SHORT TITLE
CHANGES IN SURFACE HEIGHT, 1957-1967, OF THE GILMAN GLACIER
Keith Charles Arnold, Facu1ty of Graduate Studies, Interdiscip1inary
G1acio1ogy, for degree of Master of Science ABSTRACT
Keith Charles Arnold
Determination of Changes of Surface Height, 1957 to 1967,
of the Gi1man Glacier, Northern Ellesmere Island, Canada.
Facu1ty of Graduate Studies
Interdiscip1inary G1acio10gy
Master of Science
SUMMARY
In 1967, 29 points on the Gi1man Glacier origina11y 10cated in 1957 were repositioned with a mean error of 0.36 m. Their height were redetermined with a mean error of 0.25 m. Refraction coefficients ranged from 0.047 to 0.558, with a mean of 0.162.
A profile in the accumulation area showed 1itt1e change. Down glacier from a seismic profile near the average position of the equi1ibrium 1ine, 1957 to 1967, the average height 10ss was 2.4 m.
From May 1958 to May 1967 the glacier advanced 25.4 m. A volume 10ss ca1cu1ated from height 10ss and glacier advance was 165 x 106 m3 , compared with 140 x 106 m3 ca1cu1ated from mass balance data, part1y estimated for missing years, and glacier f10w through the seismic profile. This area had a negative mass balance of 91 cm ice/yr; 69 cm ice/yr wou1d balance the vertical component of f10w, keeping the surface unchanged. DETERMINATION OF CHANGES
OF SURFACE HEIGHT, 1957-1967, OF THE GILMAN GLACIER,
NORTHERN ELLESMERE ISLAND, CANADA
K. C. Arnold
A thesis submitted in accordance with the regu1ations for the degree of Master of Science at McGi11 University. 1968
1 ® K.C. Arnold 1969 TABLE OF CONTENTS
Chapter
Preface i List of Figures ii List of Tables iH
l INTRODUCTION 1 IUGG recommendationsfor recording the variations of existing glaciers 1 Definition of thesis problem 2 Phot'ogrammetric methods 3 Non-photogrammetrie methods 5 The problem of relocating fixed positions 6 The method of "repositioning" 7 Determination of the height of fixed positions 8 Description of the field area 8
II SURVEYING ON THE GILMAN GLACIER DURING THE IGY, 1957-1958 12 ·Choice of method 12 Errors of closure 13 Determination of glacier movement 15
III FIELD PROCEDURE, 1967 23 . IV ERRORS IN REPOSITIONING 26 Theory of errors in repositioning 26 Errors in repositioning encountered on the Gilman Glacier 29
V ERRORS IN DETERMINATION OF HEIGHTS 33 The problem of atmospheric refraction 33
VI CHANGES IN HEIGHT OBSERVED ON THE GILMAN GLACIER 42
VII DISCUSSION OF RESULTS 47 Factors affecting the change in level of a ~lacier surface 47 Factors observed or estimated on the Gilman Glacier 50 Changes in the snout of the Gilman Glacier 63 The change in volume down-glacier from seismic prof~le 101 66
VIII SUMMARY 70
REFERENCES 72 -i-
PREFACE
This thesis is based 011 field work carried out on the Gilman
Glacier, Northern Ellesmere Island, during the International Geophysica1
Year, 1957 to 1958, and during the months of May and June, 1967. In
1957 and 1958 the work formed part of "Operation Hazen" organized by the Defence Research Board, Department of National Defence, Canada.
In 1967 arrangements were made by the Department of Energy, Mines and
Resources, In1and Waters Branch, for me to join a Defence Research
Board field party revisiting the Gi1man Glacier.
l wou1d 1ike to acknow1edge the great assistance extended by
Dr. G. Hatters1ey-Smith, for making it possible for me to visit the
Gilman Glacier in 1957, 1958 and 1967, and for a110wing me to use unpub1ished field data from the most recent visite The 1967 work wou1d not have been possible without the carefu1 surveying observations of F/Lt. C. D. Drew and F/Lt. P. G. Pinney of the Royal Air Force
Ellesmere Island Expedition, 1967, and assistance in the field from u. Embacher and J. van der Leeden. l wou1d a1so 1ike to thank my employer, the Department of Energy,
Mines and Resources, for educationa1 1eave during the winter of
1967-68, for a110wing time for the preparation of this thesis, and for assistance in typing and drafting diagrams.
Fina11y l would 1ike to thank my supervisor Dr. Fritz Muller" for his academic supervision, and for his encouragement to me whi1e writing this thesis. -ii-
LIST OF FIGURES
Figure
1 Location of field area Il
2 Control surveys for geophysica1 work, International Geophysica1 Year, 1957-1958 17
3 Location of seismic and gravity profiles, 1957-1958 18
4 Glacier movement determined over one year, 1957-1958 20
5 Glacier movement determined during the summer of 1958 22
6 Error figure for repositioning 28
7 Ca1cu1ation of coefficient of refraction, k 34
8 Location of height changes measured in 1967 41
9 Amount of change of surface height, 1957-1967 43
10 Long profile of the Gilman Glacier 46
Il Effect of a wave type perturbation of f10w on change of surface height 49
12 Me1t re1ated to accumu1ated me1ting degree-days 54
13 Comparison of mean dai1y temperature at A1ert and Gilman Glacier, 1957-1958 56
14 Comparison of 142 mean dai1y temperatures, A1ert and Gilman Glacier camp, 1957-1958 (Median Values) 57
15 Relation between mass balance and change in thickness, 1957 to 1967 62 -iii-
LIST OF TABLES
Table
1 Glacier movement determined over one year, 1957-1958 19
2 Glacier movement determined during the summer of 1958 21
3 Maximum errors in repositioning (m) for an angu1ar error of 10" arc in directions 29
4 Distribution of errors of directions to repositioned points 30
5 Distribution of distances to repositioned points 30
6 Distribution of errors of horizontal coordinates of repositioned points 31
7 Accuracy of repositioned points on the Gi1man Glacier 32
8 The advantage of simu1taneous reciproca1 vertical angles 36
9 Accuracy of height changes measured on the Gi1man Glacier 40
10 Summary of changes of surface height on the long profile of the Gilman Glacier 44
11 Net accumulation for the Gilman Glacier, and precipitation data for A1ert 51
12 Me1ting degree-days at the Gilman Glacier, estimated from A1ert mean dai1y temperatures by comparison of individua1 values 55
13 Me1ting degree-days at the Gilman Glacier, estimated from A1ert mean dai1y temperatures by modified 1apse rate method 58
14 Observed and estimated mass balance on the long profile of the Gilman Glacier (ice equiva1ents) 60
15 Distance of the snout of the Gi1man Glacier from West Base cairn 64 -~
cruœTm l
INTRODUCTION
IUGG recommendations for recording the variations of existing glaciers
It has long been realized that glaciers undergo changes in their extent and thickness, and that these changes are related to changes in seasonal snowfalls and summer warmth. Because of the complicated physical character of ice ·as a material in nature, the response of any individual glacier to locally measured climatic changes is not simple, and is still a matter for theoretical investigations, to be checked by field observations. In spite of this difficulty it is hoped that a large sample of glacier changes on a world-wide basis will be valuable for increasing our understanding of the glacier-climate re lationship, and of extending our knowledge of climatic change in glaciated areas into the past, finally attaining the ability to pre dict the effect of a small climatic deterioration in a glacierized area.
During the General Assembly of the International Association of
Scientific Hydrology held in Helsinkiin 1960, the Commission of Snow and Ice resolved to undertake the recording of variations of existing glaciers on a permanent basis (General Assembly of Helsinki, 1960, p. 5).
In particular, they agreed to prepare a document detailing the types of measurement desirable. A Sub-Committee was set up to prepare this report, which was published in the proceedings of the Obergurgl
Symposium of the IASH, he Id in September, 1962, (Symposium of Obergurgl,
1962, pp. 306-309). With minor modifications, this report was adopted as a basis for recording glacier variations during the International
Hydrological Decade, in IHD Resolution 1-13 (Kasser, 1967, p. 47). -2-
The report of the Sub-Committee on Variations of Existing Glaciers
to the Commission of Snow and Ice stressed the glacier-c1imate re1ation
ship as the under1ying reason for recording glacier variations, and p1aced particu1ar importance on the desirabi1ity of having the greatest number of reasonab1y simple measurements of glacier variations, rather than a more 1imited number of high1y sophisticated measurements. It was desirab1e that measurements made during the International Geo physica1 Year shou1d be incorporated in the series, and according1y a five year interva1 of measurements commencing in 1963, five years after the close of the I.G.Y., was suggested. As balance measurements on a glacier are norma11y referred to the time of minimal seasona1 snow cover, the measurements for glacier variations shou1d, if possible, be made at the same time.
The body of the recommendations of the Sub-Committee was divided
into two sections, the first dea1ing with basic observations necessary for recording the variations of a glacier, and the second dea1ing with more comprehensive measurements (Symposium of Obergurg1, 1962, pp. 307-308).
The basic observations suggested were a genera1 description of the
glacier and its situation, photographs of the snout from fixed reference
stations and measurements to estab1ish the position of the snout, the measurement of the height of the snow 1ine, and measurement of surface heights at se1ected points.
Definition of thesis prob1em
The latter prob1em, the measurement of changes of surface height
at se1ected points, forms the subject of this thesis. A method was
chosen that is suitab1e for sma11 parties without access to photo
grammetric equipment, and was app1ied to an Arctic glacier origina11y -3-
studied during the International Geophysical Year. The part of the glacier where most height redeterminations were made measured 14 km in length and 5 km in width, with distances of up to 6 km from trigonometrical control points on the land.
The recommendations of the Commission of Snow and Ice specified that these measurements were "to be absolute positions fixed relative to rock marks, not moving with the ice", and should include at least a point near the snow line, a point roughly in the middle of the accumulation area, and a point roughly in the middle of the ablation area.
Mass balance data is available for a number of points on the Gilman
Glacier for five years of the period 1957 to 1967, and an estimate is made for the mass balance data of the missing years. The change in surface height is related to this mass balance data and to the flow of ice through a known cross section, measured over the years 1957 to 1958.
Photogrammetric methods
Photogrammetric equipment has a high initial cost, and people trained in its use are not readily available for glacier surveys, but if these limitations can be overcome photogrammetric methods afford the optimum solution to the problem of recording glacier variations. The time spent in field work is much reduced, a wider area can be given simultaneous coverage, and the photographic record of the glacier called for in the recommendations of the Commission of Snow and Ice is naturally available from the field work. The number of points available for comparison is greatly increased and in effect allows a comparison of areas rather than a comparison of points. Both aerial and terrestrial photogrammetry have been used with success in glacier surveys. With aerial photogrammetry the cost for an individual remote glacier may be high, but it has the advantage -4-
of giving contemporaneous coverage of a number of glaciers in the same area. Blachut and Muller" (1966) give a probable error in height of the glacier surface of the White Glacier, Axel Heiberg Island (mapped from
1,500 m above ground at a scale of 1:10,000) of 0.47 m, based on the formula:
m' ± (0.2 + 1.0 t~n a) metres, h = where a = surface slope angle.
The probable error of a height difference from a remapping would be the root-m~an-square of twice this value, or approximately 0.66 m. This could conceivably be reduced by choosing a yet lower flying height, but this might not be possible in mountainous terrain, with the associated air turbu!~ence, and would probably involve a greater number of ground control points, which themselves might need to be located on the glacier surface immediately prior to photography. For a glacier of a certain size, in other words, there will be a limiting flying height that cannot be econ- omically reduced, and at a given level of plotting machine capability, this flying height will determine the accuracy of height determinations.
Other figures that have been given, (in terms of a comparison between ~ mappings), are: (based on Kasser, 1967)
Vernagtferner (S. Finsterwalder) : 1.65 m for a single
photogrammetrically determined point
Swiss National Topographic Service : 1.42 m in the
0 ablation area for slopes of 10 , based on (0.5 + 3
tan a) m
1.73 m in the accumulation area for slopes of
0 10 , based on (1.0 + 3 tan a) m
If the glacier is of relatively limited extent, or is long and narrow and confined between good vantage points, terrestrial photogrammetry may -5-
afford a good solution. Konecny (1965), discussing both aeria1 and
terrestria1 photogrammetry of glaciers, gives 0.2 m as the probable error
of contours in the lower part of the ablation area of the Per Ardua Glacier, northern Ellesmere Island. This wou1d imp1y a doubt of 0.28 m between two mappings, for the change in height of an individua1 point. The accuracy
of terres trial photogrammetry fa11s off according to the square of the
distance from the camera stations, and ia therefore more usefu1 for
se1ected parts of glaciers, un1esa a number of base1ines are used.
Non-Photogrammetric methods
Usefu1 work can be done, especia11y on sma11er glaciers, even though
photogrammetric equipment is not avai1ab1e. Surveying on glaciers must
be conducted with the same basic techniques that are used e1sewhere, but
some considerations of terrain influence the choice of methods. The most
critica1 one is that one is working on a changing surface, and the possi
bi1ity of using reference marks on that surface is great1y 1imited. Gener
a11y it is more usefu1 to work from fixed marks on rock. The distance of
these fixed marks from the study area will influence the accuracies attainab1e.
The atmosphere immediate1y above 8n ice surface has a strong temperature
gradient, and inversions of temperature often occur. This has an effect on
atmospheric refraction of 1ight waves, which a1ters the optica1 path in both
the horizontal and the vertical sense. The errors in vertical angles are
genera11y more troub1esome, making the accurate determination of height
differences more difficu1t.
During the ablation season open crevasses or impassab1e me1t streams may
inhibit direct access to the points where measurements are desired. On the
1arger glaciers of northern Ellesmere Island the ablation area is often
bordered by an ice cliff which makes direct access to the land difficu1t. -6-
The measurement of the change of height at an absolute position fixed relative to rock marks, not movingwith the ice, can be thought of as two successive tasks, the first being to restore the absolute horizontal position, and the second being to remeasure the height of the absolute horizontal position.
The problem of relocating fixed positions
The problem of relocation is basic to many types of surveys, especially cadastral and engineering surveys, where measurements on a plan have to be carried to the ground. The moving glacier surface also suggests that some of the techniques of hydrographic surveying may be applicable.
The simplest case implies the.measurement of a line across a glacier defined by two fixed marks on each side. If the transverse profile of the glacier is smooth, and if access to the glacier from the fixed marks is easy, simple taping can restore the positions of fixed points with sufficient accuracy. A double pentagonal prism, which gives angles of
900 and 1800 with an accuracy of one to two minutes, is a useful aid in lining out between two fixed marks, and taking a check bearing on a third mark.
If these methods do not suffice, a theodolite and steel tape traverse can be made. This suffers from the disadvantage that the accuracy of the work is not known until a closure is made on another fixed point, and that errors affect the positions of each point in the traverse. Accuracy is hard to maintain over the broken terrain characteristic of many glaciers.
Although electronic distance measurement improves the accuracy of measure ment, it is not ideally suited to setting out points, for most instruments do not give a direct read-out in terms of distance. Approximate trial -7-
positions wou1d have to be used with field ca1cu1ations fo110wed by a
short distance and bearing measurement to the required position.
The same argument app1ies to distance and bearing measurements
from a fixed point on land, 'with the aid of e1ectronic distance measuring equipment, or position fixing by two distances.A1though accurate resu1ts cou1d be obtained, the field procedure wou1d be rather slow and unwie1dy.
Resection from a trial position needs on1y one observer. This ad- vantage is offset by the necessity for a field ca1cu1ation to determine the distance and bearing from the trial to the required position.
The method of "repositioning"
Another possible method is to re10cate a point by theodo1ite inter- section from two fixed points on land. This method of re10cating stakes by reproducing the directions origina11y observed to them was used on glacio10gica1 studies in Axel Heiberg Island (Muller" and others, 1963, p. 65). Each stake is fixed separate1y, so there is not the possibi1ity of errors accumu1a.ting, as in traversing. The roughness of the terrain, or access from the land to the glacier, is not an inhibiting factor with this method. The accuracy depends on the qua1ity of the theodo1ite used, and the angle of intersection of the directions from the two land stations.
If an observer is at the intersectedpoint, a direction to a third land station supplies an immediate field check that the re10cation is satisfactory.
This technique was termed "repositioning" in Axel Heiberg Island, a term which will be retained in this thesis. The work on the Gi1man Glacier en- ables the accuracy of this method to be assessed on a glacier some 15 km in
1ength, with an average width of 5 km. The distances from fixed stations on land were as great as 6.8 km. -8-
Determination of the height of fixed positions
The most accurate field method of d~ing this is by conventiona1
1eve11ing. This is time-consuming over the steep slopes typica1 of the glacier margins, and if the 1eve11ing is done at the height of the ablation season, the changing height of the glacier surface adds difficu1ties.
Stadia 1eve11ing is more rapid, especia11y where slopes are steeper, and can give accuracies of between 5 and 10 cm per km, if the 1ines are run twice. Accumulation of error is a prob1em, as with traversing, and a serious error is not determined unti1 a c10sure has been made, in which event the who1e section is in doubt.
Elevations can be ca1cu1ated from vertical angles, and with the method of repositioning, the e1evations can be ca1cu1ated from two stations, afford- ing a check. Irregu1ar refraction over the ice is the main 1imiting factor in the accuracy of this method. The work on the Gi1man Glacier attempts to eva1uate the inaccuracies attributab1e to refraction by comparing e1evations \ ca1cu1ated by a single ray from the land station to the ice with those ca1cu1ated from a simu1taneous reciproca1 ray between the land station and t~e ice - .a procedure which in theory reduces the effect of variable vertical refraction.
Description of the field area
The mountains of northern Ellesmere Island (Figure 1) contain the highest peaks in North America east of the Cordi11era. In 1967 the highest peak was c1imbed for the first time, and theodo1ite observations determined the height to be 2603 m above sea 1eve1 (Hatters1ey-Smith, 1968, p. 196).
The central iee cap is bordered to the south by the United States Range, and to the north by the British Empire Range. Out1et glaciers f10w through both these ranges, towards Tanquary Fiord and Lake Hazen in the south, and -9-
towards the Arctic Ocean in the north. The Henrietta Nesmith and
Gilman glaciers are the principal outlets of the southeast part of the ice cap, and rivers flowing from the se glaciers enter Lake Hazen.
The central part of the ice cap is an undulating plateau at an elevation in excess of 2000 m, with local ridges and valleys of 150 m in amplitude. The high peaks form nunataks above this plateau. Under present climatic conditions a dry snow zone (MUller, 1962, p. 305) is not found in northern Ellesmere Island, but conditions might have been different in the early 1920's (Hatters ley-Smith , 1963, p. 142). The outlet glaciers flowing to the north often reach sea level, joining the ice shelf which fringes part of the north coast. Fragments of this ice shelf break off from time to time, and form the well-known
"ice islands" that drift in a clockwise path around the Arctic Ocean.
The main outlet glaciers flowing to the south do not reach sea level. The snout of the Henrietta 'Nesmith Glacier is about 2 km from the north shore of Lake Hazen, at an altitude of about 170 m. The
Gilman Glacier ends 20 km from the lake, at an elevation of 414 m above sea level. The area of the drainage basin of the Gilman Glacier is 480 km2 , of which the ablation area covered about 145 km2 in 1957 and
1958. During the decade 1957-1967 the equilibrium line has been as high as 1250 m, and as low as 830 m. ' At 1037 m the temperature of the ice b e 1 ow t h e 1 ayer 0 f seasona1 temperature cangesh i s -18oC, The glacier is thus of polar type, with a relatively slow rate of glacier movement.
Permanent weather stations were established at Eureka in April 1947 and at Alert in April 1950. Both these stations have airstrips suitable -10-
for heavy aireraft, and are the most eonvenient means of aeeess to the field area. The Defenee Researeh Board estab1ished field stations at Lake Hazen in 1957 and at the head of Tanquary Fiord in 1963. A party wintered at Lake Hazen during the l.G.Y., and parties have oeeupied both stations during the summer months. Both stations have airstrips suitab1e for 1ight aireraft. -11-
:,j !
Lancaster Sound
FIGURE 1 -12-
CHAPTER II
SURVEYING ON THE GILMAN GLACIER DURING THE IGY, 1957-1958
Choice of method
Apart from a short visit by A. W. Moore, of the northern party
of the Oxford University Ellesmere Island Expedition, 1935, who trav-
e11ed up the Gi1man Glacier on the way to his first ascent of Mount
o 0 Oxford (82 10'N, 73 11'W), the Gi1man Glacier was unknown before the beginning of the International Geophysica1 Year.
The Gi1man Glacier was chosen as the site for a programme of
glacio1ogica1 and geophysica1 investigations during the IGY, a pro-
gramme that was initiated and coordinated by the Geophysics Section
of the Defence Research Board, Canada (Hatters1ey-Smith, 1962).
At this time this area was not we11 mapped, and a better basis of
control was necessary for the location of the gravity surveys. For
the reduction of the gravity observations, latitudes were required to
0.1 minutes, and differences in e1evations between neighbouring
stations were required to 0.3 m.
Work of this type had been done before in Central and North Green-
land by Expéditions Polaires Françaises and the BriLlsh North Green1and
Expedition, for which the method of extended base subtense bar travers-
ing, to estab1ish positions, and the measurement of simu1taneous ver-
tica1 angles to carry the differences of e1evation had proved success
fu1 (Nevière, 1954; Paterson and Slessor, 1956). In 1957 the te11uro-
meter was not avai1ab1e, and the logis tics of the party set a premium
on 1ightness of survey equipment. The resu1ts of the geophysica1 work -13-
are given in Weber and others, 1960, and a detailed account of the surveying is given in Arnold, 1959.
In 1957 a Shoran station was established on John's Island, Lake
Hazen - the most northerly station of the Canadian Geodetic Survey's
Shoran network. During that year an extended base subtense bar tra verse was run from that station to a small nunatak near the head of one accumulation basin of the Gilman Glacier, described as station
110 (Figure 2). This traverse established the height of the glacier surface in 1957, from which changes in height were measured in 1967.
Errors of closure
A triangulation network was necessary to serve as a basis for glacier movement observations, and the base line of the network was taped on the river fIat immediately southeast of the Gilman Glacier snout. One station of this was incorporated in the subtense bar tra verse. When this triangulation network was later extended to "K.K", identical to station 110 of the subtense bar traverse, a check could be obtained on horizontal positions and heights for the gravity stations along the traverse. The horizontal closure was 1:3,600 in a distance of 38 km, and a zero vertical closure was obtained. This would imply that for purposes of comparing the height changes in the decade 1957 to 1967, the 1957 heights can be accepted as having their value as stated, to the nearest 0.10 metres.
The effect of the horizontal misclosure is estimated in the follow ing manner. Errors in this method of traversing increase as the square of the distance of the legs. The average distance between stations in the part of the traverse where changes in height, 1957-67, were deter mined was 1.15 km, with a maximum of 2.2 km. From here to the end of the traverse the average distance between stations was 2.55 km. The -14-
total misclosure of the traverse was 10.5 m in a length of 38 km, and the length of the part where height redeterminations were made in 1967 was 15 km. It seems conservative, therefore, to proportion the error linearly, and set a limit of 4 metres for the margin of error in the position of the subtense bar stations which were later repositioned. Because of the square law of errbr propagation in this type of traverse, the error is probably less. The steepest slope of the longitudinal profile of the glacier where height changes were o measured is 6 , and with this slope, an uncertainty in the 1957 po- sition of 4 metres gives rise to an uncertainty of about 0.3 metres in height change. This is a maximmn uncertainty, valid for the steep part of the glacier near the snout, and based on the assumption that aIl the error in position occurred on the first leg measured on the glacier in 1957.
AlI the height changes measured are with reference to the height of the ice surface of the glacier in May and June, 1957, with the exception of points of the seismic profile near station 90, which was measured in mid-July of that year. The height changes here are dis- cordant with other height changes according to the amount of the 1957 summer ablation to that date. At the poles nearest to these locations this was about 1.5 metres.
The later progress of the survey is not directly relevant to the measurement of height changes, but can be summarized as follows. In
1958 the trigonometrical levelling was extended to sea level in Clements
Markham Inlet, near the north coast of Ellesmere Island, and a tie was made between Lake Hazen and sea level in Chandler Fiord by double line stadia levelling. The misclosure between the two sea levels was 1.2 m, in a total distance of 168 km (Figure 2). Additional gravity and -15-
seismic profiles were located in the higher parts of the accumulation area, near Mount Oxford. Figure 3 shows the location of the seismic and gravity profiles.
Determination of glacier movement
The rate of glacier movement was determined over one year for 17 stakes (Table 1 and Figure 4) and over a period of about one mon th in the summer of 1958 for 27 stakes (Table 2 and Figure 5). The summer interval was too short to allow the vertical component of movement. to be measured with sufficient accuracy on a glacier as wide as the Gilman
Glacier. As the absolute changes in the short summer interval are small compared with errors in the location of the stakes, it is not possible to state conclusively that there is a difference in the rate of summer and winter movement, although the extrapolated horizontal movement for stakes M19, M12, M23 and M24 is rather higher than expected.
Meier found accelerated movement during the summer on the Saskatchewan
Glacier (Meier, 1960, p. 14) and suggested that the difference between summer and yearly velocity was related to the position of the stake within the tongue, the difference being less near the equilibrium line.
An increase of velocity measured during the summer has also been observed in Axel Heiberg Island (MUller and others, 1963, pp. 68-71). On the
Anniversary profile, White Glacier, the greatest short term increase of velocity amounted to more than 100% of the mean annual velocity.
Over a longer summer interval the increase was 36%. On the Eureka pro file, Thompson Glacier, the summer velocity increase was 12%. The
White Glacier is about 1 km wide at the Anniversary profile and the
Thompson Glacier is 3 km wide at the Eureka profile. The Gilman Glacier is 5 km wide where movement was determined both on an annual and on a -16-
summer basis. The summer ve10city increase of glacier movement is be1ieved to be caused by··me1twater 1ubricating the bed of the glacier.
In this area this may have a greater effect on a narrow valley glacier than on a wider one, but more observations are necessary before defin ite conclusions can be made.
The position of the snout relative to a fixed mark was measured severa1 times during the IGY, and again when the glacier was revisited in 1967. The measurements are given in Table 15, and the behaviour of the snout is discussed at the end of Chapter VII. -17-
, ~ .ll.. "1"
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fJ 'V 1 o 0
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..-,.- --'--"'--~:-<-_.::-...:-;;":;;,' .-- /'" '~'--':::::""
CONTROl. SURVEYS FOR GEOPHYSICAl. WORK INTERNATIONAl. GEOI'HYSICAL YEAR. 1957-56 . , \ i : 69-63-110 Sublense bDr Iraverse. 1957 O-Chrlstio Sullionsc bDr trayerse. 1956 East Bost -Christie Link by trla~~ulotion 1-135 Double lino sla~IQ su"e1. / __ .r"_~ LD~a Hazen to Cho~d!er Fiord
~'''':','"::;O;~::I):;);:I,:Z;.I-''':'' ___--- ______. __-L. i ______J , .. - .. ~.. ;",,".",,:.',;~L_'"-':;~;:"~""':dl!.i::iJ.l:RE~;!lX.j;:;;':;ili.:Z:2: FIGURE 2 - .':
• ,,' ';.. , ...... :~. -' j .... ~.,~ 1..." •• ~~:.c.., ,. ,-' ~):.~~~~t?~·. ~~~~;y 72.00 \ ",, -' , "\ ~O~,' ... --_, '" _, '11 00 1 ~.' ,-'v.:: \. \ 'r,.... l:.:, .. ~ ,"~. '-"""~• .....?~. ;, &'~h~;~ -'} '".' GILMAN GLACIER ; ",''''"j \.1"
TABLE 1 GLACIER MOVEMENT DETERMlNED OVER ONE YEAR, 1957-1958
STAKE INTERVAL HORIZONTAL VERTICAL EMERGENCE RATE (DAYS) COMPONENT COMPONENT (m/yr) (m/yr) (m/yr)
In accumulation area, seismic profile 108 (27 Ju1y 1957 to 19 Ju1y 1958)
108 357 0.8 -0.2 -0.2 108/1S 357 13.7 -0.3 0.0 108/1. 6S 357 14.9 -1.6 -1.2 108/2S 357 15.7 * * Upper profile, near seismic profile 101 (11 Ju1y 1957 to 25 June 1958)
Ml 349 20.3 -0.5 -0.3 M2 349 24.6 -1.1 -0.6 M3 349 24.8 -1.3 -0.8 M4 349 24.3 -1.0 -0.7 MS 349 23.1 -0.8 -0.5
Lower profile, near seismic profile 101 (11 Ju1y 1957 to 25 June 1958)
M6 349 19.3 -0.2 0.0 M7 349 23.1 -0.7 -0.2 M8 349 23.4 -0.7 -0.2 M9 349 23.2 -1.0 -0.7 M10 349 22.6 -1.3 -1.0
Seismic profile 98 (17 Ju1y 1957 to 25 June 1958)
98 343 19.7 0.0 +0.5
Other points on long profile be10w 98
(96 : 17 Ju1y 1957 to 29 Ju1y 1958) (M12: 16 Ju1y 1957 to 2 Ju1y 1958) 96 377 19.6 *. * M12 351 19.6 * * Estimated errors 0.1 m (horizontal) and 0.3 m (vertical)
(*) Unre1iab1e because of replacement of stake See Figure 4 for location of movement stakes. (~e 'e
MAPSCALE ~ 9 ? L-'t-JKM. 1 GILMAN GLACIER MOVEME 1957 -1958 ~• .""t''''k MOVEMENT SCALE 10B- .N. o 2,5 5,0 7,5-19° METRES PER YEAR 108/51 "' " 109/52 ...... M1 ~6, M\\'\"" M)~" 1 oN 9, 1 •
96 "M12 ~ ~ "
FIG.uRE 4 . -21-
TABLE 2 GLACIER MOVEMENT DETERMINED DURING THE SUMMER OF 1958
STAKE INTERVAL HORIZONTAL EXTRAPOLATION OF HORIZONTAL (days) COMPONENT COMPONENT (m) (m/yr)
103 30 1.5 18 102 30 2.2 27 Upper profile, near seismic profile 101
Ml 30 1.8 22 M2 30 2.0 24 M3 30 1.8 22 M4 30 1.8 22 M5 30 1.8 22
Lower profile, near seismic profile 101
M6 30 1.5 19 M7 30 1.9 23 M8 30 1.9 23 M9 30 1.8 22 M10 30 1.9 23
Between 1958 camp (station 100) and seismic profile 98
AS6 30 1.1 14 AS5 30 1.5 18 AS4 30 1.6 19 AS3 30 1.6 20 AS2 30 1.7 21 AS1 30 1.7 20
Near seismic profile 98
M15E2 23 1.1 18 M15E1 23 1.4 23 M15 23 1.4 21 M15W1 23 1.3 20
Other points on long profile be10w 98
M19 23 1.5 24 M12 23 1.5 24 M22 23 1.4 22 M23 23 1.6 26 M24 23 1.2 19 Notes: 30 day interva1 is from 25 June to 25 Ju1y 1958. 23 day interva1 is from 2 Ju1y to 25 Ju1y 1958. Estimated errors are 0.1 m for stakes ab ove seismic profile 98, and 0.3 m for the others. The re1ated errors in the extrapolation of the annua1 com ponent are 1.5 and 4.5 m. Ve10cities determined during the ablation season are frequent1y higher than ve10cities determined over a complete year. The interva1 is too short to a110w the vertical component of f10w to be determined. See Figure 5 for the location of the movement stakes. /-re-- i •
~ t( MAPSCALE ~ o '1 ~ 4 $ KM. (iè .GILMAN GLACIER MOVEMENT ~ SUMMER 1958 - ,,- MOVEMENT SCALE 1p3, L!~ __~ ___ 7~ _~oo METRES PER YEAR
102, M1~ "': MG, ~ AS8 M5~"" " M'",\~" ,"" E2 AS,,,"'\ 1 Œ> ~ ,~ - 1 M15 "" " Vl1"" " , M12 M19 ~ ~ " '\ ,A 9 M22
v \M23 . -\M24 \
, FIGURE 5 -23-
CHAPTER III
FIELD PROCEDURE, 1967
The survey party working on the Gi1man Glacier in 1967 consisted of three observers, assisted from time to time by one or more recorders.
The observers were equipped with Wi1d T2 theodo1ites, which read direct1y to one second of arc, a sma11 portable transistor two-way radio, and a signal mirror.
The bearings and distances to a11 points at which height changes shou1d be measured had been ca1cu1ated by a computer programme, and each observer had a print-out of the resu1ts. The original field notes wou1d not have been sufficient on the Gi1man Glacier, as a11 points on the glacier had not been observed from a11 the trigonometrica1 points on land that it was p1anned to reoccupy. A1so in 1957 and 1958 severa1 days often e1asped between observations from different trigonometric points to positions on the glacier. This cou1d be a110wed for in computation, but it meant that differences existed between directions recorded in the field books and directions corresponding to the fina11y adopted position of the glacier point. Such a programme is a great assistance in the field, and its use is recommended in any simi1ar work p1anned.
After the observing programme for the day had been decided, two observers occupied trigonometrica1 stations on the hi11sides, and the third party set off down the glacier by skidoo. The use of the signal mirror was he1pfu1 at this time, as the radio cou1d not be used whi1e the engine of the skidoo was running. A flash from the signal mirror of the most favourab1y situated land observer indicated that the glacier party wou1d soon approach his desired direction, and the glacier party then moved around on ski. Instructions by radio from the observers on -24-
land usually brought the observer on the glacier to the desired position within about five minutes.
This observer then set up his instrument, and set on it the reverse direction to a land station from the computer read-out. The horizontal angle was observed between the two land observers, and a check on other known trigonometric points could be obtained at once, as the instrument was prcperly oriented in the local grid system. This is a valuable field check, and if a disagreement of more than 30" is found the repositioning should be rechecked. Two rounds of horizontal angles were taken, with the instrument in direct and reverse position on each round. By resetting the horzontal circle for the second round to give an initial direction of zero to one of the land stations the arithmetical accuracy of the angle reductions is checked more rapidly.
The vertical angles were measured from telescope objective to telescope objective, and the means of two sets, direct and reverse, were compared. If these differed by more than 10", additional rounds were taken until satisfactory results were obtained. The height of the instrument above the ice surface was measured, and a check was made by digging a few shallow pits to see that the surface under the instrument was typical of the local surface. Otherwise there was a risk that the point might have been relocated on a snow-filled melt stream. If aIl was satisfactory, the observing party on the glacier then moved on to the next point.
The two observers on land were F/Lt C. D. Drew and F/Lt P. G. Pinney, of the Royal Air Force Ellesmere Island Expedition, 1967. These officers had done no surveying before coming to Ellesmere Island, except for a day and a half gaining familiarity with the Wild T2 theodolite at the School of Military Survey in the U.K. Temperatures during May on the Gilman -25-
Glacier can fall as low as -20 o F (-29 0 C), but despite these adverse conditions they were able to take consistently accurate observations.
The party was a little undermanned for the task, which meant that the land observers often had to climb with the full weight of their survey equipment, and were unable to avoid overheating on the climb. Having to record their own field notes added to difficulties caused by low temperatures. In this type of work there was little scope for a break between observations, as the party on the glacier moves rapdily from one point to another, so the task of the observers on land is the most demanding one. It is evident, therefore, that enthusiasm and persis- tence on the part of the land observers is more necessary than long ex- perience with surveying instruments, and given suitable climatic con·- ditions, accurate work of this type can be done by relatively inexper- ienced parties.
About six points per day were observed when simultaneous reciprocal vertical angles were taken. If repositioning al one had been done the number of points per day would have been much greater, possibly as many as 25, depending on the distances to be covered by the glacier party. The value of simultaneous reciprocal vertical angles is discussed in Chapter V, which is concerned with errors in the determination of heights. -26-
CHAPTER IV
ERRORS IN REPOSITIONING
Theory of errors in repositioning
Consider a point fixed by two directions, el and e2 , at distances SI and S2 from permanent stations on land, intersecting in a -point P at an angle of intersection $ (Figure 6).
A maximum for a small angular error in the directions el and e is 2 denoted by de. As the error is small, in the neighbourhood of P its effect can be represented as parallel lines on each side of el and e 2 at distances de,Sl and de.S2, respectively, where de, being a very small angle, can be expressed in radian measure.
These paraI leI lines form a parallelogram centered on the point P, having opposite sides of lengths
2 • de,Sl and 2 • de,S2 sin $ sin $
The repositioned point can lie anywhere within this parallelogram.
The formula shows that the effect of the angle of intersection $ is a o minimum when $ = 90 , and an inspection of the figure shows that for equal maximum values of deI and de the greatest departure from P 2 occurs when the)' are of opposite signe
For errors of unlike sign, the greatest possible departure from
the desired point P for a given value of de is:
de'S de 'Sl)2 + {rIe. S2)2 + 2 cos ~ ~ [( sin $, \ sin $ sin $ sin $ -27-
In p1acing a stake in a given direction, the same accuracy cannot be expected as wou1d be attained in a series of observations to a permanent target. A known direction to another permanent mark is set on the theodo1ite. The theodo1ite is then turned to the desired direction, and the necessary instructions are given to place the stake on the correct 1ine. This corresponds to on1y one reading on one face of the instrument. It wou1d be possible to make numerous sma11 subsequent corrections, but in repositioning this wou1d be too time-consuming and wou1d invo1ve unnecessary work. Consequent1y, with an instrument that reads to a single second of arc, and from which a mean square error of one second might be expected from four complete sets of observations under favourable conditions, the value for de will be greater, of the order of 3 seconds of arc.
In work close to valley glaciers, the effect of steep1y inc1ined sights on angu1ar errors should be considered. For a one second reading theodo1ite, the sensitivity of the horizontal plate of the theodo1ite is of the order of 20 seconds per mm division. The error of direction due to defective leve11ing is given by:
-1 tan de = e.tan h where e = a sma11 angu1ar dis1evelment of the horizontal axis, and h is the inclination of the 1ine of sight, measured from the horizontal.
Shou1d the theodolite become two mm divisions out of adjustment 0 while repositioning a point at an inclination of 10 be10w the observer, an error of 7" arc in the direction cou1d occur. For this reason, the permanent reference mark used to estab1ish a reference direction should be at about the same 1eve1 as the observer. -28- . ,
..
o~ u
NIe-:: . "ben~
Il.... ëi) o 0- W cr \ cr o \ la.. w \ cr \ \ ,<0 cr W o \ cr 0:: cr :::> \ w .C!> Il .ii: \ \ \ cr o \ 0: 0: \ W \ .. \ \ \ \ \ \ \ \ \ \ \
1e . -\ \ \ \ \ -29-
Remaining sources of error are defective centering, which shou1d be a neg1igib1e error over distances about 0.5 km; an unstab1e setup of the theodo1ite; inaccurate positioning of the pole to be reposi- tioned, possib1y due to its non-vertica1ity; and a gross b1under in setting the proper reading on the theodo1ite.
If 10" arc is assumed to be an upper 1imit for an error in a direction, the maximum error in position expected for certain angles of intersection is given in Table 3.
TABLE 3: MAXIMUM ERRORS IN REPOSITIONING (m) FOR AN ANGULAR ERROR OF 10" ARC IN DIRECTIONS
DISTANCE ANGLE OF INTERSECTION 0 (km) 1 20 50 100 300 60° 900
10 55.55 27.78 11.11 5.56 1.87 0.97 0.69 9 50.00 25.00 10.00 5.00 1.68 0.87 0.62 8 44.44 22.22 8.89 4.45 1.50 0.78 0.55 7 38.88 19.45 7.78 3.89 1.31 0.68 0.48 6 33.33 16.67 6.67 3.33 1.12 0.58 0.41 5 27.77 13.89 5.56 2.78 ·0.94 0.48 0.34 4 22.22 11.11 4.44 2.22 0.75 0.39 0.28 3 16.67 8.33 3.33 1.67 0.56 0.29 0.21 2 11.11 5.56 2.22 1.11 0.37 0.19 0.14 1 5.56 2.78 1.11 0.56 0.19 . 0.10 0.07
If the land stations are so situated that acute intersections are transverse to the direction of the glacier, the effect of an error in repositioning on a measured change of height will be sma11.
Errors in repositionins encountered on the Gilman Glacier
For the work on the Gi1man Glacier, a third observer, having fixed the repositioned point according to the instructions given by the two observers on land, set a theodo1ite over this point and observed the -30-
angle between the two land stations. This gave a check on the tri-
angular closure. An extra direction or two were observed to other
land stations, which gave a preliminary field check of the accuracy
of the repositioned point. The primary function of the third observer was to enable simultaneous reciprocal vertical angles to be taken, so
that the effect of vertical refraction could be investigated.
The mean triangular misclosure was 7.8 seconds (maximum 25.8).
Some of the directions had a greater difference from the desired
direction than expected: (Table 4).
TABLE 4: DISTRIBUTION OF ERRORS OF DIRECTIONS TO REPOSITIONED POINTS
Size of error Number of errors
less than 1" 5 1" - 2" 2 2" - 5" 21 5" - 10" 19 10" - and over 11
The greatest difference was 23.5 seconds. Su ch a difference might be
explained by the 1ength of time that it took to position a point properly,
a110wing the instrument to drift from the direction origina11y set on it.
The usual distance to the repositioned point was about four ki10metres
with the fo1lowing distribution: (Table 5).
TABLE 5: DISTRIBUTION OF DISTANCES TO REPOSITIONED POINTS
Distance from trigonometrica1 station on land Number of . distances 1ess than 1km 2 1 - 2km 2 2 - 3km 6 3 - 4km 18 4 - 5km 17 5 - 6km 10 6 km and over 3 -'>.1.-....
Having distributed the triangu1ar misc1osures, the corrected directions enab1ed co-ordinates to be ca1cu1ated for the point actua11y fixed.
The differences between the point actua11y located and its desired location were: (Table 6).
TABLE 6: DISTRIBUTION OF ERRORS OF HORIZONTAL COORDINATES OF REPOSITIONED POINTS
Distance from Number of Eoints desired location
1ess than 10 cm 4 10 - 20 cm 10 20 - 30 cm 6 30 - 50 cm 6 50 - 100 cm 2 100 cm and over 1
Over the distances encountered on the Gi1man Glacier, it was not possible to detect any c1ear re1ationship between an error in re- positioning and the associated angle of intersection of the directions, or the distance of the point from the land stations. One can conc1ude that if the angle of intersection is greater than 30 o , and the greatest distance from a land station is 1ess than seven ki1ometres, a satisfactory resu1t can be obtained. For intersections. greater than 30 0 , the mean error was 0.36 metres, with a maximum of 0.76 metres. In one case on1y was the angle of intersection 1ess than thirty degrees - an intersection of 5 o was associated with an error of 3.13 metres, but as this error was in a cross-glacier direction, it is thought to have little effect on the change of height measured. ~32-
TABLE 7: ACCURACY OF REPOSITIONED POINTS ON THE GILMAN GLACIER
Station From (km) O-D From (km) O-D O-D ("arc) ("arc) deg. 4> min. (m)
84 R 3.6 -6.r: W 3.7 2.3 137 16 0.13 85 R 3.8 16.3 W 4.0 5.6 122 43 0.44 86 R 4.3 -16.2 W 4.5 6.6 103 36 0.34 87 R 4.9 -10.8 W 5.4 6.7 82 55 0.33 88 R 5.4 7.1 W 6.0 7.5 73 32 0.25 89 R 6.3 2.9 W 6.8 -19.4 62 59 0.76
90 HS 4.5 6.2 NN 4.3 -8.9 87 26 0.23 90/0-3085'S HS .4.2 0.0 NN 5.3 3.9 78 24 0.11 90/0-3000'N HS 4.9 -3.8 NN 3.8 13.3 88 06 0.27 90/1N-2200'W HS 4.4 -18.7 NN 3.4 2.2 102 16 0.40 90/1N-2400'E HS 5.5 -6.0 NN 4.2 0.2 76 02 0.17
92 HS 3.7 -2.0 NN 2.9 7.1 132 13 0.17 94 HS 2.8 0.5 NN 3.3 -16.2 175 25 3.13 96 p 3.3 -5.5 S 5.5 2.1 43 06 0.19 98 p 3.0 -5.2 S 4.2 -9.1 60 54 0.19 98/1N p 2.0 5.4 S 3.8 4.4 73 48 0.09 98/2N p 0.9 7.9 S 3.7 4.8 90 24 0.10 98/1S p 4.1 1.9 S 4.8 -1.3 49 56 0.08 98/2S p 5.1 3.3 S 5.5 -4.3 41 51 0.27
100 p 3.6 23.5 S 2.4 -2.0 76 33 0.42
101 p 4.1 12.3 S 2.3 -3.6 67 20 0.28 lOI/lN Ii 3.5 6.3 S 1.5 -2.0 90 19 0.12 101/2N p 3.1 8.1 S 0.9 -2.9 139 39 0.17 101/lS p 4 •. 7 4.1. S 3.2 -3.1 53 08 0.18 101/2S p 5.5 17.1 S 4.1 -3.1 43 46 0.71
108/1S KI{ 4.3 0.5 SCOP 1.8 -2.6 85 10 0.02 108/2S KI{ 4.6 0.0 SCOP 2.8 -6.6 70 14 0.09 108/3S KI{ 5.1 -6.4 SCOP 3.8 16.3 58 41 0.48 108/3S-80OmS KI{ 5.6 6.2 SCOP 4.6 -4.1 51 20 0.29
O-D ("arc) are errors in directions, observed 1ess desired. The range is 0.0" to 23.5" and the Mean is 6.6". o-D (m) are the resu1ting differences in position. The range is from 0.02 m to 3.13 m, and the Mean is 0.36 m.
4> is the angle of intersection of the two directions. -33-
CHAPTER V
ERRORS IN DETERMINATION OF HEIGHTS
The prob1em of atmospheric refraction
In an at~osphere in which the coefficient of refraction is known,
and can be a110wed for, the effect of a sma11 errer da in a vertical
angle a over a distance S is simp1y: da.S With 10" arc assumed as a
maximum value for da, and working within a maximum distance of 10 km,
the maximum error in height expected wou1d be 0.48 metres.
A method for the determination of the coefficient of refraction
is given in the Textbook of Topographica1 Surveying, para. 242 (Ministry
of Defence, 1965). Referring to Figure 7, if the angle subtended at
the earth's centre by the 1ine joining two stations A and B is denoted
by X, and the observed (refracted) rays are denoted by R'BA and RBA
(assuming equa1 refraction at each end point):
RAO + R'BO = BAO + ABO + 2.BAR 0 0 0 or (90 + Va) + (90 + Vb) = 180 - BOA + 2.BAR
Then 2(r) = Va + Vb + X
r = (X + Va + Vb) 2
and by àefinition the coefficient of refraction k = angle of refraction angle subtended at earth's centre by 1ength of ray
k = r/x = (X + Va + Vb) /2X
where X = c/R sin 1" e. CALCULATION OF COE FFICIENT OF REFRACTION K 'e K = r 'ïx"
r" . .------.--~. A
- - w •• ,.,.,.",.":;,;";;,;;:"t;ii;~t~rM@HlMi@i!E1iil%tlml!@}tUE1I1Jr ·'o/•• ï'"~wot'
x ='SMALL ANGLE SUBT,ENDED AT EARTH'S CENTRE SV DISTANCE e.
x"= c/R SIN 1"
o -35-
Values of refraction encountered in a subtense bar level traverse across north Greenland, 1953-1954, are discussed in Paterson, 1955. He measured extreme refraction coefficients of between +0.9 and -0.25.
This was over average distances of 4 km, slopes of about 15 minutes, and a greatest difference of height between the end points of 19 m. By statistical analysis he was able to show that temperature was the main controlling factor, although cloud and the presence of drifting snow also showed a significant correlation with refraction. With more than
50% cloud cover the average value of kwas 0.06, contrasting with an average value of 0.20 for less than 50% cloud. 0.11 was an average value for k when low drifting snow occurred, without it the correspond- ing value was 0.22. From theoretical considerations, proved by actual observation, he was able to show that the time of minimum refraction occurred about three hours before that of maximum temperature.
dT 0 Whenever the value of dH was more negative than -0.034 C per metre, the value of k is negative, and the refracted ray is convex towards the earth's surface. An inversion of temperature occurs if the value of k is greater than about 0.09.
When simultaneous reciproca1 observations are not possible, vertical angles should preferably be taken under overcast and windy conditions, and around the time of local noon.
Similar observations have been made at fixed sites in north
Greenland (Hamilton, 1957) and in Antarctica (Dittrich, 1967). Hamilton used about eighty observations which he considered reliab1e to ca1culate refraction coefficients that varied from 1.5"/km to 29.4"/km for morning observations, -2.2"/km to 11.8"/km for afternoon observations, -36-
and from 0.9"/km to 17.6"/km for evening observations. The correspond- ing indices of refraction k, hS defined in Figure 7, are 0.05 to 0.91 for morning observations, -0.07 to 0.36 for afternoon observations, and 0.03 to 0.54 for evening observations. Hamilton suggested that use cou1d be made of observations of atmospheric refraction to ca1- cu1ate temperature gradients in the lowest layer of air above the ice with a standard error of 0.1o C per metre."
Dittrich (1967) made 294 observations over a distance of 565 m, at temperatures ranging from -32 o C to +3.5 0 C, and at wind speeds up to
15 metres per second. He uses a different definition for the coefficient of refraction in which the index is defined as the curvature of the earth divided by the curvature of the 1ine of sight. This index is approximate1y twice that given in Figure 7. His values ranged from
-0.18 to +3.97, with +0.6 being experienced most frequent1y.
An illustration of the use of simu1taneous reciproca1 vertical angles to reduce the effect of refraction is avai1ab1e from the work done on the Gilman Glacier in 1957, during the course of the subtense bar traverse.
TABLE 8: THE ADVANTAGE OF SIMULTANEOUS RECIPROCAL VERTICAL ANGLES
Stations
12 June 1957 (1720 hrs.) (1725 hrs.) (1730 hrs.) (1735 hrs.) From 98 to 100 +01 17 10.0 +01 17 23.0 +01 17 37.5 +01 17 54.5 From 100 to 98 -01 17 06.0 -01 17 00.0 -01 16 50.0 -01 16 31.0
Mean 01 17 08.0 01 17 11.5 01 17 13.8 01 17 12.8 -37-
Although the vertical angle at the lower station increased by
44.5", the depression at the higher station decreased by 35.0". The mean angle varied by only 5.8". Over this distance an error of 44.5" in the vertical angle would have given an error of about half a metre.
The results discussed so far involve a ray of light that is close to the snow surface for ~he whole of its path. Experiments have been made over the Juneau Icefield, Alaska (Angus-Leppan,-1:968) in which the reciprocal vertical angles were measured in the height range of 15 - 70 m above the ice. These were measured at two hour intervals over a period of 24 hours. The principal findings were (Angus-Leppan,
1968, p. 5) that a regular pattern of diurnal variation was not found, that the scale of variations was dampened with increasing height, and that reciprocal observations fitted each other more closely at higher than at lower levels. The coefficient of refraction was defined as the radius of the earth divided by the radius of the line of sight
(as by Dittrich) and values ranged from 0.35 to as high as 3.0 (0.18
- 1.50 as defined in Figure 7).
The vertical angles observed on the Gilman Glacier were ma1nly weIl above the ice surface, but it was thought to be worthwhile to observe them reciprocally so that coefficients of refraction could be calculated, and its effect assessed. The mean value., for k, as defined in Figure 7, was 0.162. It should be stressed that this only represents a mean value for observ~tions taken at a variety of local times during the month of May, and that no attempt was made to observe at the time of minimum refraction. However, most observations were within four hours of this time. An average value for minimum refraction used by -38-
the Geodetic Survey of Canada is 0.07 by day and 0.09 by night. The range on the Gilman Glacier was from 0.047 to 0.558, which suggests that the coefficient of refraction is appreciably higher. An in version of temperature seemed to be typical, for only three values were less than 0.09.
It is interesting to consider how valuable the simultaneous measurement of vertical angles proved to be. Each height difference was calculated from the vertical angle from the land station alone, applying a standard correction for earth curvature and refraction.
The difference between a single ray and a reciprocal one has been tabulated as (S-R) in the table of height changes. These values are surprisingly small, in the light of precautions that have been taken to measure vertical angles simultaneously in the pasto The mean value of (S-R) is 0.31 metres, with a range of -0.05 to 1.74 metres. The value of 1.74 metres was associated with a grazing ray that was close to the snow surface for at least 400 m. If this value is excluded, the range of (S-R) is still of the same order, -0.05 to 1.67 metr~s.
However, 33 of 58 values were less than the spread of the two height determinations, a result that shows that for the majority of obser vations errors in pointing, attention to the level index bubble, and reading the theodolite had a greater effect than variable refraction.
It is not possible to state that the larger values of (S-R) occurred at particular times of the day, or under different weather conditions, as different values of k were measured at successive stations under apparently similar conditions and at a similar time of day.
The effect of refraction gave an error of more than one metre in only three of 58 observations. It wou Id be assuring to state that in -39-
this type of work single vertical angles are sufficient, but this do es not appear possible. Under conditions experienced in May the risk of a poor result may be small, but this may not hold for the later part of the season, when the temperature contrast between ice and land might be larger, and the vapour pressure of the air greater.
Consequently, unless the programme allows vertical angles to be measured to the relocated points at several times on different days, the measurement of simultaneous reciprocal vertical angles is still to be recommended.
Each height was measured from two trigonometrical stations.
The mean difference of the two measurements for 29 points was 0.25 metres (range 0.05 to 0.52 metres). lt can therefore be seen that the method of repositioning points, and measuring height differences by simultaneous reciprocal vertical angles, gives an accuracy at least as good as the results claimed for aerial photogrammetric surveys of glacier changes, and almost as good as results quoted for terres trial photogrammetric measurements. The photogrammetric methods, however, have a great advantage in the speed of gathering data. -40-
TABLE 9: ACCURACY OF HEIGHT CHANGE8 MEA8URED ON THE GILMAN GLACIER
8tation From k (8-R) From k (8-R) Height Range (1) (m) (2) (m) Change (1 & 2) 57-67 (m) (m) ....
84 R 0.163 0.21 W 0.143 0.13 -0.5 0.31 85 R 0.105 0.06 W 0.123 0.19 -1.4· 0.05 86 R 0.086 0.05 W 0.177 0.32 -2.3 0.23 87 R 0.089 0.08 W 0.120 0.24 -2.4 0.15 88 R 0.224 0.73 W 0.361 1.67 -0.9 0.41 89 R 0.206 0.89 W 0.281 1.59 -1.8 0.52 90 H8 0.122 0.15 NN 0.160 0.25 -1.6 0.28 90/0-3085'8 H8 0.314 0.69 NN 0.160 0.41 -15.5* 0.37 90/0-3000'N H8 0.110 0.18 NN 0.137 0.16 -0.3* 0.31 90/1N-2200'W H8 0.161 0.27 NN 0.178 0.25 -0.8* 0.32 90/1N-2400'E H8 0.180 0.53 NN 0.144 0.22 -0.1* 0.43 92 H8 0.136 0.12 NN 0.118 0.06 -2.6 0.24 94 H8 0.171 0.15 NN 0.127 0.13 -2.9 0.41 96 P 0.237 0.29 8 0.075 0.04 -2.6 0.19 98 P 0.108 0.06 8 0.047 -0.05 -2.1 0.09 98/lN P 0.086 0.01 8 0.128 0.15 -2.2 0.18 98/2N P 0.157 0.01 8 0.155 0.19 -1.9 0.23 98/18 P not reciproca1 8 not reciproca1 -1.2 0.34 98/28 P 0.315 0.99 8 0.191 0.61 -11.2 0.06 100 P 0.137 0.14 8 0.167 0.12 -1.0 0.17 101 P 0.145 0.21 8 0.131 0.08 -1.3 0.20 ,...... ,- lOI/lN P 0.081 0.03 S U.l.'+::1 0.04 -1. 7 0.11 101/2N P 0.145 0.12 8 0.137 0.06 -1.2 0.16 101/18 P 0.558 1. 74 8 0.156 0.15 -0.8 0.41 101/28 P 0.127 0.30 8 0.191 . 0.37 -0.4 0.24 108/18 KK 0.087 0.06 8COP 0.052 -0.01 +0.1 0.05 108/28 KK 0.154 0.29 8COP 0.156 0.10 -0.1 0.05 108/38 KK 0.174 0.45 8COP 0.174 0.24 +0.2 0.16 108/38-80Om8 KK 0.212 0.72 8COP 0.134 0.23 -0.7 0.45
Key k is the coefficient of refraction, as defined in Figure 7. The range of values is from 0.047 to 0.558, with a mean of 0.162.
(8-R) is the difference between a height ea1cu1ated by a single ray from the land to the ice, with a standard earth curvature and atmospheric re- fraction correction app1ied, and that ca1cu1ated from the simu1taneous reciproca1 rays. It represents the effect of non-standard refraction over the glacier. The range of values is -0.05 m to 1.74 m, with a mean of 0.31 m.
Range is the difference in height as ca1cu1ated from two trigonometrica1 stations. (*) -1.5 metres shou1d be addedto these values, corresponding with the ablation to mid-Ju1y 1957, to make them consistent with the other height changes. e e
l ,; ~,\ ... ~ .. " 1" -, - ,!;,..~":} - ----y ------,------;- '. #' 1 .... ,~."'3'" - -;-.". 12-00' \ (-"-,>\.::~~,, ,<,-.!; ; ...... t':J:-._'. ,.-00'/ ~~·~\~'oC c'~-~':t:;~~ 4/:;: GILMAN GLACIER ",1 ".,"J., 1 '," t) \ _1 1 .tir.,..'.,.! Q ...... ' 1 ... t:';<.'";';,·S'--:~ ?~~?JJf!' NORTHERN ELLESMERE ISLAND -,~ '\~:-' ',\\ ".,,0 .' (~,:_ ... " ... ,o, I}t::rf.-',,?,,/?~ .0.,., .tf}~'L.}'(; HEIGHT CHANGES MEASUREO,I967 1 ): \ \..' ~ ,~ ....~, \ J,~~"+L.:~'~ °o../,..J~*$.'bi/ o " 1 l,' " , , I~...... L.Oo ~... t .. _ .fi':~ ... .t'~ //~:;.t:;:":.:ltI) ,.- J t, I~ K III o"~," ,,' ," ,.-0500. __ • /' " ", .,1J,7~--_ -"" :;,;;.- 6' '. :,:. .... ·'-d/ i i ,_.... 0 __ "..-' -- "', {~- ( "", /!--~ ,/ /;,~:.5\·~~v ",~: /, :10 o 0 Mil.. ", .."J,-:- \ ) C...... _J I/~ OO... ';::"-,·'V· .... ;;1 ·~.. ~'};;~ ..... I!\r- ContOll' InU",ol ~OO fil' \ "-' :'..-' .....~'" //~~., ;1V::~èf1" .,,-)"', 1z,:::é'::r'1 ,l',", , , 1 l ' ,\-,.'7 ,
CHAPTER VI
CHANGES IN HEIGHT OBSERVED ON THE GILMAN GLACIER
Seismic profile 108 is in the accumulation area of the Gi1man
Glacier, at an e1evation of 1400 m. At this profile there appears to be virtua11y no change in surface height. The greatest change is -0.7 metres at 108/3S-80OmS, a point in the midd1e of the cross profile of this arm of the glacier (Figure 9). The e1evations on this profile refer to the height of the 1966 firn, compared with the height of the summer surface on Ju1y 17th, 1957. The absence of any great surface change at this profile suggests that there has been
1itt1e change in accumulation patterns over the decade, and that the changes 10wer down the glacier are 1ike1y to have been caused by variations in the warmth of the different ablation seasons.
A long profile of the Gi1man Glacier be10w seismic profile 101 is shown in Figure 10, together with the observed changes in surface height. The difference of two determinations of the height changes i5 a1so indicated. The changes in the long profile show an osci11at ing pattern, with two maximum points and three minimum points. Meier found that a long profile of height changes on the Saskatchewan Gla cier (1948 to 1954) a1so showed an osci11ating pattern, but stated that the data were too erude for firm conclusions. (Meier, 1960, p. 6).
On the Nisqua11y and K1awatti glaciers, Washington, maps of equa1 sur
face change have been constructed from photogrammetrie measurements.
A long profile drawn down the median 1ine of these glaciers wou1d a1so have ShOWTl an osci11ating pattern of height change (Meier, 1966,
Figures 5 and 8, pp. 815 and 817). It is possible that this is a
characteristic of glacier surface height changes. ~ ..• ' •.
, ,·,·..... '·.1 \ fi~, 1.\;. , . .1" / - .... ~'~jR~ ~~r~~· -~ 1 ... T2-00' \ l'I'_}.,.r~"':·~' ,--..1, , ...... tlf-J -... 1 .00 1 ~~ ' ... ' \ ' ..... It~(it7f7~!;~\,1-' lt~~J~')~ GILMAN GLACIER ; " .... "J \.,.~~ " ,"",' 00 \ 1. " ~~j 00."-.. , η'-~":~{~'.;$~';'>t;'t.~ ;. ~r~..;.c NORTHERN ELLES~ERE ISLAND ,"'"::-... ~., , 1 ~ cs '...,- I~::....", 0 ;J.. "-.J~~;;:~
Table 10 gives the locations, values and distance from the
terminus of the glacier of the local maxima and minima of height changes on the long profile of the Gi1man Glacier.
TABLE 10
SUMMARY OF CHANGES OF SURFACE HEIGHT ON THE LONG PROFILE OF THE GILMAN GLACIER
Station Local Maximum Value Distance from or Minimum (m) Terminus (km)
100 Minimum -1.0 13.8 94 Maximum -2.9 8.8 88 Minimum -0.9 4.5 87 Maximum -2.4 3.8 84 Minimum -0.5 1.3
Cross profiles of height changes have been determined at the former seismic profiles 101 and 98. Except for the value at 98/2S, the differences in height changes on these profiles cou1d be exp1ained by sma11 differences in ablation rates or f10w rates from point to point.
The 10ss of -11.2 m at 98/2S was checked carefu11y, and is un-
1ike1y to be a b1under. This lies in a re1ative1y f1at part of the glacier, close to a right-ang1ed junction with a tributary glacier, a1so with a very flat profile. It is at least 2 km from the nearest point of land, so a greater rate of ablation close to the edge of the glacier is not the most like1y exp1anation. From the seismic profile measured in 1957, the ice i9 380 m deep at this point. The probable exp1anation is that this point does not lie in the main f10w of the
Gi1man Glacier, and the loss of ice due to ablation has not been com- pensated by the upward component of flow.
The greatest height 10ss observed occurs at the south end of the -45-
seismic profile shot in mid-Ju1y of 1957, near station 90. Point
90/0-3085'S 10st -15.5 m in height, and if the ablation up to mid
Ju1y is added to make this point consistent with the others the 10ss is -17.0 m. The depth at this point was not determined, but is prob ab1y considerab1y 1ess than 400 m, the me an depth of this profile.
It is probable that this point a1so lies out of the main f10w of the glacier, but as there is a steep souther1y slope at this location, increased exposure to solar radiation is an additiona1 exp1anation. • e
;
te tes !t4 fit Olt ee eT es ee e4
O~--~--~------~------~------~------~------~~----~----~------r-----r----~ CHANGE IN HEIGHT o OF SURFACE 1957-67 -1 D AMOUNT O~ ERROR -2
-li
1 ~ 1000111. '"1
LONG PROFILE OF GILMAN GLACIER
OEPTHS DY GRAV IoIEASUREMENTS
!SOO 500111.
III -l u ii: ... ~ o II) tJ) cr .... li; W CI. 3J < en 2 .... ~ u iii :ï en CI) W II>
~ . L 1 Km. 14 12 Il 10 9 e ., e e 4 li 2 FIGURE 10 -47-
CHAPTER VII
DISCUSSION OF RESULTS
Factors affecting the change in level of a glacier surface
The change in level of a glacier surface over a given time interval is the resultant between the mass balance at different points on the gla cier (expressed in ice equivalents) and the vertical component of glacier flow with respect to the glacier surface.
On a glacier in an equilibrium state the addition of mass in the accumulation area is compensated by a downward flow component, and the ablation of ice below the equilibrium line is compensated by a flow com ponent that is upwards with respect to the glacier surface. At the equilibrium line, the flow is parallel to the surface.
The factors affecting the change in height of a glacier surface can therefore be separateà into net mass balance from point to point on the glacier, and the vertical component of flow at the same points. A net mass balance can be determined from stake and pit measurements alone, and is sufficient for the study of the change in height of a glacier surface.
The net mass balance is determined by year to year climatic fluctu ations. The height of the equilibrium line can be raised or lowered by changes in annual precipitation, and by changes of summer warmth. In the polar regions precipitation amounts are low, 10 - 20 cm w.e. being typical of northern Ellesmere Island. As summer temperatures do not rise far above freezing in the ablation area of the glacier, relatively small fluctuations in the Mean monthly temperatures of the summer months cause a relatively greater variability in the effective warmth of the different ablation seasons. In contrast with glaciers in a maritime -48-
temperate environment, where the amount of precipitation is much greater, the net mass balance at different points on polar glaciers is determined to a greater extent by fluctuations in summer warmth, than by fluctuations in annua1 precipitation. Exceptiona1 snowfa11s can occur, that weaken this genera1ization. The White Glacier, Axel Heiberg Island, had an unusua11y positive mass balance in 1964, which had the effect of de1aying the normal me1t season in 1965 (MUller, 1965, p. 140) •
. On the Gi1man Glacier most of the height changes were measured be10w the mean position of the equi1ibrium 1ine, 1957 to 1967. In the warmer than usua1 summers of 1957 and 1958 the accumulation area covered at 1east
70% of the glacier, which imp1ies that a sma11 mass gain per unit area above the equi1ibrium 1ine must be ba1anced by a1arger mass 10ss be10w it, if the surface profile of the glacier is to remain unchanged. In this area of the glacier fluctuations in the summer temperatures are 1ike1y to be the dominant factor determining the net mass balance.
On glaciers in many different c1imatic regions ablation of ice shows a
1inear re1ationship with height (Haefe1i, 1962, p. 51). If a 1inear re1ation ship does not ho1d for a particu1ar glacier, two curves of mass balance from different years are near1y para11e1 (Meier and Tangborn, 1965, p. 556). A' know1edge of specifie mass balance at a particu1ar point on a glacier long profile can then be extended to other points on the long profile, if these re1ationships have been estab1ished from observations in ear1ier years.
Cumulative ablation of ice and of snowfa11 occurring during the ablation season shows a good correlation with cumulative degree-days above freezing temperatures (Kee1er, 1964, fig. 38, p. 76). These re1ationships are used to estimate mass balance data for years in which no observations are avai1- able from the Gi1man Glacier.
The movement of a glacier is caused by f10w due to deformation within -49-
the ice, and by the slip of the glacier on its bed. The deformation within
the ice is a function of the glacier thickness, surface slope, temperature
and the degree of interlocking of the ice crystals. The thickness is the
factor most likely to change over a period of ten years. The horizontal
component of flow varies as the fourth power of the glacier thickness (Meier,
1960, p. 14). On the Gilman Glacier the greatest change of height was about
3 metres in a glacier with a depth of more than 400 m for the greater part of the long profile (Figure 10). As the slope of the glacier is small, the vertical component of flow is less than 10% of the horizontal component
(Table 1). The vertical component of flow can therefore be assumed to be
a relatively constant factor during the interval 1957 to 1967.
An unknown factor is the possibility of a kinematic wave passing
down the glacier (Figure Il).
\ 1 i
1
1 'j j
1
EFFECT OF A WAVE TYPE PERT~ReAT10N OF FLOW ON CHANGE OF SURFACE HE1GHT 1 1 1 FIGURE Il \ J -50-
A sudden departure from an equilibrium condition can cause a kinematic wave to travel down the glacier with a velocity of 2.0 - 2.3 times the centre-line velocity of movement (Nye, 1965, p. 688). Figure Il illustrates
the effect on surface height of a wave displaced in phase by this amount.
Within a single wavelength two points are unaffected, and the length of profile gaining in height equals the length of profile losing in height.
On a glacier as large as the Gilman Glacier an interval of at least one year would be necessary to measure the vertical component of flow with sufficient accuracy. There is no possibility of detecting a kinematic wave unless a series of movement observations are taken. For aIl measurements of the vertical component of flow it is necessary to have stakes or other sensors drilled into the ice (Meier, 1966, p. 812). Observations taken to rock debris riding on the ice or to ice features are not sufficient.
Factors observed or estimated on the Gilman Glacier
For the decade over which the change in surface height has been measured on the Gilman Glacier, the change due to mass balance can be estimated with fair reliability, but there is little data available on
the vertical component of glacier flow with respect to the ice surface.
R. B. Sagar has published curves showing the relation between specific mass balance and height for the Gilman Glacier for the years 1957 to 1961
(Sagar, 1964, p. 51). When the glacier was revisited in 1967 G. Hattersley
Smith concluded from pit studies that the equilibrium line had been much
lower in the years 1963 to 1966 than in the first five years of the decade,
and by using theeryoconite layer at the end of the warm 1962 season as a
stratigraphic indicator, it was possible to estimate the net accumulation
above the 1966 equilibrium line. (Hattersley-Smith, personal communication).
Thus the mass balance is unknown in its entirety only for the year 1962, and -51-
that for the lower part of the glacier i9 unknown for the period 1963 to
1966.
In 1967 a deep pit was dug at the site of the 1961 upper camp, about 5 km east of Mount Oxford, and at an e1evation of 1660 m. Data from this pit (G. Hatters1ey-Smith, 1963, p. 144; and persona1 communication for years 1961-66) show that the mean accumulation for the decade was 17.2 cm w.e., s.d. 5.5 cm (Table Il). The maximum for the decade was 30.0 cm w.e. for the balance year 1961-62 (not the same year as the unusua11y high accumulation on the White Glacier, Axel Heiberg Island).
TABLE Il: NET ACCUMULATION FOR THE GILMAN GLACIER, AND PRECIPITATION DATA FOR ALERT
Year Ice Ca:ez 1660 m Alert Maximum de:eth From Eit data SeEt.-Ma~ June-Aug. Total of snow cm w.e. cm w.e. cm w.e. cm w.e. cm
1957-58 18.8 8.4 3.3 11.7 41 1958-59 10.9 9.4 4.8 14.2 56 1959-60 19.4 10.4 4.7 15.1 41 1960-61 13.8 7.2 3.0 10.2 66 1961-62 30.0 6.2 5.8 12.0 51 1962-63 21. 7 8.3 3.9 12.2 43 1963-64 17.6 8.8 7.9 16.7 64 1964-65 15.3 12.7 7.0 19.7 69 1965-66 15.4 7.0 6.3 13.3 18 1966-67 9.6 (*) 12.5 6.9 19.4 25
17.2 9.1 5.4 14.5 47
(*) to end of May, 1967 Sources:
Ice CaEz 1660 m, 1957-61 G. Hatters1ey-Smith, Geografiska Anna1er, XLV (1963) Bd 2-3, pp. 144-5. 1961-67 Ca1cu1ated by K.C.A. from field notes of G. Hatters1ey-Smith. A1ert Canada, Department of Transport, Meteoro1ogica1 Branch: Arctic Summary, Month1y Record of Met eoro1ogica1 Records in Canada, Canadian Weather Review.
This table shows that accumulation over a who1e balance year has not -52-
been a factor of major importance in changes in the height of the ablation area of the Gilman Glacier. The relationship of accumulation at 1660 m to that over the ablation area is in any event a rather dubious one, for the snow lying on the glacier surface at the start of an ablation season is more likely to be determined by the occurrence of gales during the winter.
The valley of the Gilman River is normally filled with deep snow, and a mean snow depth of 40 cm over the ablation area (corresponding to about
13 cm w.e.) is probably a high estimate. The only data on the change of height of the surface in the accumulation zone is at four points of the former seismic profile S 108, which indicates virtually no change in the surface height. This again suggeststhat the net accumulation can prob ably be regarded as a relatively constant factor over the decade.
No attempt has been made to separate summer and winter accumulation in the pit data presented in Table Il, but the available records from Alert, the nearest permanent weather station, have been summarized on a balance year basis. Alert (820 30'N, 620 20'W) is 130 km to the north-east; and
62 m above sea level. There the ten year mean is 14.5 cm w.e., with a maximum in 1964-65 of 19.7 cm w.e. The precipitation falling in the months of September to May and in June to August has been shown separately.
There does appear to have been a higher proportion of precipitation in the summer months in the last four years of the decade (41%) compared with the first six years (34%), and the absolute amount has also increased (mean of 7.0 cm w.e. for 1963-64 to 1966-67 compared with 4.2 cm w.e. for 1957-58 to 1962-63). It is likely that this has been an important influence in lowering the equilibrium line of the Gilman Glacier in recent years, as precipitation falling during the ablation season increases the reflectivity of the glacier surface, and diminishes the effectiveness of solar radiation. -53-
Using the weather observations recorded in 1957 and 1958 at the
Gilman Glacier camp near station 100 (elevation 1037 m) a correlation was made between the total ablation of ice and snow and cumulative degree days above freezing. The original observations are tabulated in Lotz,
1957 and Sagar, 1960. Figure 12 shows that these two variables were weIl correlated (r = 0.99) in both years. If the cumulative melting degree-days could be estimated for those years in which ma.ss balance data is missing or incomplete, it might form a reasonable guide for es timating the mass balance for those years.
The shortcomings of attempting to relate weather conditions on a glacier to those at a distant station are weIl known, and the difficulties are accentuated by the maritime situation of Alert, with an exposure open to' northerly winds blowing off the Arctic Ocean, contrasted with the inland situation of the Gilman Glacier, which is protected to some ex tent from winds blowing directly off the Arctic Ocean by the highest mountain ranges of northern Ellesmere Island. AlI that is attempted is an estimation of the relative warmth and coolness of the different ablation seasons.
An estirnate of degree-days at the 1957-58 Gilman Glacier camp using mean lapse rates given in Sagar, 1964 (p. 25), between Alert and the 1961 upper glacier camp, did not give good results when cornpared with the melt ing degree-days actually observed at the glacier camp during those surnmers.
Two other methods were tried.
The first was based on a plot of mean daily temperatures observed on the Gilman Glacier during the IGY against those observed at Alert. As the melting ice surface of a glacier tends to stabilize temperatures during the ablation season (Orvig, 1951, p. 188) the temperatures on the glacier were '~e •
2r SSp 7f J?O '55 CMS. OF MELT BO ~ • 1 • • CENTIGRADE MELTING DEGRE E OAYS • MELT RELATED TO ACCUMULATED • o MELTING DEGREE DAYS • (SNOW MELT VALUES -:- BY 3) •
1957· Y =-17.7 i' 0.541 X r = 0.99 .0'
0, ~ iO 1
o
o ..
1958: y = -2.4 + 0.40S·X • r:= 0.99 •
• '.
o FAHRENHEIT MELTING DEGREE DAYS . • . :;: .. .. ' ~ 60 '00 L50 ~DO 250 ~.,.." ...... ,.... -55-
separated into those of 1ess than 31 o F and those of 33 0 F and above. A regression 1ine and correlation coefficient was then ca1cu1ated for these two groups (Figure 13). The correlation coefficients were r = 0.48 for temperatures above 320 F and r = 0.65 for those be10w 32oF. Table 12 shows estimates of me1ting degree-days based on a slight modification of this method, (Figure 14) in which median values of the temperature comparisons were taken, to reduce the effect of extremes.
TABLE 12: MELTING DEGREE-DAYS AT THE GILMAN GLACIER, ESTlMATED FROM ALERT MEAN DAILY TEMPERATURES BY COMPARISON OF INDIVIDUAL VALUES (oF)
YEAR JUNE JULY AUGUST TOTAL
1959 21 60 20 101 1960 30 95 36 161 1961 14 101 9 124 1962 47 107 55 209 1963 0 64 70 134 1964 34 60 43 137 1965 0 62 33 95 1966 49 77 65 191
RELIABILITY OF ESTlMATOR FOR 1957 AND 1958 SEASONS
1957, Actua1 76 128 11 (*) 215 Estimate 49 103 17 (*) 169 (-27%) 1958, Actua1 29 76 7 (*) 112 Estimate 32 91 18 (*) 141 (+21%)
(*) to August 8th, 1957, to August 12th, 1958
The method i11ustrates the relative warmth of the 1962 summer, and the exceptiona1 coo1ness of the 1965 summer. The re1iabi1ity of this estimate was not high (-27% in 1957 and +21% in 1958). The sign of the difference suggests it is possible that this method has tended to reduce the extremes of fluctuations. In Canada the mean dai1y tem?erature is defined as ha1f the sum of the dai1y maximum and the dai1y minimum. When temp- IOOF 40
1!'.LERT • TOF(G) = 22.85 + 0.29(ToF(A» r= 0.48 •
COMPARISON. OF MEAN DAILY. • TEMPERATURES AT ALERT AND GILMAN GLACIER, 1957-1958 • 50o~ (142 VALUES) · • • • • •
• • • • • ·• • • • • 40° F • • " • .'· • , • z. • · • • · ·• • · . • • • , • • • • • • • • , • • 1 / SOoF •
• •
T°F"(G) = -21.28 +. ,. 75( TOF(A>' • • • • • • r= 0.65 .
• • • • •
'.
· GILMAN MEAN DAILY TEMPERATURE AT ALERT ,-
2
COMPARISO N OF 142 MEAN looe 50 4 DArLY TEMPERATURI;S, ALERT 2 AND GILMAN GLACIER CAMp' 1957-1958. 5 !
20: PLOTTED POSITION REPRESENTS MEDIAN OF 20 VALUES .4
4
6 fioe 4
-..
7
Il OOc
!O
1
~ 2 .- .- \\. 2 7 _Sci 2 3 20
MEAN DAILY TEMPERATURE AT GILMAN GLACIE R CAMp' 1957 - 1958
10~------.------,------~~--~ 20 ·30 40 0 F FIGURE 14 -58-
eratures f1uctuate about the freezing point, me1ting degree-days based
on mean dai1y temperatures defined in this way tend to under-estimate
the relative warmth or coo1ness of ablation seasons. (Arnold and MacKay,
1964)
The second method was 1ess e1aborate and is a modified 1apse-rate method. The temperature difference to be app1ied to the A1ert mean dai1y
temperatures to give the best fit to the Gi1man Glacier me1ting degree-
day tota1s was chosen for each of the six months in which observations were
avai1ab1e. A single temperature difference of 6o F was then chosen as the value c10sest to the mean of the separate values. This wou1d imp1y a o 1apse-rate of 0.34 C/100 m when temperatures were above freczing at the
Gi1man Glacier, which agre~s weIl with the radiosonde data given in Sagar, o 1964, p. 25 (0.330C/100 m for June, 0.38 e/100 m for Ju1y). The resu1ts
based on this method are given in Table 13.
TABLE 13: MELTING DEGREE-DAYS AT THE GILMAN GLACIER, ESTIMATED FROM ALERT MEAN DAILY TEMPERATURES BY MODIFIED LAPSE RATE METHOD (oF)
YEAR JUNE JULY AUGUST TOTAL
1959 Il 23 32 66 1960 25 138 28 191 1961 1 128 o 129 1962 30 158 84 272 1963 o 38 95 133 1964 28 25 17 70 1965 o 32 29 61 1966 60 71 59 190
BEST FIT OF ESTIMATOR FOR 1957 AND 1958 SEASONS
1957, Actua1 76 128 11 (*) 215 Estimate 66 137 18 (*) 221 (+3%) 1958, Actua1 29 76 7 (*) 112 Estimate o 114 o (*) 114 (+2%)
(*) to August 8th, 1957 to August 12th, 1958 -59-
The pattern is simi1ar to that in Table 12, with the warmest summer being 1962 and the coo1est being 1965, but the extremes of warmth and coo1ness have been accentuated to a degree that appears more rea1istic, as the 1962 ablation season was unusua11y warm on other glaciers in the
Queen Elizabeth Islands. (For examp1e, Meighen Ice Cap, in Arnold, 1965, p. 408). The cool summer at Alert in 1959 was caused by an exceptional prevalence of fog, and is not ref1ected in the specific mass balance curve of the Gilman Glacier for that year. Again, the relatively high degree-day total for 1966 does not correspond with the lower position for the equil ibrium line on the Gilman Glacier in that season. The estimate may have been unreliable in that year, or the effect of summer precipitation on the glacier may have been more pronounced.
Using this estimator for the relative warmth of the 1962 ablation season, and taking into account the 30.0 cm w.e. accumulation of that balance year from the pit data at 1660 m, it was estimated that the mass balance at station 100 in that year was -100 cm (ice equivalent). With this value an estimate for the profile down-glacier from station 100 could be made. In a similar way the mass balance was estimated for the profile down-glacier from station 89 for the balance years 1963 to 1966. The observed and estimated mass balance for the long profile of the glacier is given in Table 14.
In this table the values given by Sagar are average for stakes within cross profiles, as weIl as values for individual stakes along the long profile of the glacier. The positive estimates may be individually in error, but their sum at any single location shou1d be free from error, as they are based on pit data. The total mass balance for the decade is considered reliable to ± 10%. e e
TABLE 14 OBSERVED AND ESTIMATED MASS BALANCE ON THE LONG PROFILE OF THE GILMAN GLACIER (CM ICE)
Year Resurveyed Point
101 100 98 96 94 92 89 88 87 86 85 84
1957 -80 -90 -100 -110 -130 -140 -160 -170 -190 -200 -210 -230 1958 -60 -70 -80 -90 -100 -110 -130 -140 -140 -160 -190 -200 1959 -20 -30 -40 -60 -80 -90 -100 -110 -120 -130 -160 -170 1960 -80 -90 -110 -120 -130 -160 -180 -190 -200 -210 -240 -260 1961 0 0 -10 -10 -20 -20 -30 -40 -60 -60 -80 -100 1 1962 -90* -100* -120* -130* -140* -170* -190* -200* -210* -220* -260* -270* 0\ 0 1963 +6 +17 +20 +12* +11* +9* 0* -10* -20* -20* -60* -70* 1 1964 +13* +13* +13* +12* +11* +9* 0* -10* -20* -20* -60* -70* 1965 +13* +13* +13* +16 +11* +9* 0* -10* -20* -20* -60* -70* 1966 +13* +13* +6* +9 ..,8 +8* 0* -10* -20* -30* -70* -80*
Known -234 -263 -320 -365 -452 -520 -600 -650 -710 -760 -880 -960 Estimate-51 -61 -88 -106 -107 -135 -190 -240 -290 -310 -510 -560 TOTAL -285 -324 -408 -471 -559 -655 -790 -890 -1000 -1070 -1390 -1520 Sources: 1957to 1961 from Sagar 1964, p. 51 (converted to ice equiva1ents) 1963 to 1966 based on accumulation data from G. Hatters1ey-Smith, persona1 communication. Year refers to end of balance year. Estimates indicated by (*). Negative estimates based on degree-day tota1s estimated from A1ert temperatures. The sum of positive estimates at any point is reliable, but the allocation to different balance years is estimated. -61-
The curves of known surface 10wering and estimated mass balance are shown in Figure 15. By subtracting the surface 10wering from the mass balance at each point, a curve can be obtained which represented the mass balance (ice equiva1ent) required to keep the surface profile unchanged at each point. This varies from -0.15 m/yr at seismic profile 101 to -1.5 m/yr at station 84, the 10west point at which the change of height was measured, and 1.3 km from the end of the glacier. This represents.a 108s of 47.3 x
106m3 of ice per year over the entire surface of the glacier be10w seismic profile 101, a110wing for the increa8ed me1ting near the glacier edges
(more fu11y discussed in the section on volume changes), an average 10ss of 69 cm ice (61 cm w.e.) per unit area.
For a steady state glacier this curve shou1d be the same in amount, but opposite in sign, to the vertical component of f10w with respect to the
ice surface. The agreement with the meagre vertical f10w component data avai1ab1e from the Gi1man Glacier is not good. The curve of equi1ibrium mass balance suggests that theemergence rate shou1d be +0.15 m/yr at station
101. Movement stake M8 wa8 on1y 18 m from this position in 1957, and the vertical f10w component with respect to the glacier surface here was -0.2 m/yr
(estimated error 0.3 m/yr). At S98, 2.7 km farther down the glacier, the
equi1ibrium mass balance wou1d be compensated by an emergence rate of
+0.19 m/yr. The value there observed was +0.5 m/yr (estimated error 0.3 m/yr).
With an estimated error of 0.3 m/yr (Table 4) these values are on1y bare1y
consistent with the curve for the equi1ibrium mass balance. The value at
M8 may be affected by a steepening of the glacier above this point.
If the vertical component of f10w with respect to the glacier surface
actua11y does pass from negative to positive between seismic profile 101 and e •
... :, . i 0
-t -t
-z -z
-3 CHANGE IN HEIGHT -3 OF SURFACE n."" .___ '" _., 1957-67 .;,...... '" :t·""00 ", D ANOUNT 0" ERROR 1 n.37) -----. :-----.... ~'+C~ a 1 "S7) '95.) ~~.,~. '" ...... • "'~~O.,~. '" .. ,,) "'';;--''. '-. '.. (880) q"l(."~ X "{' ,. +. FcELATION BETWEEN MASS BALANCE ~"'C~ .~ "' (f'(f'.o X ~C ~ AND CHANGE IN THICKNESS, 1957 TO 1967 (831) ~ ~C0', ~1'A\ . "4(.~~I'J " ~(' (1037) ELEVATION IN METRES •. 1957 (79~) Ivl'J ". ~(f' . (76!" ...... ~~
(708) \ :.s-~ Il 4 z FIGURE 115 ~.. , -63- seismic profile 98, it may imply that the long term equi1ibrium 1ine to which the f10w is adjusted lies between these two points, at an e1e vation of 1020 m. In 1957 the equi1ibrium 1ine was as high as 1250 m (Hatters1ey-Smith, 1960[a], p. 620), and during the years 1963 to 1966 it has been as lowas 830 m (Hattersley-Smith, persona1 communication). A ho1e bored at 1037 m in 1958 contained ice of mean density 0.86 gm. cm- 3 in the upper 7.5 m, of mean density 0.82 gm. cm- 3 from -7.5 to 3 -18.25 m (with a minimum density of 0.77 g. cm- ), and thereafter the 3 3 mean density increased to 0.89 g.cm- , with values as high as 0.9 g.cm- • Hatters1ey-Smith thought it unlike1y that this low density ice cou1d be very old, and suggested that the equi1ibrium 1ine had been appreciably raised since this ice was deposited (Hatters1ey-Smith, 1960[a], p. 622). It is evident that on slowly moving glaciers typica1 of this part of the Arctic, vertical f10w components must be measured with considerable precision if re1iab1e conclusions are to be made from them. This wou1d involve careful attention to the insertion of the stakes, a complete record of any height changes due to redri11ing of stakes in the ablation area, and spirit 1evel1ing to de termine the heights of the tops of the stakes. The relative re1iability of different types of sensors shou1d be investigated. A calibrated steel wire frozen into a bore ho1e may render the replacement of stakes from ablation season to ablation season unnecessary. Changes in the Snout of the Gi1man Glacier During the IGY survey a cairn was bui1t about 100 metres from the snout of the Gi1man Glacier, and severa1 steel tape measurements were made from this cairn to the snout a10ng a fixed 1ine. This distance was again measured in 1967. The measurements are given in Table 15. -64- TABLE 15: DISTANCE OF THE SNOUT OF THE GILMAN GLACIER FROM WEST BASE CAIRN Distance Change Interval Rate Date metres metres days m/yr 8 June 1957 101.2 -2.6 59 -16.1 6 August 1957 103.8 +8.0 279 +10.5 12 May 1958 95.8 -1.2 60 ) Il July 1958 97.0 ) -5.8 22 ) +28.1 2 August 1958 102.8 ) -0.4 14 ) 16 August 1958 103.2 21 May 1967 70.4 +25.4 (*) 9 years +2.8 (*) From corresponding season in 1958 The greatest difficulty in making these measurements was to decide on the actual position of the snout. In the pre-melt season, drifted snow accumulated at this location, and it was necessary to probe for solid ice when making the measurement. During the ablation season, it is possible that some of this drift snow became soaked by meltwater run- ning off the glacier, and formed superimposed ice on the glacier snout, which had a slope of some 40 degrees at this locality. This was not a typical one, for elsewhere the glacier ended in an ice cliff up to 30 metres high. As far as locating solid ice is concerned, the measurements are considered to be reliable to 0.5 metres; but accumulation of super- imposed ice may affect the measurements within a single summer. In 1967 the position of the base cairn was checked from stations Roger and Wolf, on the hillsides remote from the glacier. There was no -65- evidence that it had moved during the 10 years. The ground in front of the glacier is therefore assumed to be free from thrusting from the advance of the snout, and the base station has not been affected by the erosion of the stream close bye During the IGY the glacier snout was advancing. Between June 8, 1957 and May 12, 1958, the snout advanced 5.4 metres. The greatest dif ficu1ty is to account for the change in recession rates during the two ablation seasons of 1957 and 1958. In 1957 the snout retreated 2.6 metres in 59 days, but in 1958, a season in which ablation was less than in 1957 over the rest of the glacier, the snout retreated 7.4 metres in 96 days, with a maximum rate of 5.8 metres in 22 days. This difference might be explained by a change in the rate of glacier movement at the snout (for which there was no evidence over the rest of the glacier), or by the re1atively rapid ablation of a water-soaked snowbank, with an ice covered upper surface that had been mistaken for glacier ice. With respect to the end of the two ablation seasons of 1957 and 1958, the position of the snout was almost stable, and had one taken measure ments at these times only, the advance of the snout would not have been detected. This is another illustration of the hazards of eva1uating glacier changes from snout behaviour. The melt during relatively warm seasons of 1957 and 1958 balanced the advance of the intervening winter, and it is therefore not surprising that it shouldshow an advance for the last 8 years of the decade, during which mean ablation rates were lower. It is therefore not necessary to postu1ate any surges of the snout position (although it is not possible to say that these have not taken place). If the rate of advance during' the 1957-58 winter had been maintained, the glacier snout would have advanced -66- 94.5 metres, in the absence of summer ablation. It advanced on1y 25.4 metres, which suggests an average figure of 7.7 metres for the recession during the nine ablation seasons. This wou1d suggest that the retreat during the 1957 summer was anoma1ous. The question of whether a glacier remains in contact with its bed at the snout of the glacier was considered by Nye in a p1asticity sol ution for a glacier snout (Nye, 1967, pp. 711-712). During the summer of 1958 it was interesting to observe that we11 deve10ped saxifrage plants were growing on the ground over which the glacier had advanced during the previous winter. This suggests that the actua1 snout of the glacier is on1y in contact with the tops of the 1arger rocks and bou1ders in this area. The Change in Volume Down-G1acier from Seismic Profile 101 At first sight it might appear anoma10us that the snout of a glacier that shows consistent thinning shou1d have advanced 31 metres in 10 years, but this is consistent with observations of the Thompson Glacier, Axel Heiberg Island (F. MUller, persona1 communication). Hatters1ey-Smith conc1uded from the glacio10gica1 observations on the Gi1man Glacier during the IGY that the main high 1eve1 ice caps and trunk glaciers in Ellesmere and Axel Heiberg Islands were showing 1itt1e change in area1 extent from year to year, but that thinning was taking place in their 10wer reaches. In ~ontrast, iso1ated ice masses be10w the equi1ibrium 1ine were thinning rapid1y (Hatters1ey-Smith, 1960[b], p. 11). It is of interest to de termine the net change in volume during the 10-year interva1, 1957-1967, be10w a cross-section of known area from the known change of surface height and the snout advance. This can be compared with a volume change ca1cu1ated from the estimated mass balance over the -67- same area and flow through the same cross-section. 2 The area down-glacier from seismic profile 101 is 69.4 km • In order to be consistent with the mass balance curves of Sagar (Sagar, 1964, p. 51) the total volume change was calculated using means for the same altitude areas used by him. This givesa volume loss by surface 6 3 lowering of 168 x 10 m • The mean loss of height is 2.43 m. For an estimate of the gain in volume due to the advance of the glacier, its me an width in the vicinity of the snout was assumed to be 3 km, the mean advance of the' ice to be 31 metres - the only value ob- served - and the mean height of the ice cliff at the edge of the glacier to be 30 metres. This gives a total volume gain of 2.79 x 106m3 • The net change, due to surface lowering and the advance of the glacier is 6 3 a loss of 165 x 10 m • c The area of the cross-section of the glacier at seismic profile 101 is known to be 2.31 x 106km2 (Sandstrom, 1959, p. 23). For parabolic cross-sections the mean velocity of a glacier through the whole section can be taken as the mean of the surface velocity measured at equal inter- vals across the section. (Nye, 1965, p. 685). The mean velocity averaged over stakes Ml to MIO over an interval of approximately 1 year was 22.8 m/yr. This profile does not extend over the whole glacier, and therefore does not include the slower moving ice near the glacier edges. A reason- able value for the average surface velocity would be 21 m/yr, and assuming that this flow rate has been maintained for the whole 10-year interval, the discharge through the cross-section would be 21 m/yr x 10 yr x 2.31 km 2 6 3 = 485 x 10 m • The ablation of ice at the very edge of the Gilman Glacier is much greater than that close to the long profile of the glacier, by a factor of 3 to 5 (Hattersley-Smith, 1960, p. 8; and Sagar, 1964, fig. 20, p. 51). -68- From ablation data given in Lotz, 1957 and Sagar, 1960 it is possible to estimate that the average ablation over the whole glacier width near the 1957-58 camp was from 1.05 to 1.25 greater than that given by the average of the ablation stakes. Consequently the mass bàlance given by these measurements is a minimum estimate (Hattersley-Smith, 1960[b], p. 8). Lower down the glacier is narrower, and the additional melting at the edges has a relatively greater influence. Assuming that this is important only in the last 100 metres of the glacier width, the ablation recorded at the stakes in this area should be increased by a factor of at least 1.30. A correction factor of 1.25 for that part of the glacier down-glacier from seismic p'rofile 101 is a reasonable estimate. If this is applied to the 10-year mass balanceœtimate given in Table 14, and a volume is ca1culated using the area-altitude distribution given in Sagar, 1964, 626 x 106m3 of ice has been lost by ablation during the 10-year interva1. During the same interval 485 x 106m3 has been added by glacier 6 3 flow, giving a volume loss of 140 x 10 m • This can be compared with c the volume 10ss calculated from the measurements of surface lowering and 6 3 advance of the snout, 165 x 10 m • These two estimates of volume 10s8 agree fairly weIl, considering that it has been assumed that the flow rate has been constant during the 10 years, that the observed surface lowering can be averaged over the same height intervals used for the volume loss estimated from the mass balance data, and that the mass balance data is not complete. It is clear that the thinning of a glacier is a much greater contri- butor to the change in volume than fluctuations of the glacier snout. On the Gilman Glacier the snout change represents about 3% of the total change. Quite apart from any local differences in topography between the bed of a -69- glacier and its upper surface in the vicinity of the snout, one can conclude that the advance or retreat of a glacier similar to the Gilman Glacier is not a good indicator of its change in volume. To draw any inferences of climatic change from the advance or retreat of glacier snouts, a sample of some 30 glaciers in the chosen area should be selected, and the snout measurements should be made at the close of the ablation sea- son over as long a time interval as possible. -70- CHAPTER VIII SUMMARY The method of repositioning stakes by two theodolite directions, and the determination of the change in height by the measurement of simultaneous reciprocal vertical angles has given results with an uncertainty of 0.3 metres in the height determination over distances of up to 6 km from trigonometrical stations near the Gilman Glacier. This is comparable with the published results of height changes measured by photogrammetrie methods, but ,photogrammetrie methods are superior both from the point of view of the time spent on field work, and in the detail of coverage. The mean value of k, the coefficient of refraction, was 0.162, with a range of 0.047 to 0.558. The effect of atmospheric refraction over the distances measured on the Gilman Glacier gave a mean error of only 0.31 metres. Errors exceeded one metre in 3 of 56 observations. If it is not possible to take simultaneous reciproca1 vertical angles to reposi tioned stations, it is a wise precaution to observe to a stake left at the repositioned point on at least two different occasions, to guard against an erroneous height determination due to abnorma1 refraction. This method is we1l suited to small parties without access to photo grammetrie equipment, and the results obtained on the Gilman Glacier by observers using theodolites in the field for the first time showed that 1engthy experience with surveying equipment was not necessary. The change of volume calculated from the known surface lowering and snout advance was in reasonable agreement with a change in volume calculated from an estimated mass balance and the flow of ice through a known profile. -71- It is estimated that a mean 10ss of ice of 0.69 m/yr over the 69.4 km 2 area of the glacier be10w seismic profile 101 wou1d keep the surface profile of this part of the glacier unchanged. The mean ice 108s over this area, from 1957 to 1967, is e8timated at 0.91 m/yr, with values for individua1 years ranging from 0.01 m/yr to 2.10 m/yr. Un1ess ablation stakes or other sensors can be maintained in the ablation zone over a period of severa1 years, the extreme1y sma11 vertical components of glacier f10w with respect to the glacier surface demand a high order of accuracy in their determination, if the surface 10wering is to be successfu11y re1ated to the f10w of the glacier and mass balance quantities. The snout of the Gi1man Glacier is advancing at the same time as the ablation area is thinning. This resu1t has a1so been observed in Axel Heiberg Island. In this area it is therefore more than usua11y difficu1t to relate the changes of snout positions to recent c1imatic changes. Marked1y different rates cf thinning have a1so been observed near the edges of the glacier, presumab1y due to local conditions of reduced ice f10w or increased exposure to solar radiation. Such circumstances shou1d be carefu11y considered when conclusions re1ating to average thinning rates of the glaciers in this area are drawn from trim 1ines and simi1ar features. -72- REFERENCES Angus-Leppan, P.V. 1968. An experimenta1 determination of refraction over an icefield. Unisurv Report No. 10. University of New South Wa1es, Kensington, N.S.W., Austra1ia. Arnold, K.C. 1959. Operation Hazen, Survey 1957-58. Canada, Department of National Defence, Defence Research Board, D Phys R (G), Hazen 5. Arnold, K.C. 1965. Aspects of the glacio10gy of Meighen Island, Northwest Territories, Canada. Journal of G1aci~, Vol. 5, No. 40, p. 399-410. Arnold, K.C. and MacKay, D.K. 1964. Different methods of ca1cu1ating mean dai1y temperatures, their effect on degree-day tota1s in the high Arctic and their significance to glacio10gy. Geographica1 Bulletin, No. 21, p. 123-129. B1achut, T.J. and Muller," F. 1966. Some fundamenta1 considerations on glacier,mapping. Canadian Journal of Earth Sciences, Vol. 3, No. 6, p. 747-759. Dittrich, G. 1967. Surveying in the Antarctic. Vermessungs Informationen (Surveying News) Carl Zeiss (Jena), No. 18', Geodesy, p. 33-43. (General As'semb1y of Helsinki. 1960.) Union Géodésique et Géophysique Internationale. Association Internationale d'Hydrologie Scientifique. Assemblée générale de Helsinki, 25-7-6-8 1960. Commission des Neiges et Glaces. p. 5-6. Haefe1i, R. 1962. The ablation gradient and the retreat of a glacier tongue. Union Géodésique et Géophysique Internationale. Association Internationale d'Hydrologie Scientifique. Commission des Neiges et Glaces. Publication No. 58, p. 49-59. Hamilton, R.A. 1957. The determinationof temperature gradients over the Green1and ice sheet by'optica1 methods.Proceedings of the Royal Society of Edinburgh, Section A, Vol. 64, No. 25, p.' 381-397. Hatters1ey-Smith, G. 1960 Ca). Studies of eng1acia1 profiles in the Lake Hazen area of northern Ellesmere Island. Journal of G1acio10gy, Vol. 3, No. 27, p. 610-625. Hatters1ey-Smith, G. 1960 Cb). Operation Hazen, glacio10gica1 studies: snow cover, accumulation, and ablation. Canada, Department of National Defence, Defence Research Board, D Phys R (G), Hazén 10. -73- Hat ters ley-Smith , G. 1962. Canadian Operation "Hazen". Polar Record, Vol. Il, No.'70, p. 46-48. Hattersley-Smith, G. 1963. Climatic inferencesfrom firn studies in northern Ellesmere Island. Geografiska Annaler, Vol. 45, Nos. 2-3, p. 139-151. Hattersley-Smith, G. 1968. Canadian Operation "Hazen-Tanquary", 1967. ,Polar Record, Vol. 14, No. 89, p. 194-197. Kasser, P. 1967. Fluctuations of glaciers, 1959-1965. A contribution to the International Hydrological Decade. International Commission of Snow and Ice of the International Association of Scientific Hydrology. United Nations Educational, Scientific and Cultural Organization. Keeler, C.M. 1964. Relationship between climate, ablation and run-off on the Syerdrup Glacier, 1963, Devon Island, N.W.T. Arctic Institute of North America, Research PaperNo. 27. Konecny, G. 1966. Applications of photogrammetry to surveys of glaciers in Canada and Alaska. Canad'ian Journal of Earth Sciences, Vol. 3, No. 6, p. 783-798. Lotz, J.R. 1957. Unpublished. Glacial-meteorological observations in northern Ellesmere Island during Phase l of "Operation Hazen" 1957. (A report prepared for the Defence Research Board, Department of National Defence, Ottawa, Ontario.) Meier, M.F. 1960. Mode of flow of Saskatchewan Glacier, Alberta, Canada. U.S. Geological Survey, Professional Paper 351. Meier, M.F. 1966. Some glaciological interpretations of remapping prograllls on South Cascade, Nisqually and Klawatti glaciers, Washington. Canadian Journal of Earth Sciences, Vol. 3, No. 6, p. 811-818. Meier, M.F. and Tangborn, W.V. 1965. Net budget and flow of South Cascade Glacier, Washington. Journal of Glaciology, Vol. 5, No. 41, p. 547-566.' Ministry of Defence. 1965. Textbook of Topographical Surve~. (Fourth Edition.) London, Her Majesty's Stationery Office. Muller," F. 1962. Zonation in the accumulation area of the glaciers of Axel Heiberg Island, N.W.T., Canada. Journal of Glaciology, Vol. 4, No. 33, p. 302-311. Muller," F. 1965. Note on Axel Heiberg Island. Canadian Geophysical Bulletin, Vol. 18, p. 140-141. -74- Muller," F., and members of the expedition. 1963. Preliminary Report, 1961-1962. Axel Heiberg Island ResearchReports. McGill University, Montreal. Nevi~re, J. 1954. Campagne au Groenland, 1948, 1949, 1950. Nivellement géodesique de l'Inlandsis. Annales de Géophysique, Tom. 10, Fasc. 1, p. 66-68. Nye, J.F. 1965. The flow of a glacier in a channel of rectangular, elliptic, or parabolic cross-section. Journal of Glaciology, Vol. 5, No. 41, p. 66l-E90. Nye, J.F. 1967. Plasticity solution for a glacier snout. Journal of Glaciology, Vol. 6, No. 47, p. 695-713. Orvig, S. 1951. The climate of the ablation period on the Barnes Ice Cap in 1950. Geografiska Anna1er, Bd. 33, p. 166-209. Paterson, W.S.B. 1955. Atmospheric refraction above the in1and ice in north Green1and. Bulletin Géodésique Internationale, Vol. 38, p. 42-54. Paterson, W.S.B. and Slessor, C.G.M. 1956. Trigonometrica1 1eve11ing across the inland ice in north Green1and. Empire Survey Review, Vol. 13, No. 100, p. 252-261~ Sagar, R.B. 1960. Glacial meteorologica1 observations in northern Ellesmere Island during phase III, "Operat;:ion Hazen", May-August 1958. Arctic Meteoro1ogy Research Group, Publication in Meteorology No. 29. McGil1 University, Montreal. Canada, Department of National Defence, Defence Research Board, D Phys R (G), Hazen 13. Sagar, R.B. 1964. Meteorologica1 and glaciologica1 observations on the Gilman Glacier, northern Ellesmere Island, 1961. Geographica1 Bulletin, No. 22, p. 13-56. Sandstrom, H. 1959. Geophysica1 methods in glacio1ogy. Canada, Department of National Defence, Defence Research Board, D Phys R (G), Hazen 3. (Symposium of Obergurg1. 1962.) Union Géodésique et Géophysique Internationale. Association Internationale d'Hydrologie Scientifique. Commission des Neiges et Glaces. Colloque d'Obergurg1, 10-9-18-9 1962, p. 306-309. Weber, J.R., and others. 1960. Geophysica1 surveys on Gi1man Glacier, northern Ellesmere Island. Union Géodésique et Géophysique Internationale. Association Internationale d'Hydrologie Scientifique. Assemblée générale de Helsinki, 25-7-6-8 1960. Commission des Neiges et Glaces. p. 500-511.