From 1966–67 until 1976–77, in accordance with the programme of the International Hydrological Decade, studies on heat, ice, and water balance were carried out in the Marukh mountain-glacier basin (the Caucasus; upper reaches of the Marukh River of the Kuban River system). They included snow surveys, measurements of ablation usings stakes, gauge run-off measurements at the outlet of the glacier’s basin, repeated measurements of thickness, density, and liquid content of the firn layer in the nourishment area, and repeated stereophotogrammetric measurements of the glacier’s volume. Equations of the water–ice balance are different for the areas of nourishment and ablation (Reference KrenkeKrenke, 1973).

For the nourishment area:

where P _s is solid precipitation, P _e is liquid precipitation, P _d is drift and avalanche horizontal snow transport to the glacier, E _c is condensation, E _e is evaporation, N _s is snow left on the glacier, N _in is inner nourishment due to water refreezing within the ice sequence of the glacier, and R is run-off.

For the ablation area:

where M is melting of many years’ ice.

Accumulation on a glacier (A _c) is described as

Surface ablation (A) is described as

Total ablation (A _t) is described as

Mass balance of a glacier (B) is described as

Table I demonstrates changes of mass balance in Marukh glacier over 11 years. The amount of ablation corresponds to glacial run-off, since the amount of refreezing or “inner nourishment” was subtracted from the surface melting; in various years the amount of refreezing or “inner nourishment” ranged from 13 to 25 g/cm² per unit of area of the glacier. “Inner nourishment” (or internal refreezing) has two components. One is melt water which refreezes in old firn. In determining this by densification we take into account the effects of settling and horizontal expansion (Reference KrenkeKrenke, 1972). In a pit, this was found to be 27 g/cm² in 1967 and 30 g/cm² in 1968. It was assumed as 28.5 g/cm² for the whole accumulation area for all years. The other component is melt water which refreezes in the remaining new snow. The amount of this water is equal to 7% of the mass of the remaining snow as it was determined by calori–metric and dielectric methods. The total value for mass balance over 10 years (−55 g/cm²) agrees well with that determined by the geodetic method (−51 g/cm²) over the same period.

Values for ablation calculated by a hydrological method (subtraction of liquid precipitation and melting from the non-glacial part of the basin from run-off) differ by only 6% from calculations based on stake data. Therefore, no corrections were made for data obtained by the stake–pit method.

The components of the mass balance have a small range of variation. The coefficient of variation (C _v) is 0.15 for accumulation and 0.11 for ablation. However, the net-balance figure varied within a broad range, i.e. from −121 g/cm² in 1974−75 to 26 g/cm² in 1969–70. The root-mean-square deviation of mass balance was ±46 g/cm². This is 0.18 of the mean of the norms of accumulation and ablation.

Because of a comparatively low variability in accumulation and ablation, the calculation of mass balance using meteorological parameters gives higher errors than when the climatological method is used. The climatological method means assuming each annual value equal to the multi-year mean value (Reference MenshutinMenshutin, 1977). However, remote-sensing methods now open new possibilities based on the relationship between mass balance and its components within the accumulation and ablation zones, which are easily identifiable on satellite imagery and air photographs.

Mass balance was compared with the glacial coefficient(K) (Reference KalesnikKalesnik, 1939), which is the ratio of the accumulation to the ablation area (Fig. 1). Since most of the observation period included years with a negative mass balance, to obtain higher positive values of mass balance we used the altitude of the snow line and a “transient” glacial coefficient, which was defined not at the end of but during the ablation period.

Fig. 1. Correlalion of the glacial coefficient with mass balance.

For a specific date within this period, when the old ice became snow-free, a map of the ablation area was plotted. The ablation in this area was subtracted from the accumulation in the accumulation area; the difference represented the mass balance of the glacier on the assumption that ablation had ceased after the specific date.

It transpired that the value of mass balance (B in g/cm²) is closely correlated with the glacial coefficient based on measurements made on remote-sensing photographs of the glacier. For Marukh glacier this correlation had the form:

Therefore, the correlation in Equation (7) having been established for the glacier under study, it is possible to determine the mass balance of the glacier from the photograph taken at the end of the ablation period before fresh snowfall. Extrapolation of ablation to the date of snowfall and the corresponding negative correction of the calculated balance can be based on meteorological data.

Let us consider annual variations of the components of glacier balance and their relative values. The year 1967–68 will be taken as an example of the balance just a little below the equilibrium but above the average, and 1968–69 as a case of a clearly negative mass balance with twice as much snow loss as the average over 11 years.

Corresponding to the climatic conditions, the structure of the glacier area was also changing (Table II). Thus, in 1968–69 with a negative balance, the accumulation area was higher and occupied only half of the 1967–68 accumulation area when conditions were close to equilibrium.

It can be seen from Table III, which shows components of the water-ice balance by zones, that, despite different amounts of precipitation in each year, total run-off from the basin and ablation remain the same. Higher run-off from the glacier is compensated for in years of low snow-fall by a reduction from the unglacierized part. The thickness of snow remaining in the accumulation zone shows little dependence on precipitation; it is only the area which changes and correspondingly the volume of snow remaining. This allows us to determine the remaining layer by measuring the area of the accumulation zone; this is easily done by using the remote-sensing photographs.

The components of the water balance in specific terms for each of the glacier’s zones have little dependence on the amount of precipitation; precipitation is most important for the total volume of these components in the accumulation and ablation areas, and accordingly for the components of glacial run-off from the entire basin. The balance features of the glacier in 1968 may be taken as typical. In this year the firn zone accounted for 20−25% of the run-off, the ablation zone for a little less than 50%, and the unglacierized zone for 33%.

In dry years the contribution of the firn zone in terms of run-off decreased to 10%, whereas the ablation zone increased its contribution to 66% in proportion to area of the zones. The remaining 24% is non-glacial run-off. The ratio of each zone’s contribution to run-off to its areal percentage is constant. The ratio of glacial to non-glacial run-off increases in dry years; this increase compensates in total run-off for the lower run-off from the unglacierized zone.

Calculation of all the components of the water balance is only possible if data are available for both the area of the various zones and for the air temperature (as recorded by meteorological stations). Summer precipitation can be calculated in this case using data from the nearest meteorological stations. The accuracy of such a calculation is approximately 1.5 times higher than the “climatological” one, which does not take time variation into consideration. In future, it may be possible to calculate all components of glacier balance using an integrated ground remote-sensing system of measurements of area, temperature, precipitation, and albedo of the glacier surface. To solve some of the problems, and glaciological problems in particular, it is essential to know the spatial distribution of the various components of glacier balance within the confines of the glacier. The authors have suggested that such components are similar from year to year, and have examined the possibility of using this fact for calculations. To this end, those years with somewhat different values for average accumulation and ablation were chosen. To make a quantitative comparison, all components were normalized by averaging the parameters for the total period of observation, and then averaging 11 normalized “typical” years (Figs 3 and 4).

Fig. 3. Fields of coefficients for variation Of normalized components of mass balance: (a) coefficients of variation for normalized accumulation; (b) coefficients of variation for normalized ablation.

Fig. 4. Parameters of ablation normalized for a glaciers average area using different types of weather:(a) normalized ablation for periods of cloudless weather; (b) normalized ablation for periods of rainy weather.

Thus, remote-sensing photographs allow us to assess both the relative and absolute values for the components of mass balance of the glaciers studied previously.

Since changes in the components of mass balance from year to year consist of changes in the area of each zone and of the water-equivalent layer thickness of these components in each zone, if we know the area of each zone we can considerably reduce the error in calculation of the glacier balance compared to using the climatological method. Zonal variations in the water-equivalent layer thickness for net accumulation and net ablation in the zones of accumulation and ablation are shown in Table IV.

If the root-mean-square variation scattering for an average layer of net accumulation is ±19 g/cm², and for a layer of net ablation it is ±33 g/cm², the error due to this variation recalculated for the entire area of the glacier is ±7and ±21 g/cm², respectively.

The relationship between anomalies in accumulation and ablation is somewhat weak, and therefore the theoretical error in a mass-balance calculation based only on actualareas of the ablation and accumulation zones and of the known average water-equivalent thickness of the balance layer in each of these areas is = ±22 g/cm², which is twice as accurate as the mass balance calculated on the basis of the climatological norm. The actual error using this method with our data for 11 years (Table I) is ±19 g/cm². Since there is no correlation between the specific mean balance of accumulation and ablation with the area of each respective zone, the relationship cannot be used. The error using the mass-balance glacial coefficient relationship is only a little lower (±18 g/cm²). However, this method allows assessment of individual anomalies in net accumulation and ablation, i.e. of the N _s and M components in Equations (1) and (2). The N _in parameter is determined for Marukh glacier as (28.5 + 0.07N _S)K/(K + 1). The value of 28.5 is possibly also applicable to other glaciers with temperate firn zones (Reference GolubevGolubev, 1976).

Earlier publications (e.g. Reference KrenkeKrenke, 1975) have suggested using a method of calculating total accumulation and ablation at the equilibrium line of glaciers based on mean summer air temperature extrapolated to this altitude. Using this relationship, i.e. the sum of melting temperatures extrapolated to the altitude of the transient snow line, it is also possible to calculate the surface ablation of snow and ice (A) for other altitudes. Then the total ablation (A _t) for the accumulation zone is equal to A − N _in and for the ablation area A ≈ A _t; since E is small, A _t ≈ R. Then, accumulation in the zone of nourishment is equal to A − N _s, and in the ablation zone A − M. Liquid precipitation may be calculated from the curve of precipitation versus altitude using data from meteorological stations. Solid precipitation may be calculated by dividing accumulation by the coefficient of concentration, (x _s+ x _d)/x _s, which maybe taken as constant from year to year.

Thus, in future it may be possible to calculate, for the glacier being studied, all the components of mass balance by measurements of the accumulation and ablation areas identified from remote-sensing photographs together with accumulation and ablation calculated from air–temperature data from nearby meteorological stations. Such a calculation is 1.5−2 times more accurate than the “climatological” one, which does not take into account the factor of temporal variability.

For the study area, even if direct observations are not available, it is still possible to make an assessment of the spatial distribution of mass-balance components if it is assumed that the areas of accumulation and ablation are similar from year to year. In order to get a quantitative assessment of the degree of similarity, the fields for each year were normalized by their average parameters, and then the “typical” 11 year normalized fields were calculated (Fig. 2a and b). The procedure of “normalization” means dividing the individual figures by the averages for the whole glacier.

Fig. 2. Fields of mass-balance components normalized for the average area of the glacier: (a) average normalized accumulation over 11 years; (b) average normalized ablation over 11 years.

The deviations of individual fields from the normalized ones are not large. To make a quantitative assessment, co-efficients of variation of normalized parameters at each point were calculated (Fig. 3a and b). For the ablation area the coefficients are every where below about 0.20, and on average they are 0.16. Therefore, the hypothesis of similarity of ablation area from year to year is confirmed satisfactorily. The variability in the average water-equivalent thickness for ablation is 0.11; the variability in area is weakly related to its average; total variability of ablation at a specific point is described by the coefficient of variation, .

The coefficients of variation for normalized parameters of the accumulation field are still below the admissible 20% error within most of the glacier. However, both the lower part of the glacier which is subject to strong winds from tributary glaciers and that part along the valley have highly variable fields of accumulation with coefficients of variation from 30 to 40%. Calculations for this part of the field require the introduction of additional parameters which are not readily available (e.g. velocity and direction of winds). However, for most of the glacier it is possible to calculate the area of the accumulation zone. The average coefficient of variation for normalized parameters of accumulation is 0.20. The variation in the glacier’s average total amount of accumulation is 0.1 5. Therefore, the coefficient of variation for total accumulation at specific points is .

A variance analysis was made of accumulation and ablation in warm, cold, cloudy, cloudless, dry, and rainy decades. All fields turned out to be similar (Fig. 4a and b). Isoline patterns correspond mainly to the relief of the land adjacent to the basin and not to that of the glacier itself; there is a similar correspondence of isolines for the accumlation field in the glacial system to the whole relief of the mountainous terrain. This similarity is disturbed in decades with sharply different albedos. However, year-to-year variations in albedo are not very high.

However, qualitatively the fields of accumulation and ablation show similar ratios for different glaciers; maximum ablation usually occurs close to the snout (the steep terminus itself is shadowed and part of it is buried beneath snow transported by wind); maximum accumulation occurs below back walls of cirques which are in the accumulation zones of glaciers but a little remote from them.

At the glacier margins, ablation is greatest owing to thermal radiation, etc. This similarity may be expected in glaciers of a similar morphological type. We have identified three morphological types, which correspond to the vertical distribution of glaciers. The first type includes glaciers with a maximum area in their lower (according to height) half; the second type has its maximum area near the centre; and, the third type, in the upper part of the glacier. These types correspond to increased complexity in the morphology of the accumulation areas.

To test the similarity between the fields of the components of mass balance for U.S.S.R. glaciers investigated according to the programme of the International Hydrological Decade, normalized values for ablation and accumulation were compared with normalized heights and distances from the glacier’s axis.

Normalized heights (h) were found from the expression

where H is actual height, H ₀ is height of the glacier’s terminus, and H _b is height of the highest point of the glacier. The distance from the glacier’s margin was normalized using the same procedure.

Normalized accumulation (ac) was derived from the expression

where α _c is actual accumultion, α _CO is accumulation at the terminus of the glacier, and α _cb is maximum accumulationon the glacier.

Normalized ablation (ab) was produced according to the expression

where α is actual ablation, α ₀ is ablation at the end of the moraine-free part of the glacier, and α _min is the minimum ablation on that part of the glacier which is free from continuous moraine. Changes in accumulation and ablation across the glacier were normalized in a similar way.

Finally, it transpired that the curves for normalized ablation almost coincide for glaciers of all types (Fig. 5a), and that the curves for normalized accumulation are similar for glaciers of one type (Fig. 5b).

Fig. 5. Distribution of normalized mass–balance components for various glaciers. The method of normalizing is given in the text, (a) Distribution of accumulation across various glaciers, ac, normalized accumulation; b, normalized width of glaciers. 1. Marukh glacier (Caucasus); 2. Central Tuyuksu glacier (Zaiti Alatau, Tianshan); 3. Minor Aktru glacier (Altai). (b) Vertical distribution of ablation; a. normalized ablation; h. normalized height. 1. Marukh glacier; 2. Jankuat glacier(Caucasus); 3. Abramov glacier (Alai ridge); 4. Central Tuyuksu glacier: 5. Minor Aktru glacier; 6. Glacier No. 31 (Suntar−Hayata ridge, Yakutia).

The conclusions show that fundamentally it is possible to calculate accumulation and ablation zones by using remote-sensing photographs of those glaciers; accumulation and ablation parameters had been calculated only up to the equilibrium line from extrapolation of air temperatures and without any observations on these glaciers, by using similarities of accumulation and ablation zones of other glaciers which had already been investigated.