VELOCITY FLUCTUATIONS AND WATER REGIME OF ARCTIC
VALLEY GLACIERS
By FRITZ MÛLLER and ALMUT IKEN
(Axel Heiberg Expedition, McGill University, Montreal, Canada)
ABSTRACT. Over a period of 10 years, 1959-69, surface movement, ablation and, to some extent, run-off were measured in the
ablation area of cold valley glaciers, particularly White Glacier on Axel Heiberg Island (lat. 80° N.) in the Canadian Arctic
Archipelago. The annual, seasonal and short-period velocity fluctuations were found to be most strongly linked to t h e discharge
capacity of the intra and subglacial drainage system. However, changes in glacier thickness, ice temperature near the bed and
longitudinal stress gradient are also influential. Intraglacial, water-activated glide planes were observed.
RÉSUMÉ. Variations de vitesse et regime de Veau dans les glaciers arctiques de vallée. Durant une période de 10 ans 1959-69, le
mouvement de surface, l'ablation et par une part, le débit furent mesurés sur les glaciers froids de vallées, notamment le White
Glacier sur l'Axel Heiberg Island (80° N) dans l'Archipel arctique canadien. On trouva que les variations de vitesses annuelles
saisonnières et pour de courtes périodes étaient très fortement reliées à la capacité de débit du système de drainage intra et
sous-glaciaires. Cependant des changements dans Fépaisser du glacier, de la température de la glace près du socle et du gradiant
de la contrainte longitudinale ont aussi leur influence. Des plans de glissement intra-glacîaires activés par l'eau de fonte étaient
remarqués.
INTRODUCTION
Variations both in time and space in the surface velocity of temperate valley glaciers have
been measured, sometimes in great detail, for over a century by such as Agassiz(1847), Mercanton
(1916), Meier (1960), Elliston (in [U.G.G.I.], 1963, p. 65-66), Millier (1968) and many others.
For cold glaciers, however, relatively few such measurements have been made (Battle, 1951;
Paterson, 1961; Millier, 1963[b]; Wilhelm, 1963; Friese-Greene and Pert, 1965; Pillewizer,
1965; Pillewizer and others, 1967), A variety of explanations for the observed fluctuations have
been offered, dependent on changes in : ambient temperature, mass balance, ice thickness, and
amount of melt water on and under the glacier.
To further the study of velocity fluctuations, data have been collected for the entire ablation
area of one valley glacier in the Arctic, and parts of others, over a long period (10 years) and
for various time intervals (annual to hourly) to investigate causal relationships and in particular
to assess the role played by water. Two facets of polar glaciers make them of particular interest :
the water supply from the surface ceases completely for several months during the winter, and,
at least in a large part of the glacier body, the water must circulate in distinct channels and
interfaces, as temperatures are below pressure melting point.
The measurements were carried out on Axel Heiberg Island (lat. 80° N., long. 90° W.), in
the Canadian Arctic Archipelago, during the summers 1959-69. Information on the area in
general, the survey programme carried out and the concurrent glaciological, climatological and
hydrological studies have been given in Millier and others (1961, 1963). The positions of the
stake lines are shown in Figure 1. The degree of detail in the surveying was greatest for the medium-sized White Glacier. For comparison, some observations were obtained from selected points
of profiles on the much smaller Baby Glacier and the large (40 km long) Thompson Glacier,
an outlet glacier from the McGill Ice Cap. Miiller (1963[b], p. 68-75) has given primary information on surface-velocity distribution along the centralflowline of White Glacier, transverse
166
Fritz Miiller and Almiit Iken
velocity curves, velocity increase during the summers 1957-62, marginal slip, a n d on changes
in the surface elevation and the snout positions. The results of seismic and gravity measurements
carried out on these glaciers have been given by Redpath (1965) and Becker (unpublished).
Miiller (1963[a], has reported the results of englacial temperature measurements. The ablation
and run-off patterns in the area have been described by Adams (1966).
Fig. 1. Location of surface-velocity measurements on White and Thompson Glaciers, Axel Heiberg
Island. Surveying profiles in ablation area: M "moraine", W "wind", A "anniversary",
I "ice cave", R "ridges", L. I. "lower ice", E "eureka".
THE DATA
Short-period variations
The discharge of glacial rivers in the Arctic has a marked daily cycle. The influence of these
short-period fluctuations on movement was studied on White Glacier. Three staks, 200 m
above the "anniversary" profile and aligned at 100, 300 and 300 m distance from the western
margin, were surveyed at intervals of a few hours during 12 d at the end of July a n d the beginning
of August 1968, and during several periods in 1969. The results are shown in Figures 2 and 3
together with discharge records of a river which drains an area of approximately 0.7 km 2 in the
western section of the "anniversary" profile.
167
Water regime of Arctic valley glaciers
VARIATIONS OF DAILY VELOCITY AND RUN-OFF
Anniversary Profile - 1968
Fig. 2. Short-penod vaiutions of \elocity and run-off in mid-summer on lower White Glacier. Stakes H t , H, and H 3 are situated
at 100, 200 and 300 m distances from the western margin. Error borders for stake H 3 are shown; those for H , and H2
are generally smaller as they are closer to the survey base. The discharge curve shows the fluctuation of a supraglacial
stream.
DAILY VARIATIONS OF VELOCITY AND RUN-OFF
VELOCITY
of
STAKE
H2
STAKE
H1
Anniversary Profile
1969
( cm/h )
1.0
Fig. 3. Short-period variations of velocity and run-off at the beginning of the melt season, lower White Glacier. The lower
discharge curve shows fluctuation of amount of muddy (intra- or subglacial) water spouting out of a marginal crevasse
about 0.5 km down-glacier from stake H ^ the upper curve gives discharge data from the same stream as in Figure 2.
Fritz Millier and Almut Iken
168
—.
_
!—
—i
i
:
-Ar
i*
CO
1$
$
;5
\
fi
'i
i
p l - U . ... :
i
!
B
1,
l
i
r 196
-.1-1-^
E ! f~r>
E !
1
-J ô
E
o
O <p
!^
;1 . , _
•
:-
j*
|
cr
>
Q-
-•8
L-g-™
i
I!
J
1
ï
—i-\t
l[i
• Z^$ s
u.
3
co j
*
|
Ct co
J ...
1
;
1
'•
1 î?<
i
i—,—.—,—,—L
o
1
en
:
C
h
'•
o
Q>
|
,;_
i
o
E3
o
£§
1
CD
-~
S 13
m
!
i
^ _ L
i!i i:
m £
S
i
i
. i .. _
.__
k H
CD
!
:
r:
«o
S f—i
i
!i
J
00
J2 O
i'
iï
,
CO
—J
-f
r
rji If
!
CM
=ï
i
il
Water regime of Arctic valley glaciers
169
On 20 July, when the approximately 4 h observations of 1968 started (Fig. 2), the ablation
had already past its climax but was still fairly strong, and for about half the days the weather
was clear, producing sinusoidal discharge curves. The velocity peaks usually coincided with
the discharge peaks; the time lags that occurred showed no pattern. Of the ten fully recorded
daily cycles, five have two velocity minima and one has three. Small movement fluctuations of
a few hours duration may have been averaged out as the surveying intervals were sometimes
extended up to 8 h particularly at night. The secondary movement peaks occurred any time
between 16.00 and 08.00 h. The early summer observations of 1969 (Fig. 3) when a period
of strong melt occurred showed a considerably different situation: (1) there was an almost
persistent time lag of 6-10 h between the daily discharge and movement peaks ; (2) no secondary
movement peaks were observed, except during the first few days at the stake nearest to the
glacier margin (Hj),
Medium-interval variations
The medium-term observations (a few days to some weeks), carried out since 1961 on
White Glacier at various profiles ("lower ice", "ice cave", "anniversary", "moraine" and, since
ANNIVERSARY
PROFILE
average of 3 stakes : A3 , A 4 , A5
Surface Velocity - summer 1968
A2
-X-
7
i'i '
15
!S
21
25 2> 29
3
6 8
10 12
Sr_l-
fS
15 17 19 21
r~3Ô
•Î-
î
1Ô- 12 (4
23
cm of ice / d
Rate of Melt - summer 1968
stakes As - A 9 , U s . i-49
l*
MAY~»!
Fig. 5. Summer velocity changes and ablation at "anniversary" profile, White Glacier. Stake A2 is about
the eastern margin. A 3 to A5 follow at 100 m intervais towards the glacier centre.
100 m from
170
Fritz Millier and Almut Iken
1968, "wind" profiles) revealed the most interesting velocity fluctuations when the time interval
corresponded with changes in weather and therefore run-off.
In Figures 4 and 5, medium-term velocity variations of selected stakes of the "wind" and
"anniversary" profiles are shown together with ablation data from the same area for similar
time intervals. The errors shown for the surface-velocity data are experimental errors determined
from repeated and 180° reversed readings from the two ends of a base line. The marked difference (in some cases) between the positive and negative error values arises from differential
rating of the readings from the two ends of the base. The error borders of the ablation values
show the 68 % confidence limit of the mean values.
At the beginning of the 1968 summer there was a time lag between ablation and velocity
fluctuations of about 5 d at "wind" profile, about 3 d at "moraine" profile and only 2-3 d
at "anniversary" profile. Though there was generally a fairly regular increase of movement
in all profiles from the edge to the centre, the time lag near the centre appears to be larger by
1 or 2 d, particularly at "wind" profile. Maximum velocity at "moraine" and "wind" profiles occur red 4-12 d after the ablation rate had reached its peak ; this time gap varied considerably from stake to stake in the upper half of the ablation area, while in the lower part
there was little or no delay. After the beginning of July, no time lag of more than a few hours
was observed in any of the fluctuations at "anniversary" and "lower ice" profiles.
Annual and seasonal fluctuations
The long-term velocity data (annual and seasonal values) measured between 1960 and
1968 are compiled in Table I and Figure 6. The correction procedures used are outlined in
the Appendix.
The annual velocity decreases from "moraine" to "wind" profile, and, after a slight
increase to "anniversary" profile, declines steeply to "lower ice". After the summer of 1962
SURFACE
VELOCITIES
AT
ANNIVERSARY
PROFILE
Fig. 6. Variations in (1) annual, (2) winter and summer velocities (mean of measurements at six
takes), and (3) ablation rates (mean of measurements at nine stakes) at the ''anniversary"
profile, 1960-68; dashed lines indicate error borders.
Water regime of Arctic valley glaciers
n 1 to 3 stake
5 to 10 stake
171
I
<ON
a
«^
Tt
• i! ^ s^ iz
I
a
iSSs.2
>
°-2
llll
3
S o o
... —i O
ÏD CS ï^-
•~< co m r n > ai
is
-3
-3- m oo CO
o oo
d
o
in ^t in
ON CO
es i n
d d
±1 +1
o o
". °.
^tm^
+1 +! +1 [ +1 +! +1 +1
NO ON NO 1 00 0O in ^J"
i n NO i n
NO NO NO r -
a
r-'i
-* Tfr
t-~ Tf N O Tt-
+ +| +! +i +! -H
m
ON O
i n *3* c s
o o o
+1 +! ±1
CO O CO
« • * r-
s00
•"-!
a
u
*-^
a 43
> CS
'o
i n N o o N - ^ c ow
oNOes
Z-,
S i-i P °
«Ta
•fl
611 > O ni
_a
Ë II "g
en
±!
M
NO
m ^3+1 +1
n m
t-~ NO
r - in
I +1 +1
' cs es
r- r-
*3"
+1
o
r-
-^
+
rr-
+1 +1 +!
CO CO NO
co i n m
ON NO t ^ •* •* m
T-4 t - 00
•tf NO • *
T-l O —1
ON
en
d
+!
ON
-—
*-i
+1 ~+!* CO
+
O
o
,2 43
a
P
. °. -;
es en cs
+1 +) +1
9.89
10.20
10.28
!
+1 +1 +1
ON NO m
• * ON
co
10.10±0.2
10.15 + 0.15
d
1
es es cs
CO Tt" NO
W
+! +!
es oo
odd
o o
r-T-i
O o"
+1 +1
e s ON
CO O
CS —'
8.25 ±0.0
7.99 ± 0.0
8.24 ±0.06
m
±1 +1 +1
7.78 ±0.18
8.28±0.16
7.38 ±0.01
O
•o
r^ en —i
O r-H-i
rl-
^
• •
+1 +1 +1 +1 +1 +1 +1 +1
c o d O N c n ^ - N i o
CSCOt^ONNO^eS-^
T-4 CS --<
^-! ,-* ^- CS o
+1 +1 + g +1 +! +! +
in in O N -, es eo tn ~H
O N *3- eo ; M M
CNO
(N _ O
(N en -çf
^ T t en
2.80±0.15
2.77 ±0.14
2.57 + 0.11
intern
+1 +! +1 ^'Q +! +1 +[
i n en ^ . n
, ON NO oo
N * m S
<m
ON
—a
g
<Si
>N > >
-
ft
o
2.80 + 0.03
2.70 ±0.01
2.60 ±0.03
e velo
n annua
e veJo
n winter
n summ
ice ve
rage o
créas
iccee ding
given
rect
Î ^ ' *^ <L> C I
II
T3
O
erio
$-.
J S .. S
3
. V3
m a. s.
m from
km wi
citie
tion
a
a ctf
o ^
73 °
a 3
2 "J
noi
§S
^
-t~i
3
o
3
m
m m
y
<S
u
rt
i-H
n
A
3
^
;>
o
a
S
12*
is-"
t
o
rct es nt
a a a
H
1-1
OcocoincoONcoco
winCNMONCNMNld d ON d CN ON d d
O N N O - ^ O N C O ^ ^ ^
esooCNOoincooooo
oôodr-ir^oôoo'oôoô
h
r--<<sm^-»r> oo-co
1 l I f ! I I 1
O S i — • M r 1n ' t i n
' O h
\O O'0'0'S0 NNOV«010
OS
Ë
I
ON
I
i
I
I
i
I
i
T1
1)
s a
T3
3
q q h * o h ; oo o \ oo
en t n < N c4 <N* c 4 c 4 <N T3 T3 "T3
rH M m ^
!
in «u M
a
a
S-
S-i
a
O O O
» o a o
!
A
I _L s i i
O ^ r J m ^ t i n ' N O h
o>
.2
- ° *v
r-
a
nj
T )
g
a
a
a
o
z
172
Fritz Miiller and Almut Iken
there was a marked decrease in annual and winter velocities for all profiles followed by an
increase in recent years. This was particularly noticeable at the "anniversary" profile, where
thev' a for 1964-68 equals 106% of fhev' a for 1960-64, and the v'a increased 5 % during the
same period. Furthermore, there seems to be less fluctuation from year to year and winter to
winter during the latter 4 years. Between individual annual and winter velocities there are
differences of up to 12%. The summer velocities—always larger than those of winter by some
10-60%—fluctuate considerably from year to year (up to 25%), especially in the lower half
of the ablation area and in recent summers.
Differences in the summer-velocity increase from stake to stake across comparable profiles
of White and Thompson Glaciers are shown in Tables II and III. The summer increase at the
broad "eureka" profile, where the annual velocity is almost twice as much as that of the "anniversary" profile (14 cm/d versus 8 cm/d), is in both the relative ( « 10-15% versus « 4 6 % )
and the absolute ( < 1 . 8 m versus 2.5 m) respect much the smaller.
Hydrological data
Local ablation data are only an inferior substitute for discharge measurements of the entire
catchment area above the particular profile. The relatively small amounts of irregularly distributed winter snow (minimum 5 cm, maximum 30 cm, 10 year average about 12 cm water
equivalent) melt first on exposed slopes surrounding the glacier and the water accumulates for
days or weeks in marginal ice-dammed lakes (Maag, 1969). On the glaciers also the first
melt water from winter snow and ice remains for a considerable time in supraglacial and marginal
lakes and channels. Thus, the ablation data as shown in Figures 4 and 5 tend, for the early part
of the summer, to under-rate the hydrostatic situation on the glacier and to over-represent the
run-off. The distinction between the hydrostatic and dynamic effect of the melt water has been
often ignored in the study of the hydrology of glaciers.
In summary, the difference between the "effective" water and the measured ablation is so
great that any attempt to relate the latter with ice movement has to be of a qualitative rather
than quantitative nature.
DISCUSSION O F RESULTS
Short-period variations
The similarity of the velocity and run-off fluctuations suggests a causal relationship between
water supply and glacier movement. The generally good agreement between the daily fluctuations
of widely spaced sites indicates that the phenomenon affects the glacier as a whole or at least
large parts of it, and is not only a jerkiness resulting from localized internal stress release. The
measurements carried out in the pre-melt season of 1969 do not show the marked daily variations observed in July and August 1968, and after the onset of melt in 1969, testifying clearly to
the connection with water. No explanation is offered for the secondary peaks which sometimes
occurred during the night (Fig. 2). These auxiliary peaks are not simply belated reactions to
irregularities in discharge on days with disturbed weather.
Medium-interval variations
The spring velocity increase commenced simultaneously at practically all stakes of all
profiles. The only systematic exception was found at the stakes very close to the edges (stake
A x in Table II; E u in Table III and figure 5 in Millier (1963[b])], where the glacier thickness is
drastically reduced. In contrast, on Khumbu Glacier, a temperate glacier in the Himalayas
Water regime of Arctic valley glaciers
o o m a
o
o
O
o NO
VOW"
NO
r~ NO
od-m
06 en so
CNJ
m
^
ON
c4
NO
oôrim
5-
£*-
NO
\D ^ OO
173
i
H
1— NO
Hinco
<N?
l-NM!
i~m\
!l
=- s
i n Tf oo
0 6 ^ ^
»• 5S
T3
C
S5
o
akc
•J
03
&a
00
0
0
0
a
n
NO
w m «
NO
on•a
rt
>
&Û
00
0.
<
Si
R-0
s
S
«
0
.2 O
0
depth (m)
raphic left edge
W
<
NO
imate
0
<
from
ier (m
u
**;
5
^ ON
b^
^JP
its
s^ >
-
p." M
NO
NO
ON
"O
S.^
o£o\
V
S
w
».
sT"
t-
NO
ON
^
SIS
eS*Ss^S -c'a.N
00
NO
ON
0 00
0 NO
( N ON
o5 *~*
•" 0
=>J3
< H
174
3.05*
Fritz Millier and Almut Iken
BÎ
W
«O
W
m
-tf.
O
(S
O
w-> O
ty-i
r^
oô
O
m
•<fr
r~-
t-
O
0\
00
t~- wv
~-< ^
o
o
^H
0O *3"
o
«n
o
oô
>o oo
o
O
oo
c?\ c*i
o
o
CO
CO O
oo
m oo
O
r4
<>
BJ
c4
00
BÎ
in
M
r-
o
to
urfa
son i
V
O
fc.
x. S
11
K
BÎ
s
s «T
i §
ON
ta
O
in
BÎ
o
t
in
m
O
BÎ
•
*
o
to
CM
C4
a
^ "g"
<
S-
ON
^ " ^
Stake
O c>
1
£°
.s
c
M
u
o
M)
a
o
W
X)
'o
P
a
^
P 0Q--3
tu
03
3
—. w-, _« E ^ >°
s"
<
Water regime of Arctic valley glaciers
175
(Millier, 1968, table 1), the marginal sections show the greatest percentage increase. It is concluded that White and Thompson Glaciers are not frozen to the bottom throughout the winter
except for the marginal parts, which may only be loosened later in the season. Measurements
in the 170 m long tunnel at the "ice cave" showed no basal slip; however, this tunnel could only
be entered prior to and after the melt season. Therefore, this lack of evidence in no way contradicts the hypothesis that for most of the ablation area basal slip occurs throughout the year.
Englacial temperature msasuremsnts in White Glacier (Millier, 1963[a]) support this view.
The large time lag between run-off and movement peaks at the beginning of the melt
season (Figs. 4 and 5) is caused by the drainage channels being closed during the winter. Their
re-opening is effected by a combination of energy from various sources: (1) local increase of
overburden pressure by 10-20% due to the accumulation of water in lieu of snow and ice in
the remaining moulins and channels and in marginal and supraglacial lakes ; (2) the accumulated
heat in the melt water, particularly in marginal lakes where the mean temperature may reach
+ 2°C(Maag, 1969); (3) the conversion of potential energy into heat once water has started
to flow. Early in the melt seasoarwhen the channels are scarce, small and irregular, the water will
take longer to reach the glacier bed. Later the water courses will be more direct,
particularly in the lower parts of the ablation area and therefore no, or only small, time lags
will occur. In all profiles, particularly the upper ones, the velocity was greater in the autumn
than in spring, in spite of equal or even smaller ablation rates. This phenomenon together with
the occurrence of minimum velocities in May may be explained by temperature changes in the
lowermost ice layers. Melt water descending through moulins and channels, and the summer
velocity increase, may provide sufficient energy to raise the temperature in the bottom ice.
This warmth would gradually dissipate throughout the winter, reaching a minimum by the
time the new melt starts.
The marked differences between the early and late summer velocity may be due also to slip
movement along water-activated thrust planes. On White Glacier, as on most Arctic valley
glaciers, large numbers of well-developed thrust planes are found in the lower third of the ablation area. Between 14 and 25 July 1968 muddy water was observed emerging from a thrust
plane situated at about 36 m above the level of Between Lake, which is dammed up on the
north-east side of the glacier tongue. The strongly fluctuating discharge from the thrust plane
was estimated to reach 1 m3 s - 1 . The water emerged over a horizontal distance of about 150 m,
with the main "spouts" shifting some 50-70 m during the observation period. From a second
thrust plane, only 10 m higher on the glacier, clear water discharged at a rate of a little less than
0.5 m 3 s - 1 , but ceased to flow about 19 July. An even larger thrust-plane spring on Good
Friday Glacier is documented by air photographs. These observations are surprising as at least
half, if not considerably more, of the 100 m thick White Glacier tongue is presumed to consist
of cold ice. The ice temperatures at depths of 15 and 30 m at nearby "lower ice" were found to
be —10° and — 5.5° C, respectively. These findings clearly illustrate the high degree of effectiveness of running water in glaciers. Temporary sliding on thrust planes, some of it probably
starting as far down as the glacier bed and associated local warming up of ice layers may be a
contributing factor, though probably small, to the summer velocity increase of Arctic valley
glaciers.
Annual and seasonal fluctuations
Only some of the observed differences and trends in annual and seasonal fluctuations can
readily be explained; in several cases observed changes contradict expection.
Influence of changing glacier thickness. Figure 7 shows the changes in surface level at the
176
Fritz Mutter and Almut Iken
main profiles since 1959. The data were obtained by relocating, after a time lapse of a year or so, the original
position of a stake with two theodolites working simultaneously from both ends of a base line. At all profiles,
but particularly at "lower ice", a thinning of the glacier
was observed. The influence of this change was assessed
on the example of the "anniversary" profile, where the
mean ice depth amounts to less than 200 m. It was calculated that a i m decrease in glacier thickness, as
occurred between August 1961 and August 1963, would
cause a velocity reduction of about 3.5 %, assuming
that Glen's flow law with n = 4 applies. Most, 2.5%,
of this results from changes in the differential movement
within the ice body, and the remaining 1 % is caused by
a reduction of the basal-slip velocity, which, following
Weertman (1964), was taken as proportional to the
n +1
—-— power of the glacier thickness. The observed
velocity change, however, for the same time span amoFig, 7. Elevation changes of the White Glacier
surface between 1959 and 1968; average of
unts to about 9%. During the period August 1963 to
three points each near the equilibrium line
August 1966 the change in glacier thickness at the "an(''moraine" profile), below the middle of
ablation area ("anniversary" profile) and in
niversary" profile was negligible but the mean velocity
the centre of the glacier tongue ("lower
ice" profile).
increased by about 12%. Clearly, glacier-thickness
changes only explain a small fraction of the observed
changes in annual velocity.
Influence of melt water. Figure 6 illustrates the complexity of the relationship between melt,
i.e. water associated with the glacier, and velocity changes. The summer of 1962, remarkable
in having the highest rate and total amount of ablation, failed to produce a record velocity
increase at the "anniversary" profile. Whereas in 1967, even more surprisingly, low melt was
accompanied by extremely high summer velocities at all profiles. If d values (additional distance
moved due to the summer velocity increase) are considered, the data show similar anomalies.
It was found that the total summer velocity increase of Arctic valley glaciers is not only, and
possibly not even mainly, a function of the amount of water available, but is strongly dependent
on its distribution in time, while also being influenced by other factors. Large or small quantities
of water discharged evenly over the entire summer have a lesser effect on movement than a
fluctuating discharge of the same amount. Not only the amplitude but also the frequency of the
discharge fluctuations is of importance. An optimum frequency seems to exist and this may
differ for summers with large amounts of water and for those with little. Gradual increases in
water supply affect glacier movement less than sudden ones. Usually, summers with little overall
melt show larger fluctuations and more frequent interruptions in discharge than summers with
much melt, as illustrated by the 5 d running mean temperature curves (Fig. 8), and thus may
experience a greater velocity increase.
Some aspects of the above observations may be explained by assuming, as Lliboutry (1964,
1968) and others do, the existence of a sub- and intraglacial system of channels. The size of
these channels slowly adapts to the amount of run-off draining into them, but at times of
rapidly increasing run-off they do not have time to adjust sufficiently and the pressure head
rises. It is assumed that a high pressure head in the channel system of basal sliding reduces
the friction.
Water regime of Arctic valley glaciers
177
1966
Fig. 8. 5 d running mean temperature histograms for ''anniversary" profile based on base camp and, where dashed, Eureka
weather-station data.
Longitudinal stresses. Although the influence of discharge fluctuations on velocity changes
may be large, particularly during summers of little melt, there is some doubt that this effect
alone could explain the summer 1967 situation. It is possible that the water-induced velocity
fluctuations are modified by changes in the longitudinal stress gradient which occur when the
velocities above and or below a profile change. To assess this effect some calculations
have been carried out for the "anniversary" profile.
It was assumed that (1) the strain-rate equals zero at "moraine" profile (near the equibrium line), (2) the average strain-rate between x = 0 ("moraine" profile) and x=x1 ("anniversary" profile) equals èv a value which can be calculated from the measured surface velocities,
and (3) the average strain-rate between x = 0 and x = x2 ("lower ice") equals e2 An equation
of the form
ex=ax
(l)
gives a reasonable approximation for the strain-rate changes with x, distance from the equilibrium line.
The constants a and m are determined from
/ axm dx
~
e1=
0
& m
=—*i
x1
m
and
/ axm dx
o
_
a
»
X9
x9
12
m
178
Fritz Millier and Almut Iken
therefore
log ( = j
log
.=
-l
log ( ^ )
log ( ^
me,
a=
-
The gradient of the compressive stress is then obtained, using Glen's flow law
n
a = — • s
k
after substituting
o=lT>
a
, n
n
x
and differentiating
i
-l
dcr
dx
If we assume that
/ a\
\ k I
m
n •x
is independent of the vertical direction y, the equilibrium equation
dx
dcr
dr
,
pd 2 x
' sin a + =j-5-=
0 (r = rXy)
dx
dy
d? 2
where t is the shear stress and a the slope angle, gives
da
sin a
d x -h +t(h)
• - ' ' +ogh
- "
d2x
+qh—-^-=0
dt2
where h is the thickness of the glacier and %(h) the, shear stress at the bed of the glacier.
Assuming that the sum of the first three terms of this equation equals zero in the average
over several years and that x(h) and h are constant, the deviation of an individual year would be
dx I „ "
or
A\-°-\At=oAV.
dx
dt1
Water regime of Arctic valley glaciers
179
TABLE IV. Average strain-rate and stress gradients in the ablation area of White Glacier, 1965 en 68.
17 Aug. 1965 to
21 May 1966
—0.38
—2.38
—0.94
0.0
2.75
0.63
0.586
:
17 Aug. 1965 to
21 May 1966*
—0.38
—2.39
—0.95
0.0
2.76
0.64
27 Aug. 1966 to
3 June 1967
—0.48
—2.36
—1.01
0.2
2.24
0.53
I 0.484
24 Aug. 1966 to
10 May 1968
—0.47
—2.49
—1.03
0.0 ! 2.41
0.60
! 0.528
24 Aug. 1966 to
10 May 1968*
—0.47
-2.52
—1.04
0.0 j 2.43
0.61
0.534
+ 0.06
i
0.590 1
—0.05
00
l
The constants of Glen's flow law are assumed to be: A: = 0.1 year and n = 3
* Slightly different sets of input data were used to assess errors.
Table IV gives numerical values (in c.g.s. units) for the variation in compressive stress
gradient at "anniversary" profile during the last 3 years.
d<7
àx
da
— j (M "moraine", A "anniversary", L. I. lower ice.)
A deviation from the average stress gradient A
âa
signifies an acceleration or dece-
dofor the
àx
-3
winter 1966-67 (0.05 XI0~° c m ) means that during that winter an acceleration occurred,
i. e. the summer season 1967 started with an already increased velocity before any melt took
place. It seems, therefore, that the effect of longitudinal-stress changes modifies the velocity.
leration of movement during the observation period. The negative value of A
Some explanatory comments
As further observations on medium- and short-period variations are in progress on the
same glaciers, only a preliminary interpretation is attempted now.
Influence of hydrostatic pressure on basal sliding. Weertman (1962) assumîd that an increase
of surface melt water initiates a kinematic wave in the water layer at the glacier bed, which
causes further drowning of obstacles and consequently increases glacier velocity. Hydrostatic
pressure in an open system can only produce a kinematic wave, i.e. lift the ice, when water
stands in the pipes to nine-tenths or more of the glacier thickness or has the squivalent head.
Exploratory observations in a moulin near "anniversary" profile showed that the glacier water
level in July 1969 was at less than two-thirds of the glacier thickness.
In the search for an explanation of the strong correspondence between fluctuations of melt
water and ice movement it may also be necessary to re-examine the often-made assumption
12*
180
Fritz Millier and Almut Iken
(Weertman, 1962, 1964, 1967; Lliboutry, 1968; Nye, 1969) that the tangential frictional forces
at the ice-bedrock interface are negligible and friction results solely from the ploughing of obstacles through the ice.
Conclusions
From the field data collected since 1959 on some sub-polar glaciers on Axel Heiberg Island,
it is apparent that surface-velocity variations of Arctic valley glaciers result from the interplay
of several factors, predominance varying with time and location, and the chosen duration of the
observation period. Long-term and winter velocity changes, though primarily induced b y mass
(ice-thickness) change, are also affected by variations in the longitudinal stress gradient which,
at least in part, result from differences in the water quantities associated with the glacier during
the summer. Variations in the summer velocities are more directly related to water, though in a
more complex fashion than at first assumed. The frequency and amplitude of the water fluctuations seem to be of greater importance than the total amount involved. With low discharge
capacity and frequent and large run-off fluctuations, the ground-water level in the glacier, and
consequently the hydrostatic pressure, often rise rapidly and decrease slowly, thus causing a
large overall summer velocity increase in spite of relatively low melt, as occurred in 1967. The
medium-interval (few days to a fortnight) fluctuations associated with weather changes are also
modified by the discharge capacity of the channel system, which, for example, governs the time
lag between discharge maximum and ice-velocity peak. Sheet flow of water in thrust planes has
been observed several times, in spite of below freezing-point temperatures for at least half the
ice depth. From the velocity observations it may be concluded that, in the ablation area, the
medium- and large-size valley glaciers on Axel Heiberg Island are not frozen to the bed except
near the margins during winter.
A comparison of the velocity response to hydrological change in White Glacier in the Arctic
and Khumbu Glacier in the Mount Everest region (Millier, 1968) shows so little difference that
it must be concluded that the temperature regime (temperate or non-temperate) is not of basic
importance to the hydrology of glaciers. This conclusion would tolerate, also for non-temperate
glaciers, the concept postulated by Llibotury (1964,1968) of a network of water-filled subglacial
cavities connected to the melt-water drainage system.
Detailed observations and measurements regarding the fluctuations of the ground-water
level in the different parts of the glacier, augmented by ice-temperature data, particularly at
depth, are prerequisites for a more complete explanation of the velocity fluctuations.
ACKNOWLEDGEMENTS
Financial support for this project was provided by the National Research Council of
Canada, and, in 1961, the Arctic Institute of North America. Many have contributed t o the
laborious field work and particularly David Terroux is thanked for his help in the surveying.
Professor David Bonyun advised on the computer treatment of data. Logistic assistance was
given by the Polar Continental Shelf Project, Department of Energy, Mines and Resources,
Ottawa.
Water regime of Arctic valley glaciers
181
REFERENCES
A D A M S , W . P . 1966. Glaciology, N o . 1. Ablation and run-off o n the White Glacier. Axel Heiberg Island, C a n a d i a n A r c t i c A r chipelago. Axel Heiberg island Research Reports, McGilt University, Montreal. Jacobsen-McGill
Arctic Research
Expedition
1959-1962.
AGASSIZ, L. 1847. Système glaciaire ou recherches sur les glaciers. Pt. 1. Nouvelles études et expériences sur les glaciers
actuels.
Paris, V. M a s s o n .
BATTLE ; W . R. B . 1 9 5 1 . Glacier m o v e m e n t in n o r t h - e a s t Greenland, 1949. Journal of Glaciology, Vol. 1, N o . ÎO, p . 5 5 9 - 6 3 .
BECKER, A. Unpublished. O n the d e t e r m i n a t i o n of glacial depth. [Ph. D . thesis, D e p a r t m e n t of Physics, McGilt U n i v e r s i t y 3
M o n t r e a l , 1963.]
FRIESE-GREENE, T. W . , and P E R T , G . J. 1965. Velocity fluctuations of the Bersaekerbrae, East G r e e n l a n d . Journal of
Glaciology,
Vol. 5, N o . 4 1 , p . 7 3 9 - 4 7 .
L U B O U T R Y , L. 1964. Sub-glacial " s u p e r c a v i t a t i o n " as a cause of the rapid advances of glaciers. Nature, Vol. 202, N o . 4 9 2 7 ,
p. 77.
LLIBOUTRY, L . 1968. General t h e o r y of subglacial cavitation a n d sliding of temperate glaciers. Journal of Glaciology. V o l . 7 ,
N o . 49, p . 2 1 - 5 8 .
M A A G , H . 1969. Ice d a m m e d lakes a n d marginal glacial drainage o n Axel H e i b e r g Island, C a n a d i e n Arctic A r h i p e î a g o . Axel
Heiberg Island Research Reports, McGill University, Montreal. Jacobsen-McGill
Arctic Research Expedition
1959—1962.
M E I E R , M . F . 1960. M o d e of flow of S a s k a t c h e w a n Glacier, Alberta, C a n a d a . U. S. Geological Surrey. Professional Paper 3 5 1 .
M E R C A N T O N , P . - L . 1916. Vermessungen a m Rhonegletscher. Neue Denkschriften der Schweizerischen Naturforschenden
Gesellschaft, Bd. 52.
M U L L E R , F . 1963[a]. Englacial t e m p e r a t u r e measurements on Axel Heiberg Island, C a n a d i a n Arctic Archipelago. Union
Géodésique et Géophysique Internationale.
Association Internationale cV Hydrologie Scientifique. Assemblée générale de
Berkeley,
JQ^8—31~8
1963. Commission des Neiges et des Glaces, p . 168-80.
M U L L E R , F . 1963[b]. Surveying of glacier m o v e m e n t a n d mass changes. (In Millier, V., and others. Preliminary r e p o r t 1 9 6 1 - 1 9 6 2 ,
[by] F . Mùller a n d others. Axel Heiberg Island Research Reports, McGill University, Montreal. [Jacobsen-McGill
Arctic
Research Expedition 1959-1962], p . 65-80.)
M U L L E R , F . 1968. Mittelfristige S c h w a n k u n g e n der Oberftachengeschwindigkeit des Khumbugletschers a m M o u n t E v e r e s t .
Schweizerische Bauzeitung, 86. J a h r . , H t . 3 1 , p . 5 6 9 - 7 3 .
M U L L E R , F . , and others. 1961. Jacobsen-McGill
Arctic Research Expedition to Axel Jleiberg Island, Queen Elizabeth
Islands.
Preliminary report of 1959-1960, by F. Mailer and members of the expedition. Edited by B. S. Millier. M o n t r e a l , M c G i l l
University.
M U L L E R , F . , and others. 1963. Preliminary r e p o r t 1961-1962, [by] F . Muller a n d others. Axel Heiberg Island Research
Reports,
McGill University, Montreal. [Jacobsen-McGill
Arctic Research Expedition
1959-1962.]
N I V E N , D . C. 1959. A p r o p o s e d m e c h a n i s m for ice friction. Canadian Journal of Physics, Voi. 37, N o . 3, p . 2 4 7 - 5 5 .
N Y E , j . F . 1969. A calculation on the sliding of ice over a wavy surface using a N e w t o n i a n viscous approximation.
Proceedings
of the Royal Society, Ser. A , Vol. 3 1 1 , N o . 1506, p . 4 4 5 - 6 7 .
PATERSON, W . S. B . 1961. M o v e m e n t of the Sefstoms Gletscher, north-east Greenland. Journal of Glaciology,Vol.
3, N o . 2 9 3
p . 844-49.
PILLEWIZER, W . 1965. Bewegungsstudien an eînem arktischen Gletscher. Polarforschung,
Bd. 5, Jahrg. 34, H t . 1-2, 1964, p .
247-53.
PILLEWIZER, W., and others. 1967. D i e wissenschafthchen Ergebnisse der deutschen Spitzbergenexpedition 1964-1965, Geoddtische unci GcophysikaUsche Verôjfentliehungen (Deutsche Akadeniie der Wissenschaften zu Berlin), Reihe 3 , H t . 9.
R E D P A T H , B. B. 1965. Geophysics, N o . I . Seismic investigations of glaciers on Axel Heiberg Island, C a n a d i a n Arctic A r c h i p e l a g o .
Axel Heiberg Island Research Reports, McGill University, Montreal. Jacobsen-McGill
Arctic Research Expedition
1959—
1962.
[ U N I O N GÉODESIQUE ET GÉOPHYSIQUE INTERNATIONALE.] 1963. Colloque d'Obergurgl (suite). Bulletin de VAssociation
Internationale d'Hydrologie
Scientifique, 8e A n . , N o . 2, p . 50-142.
WEERTMAN, J. 1962. Catastrophic glacier advances. Union Géodesique et Géophysique Internationale.
Association
Internationale
cV Hydrologie Scientifique. Commission des Neiges et des Glaces. Colloque d'Obergurgl, 10-9—18-9
1962, p . 3 1 - 3 9 .
WEERTMAN, J. 1964. T h e theory of glacier sliding. Journal of Glaciology, Vol. 5, N o . 39, p . 287-303.
WEERTMAN, J. 1.967. Sliding of n o n t e m p e r a t e glaciers. Journal of Geophysical Research, Vol. 72, N o . 2, p. 5 2 1 - 2 3 .
W Î L H E L M , F . 1963. Beobachtungen uber Geschwindigkeitsànderungen und Bewegungstypen b e i m Eismassentransport a r k t i s c h e r
Gletscher. Union Géodesique et Géophysique Internationale. Association Internationale d'Hydrologie
Scientifique.
Assemblée
générale de Berkeley, 19-8—3ï-8
1963. Commission des Neiges et des Glaces, p . 2 6 1 - 7 1 .
APPENDIX
CORRECTION OF SEASONAL VELOCITIES
It is almost impossible (weather, logistics, personnel) to obtain comparable survey values
from profile to profile, season to season and year to year. To align the data, correction formulae
had to be used. As measurements usually commenced several weeks ahead of the onset
of melt and terminated approximately at its end, the "winter survey periods" contain, in most
cases, only a few days of melt. Therefore, the uncorrected average velocity over a melt season
(vs) was calculated from the "uncorrected annual velocity" (v0) and the "uncorrected winter
velocity" (vw) using the formula :
365v„—wv„,
Fritz Mutter ano Almut Iken
182
where s signifies the actual summer period, defined as number of days between dates for which
the 5 d running mean temperature was above the freezing point, and w =(365 —s). When the
"whole-year survey period" is longer or shorter than 365 d by (d) d (d is defined as positive when
the observation period is more than 365 d), a correction factor is applied to obtain the "corrected annual velocity" (v/). This factor derived
from
vH(365 + d) - d ( ~ ] va = 365v'
and amounts to
d\^--l
va
365
The "corrected winter velocity" (v'w) is calculated by using t h e equation
wv'w+e ( -j-1
vw=(w+e)vH
which provides a correction factor
e being the number of melt days contained in the "winter survey period". F o r the final calculations, the values of d and e have been further adjusted, i.e. reduced, t o allow for the usually
lower velocity at the beginning and end of the melt season. Where field observations were lacking,
the values of s, d and e were established from temperature data recorded, in part by automatic
stations, at the "moraine" profile, "lower ice" and base camp; t h e latter station is located on
bare land 3 km west of "lower ice". In a few cases extrapolations from the data of Eureka
(100 km to the east-north-east) had to be used. Errors arising from the uncertainty of the length
of the melt season have been taken into consideration. The errors associated with the corrected
summer and winter velocities presented in Table I result largely from the uncertainty of s. These
are cumulative estimates of all standard experimental errors a n d therefore the velocity data
shown in Table I may well be more reliable than indicated.