T H E TEMPERATURE, MELT WATER MOVEMENT AND
DENSITY INCREASE I N T H E NZVE O F AN ALPINE GLACIER
(Publication No.
2
of the Jungfraujoch Research Party, 1938)
T. P. Hughes, Ph.D., and Gerald Seligman
(Received 1939 May 27)
GENERAL
REMARKS
When snow falls on the upper accumulation region of a glacier and
commences its journey into the valley, it undergoes a long and slow change
in its appearance and physical properties. Fallen snow has a density of
about 0.16 and its average grain diameter is less than I mm., but when it
emerges several years later in the glacier tongue it has become clear ice with
varying numbers of enclosed air bubbles and its grains are generally of the
order of I cm. in diameter. These changes are brought about by the
processes of grain growth occasioned by recrystallisation and by the closer
packing of the crystal grains. It is well known that the rate of recrystallisation is markedly influenced by the temperature. Similarly, the rate
of settling of the crystal grains must depend on the amount of water present
to lubricate relative motion between them, and on the mechanical strength
of the ice itself ; both these factors are again dependent in magnitude on
the temperatures existing in the snow and firn. It follows, then, that in
making a study of the physical changes taking place in a glacier, it is necessary
to have as complete a knowledge as possible of the temperature gradient
existing in the interior of the glacier.
This paper describes observations of the temperature gradient and melt
water movement in the nkvk region of an alpine glacier ; the results are
discussed from the point of view of their bearing on the question of the
temperature gradient in the interior of a glacier, the drainage of a glacier
and, finally, of the mechanism of the increase in density of the firn.
DEFINITIONS
The nkvk area or accumulation area is the region of a glacier in which
the annual accumulation by precipitation exceeds the ablation (by evaporation, melting and wind erosion).
The glacier tongue or ablation area is the region in which ice appears on
the surface of the glacier during the height of summer.
The $rn line separates the nCvC area from the glacier tongue.
Firn or $rn snow is granular compacted snow. It possesses intercommunicating air channels and is, therefore, permeable to water. Firn
covers the surface of the nCvC area throughout the year. It is convenient
to use the term firn to describe the actual ice crystals and nCvC for the area
in which they exist.
1939 Dec.
Temperature, etc., in the NLvL of an Alpine Glacier
617
Glacier ice is firn in which the inter-communicating air channels have
become sealed up, rendering it impermeable to water.
The Bergschrund is a crevasse at the upper margin of the n6vvC area,
separating the glacier from the ice-covered rocks above.
PART I
THETEMPERATURE
IN THE N M
OF AN
ALPINEGLACIER
(a) Introduction
Several studies have been made of the temperatures existing in glaciers,
although most of them have been concerned with Arctic glaciers, or with
the ablation areas of temperate glaciers. A critical account of the general
thermodynamics of glaciers has been given by Lagally.* Previous temperature measurements in glaciers may be considered to be either shallow
or deep observations. The shallow measurements, as the term implies,
have been made near the surface and have had as their purpose the detection
of periodic temperature waves. The penetration of the diurnal variations
has been found to be about 10 cm., while the seasonal variations have never
been detectable below a depth of 20 metres. The deep measurements,
which may be considered to be those made at depths greater than 20 metres,
have been made with a twofold purpose. First, information on the
temperature gradients existing in the ice has been necessary to assess the
heat income of a glacier; second, there was need to test the statement
that some glaciers consisted of ice at the pressure melting-point.+
Blumcke and Hess 1 measured the temperatures in bore-holes up to
148 metres in depth in the Hintereisferner in Tirol. However, it appears
probable that their results were considerably affected by the disturbing
influence on the surrounding ice of the water they were obliged to use in
their borings. The results were taken to confirm the statement that the
ice at great depths was at the temperature of the pressure melting-point.
Koch and Wegener 0 measured the temperatures at depths as great as
24 metres in the ice in East Greenland, using resistance thermometers.
They were able to observe a considerable temperature gradient both in
the upper layers, which were affected by seasonal fluctuations, and at
greater depths.
* M. Lagally, Mechanik und Thermodynamik des Stationaren Gletschers, Leipzig,
1934.
t The melting-point of ice is lowered by a pressure acting on either one or on
both phases, Hence, when a block of ice is compressed adiabatically, it becomes
cooled by a melting process to the melting temperature corresponding to the acting
hydrostatic pressure. If a large mass of ice, insulated thermally from its surroundings, is initially at oo C., then the temperature at any particular depth is finally
the " pressure melting temperature " corresponding to the acting pressure.
1 A. Bliimcke and H. Hess, Wiss. Ergh. 2.Dtsch. Oest. Alpenwerein, I , ( z ) , 1899
(summarised by Hess in " Das Eis der Erde," Handbuch der Geofihysik, 7,46, Berlin,
1933).
J. P. Koch and A. Wegener, Medd. om Grdnland, 75, 191,1930.
618
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
More recently, Sverdrup," a member of the Norwegian-Swedish
Expedition to West Spitsbergen, carried out a series of detailed temperature
measurements in the d v k region on Isachsen's Plateau on the Fourteenth of
July Glacier down to a depth of 14.7metres. He used a number of copperconstantan thermocouples which were buried at different depths in pits
and &ore-holes. He was able to obtain fair agreement between the observed
temperature-depth curve and that calculated from the known air
temperatures and the thermal constants of the firn. The rapid rise in the
firn temperatures during early summer was shown to result from the
downward percolation of melt water in the firn. The results described
below show that similar processes to those observed by Sverdrup for an
Arctic glacier occur in the m'vk region of an Alpine glacier. They are, so
far as we know, the first systematic measurements of Alpine nCvC
temperatures.
(b) Experimental
The temperature was measured by means of thermocouples. These
were buried in the firn at several points and at various depths down to
30 metres.
Thermocouples.-Three types of thermocouple were used, according
to the depth at which they were to be buried and their resistance. The
wire used at the greatest depth was twin-wound copper-constantan wire
with a waterproof insulating covering of Glazite. The wire was 0.091cm.
in diameter and its resistance was 0.76 ohm per metre. The wires used
at lesser depths were 24 and 18 S.W.G. twin-wound copper-constantan
wires, insulated with 'a coating of enamel and covered with cotton. Their
resistances were 2.1 and 4.6 ohms per metre respectively. The junctions
were made by hard-soldering the ends of the wires together ; these were
then coated with shellac and, when necessary, covered with a protecting rubber
sheath. The standard junction was kept in a mixture of snow and water
in a vacuum flask and remained indefinitely at 0" C. exactly, provided the
flask was shaken occasionally.
Galvanometer.-The E.M.F. of the thermocouples was measured as a
current on a galvanometer in a circuit of known resistance. A very robust
form of enclosed lamp and scale galvanometer was used. This had a
sensitivity of about 14.2 mm. per microampere and a resistance of 54-5ohms.
This fairly high resistance was used in order to eliminate the effects of
varying contact resistances, and also to avoid wide differences in the calibrations of the various thermocouples. The range of the galvanometer was
about 8" C. for the shortest couples, and the temperatures could be read
to about 1/50" C. Other effects, such as the zero shift and difficult
experimental conditions, increased the uncertainty to about jl oO.1 C.
on some days. In making the electrical connections the galvanometer
was placed in the copper part of the circuit and the two constantan leads
were kept pressed together by an insulated spring clip. In order to avoid
the effect of other stray thermo-electric currents, the readings were always
*
H. U.Sverdrup, Geoffrafiska Ann.,
17,53,"1935.
1939 Dec.
Temperature, etc., in the N h 6 of an Alpine Glacier
619
made in two directions by reversing the terminal connections. As the
scale was on the top of the box containing the galvanometer, it was necessary
to use a black eyeshade fitted over the scale when taking the readings in
bright daylight. In a severe blizzard the observations were made under
the protection of a portable tent fitted on to a pair of skis. Both the
galvanometer and the standard junction were contained in a specially
designed box and could be conveniently carried about the glacier.
Position of the Thermocouples.-Since
it was desired to observe the
influence of local topography on the temperatures, the couples were buried
at three different places in the glacier, represented by G, M and 0 in fig. I.
It was also necessary to investigate the relative disturbing influences of a
shaft and a bore-hole on the temperatures in the neighbourhood. This
was done by comparing the temperatures in the two when made in close
proximity to one another. The shaft (G) was 20 metres deep and z x I
metres in cross section. From the bottom of this shaft a vertical boring
was put down to a depth of 10 metres and other borings were made z to 3
metres horizontally into the walls of the shaft at various depths below the
surface. The thermocouples were all tied to one rope, lowered into the
shaft, and placed in the appropriate bore-holes. The bore-holes and shaft
were then filled with dry snow in order to minimise the change in temperature
which must always result from the digging or boring process. It was
assumed that this snow would rapidly attain equilibrium with the surrounding firn. A description of the boring and digging technique will be given
elsewhere by us.*
A check pit (I) (Auxiliary Pit No. I), 4 metres deep, was made in a
similar manner to the shaft at a spot 10 metres away, in order to confirm
the observation (see later) that the results in pits were not very different
from those in the borings.
Bore-holes I, 2 and 3 were made to a depth of about 10 metres in the
positions H, M and 0 respectively as shown in fig. I. The holes were
filled with cotton-wool plugs and, near the surface, with dry snow.
(c) Results
Temperature Variation with Depth.-It was found that the temperatures
at different depths in the shaft and Bore I lay well on a single curve below
a depth of about 4 metres. There was no difficulty in correlating the
reference level for the depth measurements since a conspicuous ice band
close to the surface, both at the shaft and Bore I, served well in this
capacity. Bores z and 3, however, gave curves which, while not tallying with
those of the shaft and Bore I , ran closely parallel to them. This was no
doubt due to the uncertainty of the depth of the reference level at a different
part of the glacier, for the ice band over the shaft and Bore I could not be
identified at Bores 2 and 3. It was found that if the depths were altered
by - 0.6 metre in the case of Bore z, and 0-4metre in the case of Bore 3,
the curves all coincided below 4 metres, as shown in fig. 2. What horizontal
+
*
In a paper to be submitted to the GeographicalJournal.
042
I
200
METRES
in metres. Contours at 20-m.intervals.
lllliI
5 0 0
FIG.I .-Altitudes
SCALE
1939 Dec.
Temperature, etc., in the Nkvk of an Alpine Glacier
62 I
variation there might have been in the position of the temperature distribution curve has naturally been eliminated by standardising the depths,
oOc
-1
-
-2
t
--
-3
Shaft, 23rd May
25th ,,
3 1 ~ 1 ,,
No. 1 Auxiliary Pit, 3rd June
Bore 1, 31st May
Bore 2, 31st May
cc Bore 3, 4th June
c
--
E
L
-tY
-5
-7
M. Bore No. 2.
N. Snow Pole No. 5 .
0. Bore No. 3.
P. Snow Pole No. 6.
Q. Auxiliary Pit No. 3.
.sa
B
w
.
622
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
time over which these first readings were spread, provided that the heat
transfer took place by ordinary thermal conduction. In fact, the points
below 4 metres would not have changed by more than about o O . 1 C. during
this time. At depths of less than 4 metres there was a considerable difference
between the temperatures of the pits and those of the borings. It will be
seen that the temperatures in the shaft have risen by I' C. during the first
week, showing that, so far as the surface layers are concerned, the disturbance in the snow and firn during the digging operations has enabled
the downward transference of heat in the form of melt water to take place
more easily-no doubt by the removal of ice crusts and layers. In the
borings where the disturbance had been less, the initial temperatures at the
same depth were considerably lower ; they also changed less rapidly with
time. T o what extent the temperatures near the surface differed from
those of the completely undisturbed firn cannot be estimated, but at depths
below 4 metres the agreement between the results in pits and bore-holes
does suggest strongly that the measured temperatures were those of the
undisturbed firn.
The temperature below 20 metres was always practically at zero, and
it seems that the whole glacier must be at the temperature of the pressure
melting-point. At 30 metres depth the pressure melting-point is - o O . 0 1 3 C.,
but such a temperature could not be measured accurately on the galvanometer. It was noted, however, that this junction always gave a small
deflection of scarcely measurable magnitude, but which corresponded
roughly to a temperature of the order of - oO-01 to - oO.02 C. The junctions
nearer the surface showed no such deflection after they had been heated
to the melting-point.
Heating of the Nkvk.-Fig. 3 shows the change in temperature with time
at any particular depth for the two pits and the three bore-holes. It will
be seen that all the temperatures rose to zero in the course of some weeks,
and that the rate at which this took place varied with the locality of the borehole or pit and with the depth of the particular thermo-junction. For
example, while the slowest thermo-junctions in the pits and Bore I had
risen to zero by July 4,those in Bore 2 reached this temperature on July 10
and Bore 3 on about August 23. The increase in the temperature often
occurred very rapidly and took place from the surface downwards-that is
to say, the shallower thermo-junctions were affected first. So rapid a
change in the temperature of the snow cannot be the result of a simple
thermal conduction process and must be due to the downward percolation
of melt water, as originally suggested by Chamberlin.* When snow on
the glacier surface is melted by conduction from the air or by the Sun's
radiation, the melt water seeps down into the firn. If the firn is at a temperature below zero, some of the water is frozen and releases its latent heat to
the surrounding ice crystals and raises their temperature to oo C. When
the water flow is rapid the temperature rises to zero in a short time, as shown
by the thermo-junctions near the surface. When the flow of water is slowed
up or arrested, either by a falling off in the rate of supply or by an im* T. C . Chamberlin, Decennial Publ. of the Univ. of Chicago, 9, 197, 1904.
1939 Dec.
Temperature, etc., in the Ndvt! of an AZpine Glacier
623
permeable obstruction in the firn, the rate of temperature increase becomes
very much less, and in some cases we found that the temperatures commenced
to decrease once more.
0.c
-2
.
t
5 -4
"
L
P
f -6
THE SHAFT
c
t
-2
-I
0
3
0
-4
Y
D
.
I
-6
-8
FIG.3.-The
change in the temperature at various depths in the Shaft, No. I Auxiliary
Pit and Bores I , 2 and 3 .
If the melt water is solely responsible for the removal of the winter cold
wave, the rate of temperature rise at any depth will depend on the following
two main factors :(a) The supply of water provided by the melting of the snow on the
surface.
(b) The permeability of the snow and firn to melt water.
The supply of melt water is naturally dependent on the temperature of the
air, the intensity of the incident radiation, the snow fall, the humidity of
the air, and to some extent on the wind. Fig. 4 shows the effect of air
temperature on the Sphinx * (4.fig. I), amount of sunshine and snow fall
on the temperatures of some of the thermo-junctions at different times.
* The temperatures in fig. 4 are those recorded at the Swiss Meteorological
Station on the Sphinx Rock, which is 120 metres above the glacier where our
observations were made. Owing to this difference, and a more exposed situation,
the Sphinx temperatures were about 14" C. lower than on the glacier during our
summer observations. Fuller details of the meteorological conditions will be given
in a paper to be submitted by one of the authors (G. S.) to the Royal Meteorological
Society.
Dr. T. P. Hughes and Mr. Gerald Seligman,
624
4, 8
It will be seen that a high temperature of the air, assisted by a recent snow
fall and abundant sunshine, caused a rapid melting of the surface snow,
which was followed soon afterwards by a sudden rise in the temperatures,
C July
C June --t
30
5
11
17
23
29
5
11
-+
17
23
-15.
-
40-
ooc
-1
-
-2
-
-
NO. 1 Aux. Pit
-8
30
I
I
5
11
-+
I
17
June
+
I
I
I
I
23
29
5
11
I
17
c July -+
FIG.4.-The influence of meteorological conditions on the rate of heating.
of the junctions-for example, during the periods June 8 to 14 and June
20 to 30. A spell of cold weather with the mean temperature below the
freezing-point slowed up this process considerably, and the temperatures
of some junctions were sometimes lowered again by loss of heat to the
cold layers at greater depths. This may be seen during the intervals June
14 to 20 and July I to 18.
23
1939 Dec.
Temperature, etc., in the Nhk of an Alpine Glacier
625
The rate at which water can percolate through snow and firn under
the action of gravity or capillarity is probably dependent on several factors,
among the more important of these being the rate of water supply, the
crystal size and density of the firn, and the thickness and frequency of ice
bands. For example, a rapid stream of water will be more effective in
heating up the firn than a slow stream, since it carries more latent heat
per unit time. A layer of loose, rounded crystals is naturally a medium
of lower resistance to water flow than a layer of tightly packed fine crystals,
but, on the other hand, the latter has the higher retentivity for water.
Many of our observations have confirmed these statements.* We also
observed that an ice band may hold up the vertical flow of water and cause
it to flow with a marked horizontal component (see Part I1 below). Experiments with dyes show that, although these bands extend in a horizontal
plane over large areas, it is possible for water to penetrate them in many places.
The results in fig. 3 show that, so far as the deeper layers are concerned,
there is little difference between the rates of heating in the.firn of the shaft,
No. I auxiliary pit and Bore I , all lying in close proximity to one another.
This suggests that the unsatisfactory results obtained in a pit by Sverdrup
had been avoided by the technique used in this work. It is evident, however,
that the greater disturbance of the firn by a pit as compared to a bore-hole
might, under some conditions of heating, result in a more rapid rate of
heating in the former on account of the destruction of ice bands and layers
of low permeability ; a bore-hole would probably give more representative
temperatures on the whole. The slower rate of heating of Bores 2 and 3
must be due to local variations in the rate of water drainage through the
firn. Bore 3 was situated on an elevation and was drained on three sides.
The vertical flow of water must have been considerably lower here than
that in the neighbourhood of the other bore-holes and pits, since the temperature at a depth of 9.5 metres did not reach zero until the end of August,
some weeks after the other bore-holes.
The change in the shape of the temperature-depth relation with time
during the penetration of melt water into the f i n is shown in fig. 5 for the
shaft and Bores I , 2 and 3. In general the behaviour was similar in each
case, but a few minor irregularities may be noted. The downward percolating
melt water heated each junction to zero in turn, while the temperature of
the deeper thermo-junctions was raised to a greater or less extent either by
localised streams of water or by the loss of heat by thermal conduction alone.
In Bore 2 it appeared that the thermo-junction at 2 metres was heated up
as rapidly as that at 0.8 metre while in Bore 3 the junction at 1.5 metres
was initially at a higher temperature than that at a depth of I metre. Such
results suggested that the melt water flow was not always vertically downwards, but that some localised horizontal flow may take place in certain
regions of the firn.
* The authors have written a short paper on the retentivity of snow and fim
which is in the press (Bulletin of the International Association of Scientific Hydrology).
t H. U. Sverdrup, Geografiska Ann., 17, 5 3 , 1935.
626
0
Dr. T. P. Hughes and MY. Gerald Seligman,
2
4
8
Depth in metres+
8
1
0
I
1
2
1
4
0
2
49 8
Depth in metres+
4
8
8
1
0
THE SHAFT
-1
-2
t
s
E
-3
-4
f
-5
BORE 2
I
I
-8
0
2
4
I
I
8
8
10
Depth in metres +
FIG.S.-The
I
I
12
14
0
2
4
8
8
10
Depth in metres +
change in the temperature-defith relation with time for the Shaft and
Bores I , 2 and 3.
(d) The Calculation of a Theoretical Winter Cold Wave
Equation of Thermal Conduction.-At the end of summer the temperature
of the upper layers of a temperate glacier is uniformly at oo C. During
the winter a cold wave is incident on the glacier surface by conduction from
the air. If the variation of the surface temperature may be represented
as a simple periodic function of the time, it is possible to calculate the
position and form of the cold wave passing down through the glacier.
The equation of heat conduction may be written as
1939 Dec.
Temperature, etc., in the N&k of an Alpine Glacier
627
where the boundary conditions take the form
v = o when t = o ,
x=o.
v=f(t) at
v is the temperature, x the depth and t the time. k is the thermometric
conductivity and is given by k =K/cp, where K is the ordinary thermal
conductivity, c is the specific heat of the firn and p is the density.
The solution of this equation is *
If the temperature wave incident on the glacier surface is represented by
v=f(t)= -C(I -cos at),
this being the function used by Sverdrup, then the solution of the differential
equation becomes of the following form :-
The two terms of the form
J
(-)P*+
sin ~k sin
cos 0 cos
ax2
&/.La
have been omitted ; they are negligible in comparison with the same integrals
between the limits ot to 0 , when t becomes large.
the mean air temperatures at the
Choice of Constants.-Although
Jungfraujoch Meteorological Station on the Sphinx .f. give a symmetrical
curve over a period of years, the winter and spring temperatures of 1937-38
were considerably different from the average curve. Fig. 6 shows that
the curve v =f (t) = - C(I - cos at) passes quite well through the measured
temperatures, when 2C = - 14O.6 C., the mean temperature of the coldest
months, and o = 2 n / T where T = 1 2 months, is the period, and t = o on
August I.
* H. S. Carslaw, Introduction to the Mathematical Theory of the Conduction of
Heat in Solids, p. 47. Macmillan, London, 1921.
t The mean air temperatures on the Monchfim are assumed to be not widely
different from those on the Sphinx. The lack of knowledge of the magnitude of
local influences on the winter temperatures in these two places did not enable a
temperature correction for the difference in altitude (120m.) to be made with any
certainty during the winter months. (See footnote on p. 623.)
Dr. T. P. Hughes and Mr. Gerald Seligman,
628
4, 8
Koch and Wegener * (pp. 332-3) have given good data for calculating k.
The thermal conductivity is represented by the formula K =6-6 . I O - ~ . p2,
and k may then be written as
k = 6-6 x IO-'P/C.
The mean density in the uppermost 13 metres in the glacier has been found
Aug.
8ept.
FIG.6 . 3 = -C(I
-cos
Oct.
Nov.
Dec.
Jan.
Feb. March April
May June
Julv
277
T where T = I Zmonths, compared
a t )for -C=7*3'C. a n d u = - ,
with the two-daily mean temperatures on the Sphinx Meteorological Station for 1938.
to be about p =0.53, and Koch and Wegener recommended the value c =0-48
for the specific heat. Then
k =6.6 x I O - ~x 0.53 + 0.48 =7.3
x I O - ~ cm.2/sec.
Also
T = I year =3.154 x
107 secs.
Hence the solution of the equation giving v becomes
I
- e - 0 . 3 6 9 6 . 1 0 - a(1.994
z ~ ~ ~ x 10-?t-0.3695 x
IO-%) - ---=
d
T
r
s-=
2
on introducing the values of the constants. The integral is a standard one
given in mathematical tables,t so that the temperature may be calculated
at various depths in the firn. Since the temperatures were measured at
the end of May, t may be written equal to 10months =2.628 x 107secs.
The Calculated Winter Cold Wave.-Fig. 7 shows the theoretical temperature distribution in the nCvC region in comparison with the whole range
*
.f.
J. P. Koch and A. Wegener, M e d d . om. GriSnland, 75, 191,1930.
J. Burgess, Trans. Roy. SOC.
Edin., 39, 257, 1899.
1939 Dec.
Temperature, etc., in the NhC of an Alpine Glacier
629
of all the earliest measurements. It will be seen that although the theoretical
curve follows the observed one quite closely, two main differences are
apparent. The observed curve has a lower minimum than the calculated
one and rises above it at depths between 8 and 15 metres. While it is not
to be expected that the fit between the two curves should be very close on
Shaded area includes all initial
observed temperatures measured
at the end of May.
Full curve represents a calculated temperature-depth relation
for t =lO months.
0
2
4
6
I
I
I
I
I
8
I0
I2
14
16
I
18
2
DEPTH IN METRES -+
FIG.7.-The calculated temperature-depth relation compared evith the range of initial
measured temperatures.
account of varying thermal constants and. the wide range of the air
temperatures about the curve selected for the calculation, these two differences
in shape between the two curves may be explained very simply. The
lower minimum of the observed curve was almost certainly the result of the
exceptionally low temperature prevailing during April, when the mean
monthly temperature was equal to that of the coldest month. If t is taken
to be 9 months in the theoretical curve to allow for this, then the calculated
minimum is at - 8 O . 2 5 C. at a depth of 1.2 metres, while the position of
thq deeper points is very little different to those on the curve for t = 10months.
The marked rise of the observed curve above the theoretical curve at greater
depths was also apparent in Sverdrup’s results, and, as suggested, may have
been due to a gain of heat during the early incidence of the winter cold wave
by the freezing out of melt water present in the firn at the end of summer.
In addition, the gradual change in the thermal constants with increasing
depth may also have a similar effect.
The snow fall during the winter has not been taken into consideration
in the above calculation, since it makes no essential difference to the result,
Dr. T. P. Hughes and Mr. Gerald Seligmm,
630
4, 8
provided that it is not exceptionally heavy. The reason for this is that
when a layer of snow arrives on the glacier surface at the temperature of
the air, it prevents further heat conduction between the snow and the air,
0" c
-1
-2
Y
r
*
2 -a
f
f
-4
-5
IAY
-6
0 5
JUNE
1
I
100
105
JULY
I
I
I
11.0
11.5
12.0
AUG.
125
Time (t) in Months
0-0 Calculated values at I, 9.5 m.; and 11, 3.9 m. depth.
n-n
Observed values at 9.9 m.in Bore I.
Observed values at 9.5 m.in Bore 111.
x - x Observed values at 3-9 m.in the Shaft.
+- +
FIG.8.-A comparison of the observed and calculated temperature-time relations at two
depths in thejirn.
since they are already in thermal equilibrium. As long as the quantity
of snow falling is not sufficiently great to give lower temperatures in the
surface layers than those possible according to ordinary thermal conduction
processes, the temperature distribution is practically unchanged by the
arrival of snow. If, however, the snow fall is very great and the temperatures
of the upper layers of firn are lower than those possible by normal thermal
conduction, then it is possible that the shape of the temperature-depth
1939 Dec.
Temperature, etc., in the Nhk of an Alpine Glacier
63’
curve may become considerably changed. Since the penetration of the
winter cold wave is about three to four annual layers of snow at the altitude
of our observations, it appears to be unlikely that the winter snbw fall can
make any appreciable difference to the temperature distribution obtained in
its absence in the upper layers of the firn.
The Heating of the NkuL-It is possible to calculate the change in
temperature with time at a certain depth from the equation relating these
three variables, on the assumption that the heat exchanges take place
according to the laws of thermal conduction. Fig. 8 shows both the calculated
and observed changes in temperature with time at depths of 3.9 metres and
9.5 metres during the interval between the end of May and the middle of
August. The theoretical curve shows that at 3-9 metres the temperature
minimum has passed during this period, and that the temperature is rising
steadily, but at 9.5 metres the temperature minimum is approaching and
the temperature is still falling slowly. It will be seen that the measured
temperatures in the shaft at 3-9 metres showed a much more rapid rise in
temperature until June 8, at which time they suddenly rose to 0” C. This
difference between the calculated and the observed temperature-time
relations indicates that the heating at 3.9 metres was not at any time due to
the effects of thermal conduction alone, but that it must have been influenced
by the downward movement of melt water from the surface, as described
previously. The observed temperatures at 9.5 metres in Bore I and at
9-9 metres in Bore 3 followed the theoretical curve for two or three weeks,
but were then influenced by the changing temperature gradient, due to
approaching melt water, and began to rise steadily to zero.
(e) The Temperature of the Ice on the Sphinx Plateau
The Sphinx Plateau (3460 metres) is a comparatively flat area between
the ridges of the Sphinx and the Jungfrau and is, in fact, the Jungfraujoch
itself (see fig. I). It is situated at the head of the valley containing the
Jungfraufirn and is roughly of the same altitude as that part of the Monchfirn
in which Bore 3 was made. A hollow in this plateau is filled with a mass of
solid, glassy ice, which has grown by the freezing of melt water from the
rocks above. This ice is stationary, except for a minute creep in places,
for it lies above the bergschrund and forms a frozen-on “ ice-apron ” covering
the plateau and bases of the rocky slopes around.
For many years the temperature of this ice-apron has been known to
remain below zero all the year round. Even in the “Eisgrotto,” which is a
series of tunnels and caves dug into this ice for the benefit of tourists, the
air temperature rarely rises above -2” C. despite the large number of
visitors. The crystallographic and other experimental work on ice was
carried out by the Jungfraujoch Research Party in a cold laboratory excavated
in the ice of this ice-apron. During the summer the temperature of the
air in this laboratory remained between - 3” and .- 4” C. rising about a
degree when two people were working in it, and dropping down once more
after their departure. In order to determine the temperature gradient
near the surface of the ice, a bore-hole was sunk near the cold laboratory
632
Dr. T. P. Hughes and Mr. Gerald Seligrnan,
4, 8
and a few thermo-junctions were buried in it. The wires became frozen
in the hole after about 24 hours, and temperatures below zero were registered
very near the surface during warm weather in early August. The results
showed that the temperatures fell from oo C. at the surface in an almost
linear manner to - 2 O . 1 C. at a depth of 2 metres. This temperature
gradient was continued at greater depths since temperatures taken by
thermometers buried in deep holes inside the laboratory indicated that at
about 4 5 metres depth a minimum of - 4
' C. was reached ; this temperature
persisted without appreciable variation to the point where the ice-apron
joined the rock of the ridge. June temperatures were some 8" C. lower than
this value.
The importance of this result is that it shows that ice can and does exist
at temperatures well below zero at this altitude, provided that the ice is
impermeable to melt water. The transition between the snow covering
and the ice underneath was quite sharp and there was little or no layer
corresponding to firn between the two. During a spell of fine weather
the snow was often melted completely off the ice, exposing typical blue ice
on the surface.
(f) Discussion
The Winter Cold Wave.-The
results described above show that the
glacier is at a temperature in the neighbourhood of zero down to a depth
of 30 metres at the end of the summer. All previous results and theories
have supposed that the temperature gradient in a glacier is such that the
temperature rises with increasing depth and it may, therefore, be concluded
that, in summer, the nkve' temperature is that of the pressure melting-point
throughout the whole Aletsch Glacier.
At the end of the summer the nkvvk contains a considerable quantity of
melt water, which is held in the inter-crystalline channels by capillary
action. As the air temperatures become lower during autumn and winter,
the snow and firn lose heat to the air above, and this water is frozen out
on the firn grains. This flow of heat upwards to the surface may be described
as the passage of a cold wave in a downward direction, and it follows the
ordinary laws of heat conduction. If the incident cold wave is expressed
as a harmonic function of the time and the constants are chosen so that this
curve represents as well as possible the actual air temperatures during the
winter, a temperature-depth relation in the firn may be calculated which
is in good agreement with the observed values at the end of the winter.
Since the meteorological observations show that the month of April was
exceptionally cold, it was to be expected that the temperatures measured
in the firn some weeks later would show lower temperatures near the surface
than those anticipated from the theoretical curve. This was found to be
the case ; the lowest temperatures recorded near the surface were about
I' to 1 O . 5 lower than the calculated values. If we attempt to compensate
for this late cold month by making the calculation for the case when the
position of the cold wave is estimated a month earlier, that is for t = g months,
the minimum of the calculated curve is only oO.5 lower than the actual
1939 Dec.
Temperature, etc., in the N h d of an Alpine Glacier
633
lowest temperatures recorded in the bore-holes. Therefore it seems that
the application of thermal equations to conduction phenomena in glaciers may
show reasonable agreement between theory and observation, provided
that the theoretical conditions are made to resemble the experimental ones
as far as possible.
The Temperature of a Temperate Glacier.-A discussion of the heat
income of glaciers has been given by Lagally.* The main sources of thermal
energy are the following :(I) The generation of heat within the glacier from mechanical energy
due to the movement of the ice mass.
(2) The heat flux passing from the Earth into the glacier.
(3) The entry of heat from above the glacier by conduction, convection
and radiation processes.
The heat produced from the loss in potential energy, which is the main
source of heat from mechanical energy during the downward flow of a
glacier, may be estimated roughly. The work done by the falling mass of
ice may be written
A =%opgh sin a
for a vertical column of firn or ice of unit cross-section extending from the
surface to the bottom (cf. Lagally, p. 69). In this equation uo is the surface
velocity, a is the angle of slope of the glacier, p the density of the firn or ice,
h the height of the column and g is the acceleration of gravity.
Taking the conditions on the Monchfirn we may estimate uo= 24 metres
per annum sin a =0.14and p =0.8,the heat generation amounts to
A =%x 2400 x 0.14x 0.8x 981h.
= 1.76x 105 h ergslyearlunit cross-section.
Hence, assuming the energy to be liberated equally throughout the whole
column of height h, the rise in temperature is
1.76x 105 x h
=oo.oo8 C . per annum,
4.18 x 107 x o.gh
where the specific heat is taken to be 0-5 and I cal. =418x 107 ergs.
T=
This heat would not be given out uniformly throughout the whole glacier
interior, but would be liberated more rapidly at great depths to give rise
to a temperature gradient. Where the mean annual temperature is below,
say, -1' C., this annual temperature rise of 0°.008 C. would not greatly
influence any existing temperature gradient in the younger nCvCs of a glacier.
Towards the glacier tongue, where the speed is greater and the frictional
heating has taken place over a period of many years, the temperature gradient
may become modified due to this cause, but the effect can hardly be of major
importance in heating up the glacier in cases where the mean temperature
is several degrees below zero. This conclusion is not in complete accord
with the views held by some writers.?
* M. Lagally, Mechanik und Thermodynamik des Stationarm Gletschers, Leipzig,
1934t See, for example, A. Holl, Les Alpes, 13,298, 1937.
634
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
Lagally has estimated that the heat flux from the Earth is of the order
of 2.5 x 1 0 - 6 cal./cm.2/sec. If all this heat goes to melt ice at the bottom of
the glacier, it will be sufficient to melt a layer of ice I cm. in thickness per
annum. When the 0" C. isotherm lies below the surface of the Earth the
heat flux from the Earth will produce a temperature gradient in the glacier
of the same order of magnitude as that in the Earth, i.e. about 20 to 40
metres per I' C. When the 0" C. isotherm lies above the surface of the
Earth and is in the glacier there will be a melting layer at the glacier bottom.
Part of the heat flux from the Earth will supply the necessary latent heat
for melting, while the rest may flow up to the glacier surface in the temperature gradient. On this hypothesis the temperature gradient in a glacier
would thus fall from oo C. or less at the bottom of the glacier to the mean
annual temperature near the surface, neglecting the seasonal fluctuations.
The energy set free within the glacier during its movement would change
the temperature gradient somewhat, and any melting zone near the glacier
bottom would gradually extend towards the surface on passing down the
glacier.
In actual fact, however, the results obtained on the Jungfraujoch and
those of previous workers show that the temperature throughout the whole
glacier is that of the pressure melting-point, although the mean annual
temperature of the surface is of the order of -7" C. The explanation of
this result is that during the summer heat flows into the glacier in the form
of melt water, which is far in excess of the heat lost by thermal conduction
alone during the winter. If the glacier could only receive heat by conduction
from the air alone, a temperature gradient would exist in its interior. This
is supported by the fact that the ice mass on the Sphinx Plateau is at a
temperature considerably below zero throughout the whole year, since the
ice mass is impermeable to water. The ice can only gain and lose heat
by thermal conduction from the air and by absorption of radiation. Any
melting which may occur on the surface results in a loss in energy as the
latent heat carried away in the melt water streams. In the n&w&region of
a glacier, however, this latent heat passes rapidly into the firn where it is
set free when any water freezes out. In this way heat is transported into
the glacier at a far greater rate than possible by purely thermal conduction.
Sverdrup * has estimated the relative importance of the various factors
controlling the heat income of the glacier surface. The ablation was calculated from the heat energy income and was found to be in good agreement
with the measured ablation of the Fourteenth of July Glacier. The figures
showed that the amount of melting due to radiation was 52.4 per cent.
while the amount of melting due to conduction from the air was 29.4per cent.
No measurements of the radiation income were made at the Jungfraujoch,
but it is certain that the part played by the radiation is greater there, since
it becomes very intense at these high altitudes and low latitudes. As there
is no reason to suppose that similar conditions to those on the n h & region
of the Great Aletsch Glacier do not exist in any of the other Alpine glaciers,
the above considerations may be regarded as quite general.
* H. U.Sverdrup, Geogrufiku Ann., 17,145, 1935.
1939 Dec.
Temperature, etc., in the Ndvd of an Alpine Glacier
635
PART I1
THEMOVEMENT
OF MELTWATERIN
THE
N M
REGION
(a) Introduction
Sverdrup,* working on a Spitsbergen glacier, showed that the amount
of energy absorbed during the summer far exceeds that lost by conduction
during the winter. The difference is utilised to melt snow and ice, and
the lost energy finds its way into the glacier streams.
In the Alps the amount of snow and ice melted during the summer is
probably much greater than in Spitsbergen. Even above the upper ndvds
at a height of 3500 to 4000 metres the snow slopes melt rapidly in warm
weather and streams can be seen running down over rocky slopes and from
hanging glaciers to disappear into the body of the main glacier or its
tributaries. Sverdrup * and Ahlmann t estimated and measured the
amounts of ablation by evaporation and melting on Isachsen’s Plateau on
the Fourteenth of July Glacier. Their results, however, refer to the. loss
of water at the surface and give no information concerning the amounts of
water in motion at various points in the glacier.
This section of the paper describes some experiments which we carried
out during the summer months on the Monchfirn. They were devised
in order that we might gain an approximate idea of the quantities of water
flowing through the firn. Exact results were not necessary and, in any
case, could not have been attempted in the time available, so that the
experiments made were simple.
The results show that large amounts of water are continually passing
down through the firn and that the actual magnitude of flow is dependent
on the supply of melt water-that is to say, on the meteorological conditions.
Layers of lower permeability which normally run parallel to the surface
often cause the flow to take place with a marked horizontal component.
(b) Experimental
The movement of melt water was studied both qualitatively and quantitatively. Fig. I shows the sites of No. z and No. 3 auxiliary pits (R and Q
respectively) in which the observations were made. They were both supplied
with covers which were kept closed. The dimensions of both pits were
frequently changed for various reasons, but their approximate size wasdepth 2.5 to 3 metres, length 2 metres and width I to z metres.
Measurements of the Melt Water.-Two methods were tried. The first
consisted of burying cylindrical aluminium pans filled with snow and
covered with fine cotton gauze. They were left in position for some weeks
and then dug up. The weight of the pan and its load of snow before and
after the experiment gave the amount of water that had entered. The
results so obtained were not wholly satisfactory.
* H. U.Sverdrup, Geografika Ann., 17,145, 1935.
t H.W.Ahhann, Geografiska Ann., 17,43,1935.
G43
636
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
A series of continuous observations was next made with specially
designed pans which allowed the water collected to run out at the bottom
into a receptacle for measurement. Fig: g shows one of these pans made of
galvanised iron. The water drained down through the depression in the
centre of the pan and ran out through an outlet; to this was connected
a rubber tube dipping into the receiving vessel. In order not to change
the conditions of flow in the pans they were completely filled with snow at
the start and were placed in niches excavated in the walls of the pits. When
in position, they were walled in again with snow to a horizontal depth of
about 30 cm., so that they could not be influenced by radiation while the
pits were open. When the water flow was rapid, as was the ease in the pans
FIG.9.-A melt-water collecting pan. Both wood and
galvanised iron pans were used.
near to the surface, it was found that the firn in the pans was little different in
texture to the surrounding firn and that no melting had occurred. In the
cases of pans buried at greater depths, however, where the rate of flow
was less, the water often became frozen in the bottom of the pans.
An attempt was made to measure the magnitude of the horizontal
component of melt-water flow by removing the upstream side of the pans
and covering the tops with a waterproof cover, so that vertically falling
water would be unable to enter. Here, again, the results were unsatisfactory, probably on account of the water freezing in the bottom of the
pans.
Throughout the course of the research several qualitative experiments
were made to investigate the path taken by melt water in the different
layers of firn. Dyes and other simple apparatus were employed.
(c) Results of the Measurements
The buried cylindrical pans gave a mean water flow of 0.01c.c./cm.2/hour
at a depth of I to 2 metres. This rate of flow was some 10 to 20 times less
than that measured by the draining pans in the pits. This result might
either have been due to a cold spell of Geather during the earlier experiment,
Temperature, etc., in the N&k of an Alpine Glacier
1939 Dec.
637
or to the saturation absorption capacity of the non-draining pans being
reached in the early stages of the experiment so that the amounts absorbed
were representative of a shorter time. In any case, they must not be treated
as typical of summer melt-water flow. Readings of the quantitity of melt
water collected per hour in the draining pans are shown in fig. 10, plotted
against the time. Some meteorological data are also shown for the sake
f July +
7 0 11 13 15 17 10 2l 23 25 27 20 31 2 4
1 " " " " " " " " ' " " " " " ' " " ' '
Temperature
on Sphinx
t
Daily Houra
o f Sun
t
Daily Snow
Fall in cms.
C August +
6 8 10 12 14 16 18 20 22
"
'
-5
1
-5
-10
12
8
4
0
- 10
12
8
4
0
40
20
0
40
20
0
0.4
04
0.3
0.3
0.2
02
01
01
t
Melt Water
Collected in
c.c./cm.'/hour
0
0
7
0
11 13 15 17 10 21 23 25 27 20 31 2
4
6
8 10 12 14 16 18 20 22
3 C August +
f July +
FIG.io.-The influence of the meteorological conditions on the rate of flow of melt water
through the firn.
of comparison. The times of the various observations were taken to be
the means of the times at which the water quantities were measured. Pan I
and Pan I1 were placed in No. 2 Pit, and Pan I11 and Pan IV in No. 3 Pit.
Pan I was in the upstream wall and at a depth of 0.9 metre, while Pan I1
was in the side wall at 2.9 metres depth. Pans I11 and IV were both at
a depth of 1.1 metres, Pan I11 being in the upstream wall of No. 3 Pit and
Pan IV in the side wall of this pit. The No. 3 Pit was dug specially for the
melt-water pans in case the conditions in No. z Pit had become disturbed
during its two months of existence.
The results show that Pan I a t 0.9 metre depth collected a much greater
quantity of water than Pan I1 at 2.8 metres depth in the same pit. In the
early readings for Pan I the flow was greater during the night than during
the day, on account of the time taken for the water to percolate down from
the surface to the pan. However, after July 21 the flow was greater during
638
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
the day, due presumably to the lowering of the snow surface and the permeability of the firn gradually increasing as the smaller crystals were melted
away. The maxima of the line for Pan I11 will be seen to occur at the
same time as the minima of the line for Pan I, since a sudden flow of melt
water only reaches the lower pan some hours after the upper one.
In the No. 3 Pit the quantity of water collected by Pan I11 was usually
greater than that collected by Pan IV, as it was in a better position to collect
a downward flowing water stream.
The influence of meteorological conditions on the melt-water flow was
quite striking. As might be expected, periods of cold weather with temperatures below zero tended to arrest the flow ; this happened during the
periods July 10 to 14,24 to 25 and August 6 to 8 and 21 to 23.
A fall of snow naturally increased the rate of melting, for the small
needle crystals of fresh snow are melted more easily than the larger and
rounder crystals of old snow crusts.
The amount of radiation falling upon the snow surface, as indicated
roughly by the sunshine record, was probably the most important factor
influencing the rate of melting and the supply of melt water. The sunshine
record, which was naturally very similar to the temperature record, showed
a correlation with the rate of melt-water flow.
The amount of melt water collected in the pans during warm weather
was of the order of 0.2 C.C. per square centimetre per hour.
The flow of water in a horizontal direction was always found to be much
less than we had expected from qualitative observations. Even in No. 3
Pit which had been dug in rather steeper slopes than the average inclination
of the glacier at this point, the amount of water collected was never more
than 0.005 c.c./cm.2/hour. We do not believe this result to be correct
and more elaborate apparatus will be required to arrive at the true figure.
(d) Qualitative Experiments
The experiments to be described here were made with two objects in
view. First, we wished to ascertain the general direction and velocity of
melt-water flow in a glacier, and, second, we wanted to find out what influence
was exerted by bands of ice on water movements in the firn. Previous work
has been carried out on this subject by Paulcke and Welzenbach,* and by
one of the auth0rs.t
When fluorescein was strewn on the surface 4 metres above No. 2 Pit
it reached the upstream wall of the pit in 48 hours, a rate of flow of 8.3 cm.
per hour. (It is, perhaps, only a coincidence that Welzenbach 1found this
identical speed--8.3 cm. per hour-for water movement on a slope of
slightly less inclination, but through firn of rather better water conducting
qualities.)
* W. Paulcke and W. Welzenbach, 2. Gletscherkunde, 16,46,1928.
t G . Seligman, Snow Structure and Ski Fields, chap. xi, Macmillan, London,
1936.
1 W. Welzenbach, Wiss. Veriflich. Dtsch. Oest, Alpenverein (Innsbruck), ( 9 ) ,
13, 1930.
1939 Dec.
Temperature, etc., in the Ntvk of an Alpine Glacier
639
Yellow ochre spread on the surface was traced to a point some 25 metres
downstream and in the whole course of this travel never penetrated deeper
than 70 cm. below the surface. Its travel vertically downwards was apparently arrested at some ice bands, but it does not follow that small
quantities of water did not penetrate deeper, because the ochre was carried
in suspension and the ice bands may have exerted a filtering action on it.
These experiments also showed that ice bands as thick as 10cm. were
penetrated in certain places by dyed solutions, such as fluorescein and
methylene blue. For this to occur it was necessary for the liquid to flow
round the grain boundaries of the closely packed crystals.
(e) Discussion
The results of the melt-water measurements show that during warm
weather large quantities of water percolate through the surface layers of
the accumulation areas of gJaciers, even at high altitudes. It is not surprising, therefore, that the effects of the winter cold wave are destroyed so
rapidly during warm periods, especially when it is realised that it only
required about 3 calories to raise one gram of snow (specific heat =om5 cal./g.)
from - 6" C. to zero, this being the heat liberated when 0.037 C.C. of water
freezes. During fine weather the amount of water flowing downwards at
a depth of one to two metres is often of the order of 0.2 c.c./cm.2/hour,
which liberates 16 calories on freezing. As will be described in Part I11
of this paper, melt water passes downwards through the firn during the
early summer and a certain amount of it, depending on the temperature of
the firn and other factors, freezes on to the firn crystals. Finally a stage is
reached when the whole of the upper layers of the glacier have been raised
to oo C., and the firn consists of an equilibrium mixture of ice and water at
the melting-point.
For the sake of comparison it might be mentioned that Sverdrup *
calculated the surfme ablation on the nCvC region of a Spitzbergen glacier
to be of the order 0.07 - 0.09 c.c./cm.2/hour during fine weather, while
the measurements on the nCvt region of an Alpine glacier show that the
melt-water flow at a depth of I metre was of the order 0.1- 0.3 c.c./cm.2/hour,
corresponding to melting during the days, and of the order 0.025 - 0.1
c.c./cm.2/hour for the nights.
If the downward stream of water is held up by an impermeable layer,
or if cold weather cuts off the supply, it is possible for heat to pass downwards by ordinary thermal conduction. The water may then be frozen
out in this stationary position to form or increase an ice band or denser
layer of firn.
Both the temperature and the dye experiments prove that the downward
flow of melt water is checked by ice bands. They cause the water to flow
along them until a permeable spot is reached through which it can continue
its downward path. If the ice band is near the surface and the water flow
rapid a slight melting may take place at the grain boundaries, due to local
*
H. U. Sverdrup, Geogmfika Ann., 17, 145, 1935.
Dr. T . P. Hughes and Mr. Gerald Seligman,
640
4, 8
inequalities in temperature. Such a process can hardly be imagined to take
place more than about two metres from the surface.
The ice bands sometimes extend over considerable areas as uniform
impenetrable layers and can hold up the descent of melt water for some time,
but eventually the water seems to be able to find its way through in thin
or permeable places. One band was traced over an area of 150 x 160 metres
and may have been of still greater extent, although there is reason to think
that there were pervious flaws in it. Under certain conditions water travels
on runnels on the surface itself. This is believed to be due to the presence
of an ice band very close indeed to the surface, or to a crust.
In the present state of glaciological knowledge the later fate of the meltwater stream is not known. It seems very likely that a considerable portion
of it is carried for long distances horizontally before reaching the glacier
bed. This was shown by the crystallographic studies made at the
Jungfraujoch.* These demonstrate that the only part of the nCvC region
comparatively readily permeable to water is very small in extent.
At an altitude of 3500 metres the permeable zone is considerably thicker
than 30 metres and there are some grounds for the belief that it extends
as far as the glacier bed. But at 3300 metres it is less than 25 metres thick
and forms an ever-narrowing wedge from there to the firn line. This does
not imply that any part of the glacier bed is dry. In addition to water
making its way down to the bed at the 3500 metres level in the manner
described above, enormous volumes of water find their way from the
radiation absorbing rocks above the glacier into the bergschrund and on
to the glacier bed. Perhaps more water is received by the glacier at this
point than anywhere else over its whole surface. It is also possible, although
no information on this point is available, that the “impermeable zone” of the
nCvC area may be riven by cracks and perforated by glacier mills.
In a much crevassed glacier a great deal of water falls into crevasses.
In the nCvC region an appreciable amount of this water becomes frozen on
the crevasse walls since crevasses carry the negative air temperatures into
the glacier body more rapidly and further than those propagated through
the firn by the diurnal or seasonal cold waves. Melt water flow over,
through, and beneath the tongues of glaciers has been dealt with by many
authorities and needs no elaboration from us in connection with glacier
run-off, although its influence on crystal growth in the ice regions is
important and will be dealt with by us elsewhere.
PART I11
THEINCREASE
IN DENSITYIN
THE
UPPERLAYERS
OF FIRN
(a) Introduction
The change in the density of the firn with depth was measured during
the excavation of the shaft and the results obtained are shown in fig. 11.
This diagram also gives the range in crystal sizes in the firn at different
*
M. F. Perutz and G . Seligman, Proc. Roy. SOC.,
A, 172,335, 1939.
1939 Dec.
Temperature, etc., in the Nkerk of an A&im Glacier
641
depths. The density rises from 0.3 for old snow on the surface to 0.6 in
the first 7 metres and then increases more slowly to 0.68 at a depth of
3 0 metres.
The following experimental results and discussion are concerned with
the comparatively rapid density change in the first 7 metres. A more
general account of the density changes in firn in relation to crystal size and
glacier structure will be given elsewhere. (See footnote, p. 619.)
t
EE
3
.-c
o
d
o
07
0.8
-
-
~
0
5
~~
10
'
15
Depth in Metres
20
~
25
30
+-
FIG.I I .-The change in density and grain si2e with &th in the shaft.
The density of snow or firn may be changed in the following ways :( I ) By the arrival and subsequent freezing of water.
(2) By the relative motion of crystal grains or aggregates into closer
packing. This process is assisted in the early stages of firnification by the
removal of small crystal projections by sublimation and surface migration
of water molecules. In glacier ice the process is assisted by the recrystallisation involved in flow by plastic deformation.
(3) By wind packing on the surface. As this has been discussed previously at some length by one of the authors * and is a surface phenomenon,
it will not be mentioned here.
The two main physical processes which increase the density of fim,
included in (I) and (z), are discussed below in the light of the results obtained
from the experimental work.
* G . Seligman, Snow Structure and Ski Fields, chapters Vii and viii, Macmillan,
London, 1936.
642
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
(b) The Density Increase by the Freezing of Melt Water
Water may become frozen out in the firn (i) during winter by the incidence of the cold wave and (ii) during summer, when the winter cold wave
is destroyed by the descending melt water.
(i) The increase in firn density due to the freezing of water held in the
firn at the end of the summer by the slowly penetrating frost was concluded
to be very small by Sverdrup,* since the greater part of the water present
in the firn at the end of summer has time to percolate away before the
temperature falls below zero. In addition, the slight discrepancy between
the calculated and observed winter cold waves at depths below 8 metres
(see fig. 7) shows that any gain in heat by the freezing of water present in
the firn at the end of summer is very much less than the heat required to
destroy the cold wave completely. That is to say, the amount of water
frozen during early winter is very much less than that frozen during early
summer, while the firn is slowly heated up uniformly to the melting
temperature.
(ii) Measurements of the quantities of melt water flowing down through
the firn in summer (see Part 11) show that they are sufficient to heat up the
cold firn to the melting-point during early summer in a comparatively short
time. During this process a certain amount of the descending water becomes
frozen out to increase the density and crystal size in the firn. If the
temperature in the firn is - t o C. during the descent of water, the density
of the dry firn becomes increased by pct/8o g./c.c., where p is the initial firn
density, and c is the specific heat. For example, if p =0.5, c =0-48 and
t = - 5' C. then the increase in density amounts to 0.015. This calculation
assumes, of course, that little or no heat conduction to neighbouring layers
of firn takes place. The change in the shape of the temperature-depth
curves with time in fig. 5 suggested that the heat transfer by normal thermal
conduction was usually very much less than that carried by the melt-water
stream, since the junctions were heated up one by one as a rule. In the
case of Bore 3, where the rate of heating was much slower and the temperature-depth curve tended to move as a whole towards the oo C. line, it
is possible that the rise in temperature of the lower couples was the result
of ordinary thermal conduction.
Under the condition obtaining in Bore 3 the above calculation would have
to be modified to allow for the transport of heat without water, and relatively
more water will freeze in the firn nearest the surface. The calculation of
the density change was originally carried out by Sverdrup * in this manner,
and, although his calculated densities were higher than the observed values,
the trend of his results showed general agreement between experiment and
theory.
In the case of Sverdrup's work at Spitsbergen, the annual surplus of
snow was of the order of 0.4metre and the cold wave penetration was about
10 metres. An annual layer of firn could thus undergo up to 25 seasons of
frosts and thaws of varying intensity before reaching a depth out of reach
* H. U. Sverdrup, Geogrufika Ann., 17,53, 1935.
1939 Dec.
Temperature, etc., in the N h k of an Alpine Glacier
643
of the cold wave. On the Monchfirn at the Jungfraujoch the annual surplus
varied between 3 and 5 metres and the cold wave penetration was about
15 metres, so that the firn was only frozen and thawed during 4 or 5 seasons
at the most and any resulting density increase due to this cause was necessarily considerably less than that at Spitsbergen. In the work at the
Jungfraujoch no study of the snow densities near the surface was carried
out over any extended period, but determinations made at the beginning
and at the end of summer showed that at a depth of about 1.2 metres the
density increased from 0.35 to 0.53. This increase was much greater than
could be accounted for by the freezing of the descending melt water of a
single season. Measurements made in the Monchfirn have shown that a
more important factor than melt water was the slow settling of snow and
firn, which was quite large enough to explain any of the observed density
changes.
(c) The Density Increase by the Settling of Snow and Firn
Results : Snow Settling.-The observations on snow settling, which
are described in detail elsewhere (see footnote, p. 619), showed that the rate
of settling of new snow was as much as 0.8 cm./cm./day during the daytime
at a depth of 20 cm. when the temperature was above zero and the surface
was melting. When the temperature was below zero new snow had a
settling rate of about 0.13 cm./cm./day. As the snow became more closely
packed the settling rate fell off gradually. The rate of settling was always
greater during the daytime than during the night, on account of temperature
differences. The process of settling was thus accelerated by the presence
of a lubricating layer of water around the snow crystals.
It will be seen that the density of new snow could increase very rapidly
near the surface when the temperature was above zero. For example, an
initial density of 0.15 could be increased to 0.25 in 12 hours, assuming
that a settling rate of 0.8 cm./cm./day was maintained. When the settling
was slower in the absence of melt water, a settling rate of 0.13 cm./cm./day
could increase the density from 0.15to 0.25 in the course of 3 days.
Other settling experiments have been described by one of the authors.*
Firn Settling.-These studies were followed by experiments made in
No. z auxiliary pit dug in the Monchfirn to a depth of nearly 3 metres.
The settling was observed by two methods:
(a) by measuring the gradually lessening separations of a vertical row
of pegs in a wall of the pit, and
(b) by means of a sensitive measuring instrument called a “firn compression meter.”
(a) A vertical row of wooden pegs, X, A, B, . . . J, was placed in the
“downstream” face of this pit. The peg X was just below the surface and
the peg J was 2.5 metres below at the start, while the remaining pegs were
placed at intervals between these two. The distances between successive
pegs were measured every day and checked by the overall measurement
*
1936.
G . Seligman,Snow Structure and Ski Fields, pp. 145-146,Macmillan, London,
644
Dr. T. P. Hughes and Mr. Gerald Seligman,
4, 8
XJ. Fig. 12(a) shows the change in the distance XJ for the settling during
the month of July. With the exception of the initial readings, the settling
appears to have proceeded in a regular manner, and gave a linear distance/
time relation. Over the linear range the average settling was 2-5x I O - cm./
~
cm./day. The greater rate of settling at the start of the experiment was
probably due to the peg X being in a surface firn of a very low density,
FIG.12.-The observed rate of settling in$rn.
where the settling rate was higher. The rates of settling between successive
pairs of pegs varied somewhat among themselves, but gave a mean of
2.25 x I O - ~cm./cm./day. The differences in the rate of settling could not
be correlated with obvious structural irregularities in the firn, although
here too it was noted that the layers of firn nearest the surface settled most
rapidly. The settling experiments are described by us in greater detail
elsewhere.
(b) The Firn Compression-Meter was identical with that used by MOSS,*
and consisted of a simple wooden mechanism to measure small vertical
displacements by a 10to I lever magnification. The base of the instrument
was fixed firmly in the firn at the bottom of the pit, about 28 metres below
the surface. The shorter end of the lever was placed under a long stake
sunk firmly into the firn at a distance of about 2 metres above the base.
* R. Moss, Geog. Jour., 92, 220, 1938.
1939 Dec.
Temperature, etc., in the Nkerk of an Alpine Glacier
645
As this stake slowly settled with the firn it caused the long end of the lever
to move across a scale. Readings were taken twice daily and the scale reset
frequently. Fig. 12(b) shows the settling over 2 metres plotted against the
time. Once again the settling-time relation was an almost linear one and
gave an average rate of settling of 1.9 x I O - ~cm./cm./day.
(d) Discussion
The results of the determinations of the rate of settling show without
doubt that an important initial increase in the snow density is due very
largely to the slow settling of the snow and firn. In summer freshly fallen
snow may at first have a settling rate of from 0.1 to 0.8 cm./cm./day, so
that a layer of density 0.1 can increase in density to 0.4 in the course of a
few days. In the firn below a depth of about 0.2 metre, which is out of
reach of the night frosts, the settling went on at a much slower but constant
rate throughout July. The average daily settling in this region was
2.3 x I O - ~cm./cm./day. If we assume that this rate of settling continues
throughout a summer of IOO days the amount of settling is 0.23 cm./cm.
at the end of this time, and the density will have increased by a factor of
1.3. For example, firn of density 0.4 would increase in density to 0.52.
This change is roughly of the same order as that actually measured at a
depth of 1.2metres in the firn during the summer.
Previous work on the density changes .inthe fim by Sverdrup* appeared
to show that the density increase could be wholly accounted for by the
freezing of melt water at the crystal boundaries. The measurements
described above show conclusively that the increase in snow and firn
densities during summer in an Alpine glacier is due very largely to a
slow and long-continued settling process. One interesting observation in
support of this conclusion emerged from the crystallographic work (described
elsewhere, see footnote, p. 640), namely, that there was no important increase
in the crystal size during the latter stages of firnification (4.fig. I I). Sorge t
found this to be the case in the Arctic as well-in fact he appears to attribute
the density increase almost wholly to the consolidation of the firn. If
the density increase had taken place by the freezing of melt water at the
crystal boundaries a considerable growth of the crystals would be entailed.
If, on the other hand, the density were increased by the closer packing of
the crystal grains little or no grain growth would be expected. The fact
that there is only a slight grain growth during the increase in density is
thus strong evidence in support of the statement that the firn increases in
density during summer largely by a slow process of settling.
* H. U. Sverdrup, Geografisku Ann., 17,53, 1935.
t E. Sorge, Wiss. Erg. Deutsch. Gron. [email protected] . Wegener, I929-3I, 3, 156, 1935.
646
Dr. T. P. Hughes and MY. Gerald Seligman,
PART IV
ACKNOWLEDGMENTS
The above work was carried out as part of the programme of the
Jungfraujoch Research Party, which was organised and led by one of us
(G. S.) for the study of glaciological problems on the Great Aletsch Glacier.
The expedition was largely financed by a grant from the Leverhulme Trust
awarded to one of us (G. S.) and by grants from the Ski Club of Great
Britain, the Alpine Ski Club and the Royal Geographical Society.
We also express our gratitude to Dr. F. P. Bowden of the Physical
Chemical Laboratory, Cambridge, who has not only guided and advised
us at every stage in this research but. has made two separate journeys
to the Jungfraujoch in order to give us the benefit of his experience on the
spot.
We have to thank Dr. A. E. Benfield for carrying out the initial part
of the temperature work, including the burial of the thermo-junctions and
some early measurements. We likewise have to thank Mr. E. A. Ferguson
for his constant assistance in many ways, notably in the burial of the thermojunctions and the melt-water pans, and in making most of the melt water
and settling measurements.
Our thanks are also due to. fIerr Liechti, Chairman of the Jungfrau
Railway and to Professor A. von Muralt, the Trustees and the Council
of the Jungfraujoch Scientific Station for the facilities and many kindnesses
shown to us.
Finally, one of us (T. P. H.) has to express his gratitude to the Trustees
of the Ramsey Memorial Fellowships Trust for having allowed him to take
part in this expedition during his tenure of a Ramsey Memorial Fellowship.
SUMMARY
Part I.-The temperatures in the ntvt region of the great Aletsch
Glacier have been measured to a depth of 30 metres and the position of
the winter “cold wave” established. During early summer the ntvt
temperatures rose to zero, and the rate at which heat entered was much
greater than was possible by thermal conduction alone. It was concluded that
the heat was carried into the firn by melt water from the surface, which
became frozen out when temperatures below zero were encountered, and
its latent heat liberated. A temperature distribution in the firn at the end
of winter was calculated from the equation of thermal conduction, and this
followed the observed values quite closely.
The fact that there was no temperature gradient (apart from seasonal
fluctuations) in the ntvt region of the Aletsch Glacier, where the mean
annual air temperature was of the order of -7” C., was considered to be
due to the large gain in heat from the melt water penetrating downwards
into the glacier during summer, since a large mass of impermeable ice at
the same altitude as the nCvC region remained at a temperature below zero
1939 Dec.
Temperature, etc., in the Nkvk of an Alpine Glacier
647
throughout the whole summer. There was thus no net gain in cold by the
glacier throughout the year. The above source of heat was thought to be
of greater significance in determining the temperature of the interior of the
glacier than the heat flow from the Earth and that generated by glacier
movement.
Part 11.-Actual measurements of the quantity of melt water flowing
downwards in the firn have shown it to be of the order of 0.2 c.c./cm.2/hour
at a depth of I metre during fine weather. The rate of flow was greater
near the surface, and depended on the amount of surface melting, i.e. on
the meteorological conditions. This flow of water in the firn occurred with
a marked horizontal component of flow down the glacier. Qualitative
experiments have shown the descending water stream to be held up by ice
bands, although these became permeable in certain places.
Part 111.-The density changes in the firn to a depth of 30 metres have
been followed. Although the freezing out of melt water in the firn plays
an important part in increasing its density, measurements of the rate of
settling of snow and firn have shown that the settling process was mainly
responsible for consolidating the fim in Alpine glaciers.