on maps of the South Polar region as mean annual albedo α s, absorbed short-wave (R k + I a) and outgoing long-wave radiation E ∞, and radiation balance R s of the ice/atmosphere system. The numerical values of the radiation balance components for Antarctica have been published by the author (Reference Aver’yanovAver’yanov, 1979[b]).
The usual difficulties due to the lack of the necessary amount of data of instrumental measurements arise when attempts are made to determine long-wave radiation fluxes described by the following equations.
The surface long-wave radiation balance is given by
where E 0 is the effective radiation of the surface calculated by Equation (8) in which R and R k are measured variables (Reference Dolgin, Dolgin, Marshunova and PetrovDolgin and others, 1976; Reference MarshunovaMarshunova, 1980), E z is the surface radiation calculated by the Stefan–Boltzmann formula E z = δσT 4 for T = 237.7 K which is equal to the mean annual temperature of the ice surface (Reference Shumskiy and TolstikovShumskiy, 1969), and E a is the atmospheric counter-radiation defined as E 0 + E z.
The long-wave radiation balance of the atmosphere is given by
where (E ∞ − E 0) is the atmospheric radiation into space, E ∞ being a measured variable (Reference RaschkeRaschke and others, 1973), and E k is the absorption by the atmosphere equal to E z − E w where E w is that part of the ice surface radiation outgoing into space.
It is known that most of the ice surface radiation is absorbed by atmospheric water vapour, CO2, and ozone, but mainly by the water vapour which is transparent to infra-red radiation only in a narrow spectral band known as the atmospheric window. We do not know yet the amount of heat E w outgoing through that window in Antarctica. To close the long-wave radiation balance we can assume this part of the radiation outgoing into space to be approximately numerically equal to the effective ice surface radiation E 0 (in fact it can be a little lower), i.e. E w = E 0. Then the long-wave radiation absorbed by the atmosphere E k would be equal to the atmospheric counter-radiation E a, through the nature of this coincidence is considered to be irregular.
The balance of long-wave radiation in the ice surface/atmosphere system can be then given by
where E ∞ is the instrumentally measured value (Reference RaschkeRaschke and others, 1973), (E ∞ − E 0) is calculated as shown above, and E w is taken from the consideration that E w = E 0.
Advective heat (Ad) and turbulent exchange P are determined as residuals of Equations (5), (6), and (7). Table II shows the components of radiation and heat balance, obtained as described above.
The accuracy of absolute values in Tables I and II seems not to be very high due to errors caused by different measuring methods and paucity of observational data, because of this the data taken for averaging were not homogeneous in quality and time. This is primarily true for moisture parameters, while the radiation balance components in a number of cases were calculated with an accuracy comparable with the probable measuring error. These data, however, allow us to assess the order of magnitude of major heat and moisture fluxes participating in the Antarctic glacierization. They are also indicative of the structure of the moisture and heat balances.
Table II Components of radiation and heat balance
Moisture balance (Table III)
Ninety-nine per cent of the total surface discharge Q′ (Q′ = A + q + f) is the solid-phase moisture. Weak evaporation causes the discharge coefficient Q′/r (= 0.89) to be much larger than it is in the Arctic (0.70). The moisture turn-over coefficient r/r a( = 1.03) is lower than it is in African deserts, indicating that there is no local precipitation due to evaporation. The ratio of the total outflow of the atmospheric moisture to the precipitation amount c/r ( = 0.16) indicates a relatively high intensity of precipitation formation processes and degree of usage of advective moisture. That is why the ratio of the total surface discharge to the atmospheric moisture outflow in Antarctica Q′/c is very large (5.6), it is 2.7 times larger than it is in Greenland. If we consider the fact that 83% of the advective moisture coming to the Antarctic mainland is stored in the Antarctic ice sheet, we can agree that it is the largest area of atmospheric moisture discharge on the Earth’s surface. It is a well-known fact that the Antarctic ice sheet stores 90% of the fresh water available over the Earth’s surface.
Table III Moisture balance
Radiation balance (Table IV)
The negative sign of the ice sheet radiation balance seems to be due to a very high reflectivity of the ice surface rather than a large effective radiation. The positive balance of the short-wave radiation is three to four times less than it is in those areas where there are nunataks.
Radiation measurements from Nimbus-3 helped us to estimate the radiation balance of the Antarctic atmosphere Reference Raschke(Raschke and others, 1973). It appears that the top of the atmosphere gets 12% more radiation than is predicted by theoretical calculations Reference Kondrat’yev(Kondrat’yev, 1965; Reference BudykoBudyko, 1971). The albedo of the atmosphere is very low due to its extreme transparency. The long-wave radiation of the atmosphere is 55% of the radiation directed to the surface of the Earth and 45% is the outgoing radiation from the top of the atmosphere, while for the Earth’s atmosphere as a whole these fluxes are 70% and 30%.
The ice surface/atmosphere system gets 57% of its radiation from the Sun and 43% is the long-wave radiation emitted from the ice surface and absorbed by the atmosphere. The radiation losses are as follows: reflected short-wave radiation is 28% and long-wave radiation lost to space is 72%. This is explained by the very high albedo of the system resulting in a smaller flux of absorbed short-wave radiation in Antarctica which is 3.2 times less than elsewhere.
Table IV Radiation balance
Table V Heat balance
Heat balance (Table V)
Antarctica is the only land area where the turbulent heat flux is directed from the atmosphere to the ice surface, that is the continent can be regarded as a huge heat sink. The turbulent heat flux is 33% of the solar flux absorbed by the ice surface.
Speaking of the heat coming to the atmosphere, we have to mention heat advection (which includes latent heat due to precipitation) which is 1.5 times higher than that of the absorbed short-wave radiation, provided the Earth’s atmosphere gets equal amounts of advective and radiant heat.
In the ice/atmosphere system the heat income is equally represented by the absorption of short-wave radiation and by non-radiational exchanges, their relative amounts being 39% of the solar radiation coming to the top of the atmosphere. The expenditure of thermal energy in Antarctica is almost exclusively due to long-wave radiation from the ice surface and from the top of the atmosphere. The total loss of radiant energy caused by the negative radiation balance of the ice/atmosphere system related to the total area of the ice sheet (13.94 × 106 km2) per year is 3.3 × 1013 GJ. It should be mentioned that a similar value was obtained by Reference Rubin, Wexler, Wexler, Rubin and CaskeyRubin (1962) though he used another method.
Figure 1 shows the major heat fluxes participating in the energy exchange processes between the Antarctic ice sheet and the atmosphere, the flux values are given in per cent of the radiation Q s coming to the top of the atmosphere over Antarctica. It should be noted that this scheme shows major features of the radiation and heat balances of Antarctica, however the components of radiation fluxes are not fully taken into account. For example, the short-wave radiation I a absorbed by the atmosphere originates not only from the absorption of part of the radiation when flux Q s passes through the atmosphere to the ice surface, as the atmosphere also itself absorbs part of Q α, the radiation reflected from the surface.
The glaciological significance of the thermal losses from the Antarctic ice sheet (3.3 × 1013 GJ) and the corresponding heat from lower latitudes becomes evident when we compare this value with the changes of the heat content of the atmosphere caused by climatic temperature changes. The marginal heat losses exceed by two orders of magnitude the changes of heat content of the Antarctic atmosphere (1.0 × 1011 GJ) and are an order of magnitude larger than the changes of the heat content of the whole of the Earth’s atmosphere (5.3 × 1012 GJ) if the temperature changes by 1 K. Thus a contemporary climatic change could not trigger any qualitative changes of the Antarctic glacial climate.
The heat and moisture advection onto the ice sheet, the amount of atmospheric precipitation and accumulation, and the radiation balance are believed to be significant glacio-climatic indices of the Antarctic glacierization regime. The invariably negative radiation balance here determined results in such low temperatures of the ice surface that the glacier would maintain itself with the smallest possible amount of precipitation. This is confirmed by the position of the snow-line at sea-level beyond the ice sheet. Considering these natural features and the above-mentioned enormous inertia of the cold ice-covered mainland in response to any external forcing, we can believe the modern Antarctic glaciation to be steady with respect to presently occurring climatic change.
