Hydraulics and hydrology of glaciers
Mark F. Meier
U. S. GeoZogicaZ Sumey, Tacoma, Washington, U. S.A.
ABSTRACT: Snow accumulation on glaciers is due to precipitation,
wind-blown snow, and avalanches. Glacier melting is strongly influenced by surface albedo so that thick snow cover produces less meltwater. The significant quantity most easily measured is balance
(change in ice mass over a period of time). Net or annual balance
can be determined several ways; the new combined system of reporting
balance is recommended. Snow changes to firn and then to ice in a
complex way that depends on temperature and meltwater. Glacier flow
permits adjustment of the ice reservoir to changes in input and output. Although the physics of ice deformation is well known, the laws
governing sliding of a glacier on its bed are poorly understood.
Water in a glacier moves through snow as through an unsaturated
porous medium. Water probably moves through and under ice in discrete conduits and perhaps also as a thin film at the icebedrock
interface. This conduit system in a glacier continually changes by
melting and plastic flow of the ice. Glacier outburst floods result
from the release of a glacier dammed lake or water body under the
glacier.
RESUME: L'accumulation de neige sur les glaciers a son origine dans
les précipitations, les rafales de neige et les avalanches. La fonte
sur les glaciers est soumise à l'influence de l'albédo de la surface,
de sorte qu'une neige épaisse produit moins d'eau de fonte. La
quantité la plus facile 2 mesurer est le bilan (la variation massique
de glaces dans un intervalle de temps). Le bilan net ou annuel est
déterminé par différentes méthodes; le nouveau système combiné sur le
bilan est recommendé. La neige change en névé puis en glace selon un
processus complexe dépendant de la température et de l'eau de fonte.
L'écoulement glacial ou fluage permet au réservoir de glace de
s'adapter aux changements d'alimentation et d'évacuation. Quoique la
déformation des glaces est bien connu, le glissement du glacier sur
sa pente est encore mal compris. L'eau se déplace dans un glacier 2
travers la neige comme s'il s'agissait d'un matériau poreux non
saturé. L'eau se déplace peut-être aussi dans la glace par des
conduites discrètes et sous forme d'un film mince à l'interface des
glaces et des roches. Ces conduites discrètes changent continuellement par la fonte et par fluage plastique de la glace. Les augmentations soudaines du débit des glaciers sont causées par la libération soudaine des eaux d'un lac barré par un glacier en cours de
€onte ou par des eaux sous le glacier et libérées de la même manière.
INTRODUCTION
Snow is recognized as an important element in the hydrologic
cycle in most parts of the world. Almost every general textbook on
hydrology includes a chapter on snow: measurement, melting, calculation of snowmelt runoff, and forecasting of snowmelt floods. By way
Publication authorized by the Director, USGS.
353
of contrast , the unique problems and methods associated with glacier
hydrology receive the attention of only a small group of specialists.
Few hydrologists know much about measurement of glacier growth and
wastage, predicting glacier runoff, the buffering effect of glaciers
on streamflow variations, glacier outburst floods, or the internal
structure and hydraulic properties of glaciers. Few nonglaciologists
realize how glacier hydrology differs , both qualitatively and quantitatively, from the hydrology of conventional streams and even the
hydrology of snow. Yet about three-fourths of all the fresh water on
the earth is temporarily detained as glacier ice (equivalent to the
world's precipitation for about 60 years), and in many parts of the
world hydroelectric, irrigation , and domestic water resources are
directly dependent on glacier runoff.
Perhaps in this symposium we can build additional bridges of
understanding between those scientists who are interested in basic
research on glaciers and those hydrologists who are concerned with
analysis and forecasting of streamflow and floods in regions that
contain glaciers. The physics of the production and flow of water
through glaciers will be considered in this session. Attention will
be given to specific matters of modelling and forecasting of glacier
runoff in a session to follow.
The relation of a glacier to its environment can be pictured as
a chain of distinct processes El]. The general meteorological environment together with the local surface topography controls the local
mass and heat exchange processes at the glacier surface, producing
changing rates of accumulation and ablation. The difference between
accumulation and ablation at a given point is called the ice or mass
balance at that point. If the mass balance averaged over a whole
glacier is positive the glacier grows by storing precipitation, and
the resulting change in thickness causes an increase in the rate of
flow of the glacier, thus extending its length and area. A series
of positive balance years, which might be caused by increased snowfall, cause the glacier to grow and extend to lower altitudes exposing more area to an environment of increased ablation. This
increased rate of ablation tends to compensate for the change in
balance. Thus a feedback occurs, and the glacier size adjusts to a
change in climate in such a way as to bring the balance back to zero
when iategrated over the new area.
Tkjs chain of events embraces a wide spectrum of problems in
glacier physics-from the meteorological input to the rheology of ice
flow-and it cannot be said that we are very close to a complete
understanding [2]. Hydrologically, perhaps the most significant
aspect is that when the glacier is in the process of adjusting to
climate change (this occurs continually because climate changes
quickly and glaciers slowly) , precipitation is being stored or released from storage [3]. Not everyone is aware that, during the
1920-45 period when many runoff I'base" or "normal" periods are defined, glaciers in most populated parts of the world were receding
and releasing streamflow greatly in excess of precipitation [4].
In this paper I will try to briefly outline what we know about
hydrologic properties and processes of glaciers, and to show how
these processes may be quite different and more complex than those
of conventional landscapes and snowpacks. In doing this we will
proceed from the mass exchange at the glacier surface and the mass
balance to the materials and temperatures within the glacier,
Glacier flow will be discussed only briefly. Gur state of knowledge
of hydraulic conditions within a glacier will be explored, and this
354
will lead to brief mention of glacier dammed lakes and glacier outburst floods. Mountain glaciers in temperate and subpolar latitudes
are emphasized because of their importance as water resources.
ACCUMULATION AND ABLATION
The accumulation of mass on most glaciers is primarily due to
snowfall, but a few glaciers are nourished primarily by avalanches,
by wind-blown snow, or by refrozen meltwater. Accumulation traditionally is measured by daily observations of the snow level on
stakes, snow boards, or the snow caught in precipitation gauges, and
snow density. The difficulties inherent in continuous wintertime
measurements over complete glacier areas and the fact that no precipitation gauge that will accurately catch blowing snow has yet been
devised have been major obstacles; in fact, very few if any true accumulation measurements have ever been accomplished. This has seriously retarded the study of glacier meteorology and hydrology.
Ablation of mountain glaciers occurs primarily by melting.
Evaporation, wind erosion, calving, and the breakoff of ice and snow
avalanches are usually minor items , except in polar regions or
certain large tidewater glaciers where calving is important, Ablation over time periods of a week or more is not too difficult to
measure using stakes emplaced in the ice or snow, probing snow thickness, measuring densities in pits or cores, and mapping changes in
the transient snow line [SI, coupled with a monitoring of precipitation.
Unfortunately, a complete understanding of the relation of heat
and ice balances at glacier (as well as snowpack) surfaces requires
data on melt at much shorter time intervals (hourly, for instance).
With the present state of knowledge this appears to be impossible
because of difficulties in continuous measurement of near-surface
profiles of bulk density and liquid water content [6]. No solution
to this problem is in,sight, at least to my knowledge.
The timing and amount of meltwater produced from mountain
glaciers is different from that derived from snowpacks on land. In
early spring, the rates of melting (for similar climatic environments) at the surface may be very similar, but glacier meltwater is
appreciably delayed in its trip through the glacier before joining a
stream or groundwate reservoir. Later in the summer, the seasonal
snowpacks disappear, except on glaciers, and glacier melt becomes
more intense. Altho gh insolation reaches a peak in June (Northern
Hemisphere), the ave age albedo (reflectivity) of the snow-covered
glacier surface is then relatively high causing a low or moderate
melt rate. In July and August, insolation is slightly reduced but
the mean albedo of the glacier surface is dropped markedly because
old dirty ice is now exposed, so that the rate of melt is actually
higher than in June [7].
A virtually unlimited volume of material is potentially available for melting and rhoff from a glacier; the amount produced
depends on the heat balance. A year of heavy snow accumulation
results in a layer of high-albedo snow persisting longer into the
summer season and curtailing melt. A dry winter or a hot sunny summer results in increased melt. Thus production of meltwater from
glaciers tends to compensate for unusually wet or dry, or hot or cold
years-a natural regulation of streamflow. Analysis of modelling of
the seasonal or yearly VariTtions in glacier melt is limited by our
present inability to accuratFly determine heat flux by eddy
'
4
1
355
convection [8], a lack of meteorological instrumentation in the high
mountains, and unknown amounts of water temporarily stored in the
glacier [9].
NET OR ANNUAL BALANCE
Ice balance is far easier to measure than true accumulation or
ablation. The difference in ice mass from beginning to end of a
certain time interval is the balance change; this value has clear,
unambiguous meaning. Accumulation or ablation, on the other hand,
cannot be defined so clearly, because both accumulation and ablation
processes may have occurred during the prescribed time interval
(occasionally, both at the same time). Thus the value of “accumulation” measured during a month, with both accumulation and ablation
occurring, depends on the time scale of observations [lo]: hourly
measurements are likely to detect brief periods of melting or evaporation whereas weekly or monthly measurements will not. This difficulty is certainly ignored all too often in the measurement of snowpacks as well as glaciers.
Two methods of measuring balance on glaciers are commonly
employed [ll] : The stratigraphic method measures the residual snow
above a time-transgressive summer horizon which is clearly identifiable in the field, together with the loss of ice and old firn
during a summer. The fixed-date or annual system measures the change
in glacier mass (snow, firn, and ice) over a hydrologic year, often
defined as October through September 30, but no aid can be derived
from the observable summer horizons or contacts in the glacier. The
change in glacier mass from beginning to end of a balance year as
determined by the stratigraphic method is called net balance; two
different kinds of net balance can be calculated. The balance change
over a hydrologic year according to the fixed-date system is called
annual balance. Both methods have important advantages and disadvantages. In order to retain the efficiency of field surveys using
summer horizons and yet produce results directly comparable with
hydrologic quantities such as runoff, it is neicessary to meld the two
systems. The new combined system of units is ertainly more complex,
but it is the only hybrid system yet devised t at includes an unambiguous and specific description of each balance term measured, and
in which each term is clearly defined in time [12].
Annual or net balances can be calculated in other ways. The
distribution of density in a glacier is usually well known, so
changes in glacier volume can be measured to derive mass balances.
This geodetic method is of greatest usefulness in determining average
balances over long periods of time [13]. Thelbalance is also a
change in storage of the ice-reservoir, and therefore can also be
determined by combining measurements of runoff, precipitation, and
evaporation-the hydrologic method [14]. However, several recent
attempts to compare balance-values measured by several independent
methods have shown great discrepancies. A major problem is evaluation of sampling error [15]. Absolute me‘ urements of ice balance
by the hydrologic method are limited by th difficulty of measuring
snowfall in the high mountains, but index echniques have been used
to extend records of glacier balance over long periods of time [16].
Net balance histories can be determined in pits or cores. Individual
years can be identified by a host of differe‘t methods including
stratigraphy [17], isotope chemistry [18], flpw dynamics [19], and
detection of atomic or hydrogen bomb products \[20].
k
1
7
356
1
I \
A most exciting recent development is the continuous yearly
record of ice balance and other climatic parameters extending back
100,000 years, obtained from a core from the Greenland Ice Sheet
[Zl]. It would appear that this would provide excellent basic data
for those who enjoy analyzing hydrologic time series by stochastic or
other non-deterministic techniques. One wonders if these data could
not be worked over more completely by hydrologists; these results
might be used to lay to rest arguments on the reality (or lack
thereof) of subtle periodicities or climatic changes [22].
Mass balance values at points on mountain glaciers vary more
with altitude than with any other parameter. Therefore it is common
practice to plot mass balance values as a function of altitude in
order to compare different glaciers or different glacier environments.
Yet the activity index (gradient of the balance/altitude curve)
depends very much on the size of the glacier and is entirely determined by local topography. Attempts to use activity index and/or
equilibrium line altitude to define climatic environments have not
been completely success€ul . Can we devise a better procedure?
SNOW, FIRN, AND ICE; WARM AND COLD GLACIERS
The winter snowfall onto a glacier surface is partly removed by
melting and runoff in the summer. The part that remains at the end
of a summer season and is buried by snow of the subsequent winter is
usually called firn. Some authors define firn on the basis of
density. Firn normally has a density of 500 kg/m3 or more. As this
new firn is subsequently buried by additional years of snow and firn
accumulation it is compacted and metamorphosed causing the density to
increase and the porosity to decrease. Liquid water may freeze in
the pore spaces, which also increases the density. At a density of
about 840-850 kg/m3 the interstices in the ice mass become sealed off
into discrete bubbles/and the material is relatively impermeable. At
that point, the material is defined as glacier ice. This brief discussion of firnification is not meant to imply that all problems are
solved; many interesting questions remain involving the sintering
processes, recrystallization, and the time/density/temperature/depth
functions in different environments [23].
The firnification process and the techiiiques used to measure
accumulation and bal&ce depend on the thermal conditions in a snowpack. The Benson-Müller classification of snow facies [24] is widely
used in Western countries: it includes a dry snow zone where the snow
and firn are always bklow freezing and negligible meltwater occurs; a
percolation zone whereI small amounts of meltwater may be generated
but which percolates only a short distance into the snowpack and refreezes there; a soaked zone where meltwater produced during the
summer percolates completely through the snowpack raising its temperature to O'C;
and a superimposed ice zone where water percolating
through the snowpack and refreezing at the base of the snowpack
builds a large deposit of superimposed ice which is later exposed by
melting of the snow. Shumskiy's classification [25] used in the
Soviet Union is somewhat similar but is semiquantitatively related to
the annual sums of liquid and solid precipitation, heat balance at
the upper surface, and temperatures at the base of the layer of
annual fluctuations. This scheme has been successfully used to determine the hydrologic regimes of various zones in the glacier environment [26]. This is a si'tuation where a synthesis of the Eastern
\
357
and Western schemes ought to contain the elements of a still better
and more useful classification scheme.
Glaciers have been classified according to internal temperature,
ie., polar, subpolar, and temperate according to Ahlmann [27] or dry
polar, moist polar, cold, marine, or continental according to Avsyuk
[28]. Recent work has suggested that the simple definition of
temperate (or marine) glacier is not sufficiently precise; the presence of even tiny amounts of solutes in the ice and in the water
causes changes in the temperature and the thermal properties of this
kind of glacier [29]. Therefore the definition of a truly temperate
glacier is best done on a basis of the effective heat capacity of the
glacier [30]. This conclusion introduces another complication to the
study of thermodynamics and rheology of glaciers, which is something
we really do not need. Glaciers may be polar in nature in their
upper regions and subpolar or temperate in their lower areas. On the
other hand, firn is permeable to meltwater and meltwater percolating
downwards is very effective in raising temperature to O°C. Therefore
some glaciers can be temperate in their upper permeable layers and
subpolar in the lower, relatively impermeable ice tongues.
MECHANISM OF GLACIER FLOW
Ice is a weak solid which can deform by gliding along slip
planes within the crystal or by recrystallization in an aggregate of
many crystals. Experiments in the laboratory and in the field show
that this rate of shearing strain of a polycrystalline aggregate is
roughly proportional to the shearing stress raised to a power of
about 3 (Glen's law) [31]. Variations in this flow law have been
suggested 1321, but the simple power law dependence is sufficient for
most analyses. The rate of strain is also very sensitive to temperature. The shearing stress at any depth within a glacier of simple
shape is roughly proportional to the weight of the material overlying
that depth times the sine of the surface slope angle. Most of the
thickness of the glacier has a density of about 0.9 so that the
increase in shear stress with depth is approxi ately linear. The
rate of deformation within the ice therefore increases at approximately the fourth power of the depth. The velo'city field can be calculated exactly for glaciers of simple shape such
l as two-dimensional
sheets or valley glaciers flowing in cylindrical channels [33].
Numerical methods have been used to calculate the velocity fields
flowing in channels of other certain shapes [34]. However, a truly
three-dimensional analysis of glacier flow in a channel of arbitrary
shape has not yet been accomplished because of the highly nonlinear
flow law. Polar glaciers, and especially polar ice sheets, have
strong temperature gradients with depth, parti ularly near the bed.
Because of the temperature dependence of the f ow law, the thermal
and flow regimes must be considered together [51.
Much less is known about how glaciers slide on their beds. Two
processes are important [36]. Ice can flow around bumps or obstacles
on the bed because stress concentrations enhance shear strain rates.
The other process is regelation: increased hressure on the upstream
side of an obstacle causes the ice there tobelt; the meltwater flows
\
around the obstacle and refreezes in the zong
of decreased pressure
in the lee of the obstacle. If the glacier flow is sufficiently
rapid a water-filled cavity may form in the Ike of the obstacle.
Several theories are extant on the sliding of 'glaciers on their beds;
these differ largely on their treatment of the 'geometry of bed
7
i
358
/
i
roughness [37], Some theories involve instabilities or multiple
sliding velocities for a given stress. Because of the difficulty of
making observations none of the theories has yet been adequately
tested in the field.
If water exists as a film between the ice and bedrock it should
have a pronounced affect on the sliding velocity. An increase in
water thickness may drown out smaller obstacles and may cause an acceleration in rate of sliding. Such an effect has been inferred by
many workers as an explanation of the observed short and mid-tern
fluctuations in the speeds of glaciers [38]. However, direct evidence is essentially lacking. Thus the hydraulic conditions in a
glacier may affect its flow dynamics.
Some glaciers have been observed after many decades of quiescence or sluggish behaviour to suddenly flow at very rapid speeds
[39]; these are called surging glaciers. Normal glacier flow ranges
from a few centimetres to a metre or so per day; surging glaciers may
attain speeds of metres per hour and ice near the termini may advance
kilometres in a few months. It is reasonably well established that
glacier surges are caused by some abrupt decoupling of a glacier from
its bed and that this decoupling is probably related to some unusual
amount or condition of water. However, the actual process is yet to
be explained [40]. Some outlet glaciers in Greenland flow at surging
speeds continually and attention has been directed to the water
emerging below them [41].
HYDRAULICS OF GLACIERS
Glaciers are usually composed of three materials: snow, firn,
and ice. The characteristics and distribution of these materials
determine the hydraulic properties of the glacier. A surface layer
of snow occurs over nearly all glaciers most of the year. The flow
of water in this snowpack must not be different in principle from the
flow of water in snowpacks situated on soil or rocks. Flow is normally unsaturated (permeability depends on water saturation) and is
partly controlled by ice layers or lenses [42]. Below the snow may
be a layer of firn, but little is known about water flow in it. One
can infer that the hydraulic characteristics of firn are different
from those of snow in that the permeability is less and semipermanent
conduits may develop because firn persists for many years.
The snow or firn mass may be at below freezing temperatures when
meltwater begins to percolate from the surface. This produces an
unstable situation. If meltwater is concentrated slightly more in
one place, the heat released when this meltwater freezes causes a
warming in this local spot. Thus a "dimple" is formed in the top of
the chilled layer and meltwater may percolate further into the cold
mass at this one point than in other locations. In this way meltwater can "drill" its way through cold layers in the snow or firn.
In temperate glaciers the cold layers are eventually dissipated and
the only traces of this unstable drilling process are peculiar vertical channels, pipes, and lenses of ice developed in the snow and firn
[43]. Unfortunately, the physics of this interesting process has not
yet been studied properly.
Much less is known about how water moves through ice. Some
water is produced at the ice/rock interface due to friction and geothermal heat and some water is produced by ice flow within the
glacier, but these are normally inconsequential compared to the water
359
moving down through the ice from the surface. Glacier ice even at
the melting temperature was long held to be impermeable because the
liquid water was thought to be concentrated in small tetrahedra at
four-grain intersections [44]. Recent theory and observations show
that this is not true and that water may move through glacier ice
along a complex three-dimensional network of tiny prisms along threegrain intersectiom, although this motion might be blocked by bubbles
in certain situations. It has been calculated that about 1 m 3 of
water per m2 of ice surface can travel through a typical glacier in
1 year [45].
It is also known that open conduits exist in glaciers. Open
water on the surface of a glacier can be seen disappearing into vertical holes called moulins. These moulins are known to extend several hundred metres into the ice [46] and may, in fact, reach the ice/
bedrock interface. Open conduits (or at least large cavities) deep
in the ice have been intersected by drills [47]. However, it is not
known how the water which percolates through firn travels through the
less permeable ice below. A water table has been observed in many
temperate glaciers but this water table shows marked changes with
time. Fluctuations of as much as 131 m have been recorded [48].
Furthermore the spatial distribution of the water table appears to be
very complex; the water table surface in the vicinity of crevasses is
especially irregular indicating that the crevasses may lead to open
conduits .
One can make additional observations to gain insight on the internal plumbing of glaciers. Tracers, such as fluorescent dye, salt,
or radioactive isotopes, can be injected at the glacier surface and
the time taken for them to move to the glacier terminus measured
[49]. These experiments seem to indicate that water flows through
moulins and open channels in the ice at rates in the order of kilometres per hour, but that water percolating through snow, firn, and
ice travels at least two orders of magnitude more slowly. Geochemical isotopic studies of the water naturally discharged at the terminus can be used to infer the source of the water and the rate at
which water moves through the glacier [SO]. Finally, one can drill
or tunnel to the ice/bedrock interface [51] and attempt a direct
examination.
Numerical calculations have been used to compare the meltwater
input with the outflow hydrograph using either a porous medium model
or other hydrologic techniques [SZ]. Another instructive calculation
is to examine the difference between meltwater inputs and outputs
from a glacier to determine the transient storage of liquid water.
These calculations generally indicate a seasonal change in the amount
of liquid water storage [53], which clearly implies a change in
hydrologic characteristics within the glacier during the season.
It would appear that water travels through a glacier in several
distinct ways. In the snow and firn part of the glacier, percolation
is relatively slow. Flow in this unsaturated porous medium must
proceed at varying rates because of continual changes in the amount
of water saturation at any level. When water has percolated through
some metres of old firn it seems likely, although it has never been
confirmed, that the porous medium type of flow gives way to flow
through many small tributary channels. These channels must join others to form larger channels so that water finally arrives at the base
of the glacier in a relatively small number of fairly large channels.
After penetration to the bed of the glacier, water must flow
along the bed toward the terminus. It may flow in conduits of
360
appreciable size [54] (RÖthlisberger channels), which are carved in
the ice at or near the icebedrock interface. Channels may be carved
in the rock below the glacier, but these are rarely seen in deglaciated channels except in certain situations [ S I . Water may also be
distributed as a thin layer (Weertman film) between the ice and rock
[56]. Whether discrete channels can capture water from a film or
vice versa is a matter that may not yet be settled. Finally water
emerges from the terminus in one or several discrete streams.
This hydraulic system must change continuously with time. Water
pressure in the ice must vary with the varying water supply and resistance to flow. Meltwater streams on the surface may pick up heat
and enter the glacier at a temperature slightly above 0°C. Viscous
dissipation of potential energy in this moving water also generates
heat. The heat may go into enlarging channels permitting water to
flow through more rapidly. However, one set of temperature measurements indicates that viscous dissipation due to loss of potential
energy in the water served only to raise the temperature of the water
and little of this heat was applied to melting ice [57].
Glacier flow also has an effect on the hydraulics. As the ice
deforms, the channels are deformed. This may cause temporary blockage or release of water. Because water is more dense than ice, the
pressure in a water-filled hole may be higher than the pressure in
the ice around it. This can cause plastic deformation of the ice
which serves to enlarge the channel [58]. Thus the hydraulic conduits may enlarge slowly as the water input increases, a fact which
can explain calculations of the water balance within glaciers. The
rate of ice deformation in response to differences in pressure between ice and water also depends on the stress imposed by glacier
flow. Because of the density differences water-filled cavities can
also migrate downward through a glacier [59].
The complex interactions between the plastic deformation of ice,
glacier flow, the amount of water at the bed and the sliding of the
bed, and the movement of water through a glacier are as yet dimly
understood. Much thinking has been done on the physics of water
movement at the bed of a glacier; we need more observational data.
Few studies have been made of water flow within the mass of a
glacier; here we need more theory and E observational data.
GLACIER DAMMED LAKES AND OUTBURST FLOODS
Careful examination of the hydrographs of many glacier-fed
rivers will disclose some unusual flood events that do not appear to
be related to rainstorms or periods of intense melt [60]. These
floods may be so small that they are barely discernible on a good
streamflow record or they may be so large as to cause major disasters. Perhaps the largest known of these glacier outburst floods,
or jökulhlaups, is the 1922 outburst from GrimsvÖton, Iceland, which
reached a peak discharge of about 49,000 m3/s [61]. These outbursts
may pick up large amounts of unconsolidated rock or soil producing
devastating debris flows [62].
A glacier may dam a subglacial basin, an embayment, or a valley
causing a lake to form; this may occur in many ways and in many environments. The water from such a lake may then discharge abruptly
over, under, or through the glacier and emerge as a flood. The outburst of a glacier dammed lake is often a yearly event or it may
occur more or less frequently or be completely unpredictable [63].
361
Extremely large glacier dammed lake outbursts may occur suddenly with
attendant loss of life and property.
Whether a visible lake is present or not, the mechanisms of outburst are probably similar. Several mechanisms are possible, including drainage through small pre-existing channels at the ice/bedrock
interface or through the glacier, raising of the ice dam by floating,
plastic yielding of the ice due to higher pressure in the water,
crack progression due to combined stresses of glacier flow and highwater pressure, overflowing of the ice dam usually near a glacier
margin, subglacial melting by volcanic heat, or weakening of the ice
dam by earthquakes [64].
Probably the most common mechanism leading to jökulhlaups or
outbursts from glacier dammed lakes begins with a tiny trickle of
water forcing its way under or through the glacier. The ensuing flow
in this small channel causes an enlargement by melting of the ice
wall of the channel due to heat produced by viscous dissipation in
the moving water, or stored in the water before it entered the ice
tunnel. This enlargement proceeds at a rate that depends on water
flow and temperature. Thus the channel area is increased at an ever
more rapid rate until no water is left. This explains a typical
hydrograph at a glacier terminus of an outburst flood-a slow
increase in the beginning, building exponentially to a very fast
increase in the rate of flow until a maximam is reached, and then a
decrease very rapidly back to zero or the normal condition [65].
However, dye experiments suggest that some lakes may have a continuing leakage [66]. Much more observational and theoretical work needs
to be done on this interesting, and very practical problem. Even
more important, existing or potential outburst situations must be
recognized and appropriate measures taken to minimize the danger to
life and property.
CONCLUSION
The study of the hydrologic processes and properties of glaciers
is a fascinating subject. This is a truly interdisciplinary topic,
involving the meteorology of accumulation and melt, the rheology of
ice flow, the hydraulics and thermodynamics of the movement of a liquid phase through the solid phase. The results of these studies can
apply directly to practical needs such as use of glacier variations
to construct climatic histories, forecasting of glacier-derived
streamflow for hydroelectric or irrigation purposes, prediction and
avoidance of catastrophe due to glacier outburst floods. At present
we know how to measure mass balance at the surface of the glacier but
OUT ability to measure heat balance is limited. We know in principle
how glaciers deform, flow, and adjust to changes in mass balance, but
we can only hypothesize on exactly how the glacier is coupled to its
bed. The flow of water through homogeneous snow is reasonably well
understood, but we are almost completely ignorant of the mode of flow
of water deep in a glacier. The obvious conclusion is that we need
this symposium, and the new research ideas it will undoubtedly spawn.
REFERENCES
[l]
362
MEIER, M.F. (1965). Glaciers and climate. In the Quaternary of
the United States, H.E. WRIGHT, Jr. and D.G. FREY (Ed),
Princeton Univ. Press, pp. 795-805.
PATERSON, W.S.B. (1969).
Press, New York, 250 pp.
The physics of glaciers. Pergamon
HOINKES, H.C. (1964). Glacial meteorology. 5 Research in
Geophysics, 2, H. ODISHAW (Ed), M.I.T. Press, pp. 391-424.
~ 3 1 KASSER, P. (1959). Der Einfluss von GletscherrÜckgang und
Gletschervorstoss auf den Wasserhaushalt. (The influence of
glacier recession and glacier advance on the water budget.)
Wasser- und Energiewirtschaft, 6, pp. 1-16.
~41 MEIER, M.F. (1969). Glaciers and water supply. J. Amer. Water
Works Assoc., 61, pp. 8-12.
[51 @STEM, G., and STANLEY, A. (1966). Glacier mass balance
measurements, a manual for field work. Can. Dept. Mines and
Tech. Surveys, 81 pp.
UNESCO/IASH (1970). Perennial ice and snow masses. Tech.
Papers in Hyd,, 1, 59 pp.
UNESCO/IASH (1970). Combined heat, ice and water balances at
selected glacier basins. Tech. Papers in Hyd., 5, 20 pp.
r61 HUBLEY, R. C. (1954). The problem of short term measurements of
snow ablation. J. Glaciol. , 2, pp. 437-440.
LaCHAPPELLE, E. (1959). Errors in ablation measurements from
settlement and subsurface melting. J. Glaciol., 3, pp. 458-467.
MüLLER, F., and KEELER, C.M. (1969). Errors in short-term
ablation measurements on melting ice surfaces. J. Glaciol., 8,
pp. 91-105.
[71 DIRMHIRN, I., and TROJER, E. (1955). Albedountersuchungen auf
dem Hintereisferner. (Albedo investigations on
Hintereisferner.) Archiv. f. Meteor., Geophysik. u. Bioklimat.,
B, 6, pp. 400-416.
HOINKES, H., and RUDOLF, R. (1960). Abfluss und Ablation am
Rotmoosferner. (Runoff and ablation on Rotmoosferner.) Aug.
28 to Sept. 6, 1955: Wetter u. Leben, 12, 14 pp.
SAUBERER, F. , and DIRMHIRN, I. (1952). Der Strahlungshaushalt
horizontaler Gletscherflächen auf dem Hohen Sonnblick. (The
radiation balance of horizontal glacier surfaces in the Hohen
Sonnblick.) Geog. Ann., 34, pp. 261-290.
HOINKES, H. (1964). Glacial meteorology. In Research in
Geophysics, 2, FI. ODISHAW (Ed) , M.I.T. Press, pp. 391-424.
HOINKES, H. (1970). Methoden und Moglichkeiten von
Massenhaushaltstudien auf Gletschern. (Methods and possibilities for mass balance studies of glaciers.) Z. Gletscherkunde
u. Glazialgeol., 6, pp. 37-90.
STENBORG, T. (1970). Delay of runoff from a glacier basin.
Geog. Ann., 52A, pp. 1-30.
TANGBORN, W.V., KRIMMEL, R.M., and MEIER, M.F. (in press). A
comparison of glacier mass balance by glaciologic, hydrologic,
and mapping methods, South Cascade Glacier, Washington. Moscow
Gen. Assembly 1971. IAHS Publ.
363
MacDOWALL, J. (1960). Some observations at Halley Bay in seismology, glaciology and meteorology. Proc. Roy. Soc., 256A,
pp. 194-197.
ur\rESCO/IASH (1970). Combined heat, ice and water balances at
selected glacier basins. Tech. Papers in Hyd. , 5, 20 pp.
ANONYMOUS (1969).
pp. 3-7.
Mass balance terms. J. Glaciol., 8,
r121 MAYO, L.R., MEIER, M.F., and TANGBORN, W.V. (1972). A system
to combine stratigraphic and annual mass balance systems. J.
Glaciol. (in press).
r 131
FINSTERWALDER, R. (1953) . Die Zahlenmässige Erfassung des
Gletscherrückgangs an Ostalpengletschern. (The numerical
determination of glacier recession of East Alpine glaciers .)
Z. Gletscherkunde u. Glazialgeol., 2, pp. 189-239.
KASSER, P. (1954). Sur le Bilan Hydrologique des Bassins
Glaciaires avec Application au Grand Glacier d'Aletsch. (On the
hydrologic balance of glacier basins with application to the
Aletsch Glacier.) Rome Symposium. IAHS Publ. 39, pp. 331-350.
ANONYMOUS (1967). Hydrology of the Lewis Glacier, north-centra1 Baffin Island, N.W.T., and discussion of reliability of
the measurements. Geog. Bull., 9, pp. 232-261.
M G B O R N , W.V., KRIMMEL, R.M., and MEIER, M.F. (in press). A
comparison of glacier mass balance by glaciologic, hydrologic,
and mapping methods, South Cascade Glacier, Washington. Moscow
Gen. Assembly 1971. IAHS Publ.
TROITSKIY, L.S. , and 6 others (1966). Oledeneniye Urala.
(Glacierization of the Urals.) FNGG. IX Razdel Programmy MGG,
16, 308 pp.
TANGBORN, W.V. (1968). Mass balances of some North Cascade
Glaciers as determined by hydrologic parameters, 1920-65.
Bern Gen. Assembly 1967. IAHS Publ. 79, pp. 267-274.
TANGBORN, W.V. (1966). Glacier mass budget measurements by
hydrologic means. Water Resources Res., 2, pp. 105-110.
HOINKES, H. (1957). Zur Bestimmung der Jahresgrenzen in
mehrjährigen Schneeansammlunger. (Determination of annual
layers in snow accumulations of several years.) Archiv.
Meteor. , Geophys. u. Bioklimat., B, 8, pp. 56-60.
KOTLYAKOV, V.M. (1961). Snezhnyi pokrov Antarktidy i ego rol'
v sovremennom oledenenii materika. (The snow cover of the
Antarctic and its role in the present-day glaciation of the
continent.) Glaciol. Researches, Sec. IX, 7, IGY Glaciol.
Program, Izdatel'stvo &ad. Nauk USSR, Moscow. Trans. 1966,
256 pp.
AMBACH, W., and EISNER, H. (1970). Grundlagen und Ergebnisse
von Kernphysikalischen Untersuchungen auf Alpengletschern.
(Fundamentals and conclusions of nuclear-physics investigations
on alpine glaciers.) 2. Gletscherkunde u. Glazialgeol., 6,
pp. 91-105.
364
Oxygen-isotope variations
EPSTEIN, S., and SHARP, R.P. (1959).
in the Malaspina and Saskatchewan Glaciers. J. Geol., 67,
pp. 88-102.
LORIUS, C., et al (1969). Dating of firn layers in Antarctica:
application to the determination of the rate of snow accumulation. ISAGE Symposium, Hanover 1968, IAHS Publ. 86, pp. 3-15.
MELLOR, M. (1968). The Greenland mass balance flux divergence
considerations. Gen. Assembly Bern 1967. IAHS Publ. 79,
pp. 275-281.
DANSGAARD, W., and JOHNSEN, S.J. (1969). A flow model and a
time scale for the ice core from Camp Century, Greenland. J.
Glaciol., 8, pp. 215-223.
PICCIOTTO, E., and WILGAIN, S. (1963). Fission products in
Antarctic snow - A reference level for measuring accumulation.
J. Geophys. Res., 68, pp. 5965-5972.
DANSGAARD, W., JOHNSEN, S.J,, MOLLER, J., and LANGWAY, C. C.
(1969). One thousand centuries of climatic record from Camp
Century on the Greenland Ice Sheet. Science, 166, pp. 377-381.
LANGWAY, C.C. (1970). Stratigraphic analysis of a deep ice
core from Greenland. Geol. Soc. Amer. Spec. Paper 125, 186 pp.
[221 YEVJEVICH, V. (1968). Misconceptions in hydrology and their
consequences. Water Resources Res., 4, pp. 225-232.
r231
SHUMSKIY, P.A. (1955). Osnovy strukturnogo ledovedeniia.
(Principles of structural glaciology.) Izdatel'stvo Akad.
Nauk USSR, Moscow. Trans. by D. KRAUS, Dover, New York,
497 pp. (1964).
BENSON, C.S. (1961). Stratigraphic studies in the snow and
firn of the Greenland Ice Sheet. Geog. Danica, 9, pp. 13-37.
MüLLER, F. (1962). Zonation in the accumulation area of Axel
Heiberg Island, N.W.T., Canada. J. Glaciol., 4, pp. 302-310.
SHUMSKIY, P.A. (1955). Osnovy strukturnogo ledovedeniia.
(Principles of structural glaciology.) Izdatel'stvo &ad. Nauk
USSR, Moscow. Trans. by D. KRAUS, Dover, New York, 497 pp.
(1964).
GOLUBEV, G.M. (in press). On water regime of the glaciological
zones. Gen. Assembly Moscow 1971. IAHS Publ.
AHLMA", H.W. (1935). Contribution to the physics of glaciers.
Geog. J., 86, pp. 97-113.
AVSYUK, G.A. (1955). Classification of glaciers by temperature
regime. Isvestiya Akad. Nauk USSR, Seriya Geograficheskaya,
pp. 14-31. English abs. J. Glaciol., 3, p. 7 (1957).
r291
RENAUD, A. (1958). Sur la présence et le rôle des impuretés
dans les glaciers. Chamonix Symposium. IAHS Publ. 47,
pp. 241-243.
LLIBOUTRY, L. (1971). Permeability, brine content and temperature of temperate ice. J. Glaciol., 10, pp. 15-29.
SHREVE, R.L., and SHARP, R.P. (1970).
Internal deformation and
thermal anomalies in lower Blue Glacier, Mount Olympus,
Washington, U.S.A.. J. Glaciol., 9, pp. 65-86.
365
[301
HARRISON, W.D. (1972).
Glaciol. (in press).
Temperature of a temperate glacier. J.
c311
GLEN, J.W. (1955). The creep of polycrystalline ice. Proc.
ROY. SOC, 228A, pp. 519-538.
c321
MEIER, M.F. (1960). Mode of flow of Saskatchewan Glacier,
Alberta, Canada. U.S. Geol. Surv. Prof. Paper 351, 70 pp.
LLIBOUTRY, L. (1969). The dynamics of temperate glaciers from
the detailed viewpoint. J. Glaciol., 8, pp. 185-205.
NYE, J.F. (1952).
2, pp. 82-93.
The mechanics of glacier flow.
J. Glaciol.,
NYE, J.F. (1965). The flow of a glacier in a channel of rectangular, elliptic or parabolic cross-section. J. Glaciol., 5,
pp. 661-690.
ROBIN, G. de Q. (1955). Ice movement and temperature distribution in glaciers and ice sheets. J. Glaciol., 2, pp. 523-532.
RADOK, U., JENSSEN, D., and BUDD, W. (1970). Steady-state
temperature profiles in ice sheets. ISAGE Symposium, Hanover
1968. IAHS Publ. 86, pp. 151-165.
PHILBERTH, K. , and FEDERER, B. (1971). On the temperature
profile and the age profile in the central part of cold ice
sheets. J. Glaciol., 10, pp. 3-14.
SHUMSKIY, P.A., KRENKE, A.N., and ZOTIKOV, I.A. (1964). Ice
and its changes. In Research in Geophysics, 2, H. ODISHAW (Ed),
M.I.T. Press, pp. 425-460.
WEERTMAN, J. (1957).
3, pp. 33-38.
On the sliding of glaciers.
J. Glaciol.,
WEERTMAN, J. (1964). The theory of glacier sliding. J.
Glaciol., 5, pp. 287-303.
LLIBOUTRY, L. (1968). General theory of subglacial cavitation
and sliding of temperate glaciers. J. Glaciol., 7, pp. 21-58.
NYE, J.F. (1970). Glacier sliding without cavitation in a
linear viscous approximation. Proc. Roy. Soc. Lond., 315A,
pp. 381-403.
KAMB, B. (1970).
Sliding motion of glaciers: theory and
observation. Revs. Geophys. and Space Phys., 8, pp. 673-728.
1381
MEIER, M.F. (1960). Mode of flow of Saskatchewan Glacier,
Alberta, Canada. U.S. Geol. Surv. Prof, Paper 351, 70 pp.
ELLISTON, G.R. (1963).
Discussion of J. Weertmen's paper
"Catastrophic glacier advances". Bull. IAHS, 8th Ann., 2,
pp. 65-66.
HAEFELI, R. (1970). Changes in the behaviour of the
Unteraargletscher in the last 125 years. J. Glaciol., 9,
pp. 195-212.
POST, A.S. (1960).
The exceptional advances of the Muldrow,
Black Rapids and Susitna Glaciers. J. Geophys. Res., 65,
pp. 3703-3712.
~401 MEIER, M.F. , and POST, A. (1969). What are glacier surges?
Can. J. Earth Sci., 6, pp. 807-817,
366
WEERTMAN, J. (1969). Water lubrication mechanisms of glacier
surges. Can. J. Earth Sci., 6, pp. 929-942.
COLBECK, S.C. (1971). One-dimensional water flow through snow.
U.S. Army Cold Regions Res. Eng. Lab. Res. Rept. 296, 16 pp.
SHARP, R.P. (1951). Meltwater behaviour in firn on upper Seward
Glacier-St. Elias Mountains, Canada. Brussels Gen. Assembly.
IAHS Publ. 32, pp. 246-253.
SHARP, R.P. (1951). Features of the firn on upper Seward
Glacier, St. Elias Mountains, Canada. J. Geol., 59,
pp. 599-621.
STEINEMA", S. (1958). Thermodynamics and mechanics of ice at
the melting point. Chamonix Symposium. IMIS Publ. 47,
pp. 254-264.
N E , J.F., and FRANK, F.C. (in press). The hydrology of the
intergranular veins in a temperate glacier. Cambridge
Symposium 1969. IAHS Publ. 95.
LLIBOUTRY, L. (1971). Permeability, brine content and temperature of temperate ice. J. Glaciol., 10, pp. 15-29.
VALLOT, J. (1898). Exploration des moulins de la Mer de Glace
Ann. Observ. Météorol. Mont Blanc 3, Paris.
STENBORG, T. (1968). Glacier drainage connected with ice
structures. Geog. Ann. , 50A, pp. 25-53.
PATERSON, W.S.B. , and SAVAGE, J.C. (1970). Excess pressure
observed in a water-filled cavity in Athabasca Glacier, Canada.
J. Glaciol., 9, pp. 103-107.
SHREW, R.L., and SI-IAW,R.P. (1970). Internal deformation and
thermal anomalies in lower Blue Glacier, Mount Olympus,
Washington, U.S.A. J. Glaciol., 9, pp. 65-86.
1481 MATHEWS, W.H. (1964). Water pressure under a glacier. J.
Glaciol., 5, pp. 235-240.
E49 1
STENBORG, T. (1969). Studies of the internal drainage of
glaciers. Geog. Ann., 51A, pp. 13-41.
r501
RAINWATER, F.H., and GUY, H.P. (1961). Some observations on
the hydrochemistry and sedimentation of the Chamberlin Glacier
area, Alaska. U.S. Geol. Surv. Prof. Paper 414-C, 14 pp.
[5 11 VIVIAN, R. (1970). Hydrologie et érosion sous-glaciaires.
Revue Gdog. Alpine, LVIII, pp. 241-264.
WEERTMAN, J. (1970). A method for setting a lower limit on the
water layer thickness at the bottom of an ice sheet from the
time required for upwelling of water into a borehole. ISAGE
Symposium, IIanover 1968. IAHS Publ. 86, pp. 69-73.
STENBORG, T. (1970). Delay of runoff from a glacier basin.
Geog. Ann., 52A, pp. 1-30.
DERIKX, L., and LOIJENS, H. (1971). Model of runoff from
glaciers. Symposium 8, Runoff from Snow and Ice, Quebec City,
1, pp. 153-199.
367
CAMPBELL, W.J., and RASMUSSEN, L.A. (in press). The production,
flow, and distribution of meltwater in a glacier treated as a
porous medium. Cambridge Symposium 1969. IAHS Publ. 95.
MATHEWS, W.H. (1964). Water pressure under a glacier.
Glaciol., 5, pp. 235-240.
J.
TANGBORN, W.V., KRIMMEL, R.M. , and MEIER, M.F. (in press). A
comparison of glacier mass balance by glaciologic, hydrologic,
and mapping methods, South Cascade Glacier, Washington. Moscow
Gen. Assembly 1971. IAHS Publ.
RÖTHLISBERGER, H. (in press). Water pressure in subglacial
channels. Cambridge Symposium 1969. IAI-IS Publ. 95.
EMBLETON, C., and KING, C.A.M. (1968). Glacial and periglacial
geomorphology. Edw. Arnold Ltd., London, 608 pp.
WEERTMEN, J. (1969) . Water lubrication mechanism of glacier
surges. Can. J. Earth Sci., 6, pp. 929-942.
WEERTMAN, J. (1972). General theory of water flow at the base
of a glacier or ice sheet. Revs. Geophys. and Space Phys.
(in press).
ZOTIKOV, I.A. (in press). Heat regime of subglacial waters of
mountain glaciers. Moscow Gen. Assembly 1971. IAHS Publ.
GLEN, J.W. (1954). The stability of ice-dammed lakes and other
water-filled holes in glaciers. J. Glaciol., 2, pp. 316-318.
WEERTMAN, J. (1971). Velocity at which liquid-filled cracks
move in the earth’s crust or in glaciers. J. Geophys. Res.,
75, pp. 8544-8553.
MATHEWS, W.H. (1963). Discharge of a glacial stream. Berkeley
Gen. Assembly. IAHS Publ. 63, pp. 290-300.
Some new aspects of the Grimsvötn
THORARINSSON, S. (1953).
problem. J. Glaciol., 2, pp. 267-274.
CRANDELL, D.W. (1971). Postglacial lahars from Mount Rainier
volcano, Washington. U.S. Geol. Surv. Prof. Paper 677, 75 pp.
POST A., and MAYO, L.R. (1971). Glacier dammed lakes and outburst floods in Alaska. U.S. Geol. Surv. Hyd. Inv. Atlas
HA-455, 10 pp., 3 sheets.
r641
LIESTØL, O. (1955-56). Glacier dammed lakes in Norway. Norsk
Geog. Tidsskrift, 15, pp. 122-149.
MARCUS, M.G. (1960). Periodic drainage of glacier-dammed
Tulsequah Lake, British Columbia. Geog. Rev., 50, pp. 89-106.
TRYGGVASON, E. (1960). Earthquakes, jökulhlaups and subglacial
eruptions. JØkull, 10, pp. 18-22
GLEN, J.W. (1954). The stability of ice-dammed lakes and other
water-filled holes in glaciers. J. Glaciol., 2, pp. 316-318.
THORARINSSON, S. (1939). The ice dammed lakes of Iceland with
particular reference to their values as indicators of glacier
oscillations. Geog. Ann., 21, pp. 216-242.
MAAG, H. (1969). Ice dammed lakes and marginal glacial drainage on Axel Heiberg Island. McGill Univ., Axel Heiberg Island
Res. Rept., 147 pp.
368
[65] MEIER, M.F. (1960). The outbreak of a glacier-dammed lake
labs). J. Geophys. Res., 65, p. 1315.
[66] FISHER, D. (in press).
Subglacial leakage of Summit Lake,
British Columbia, by dye determinations. Cambridge Symposium
1969. IN-IS Publ. 95.
GILBERT, R. (1971). Observations on ice-dammed Summit Lake,
British Columbia, Canada. J. Glaciol., 10, pp. 351-356.
DISCUSS ION
C.F. Bohren (U.S.A.) - I was interested by your description of
the internal plumbing in glaciers. I would like to know the effect
of the crevasse field on the water flow. Has any work been done on
relating the site and spacing of crevasses to water flow?
M.F. Meier (U.S.A.) - Crevasses extend only to a comparatively
shallow depth in a glacier. Normally they are not deeper than a few
of metres whereas glaciers are frequently tthundreds”of metres
thick. Thus, crevasses are most important in the surface zone of a
glacier. Many studies have been made in which dye tracers were introduced into crevasses and these have shown that water travelling on
the surface in the ablation area - the ice zone - does in fact funnel
into crevasses. These crevasses then act as loci of conduits which
must extend below the crevasse into the unknown depth of the plumbing
sYstem.
-
C. Benson (U.S.A.)
When crevasses occur in snow- and firn-covered parts of a glacier they introduce a channel for water to penetrate deeper into the firn than it could in the absence of the crevasses. This is because ice layers, which are parallel to the surface,
prohibit water percolation. The crevasses, by breaking the ice layers, provide vertical paths for the water to move down and spread
laterally on deeper ice layers. This appears to cause growth of ice
layers at depths of 3-5 m below the snow surface on the McCall Glacier
in Alaska. This phenomenon is being studied on the McCall Glacier
by Dr. G. Wakahama, Institute of Low Temperature Science, I-Iokkaido
University, Sapporo, Japan, in cooperation with our group from University of Alaska; however, it must occur elsewhere as well.
-
M.F. Meier (U.S.A.)
I realize that I did not mention the occurence of a water-table in a glacier. A number of measurements have
recently been made by drilling holes in glaciers and observing the
water level. In the vicinity of crevasses the water table is depressed. This also suggests that crevasses are effective in funnelling water into a conduit system.
-
F. MÜZler (Switzerland) Our group has done some investigations
on the semi-cold Wiite Glacier on Axel Heiberg Island in the Canadian Arctic. There is evidence that this glacier is not frozen to its
bed, ie., it has this much discussed layer of water at the ice-rock
interface. Miss A. Iken measured large daily and seasonal fluctuations in the water table of this glacier using pressure cells lowered into moulins down to depths of more than 200 m. Some of the
crevasses appear to be linked to moulin-type extensions that reach
down to the glacier bed.
369
In your conclusion you point out that our ability to measure
the heat balance, which is needed to relate the behavior of glaciers
and climatc, is very limited. Statements about the relationship
between the behavior of glaciers and climate have been in the literature for more than 200 years. However, as to this date we have not
yet solved the problem, Would you express your opinion on this subj ect?
M.F. Meier (U.S.A.) - Dr. Kraus gave us an excellent review of
our ability to measure a heat balance. To actually measure the heat
and momentum fluxes directly is expensive. The problem with glaciers
is that the heat halance at a point is still insufficient, even if
funds are available to measure it. One has to know the whole mesoscale heat balance of the glacier basin. Someone should cover a
whole glacier basin with a network of good micrometeorological instrumentation. Nobody has been able to do this yet and until we
learn something from projects such as these, it will be very hard to
extrapolate point inferences obtained from the middle of a glacier
to the general relation of that glacier to its whole environment.
It is a matter of converting point measurements to mesoscale measurements.
F. MUZZer (Switzerland) - Dr. Meier was very kind not only to
those glaciologists, who have limited their heat balance measurements
to a single station on the glacier, but in particular to all those
(who have written perhaps 80% of the literature on the subject) who
have used a station some kilometres - if not hundreds of kilometresaway and related it to conditions occurring on the glacier.
One interesting aspect that is not discussed in Dr. Meier's
paper is how glaciers on a large scale grow and disappear. How do
large ice sheets grow in periods of climatic deterioration, and vice
versa? More information is available about the retreat situation
than about the build-up situation. The theory that ice ages start
at the edge of the continents along the seas that provide the moisture and then gradually flow into the continental plains is questionable. Under suitable climatic conditions snow patches remain over
large areas. A feed-back system will speed up the amalgamation of
these snow patches to form a thin ice sheet of very large size.
Meso- to macro-scale modelling with numerical iteration of the energy
and mass fluxes will bring progress in this field. The much improved
network of climatological stations in the regions of snow and ice is
producing the necessary input data for these large-scale models.
M.F. Meier (U.S.A.) - I agree entirely on this. Some numerical
modelling has been done, but I should emphasize again that there are
two problems connected by the mass balance: firstly, the meteorological problem, ie., what determines these heat and mass fluxes
that produce a mass balance, and secondly, the flow dynamics problem,
ie., what is the response of the glacier to changes in mass balance?
The latter problem is fairly-well defined, except for some uncertainty with respect to sliding of the glacier on its bed. Some numerical
modelling of macro-scale accumulation and ablation process (a problem in meteorology) is still in a very poor state. Perhaps we must
wait until these huge new computers that are being developed for
modelling o f world-wide atmospheric circulation come into more general use. Then we will be able to actually feed in all necessary
meteorological parameters to grow a major ice cap.
370