I. Introduction
McCall Glacier is a small glacier (6.22 km2) located in the Romanzof Mountains of the Brooks Range in Alaska, at lat. 69° 18’ N., long. 143° 48' W. (Fig. 1). It is the only Arctic glacier currently being studied in the United States, and is of special importance as it lies on two glacier "chains" recommended for intensive study in the International Hydrological Decade. These two chains are the Arctic Circle chain and the Western American chain. McCall Glacier was first studied during the I.G.Y. (Reference SaterSater, 1958,1959; Reference KeelerKeeler, 1959; Reference MasonMason, 1959; Reference Meier, Wright and FreyOrvig, 1961; Reference WendlerOrvig and Mason, 1963).
The mass balance of the McCall Glacier has been measured for the hydrological years 1968/1969 and 1969/1970 (Reference Wendler, BensonWendler, BensonFahl and BensonCorbinWendler and others. 1972) and for 1970/1971 and 1971/1972 (Trabant and others, unpublished). However, four years of mass-balance data is a very short interval to determine general trends (e.g. Reference Paterson.Paterson, 1969), hence other methods were used to obtain mass-balance estimates for a 15-year period. This attempt was considered useful, since there are only very few long-term mass balance studies, most of them in lower latitudes (Reference SableSchytt, 1962; Reference Hoinkes and OdishawHoinkes and Rudolf, 1962; Reference LaChapclleLaChapelle, 1965; Reference Meier, Wright and FreyMeier and Tangborn, 1965).
Fig. 1. Location map of the McCall Glacier basin.
II. Photogrammetry
Reference Hoinkes and OdishawFinsterwalder (1953) first showed that photogrammetry is a powerful tool in obtaining mass-balance changes over a long period of time. Best results are obtained, not with annual photographs, but with photographic coverage over intervals of 10 years or more. Otherwise the error in the accuracy of the evaluation as compared with the actual change of the glacier may be disproportionally large.
In the summer of 1958, as part of the I.G.Y. program, aerial photograrmmetric pictures on a scale of 1: 24 000 were obtained of McCall Glacier, which resulted in a I; 10 000 scale map with 5 m contours (Reference FahlCase, 1958), In the summer of 1971 we repeated the photogrammetric flight (Fig. 2) this time with color photography at a scale of 1: 20 000 mainly for reasons of better interpretability. The time lapse of 13 years between 1958 and 1971 was considered to be sufficient for a quantitative determination of glacier height changes. Normally, such changes are found indirectly by comparing two contour maps of the same region, but compiled from photographs taken at two different times ("topographic" method). The fact that no ground control data were available from 1958, and that the glacier height changes might be less than expected, i.e. less than about 5 m, made it advisable to establish, survey, and signalize a completely new ground control. High accuracy could only be obtained by evaluating the new photographs together with the old ones, viz. via identical features or points.
During July and August 1971 a local three-dimensional triangulation network consisting of some 30 stations was observed by a group of three persons. Angle measurements were carried out with a Wild T2 theodolite, the scale was determined by some ten distances measured with a Hewlett-Packard 3800B distance meter. Ten stations were signalized by crosses 2-3 m long laid out with fluorescent red plastic material. The accuracy obtained after a simultaneous least-squares adjustment of the network (Amaresekere, 1972) showed mean standard errors of 0.2 m for the horizontal coordinates and 0.15 m for the elevations.
Fig. 2. Aerial photo-mosaic of McCall Glacier,1971
Due to poor third generation quality of the 1958 photography, and completely missing camera calibration dataFootnote *, only a purely "analytical" method could be considered as giving sufficiently accurate results. Λ variety of solutions to this so-called block-analytical aerial triangulation do exist and are commonplace in photogrammetrk practice (e.g. Reference DreiseitlBrown, 1973). Systematically overlapping photographs are related to each other by means of transfer points. As the image contrast on the 1958 photographs was extremely poor, particularly on the glacier surface (Fig. 3), since rather different illumination effects and snow coverage prevailed during the two photo missions, and since the photo scales differed by about 20%, it was virtually impossible to locate a sufficient number of transfer points between the 1958 and 1971 photographs. We therefore decided to make use of a rigorous stereo-block analytical triangulation similar to a suggestion published by Albertz. (1972). No transfer points are required with this method, but possibly all overlapping photographs must be measured stercoscopically in stereo comparator. Figure 4 shows the geometric configuration of" the 2x3 photographs selected for this project. The straight lines connecting the six camera stations indicate that in total eleven stereopairs were measured, viz. two pairs with 1958 photos, two pairs with 1971 photos, and seven pairs with combined 1958/1971 photographs. The actual photogrammetric solution is described in Reference DorrerDorrer (1975).
Fig. 3. (a) Enlarged section of 1958 photography (left) (a) Enlarged section of 1971 photography (right).
Fig. 4. Fig. 4 Schematic photographic coverage of McCall Glacier area for stereo block analytical triangulation. 1958 photographs 05,04,03; scle 1; 24 000. 1971 photographs 19.17,15; scale 1;20 000.
The camera stations and exterior and—for the 1958 photos— interior orientation parameters are related to each other by means of three types of non-linear condition equations, viz. a coplanarity condition for each pair of measured points, a control condition for each measured control point, and a transfer condition for a measured reference point. In a first phase, an iterative simultaneous least-squares procedure was used to solve for the 32 unknown parameters. A total of 516 points were measured stereoscopically, viz. control points, stereo-pair points, glacier points, and a few reference points on bedrock close to the glacier for eliminating or reducing local systematic error sources (bias) inherent in the two types of photographs. Already at this stage it became clear that, due to poor contrast conditions, only a few regions on the glacier surfaces were suited for selecting measurable glacier points. The néve region was entirely unsuitable due to snow coverage of the 1971 photographs.
The second phase of the procedure consisted of intersecting spatially all control, glacier, and pass points. The residual y-parallaxesFootnote * agreed very well with random variables taken from a normally distributed population. As expected, for the 1958 photographs, the root-mean-square values are roughly twice as large (0.85 m) as for 1971 (0.40 m). Though not determined explicitly, corresponding elevation errors are of the same order of magnitude.
In its third phase, the procedure performed an absolute orientation into the given ground control. An existing computer program (Ackermann and others, 1970) was used, which resulted in surprisingly small root-mcan-squarc values for the coordinate residuals of all control points, viz. 0.15m for X, 0.21 m for Y, and 0.14m for Z (1971 photography only). For an average flying height of 3 000 m, the relative elevation error is thus below 0.5 × 10 4. This accuracy could have never been achieved by a purely topographic method.
The last phase was to determine representative glacier elevation changes for a few characteristic cross-sections. It was intended originally to describe the glacier surfaces by two-dimensional polynomials and to condense all information into one value for each cross-section, thus averaging out many error sources. This method, however, failed due to poorly ordered and unfavorably related point distributions on the glacier surfaces. Instead all measured glacier points and reference points were plotted on a scale of I : 10 000, and, by manual and graphical· procedures only, spot heights of the two glacier surfaces were corrected for local bias (reference points), and related to each other.
The results of the graphical method were improved by a numerical procedure. For each of the three glacier regions at least four reference points were carefully selected. Their elevation differences ΔZ were used to interpolate a least-squares bi-linear trend surface. The elevations of glacier points were corrected prior to comparing the two glacier surfaces represented by unordered sets of spot heights. The standard error of glacier elevation change is a function of its position. Computed values for each region can be considered representative for the final elevation changes shown in Table I. The standard errors ΔZ are representative for a single elevation difference average over each of the regions. Since for each region a single elevation change ΔZ was determined from several interpolated spot heights, the actual standard errors ΔZfor the meaned height change is smaller. Assuming no further bias, the standard errors ΔZ of the mean may be considered around 0.5 m (last row in Table I). The quantity σ0 represents the standard error of an original reference point elevation difference prior to eliminating a local bi-linear bias.
Table I. Glacier elevation chances 1958-71 as determined by aerial photogrammetrt
In addition, Figure 5 shows a reasonable exponential curve interpolated into the three regional elevation changes. The σ-confidence band indicates, however, that extrapolating the elevation changes beyond an altitude of 2 100 m gives rise to rather large uncertainties, and may lead to wrong conclusions.
Fig. 5. Fig. 5 Elevation change of McCall Glacier obtained from aerial photogrammetry in 1958 and 1971 plotted as a fun glacier altitude.
Using this regression curve, the glacier became in the mean 185 cm thinner, which represents a loss of 11.6X106mJ ice or snow. This would result in a mean annual balance of —128 mm water equivalent for the 13 year period. For this calculation it was assumed, that the mass loss was all ice of density 0.9 Mg m-3 This assumption should be reasonable, as the photogrammetric overflights were both made at about the same time in summer and the total amount of snow on the glacier may well have been similar. However, if part of the amount lost had consisted of snow or firn. a mean annual mass balance somewhat nearer to zero would have been found.
III. Climatology
Reference HamiltonHoinkes (1971) has shown that it is possible to obtain a good estimate of the mass balance of a glacier by using the climatological data of a nearby valley station. Using the mass-balance data of the Hintereisferner, Austria, and the climatological data of the valley station Vent, he established so called TS functions (T = temperature, S = snow). Basically, temperature summations were used after applying a correction for the altitude difference between the station and the glacier. These were then corrected for snowfall which occurred during the summer. Owing to its high albedo, the snowfall retards the ablation substantially (Reference TronovTronov, 1962). The relationships he found are good. Initially this is surprising, since the ablation on a glacier is mostly caused by radiation and not by sensible heat (e.g. Reference Hoinkes and OdishawHoinkes, 1964; Reference Wendler, BensonWendler, BensonIshikawa and BensonStretenWendler and Weiler, 1974). However, there exists a good relationship between the radiation balance and the temperature, which means that a sunny day with a positive radiation balance is also normally warmer than a cloudy day with a less positive radiation balance. Ambach (1972) and Drciscitl (unpublished) have successfully used the method developed by Hoinkes.
The nearest climatological station from McCall Glacier was Barter Island, about no km to the north of the glacier. Arctic Village, some 160 km to the south, had poor and irregular records, and Fairbanks, more than 500 km to the south, was considered to be too far away.
An attempt was made to apply the method developed by Hoinkes for the relationship between the mass balance of McCall Glacier and the climatological data of Barter Island. Although several variations of this method were applied, no relationship could be established. To discover if there was any relationship between the climatological data of Barter Island and the mass balance on McCall, the daily mean temperatures at Barter Island were plotted against the daily values of ice ablation (Fig. 6). The ice ablation data were obtained as the mean measurements of ten small ablation slakes al 1 740 m altitude, carefully read twice daily. It can be seen, that no well-established relationship exists and no further attempt was made to use the Barter Island climatological data to obtain estimates of the mass balance of McCall Glacier. The result suggests that the climate of McCall Glacier is substantially different from that of Barter Island. This has been shown elsewhere by Wendlcr and others ( 1974). McCall Glacier lies on the divide of the continental climate of interior Alaska and the Arctic climate of the slope, while Barter Island is primarily under the influence of the climate of the Arctic Ocean (Searby, 1968).
Fig. 6. Daily amount ice ablation on McCall Glacier at 1 740 m [the mean value from ten ablation stakes) plotted against the daily mean temperature at Barter Island, no km to the north..
IV. Height of Annual Equilibrium Line and Mass Balance
During our field work, on McCall Glacier between 1969 and 1972, two I.G.Y. ablation stakes were found at an altitude of about 2 065 m. These stakes had neither melted out of the ice nor been covered by the snow during the period from 1958. This means that over this time period this location had to be, on the average, near the annual equilibrium line of the glacier.
Several authors (e.g. Reference Palgov.Palgov, 1962; Reference OrvigMeier and Post, 1962; Reference Wendler and WellerWendler, 1967) have shown that there is a linear dependence between mass balance and the AAR, or, equivalently, between the mass balance and the height of the equilibrium line. Using this relationship and considering the movement of the glacier of about 10 m per year, a mean mass balance of — 265 mm per year could be calculated. However, one has to be somewhat careful with this value. The stakes were just penetrating through the surface when found. We do not know, how far the stake had been exposed above the glacier surface in the summer of 1958. If, at that time, the stake had been exposed to its full length (4-5 ft, 1.2-1.5 m), which would be the other extreme, the mass balance would be less negative by about 100 mm water equivalent and values of about —165 mm per year would be found.
V. Height of the 500 Mbar Level and Mass Balance
Schneider (unpublished), Reference HoinkesHoinkes and others (1968), Fahl (unpublished), and Dreiseitl (unpublished) have shown that there is a relationship between the height of the 500 or 700 mbar synoptic pressure level in summer and the mass balance. A negative deviation from the mean in the height means cool weather with precipitation which is "healthy" for the glacier, while a positive deviation means sunny weather with increased ablation, which is hence "unhealthy" for the glacier.
For the four years in which detailed mass-balance data were available, the mass balance was plotted against the deviation from the mean of the 500 mbar level for McCall Glacier in summer. However, the relationship found was not very good. This is understandable, as two factors influence the annual mass balance. The first is the ablation in summer, for which the deviation of the 500 mbar level might be a good indicator; the second is the accumulation throughout the year for which this value is not a good indicator. The mass balance value was therefore corrected for a precipitation deviation from the mean. Reference Wendler, BensonWendler, BensonIshikawa and BensonStretenWendler and others (1974) showed that the precipitation at McCall Glacier (about 500 mm) is about three times higher than that of Barter Island (long-term mean 160 mm). Despite the shortcomings of Barter Island as a guide to the McCall climate, a first approximation of the precipitation deviation could perhaps be made by using three times the precipitation deviation at Barter Island. This assumes that all precipitation falls in solid form, which is generally true for McCall Glacier even in midsummer.
For the deviation from the mean of the 500 mbar level, June and July were given twice the importance of May and August. The ablation season, lasting about three months, is short on McCall Glacier (Trabant and others, unpublished), and June and July contribute most to the melt, with less melt occuring in May and August. A similar method was used by Reference HoinkesHoinkes and others (1968).
If the corrected mass-balance figures are plotted against the deviations of the 500 mbar level, a relatively good relationship is found (see Fig. 7). The mean difference in the mass balance between observed and calculated values is 22 mm, a relatively small amount.
Fig. 7. The deviation from the mean height of the 500 mbar level in meters for summa plotted against the specific mass balance of McCall Glacier. The mass-balance values were corrected fur anomalies in precipitation for the hydrologica! years by applying the Barter Island data. The. summer deviations of menu height are found by adding the values for May and August and twice the values for Jane and July and dividing the sum by six.
Using this relationship, the mass balance could be calculated back to 1957 (see Fig. 8). One can see that the period 1961 -67 had positive or only slightly negative values, which is in agreement with Reference CaseFahl (1973). Altogether, the negative values dominate, a mean mass balance of —94 mm per year being found for the period 1958-71 by this method. This means that the glacier became thinner on the average by 1.36 m of ice or lost a total mass of 7.6 × 106 m3 water.
Fig.8. The calculated mass balance of.McCall Glacier, using the relationship between the height of the 500 mbar level and the mass balance (Fig. 7).
VI. Conclusion
Calculation of the mass balance of McCall Glacier using different methods showed that the glacier has lost mass for the period 1958-71 (Table II). The actual values are relatively small; one should consider, however, that annual ablation and accumulation rates are much smaller there than at lower latitudes. This trend of glacier retreat seems to be typical and has apparently been going on for a long time in the Brooks Range. Reference SableSable (1961) reported that the Opilak Glacier, about 15 km to the south-west, had been receding for 50 years ( 1907-58).
TABLE II. Estimates of the specific mass balance of· mccall glacier, for the period 1958 to 1971
Further, he found that the rate of depletion had increased since 1950. Reference FahlHamilton (1965) found that glaciers in the south-central Brooks Range had been receding for at least 50 years (1911-62). This trend of glacier retreat for the last 50-60 years found in the Brooks Range agrees well with the simultaneous retreat of the majority of the glaciers in the Northern Hemisphere (Reference DreiseitlGrosval'd and Krenke, 1962; Reference Meier and TangbornMeier, 1965; Reference HoinkesHoinkes, 1968, and Reference Meier and TangbornMeier and others, 1971 )
Acknowledgement
The research was supported by the Atmospheric Science Section, National Science Foundation, under Grants GA-37306 and DES 75-06184. We would like to thank our colleagues and students who helped with the field work. Professor N. Strctcn read this manuscript, and made many valuable comments, for which we are thankful.
