SOME VIEWPOINTS ON THE INTERNAL DRAINAGE OF GLACIERS

By THORSTEN STENBORG

(Department of Physical Geography, University of Uppsala, Uppsala, Sweden)

ABSTRACT. This paper is a survey of problems of the near-surface and internal hydraulic drainage of mainly non-polar valley-glacier tongues. Reference is made to the authors earlier papers, which contain detailed investigations of some valley glaciers in northern Sweden (Stenborg, 1968, 1969). Field work is reported from Mikkaglaciâren (drainage structures a n d internal drainage) and Storglaciâren (internal drainage).

The superficial systems of oblique tensile crevasses on a glacier tongue will lead to a division of the drainage, which has, on the two glaciers studied, been found to persist even down to the frontal streams. The general possibilities and cond i t ions for this model with two quite separate internal drainage systems are discussed in relation to the glaciers studied a n d , in some respects, with reference to similar glacier tongues in general. Some possibilities of drainage penetration are also discussed from a theoretical point of view.

Firn areas are not considered in this study but some of the ideas presented may also be useful in such studies. ïn the final section, the mutual influences of run-off, movement and drainage are discussed with special reference to the influence of movement on the drainage.

RÉSUMÉ. Quelques points de vue sur le drainage interne des glaciers. Le rapport est une étude des problèmes du drainage hydrauli­que superficiel et interne principalement des langues des glaciers de vallée non-polaires. Des références sont faites aux rapports précédents de l'auteur, qui contiennent des investigations détaillées de quelques glaciers de vallée au nord de la Suède (Stenborg, 1968,1969). Le travail sur le terrain est reporté du Mikkaglaciâren (structures de drainage et drainage interne) et de Storglaciâren (drainage interne).

Le système superficiel des crevasses obliques de tension dans la langue d'un glacier amené une division du drainage qui , chez les deux glaciers étudiés, a été trouvée persister même jusqu'aux courants frontaux. Les possibilités et les condit ions générales de ce modèle de deux systèmes de drainage interne tout à fait séparés sont discutées pour les glaciers étudiés et, sous quelques rapports pour les langues de glaciers similaires en général. Quelques possibilités de la pénétration de drainage sont également discutées du point de vue théorique.

Des basins de névé ne sont pas compris dans l'étude, mais quelques des idées présentées peuvent aussi être utiles pour de telles études. Dans la partie finale, les influences mutuelles de l'écoulement, du mouvement et du drainage sont discutées, spécialement de l'influence du mouvement sur le drainage.

The internal drainage of glaciers has a wide range of significance in different scientific fields. It is not only in many ways of interest to the glaciologist but also to glacial geologists and geomorphologists, who require a knowledge of drainage for their interpretations o f glacial features or discussions of déglaciation sequences. The hydrologist is interested in the rate of internal drainage as a main characteristic of a glacier catchment area.

In spite of the great demand for knowledge of internal drainage, the subject has been very little studied in the field at recent glaciers. One reason for this may be the practical difficulties involved, as the main parts of drainage courses can be only studied indirectly. However, it is astonishing that until recently very little study has been devoted to those parts of internal drainage courses which are directly accessible, namely, the glacier mills and corresponding "intakes" at the ice surface and the streams emerging at the glacier front.

During the period 1956-68 I studied different subjects within the field of glacier hydrology at some glaciers in northern Sweden, mainly at Mikkaglaciâren in the Sarek district. T h e results of these studies have in part been published. (Stenborg, 1965, 1968, 1969), papers including t o the special investigations on glacier mills and other drainage structures, the measurements of in­ternal drainage connections by injections of brine, the addition of salt and the discussion of the winter run-off from glaciers. The present paper, including a compilation of the two papers on internal drainage in the upper ice layers and further on to the glacier front, is a general sur-veyof some drainage problems concerning non-polar valley glaciers.

(18 Thorsten Stenborg

The following discussion deals with the internal drainage of water generated at the glacier surface. This means that superficial melting should occur and tha t the ice temperatures should permit water penetration. As the field studies were under taken on the tongues of some valley glaciers, the generalization of the discussion is, with some exceptions, restricted to the corre­sponding parts of glaciers with summer ice temperatures at o r not too far below the pressure-melting point. With temporary or local exceptions in their marginal parts, the glaciers studied are at the pressure-melting point in their deeper layers. Negative ice temperatures have a re­markable influence on the superficial or internal drainage only during a short period at the beginning of the summer.

DRAINAGE STRUCTURES AND NEAR-SURFACE I N T E R N A L DRAINAGE

The basic conditions for the initiation of internal drainage at the ice surface are the exis­tence and collection of superficial run-off and possibilities for t h e water to penetrate down into the ice body and from there to be drained off further. The first condition means that the develop­ment of internal drainage courses is restricted to a small part of the year, and that the determin­ing superficial characteristics are somewhat variable also dur ing this time, as a consequence of the change of the superficial structure and micro-relief during the melting period. The second condition means that the upper parts of internal drainage courses are determined by crevasses during their development and that possibilities of immediate further drainage of the water must exist, if the crevasses are not to be filled up by standing water and drained off superficially by "spilling" water.

It should be stressed at once that water-filling of fresh cracks in the phase of mill develop­ment was not observed on Mikkaglaciàren during my studies o n drainage structures during the years 1961-66 or during my earlier field work or. the same glacier. It should also be emphasized that water-filled mills do not (with a few exceptions, explained by special circumstances) develop into draining mills (cf. Stenborg, 1968). Consequently, vents mus t exist, which can drain off further the water debouching into a crevasse during mill development. Before discussing the continuation of the drainage courses from the glacier mills, some attention should be given to influences in the superficial ice layer, since the crevasses in this layer must have a decisive in­fluence on the further distribution of the surface run-off.

Influence of crevasses

From a general, point of view, and on an observational basis, regarding the conditions on Mikkaglaciàren, the crevasses of greatest importance to internal drainage are the oblique tensile crevasses, forming one series on each lateral half of a glacier tongue. According to the theoretical determination by Nye (1952), these crevasses, at zero longitudinal, stress, form straight lines at an angle of 45° to the margin and approach the centre line of the glacier (Fig. la). The direction and form of the crevasses are modified by compressive longitudinal stress, as shown in Fig. lb . In the latter case there apparently exists a central strip, lacking crevasses, where only surface run-off occurs. On both sides of this strip, at the outer extensions of crevasses from the border­ing areas, there are zones of favourable conditions for the development of heavily draining glacier mills (Fig. Ic). I found on Mikkaglaciàren that mills in these positions survived for a longer time than most of the other mills.

The above model is modified when irregularities or deviations occur in the conditions determining the ice flow. On Mikkaglaciàren, the longitudinal shear strain-rate component has

Internal drainage of glaciers 119

its maximum, on the whole, at some dis­tance from the lateral margins (Stenborg, 1968, fig. 5). In conformity with this, the crevasses frequently do not reach down into the lateral depressions, and the few crevasses cutting these depressions thus initiate mills with large catchment areas and large drainage. A slight asymmetry also appears, as the maximum longitu­dinal shear occurs closer to the lateral margin on the western half of the glacier than on the eastern one.

//.< • \ \ / ÂS\''^

//V\\ // \ \

1

/ / ' /, / /

• ' ' /

/ /

> \

\ \ \ \ \

\ \

- % •'A

1 - '.<•

X;

>'. I Fig. 1. The influence of crevasses on surface drainage. Crevasses

at neutral (a) and compressive (b) flow according to ISlye (1952, fig. 9). In (c) the resulting main strips of drainage at slightly compressive ice flow are suggested; areas with fa­vourable conditions for development of glacier mills are stippled.

Development of glacier-mil! systems with reference to Mikkaglaciàren

The systems of glacier mills that develop in the superficial oblique crevasses are determined by water supply, ice structures and time. Along the glacier tongue, zones of crevasse formation occur with the new crevasses formed at the upper edge of each zone repeatedly in nearly the same position. Mill series are consequently also initiated especially in these positions at the upper edge of crevasse zones and with water supply from an up-glacier area of fossil structures only. The number of glacier mills developed simultaneously in one crevasse mainly depends on the intersecting structures, ice-surface topography and micro-relief (e.g. crack formation during the period of superimposed ice). On Mikkaglaciàren five to seven mills normally occur.

The mills of any crevasse are developed mainly synchronously to the mature and old stages, and finalîyfossilize. Differences between the mills,as regards their development, are caused by inter­secting structures and water-supply differences.

The fossilization of mills, as well as the closing of cracks and the fossilization of crevasses, is associated with the transport and rotation of the initiating crack due to the ice movement. By transport, the crevasse and mill system may be moved into a zone of compressive tendency; through the rotation the crevasse and the mill series will obtain less favourable strain conditions, compared with the initial direc­tion. Studies on the rate of tran­sport and rotation, and the cor-

fig. :. examples of coital quirks, MikkagUciaren, .\ugust 1966. Notice r e s p o n d i n g m i l l t y p e s , a n d d i r e c t the compass as scje which is approximate!} the same for the ctuHips r>n mi l l d p w l n n m p n f h a mset. (Se.- jso stenborg, 1968. p. 42-43.) studies on mm development, na-

120 Thorsten Stenborg

veshown that the life of mills on Mikkaglaciâren is normally 3-7 years. Extreme ages are difficult to determine without long series of direct observations but no clear proof of mills older than 10 years has been found by indirect methods.

The majority of developed mills are fossilized by blocking in their sub-surface courses, water-filling and freezing up. In this way, characteristic ice structures are formed, which I have termed "crystal quirks" (Fig. 2). The depth of freezing is at least a few metres, because ail frozen-up water-filled mills have been recognized as crystal quirks after some years of ablation ; ice shells in freezing-up water-filled mills have been measured at a depth of 15 m and water-filled mills, 30 m deep, have formed crystal quirks within 1 year. Old crevasses can be recognized by the differential melting at the ice surface or, when the crevasse has contained a mill series, by the linear appearance of point structures (crystal quirks).

Sub-surface connections

The detailed studies of glacier mills and related structures on Mikkaglaciâren h a v e shown that a mainly simultaneous development of the different mills occurs along any crevasse. As one main condition for the development of mills is the possibilities of further draining off, and as the "parent crevasse" at the initiation of the mills offers a natural drainage course, it i s also to be expected that there will be a physical interconnection between the mills along the crevasse. There is no reason to pre-suppose that such a circumstance would be changed by the superficial fossilization of the crevasse.

Indications of the actual occurrence of sub-surface courses on the planes of fossil crevasses and indications of drainage directions laterally along these courses can be found by observing different features on the glacier, such as blow holes, ejecting water, debris cones, mil l depths, occasional emptying of water-filled mills, position and form of old mills and crystal qu i rks , and by direct observation of the sub-surface courses of mills. These features have been discussed and references given by Stenborg (1968). Indications of sub-surface courses and drainage directions laterally along old crevasse planes were found on Mikkaglaciâren.

It is interesting to note in this connection that the greatest mill depth measured o n Mikka­glaciâren (39 m), which is nevertheless much larger than the maximum depths in m o s t local areas, corresponds to less than two-fifths of the ice depth at the glacier centre line 1 k m from the front and about one-fifth of the ice depth 2 km from the front (see also Fig. 6). To g e t closer to the bottom, the water has either to move laterally to strips of thinner ice or to penetrate vertically through uncrevassed ice. It should be mentioned that any mill normally reaches its maximum ice depth during the first or second year and does not deepen vertically du r ing its remaining lifetime.

Conclusions on near-surface drainage

In different ways it has thus been indicated that a mill system implies a deflection of the drainage, the main direction of which is obliquely towards the lateral margin of the glacier. For the continuation of these drainage courses, we should preferably search in lateral o r semi-lateral positions, all the more so as the comparatively greater shear rates near the marg in , com­pared with the central parts of the glacier, must yield better possibilities for the initial tectonic openings that must be assumed, if the superficial crevasses are not to be water-filled d u r i n g the first phase of mill development.

Internal drainage of glaciers 121

INTERNAL DRAINAGE OF MIKKAGLACIÂREN

Areal ablation and discharge relations

The main areas of surface and crevasse drainage on the tongue of Mikkaglaciâren are shown in Figure 3. The partition and deflection of the drainage, discussed above, do not ne­cessarily mean that the drainage issues at the glacier front through separate streams. However, where two separate main streams occur at the glacier front, as is the case at Mikkaglaciâren (Fig. 3), a necessary condition for these outlets to be regarded as the outlets of wholly separate

Fig, 3, Generalized map of the tongue of Mikkaglaciâren, comprising observations from the years 1956-58 and 1961-66. The following symbols are used: (1) crevasses, (2) surface run-off, (3) glacier mill, (4) boundary between areas of crevasse striking east and west, respectively. Part of the surface run-off of the western area terminates in the drainage structures of the eastern half. The stippled area on the inset shows the ablation area supplying the western frontal stream (W).

drainage systems is that their discharges should correspond to the amounts of surface run-off (melting) within the separate feeding areas on the glacier surface. Such a correspondence exists on Mikkaglaciâren, where the western stream discharged 20% of the run-off and the areal ablation of the western part was calculated as being about 19 ( ±2)% of the total ablation.

122 Thorsten Stenborg

Internal drainage connections

Internal drainage connections have been traced and flow times measured on Mikkagla-ciâren by injecting salt solutions. Some results, compiled in F igure 4, confirm the existence of two separate drainage systems, which on the glacier surface correspond strictly to the areas of east- and west-striking, oblique tensile crevasses (cf. Fig. 3). Furthermore, the western system was traced in a true lateral position (L in Fig. 4) at a rather high level.

Fig, 4. Observations of internai drainage on Mikkaglaciâren, I958. The following symbols are used: (!) moraine cover on ice, (2) glacier mill with connection traced (only) to the frontal stream P, (3) glacier mill with connection traced (only) to the sub-lateral stream at L and further to the frontal stream W, (4) the sub-lateral stream, L, (5) isochrone approximating the shortest drainage times from different local areas, (6) boundary between areas of internal drainage, coinciding with the boundary in Figure 3. Flow times of internal drainage to the front are given in minutes.

Large differences of flow times between different mills are recorded even within one and the same area. This reduces the possibilities of determining the most favourable positions for rapid drainage. However, a slight tendency for semi-lateral positions to be the most favourable on the eastern half of the glacier may be suggested from the recordings,

Drainage model

The existence of two separate drainage systems, through which the run-off was primarily divided by the separate systems of superficial crevasses of different strike directions, indicates a model with a superficial drainage deflection to near-lateral positions and down-glacier continua­tions of the drainage courses situated in lateral or semi-lateral positions. These continuations

Internal drainage of glaciers 123

may be wholly subglacial or partly englacial, consist of pseudo-parallel sub-courses or con-flow to main courses. On the western side of Mikkaglaciâren the existence of a lateral main stream was established (at L in Fig. 4). The asymmetry between the positions of the main streams of the two drainage systems (cf. Fig. 6) corresponds to the above-mentioned asymmetry of the longitudinal shear-strain component, whose maximum falls in a relatively more lateral position in the western half of the glacier.

Generally speaking, in the near-lateral positions, comparatively high shear-strain rates or bottom- (side-) slipping should offer relatively favourable conditions for the development of (ephemeral) cracks or vents that could be used in the initiation of new drainage courses. A p ­parently, at least, the possibilities of melt-water penetration beyond the depth of superficial cre­vasses should be larger in these lateral or semi-lateral positions (cf. Fig. 6) than within the non-laterai parts of the ice body with their lower shear strain-rates and higher hydrostatic pressures at greater ice depths (cf. Glen, 1958, p. 191).

The occurrence of one single main stream at the front of any glacier does not, of course, disprove the existence of separate drainage systems in non-central positions farther up-glacier. The location of streams inside the front at small ice depths depends largely on the bottom to­pography and may change from time to time, whether combined with ice-front regression or not. Changes between one and two main frontal streams have been observed at Mikkagla­ciâren during a recent 15 year period, and earlier changes can be observed from morphological evidence within the moraine area in front of the glacier (Stenborg, 1969, p. 23-26).

INTERNAL DRAINAGE OF STORGLACIÀREN

Conditions in 1960

The field investigations of internal drainage were continued by an investigation on Stor-glaciâren. Some results from the main investigation in 1960 are shown in Figure 5. Apparently, the glacier conforms to a "two-system model" of internal drainage as far as the boundary be-

Fig. 5* Superficial and internal drainage of Storglaciâren, i960. The following symbols are used: (1) crevasse, (2) surface streamlet or direction of surface drainage. (3) the northern area of surface run-off, (4) glacier mills (with and without Injection) having drainage connections to the frontal stream S, (5) glacier mill with drainage connection to the stream Ar, (6) glacier mills with indirect drainage connections to the stream S (no response in any of the frontal streams by injection). Flow times given in minutes. L (1968) shows the position of the lateral stream in 1968.

124 Thorsten Stenborg

tween areas of different internal-drainage behaviour coincide with the boundary between the main areas of oblique crevasses of different strike directions.

The lower part of the tongue, below the upper edge of the northern area of surface run­off (Fig. 5), was dominated by superficial drainage but also showed a division of its internal drainage into the two main streams. Higher up the tongue showed the corresponding division in a special sense. In accordance with the two-system model, the southern half of the tongue was drained internally to the southern main stream. The corresponding part of the northern pa r t of the tongue had no direct drainage to any of the frontal streams.

As the areal ablation within the northern surface run-off area (Fig. 5) was relatively a lmost as large as the discharge fraction through the joint northern stream (18-20% versus 2 0 % ) , it can be stated that the northern half of the tongue above a "critical locality" (corresponding to the upper edge of the surface run-off area just mentioned) was drained internally (possibly sub-gJacially) to the southern main stream. This draining was indirect, i.e. with considerable flow times, which made it impossible to record the drainage connection by the salt-injection method .

Thus, as a deviation from a simple two-system model of internal drainage, the upper par t of one of the drainage systems (the northern) seemed to have been obstructed at the above-mentioned "critical locality", which, as regards ice-surface topography, structural features (cf. the crevasse area in Figure 5) and ice-velocity conditions, can be assumed to correspond to a topographical bottom anomaly.

Conditions in 1968

On a later occasion, in 1968, a re-arrangement of the drainage from the pertinent area was found. The water was dammed at the anomalous locality and was drained by overflow th rough a high-lying lateral stream (Fig. 5), which farther down joined the northernmost frontal s t ream. At extreme low water during a period of cold weather, this lateral stream contributed half of the water discharged from the glacier. During a previous, short high-water period, the nor thernmost stream at the front (comprising the drainage of the lateral stream plus most of the drainage from the northern surface run-off area on the lower tongue) contributed about half of the total discharge. The relatively increasing proportion that was drained laterally at recession discharges can be explained by the gradual emptying of the dammed water.

During the observation week beginning at the middle of the short high-water per iod, the ablation within the northern and southern halves of the entire glacier corresponded in absolute amounts to the discharge through the northernmost fontal stream and to the sum of the dis­charge through the more southerly frontal streams, respectively (Stenborg, 1969, p. 32-34). The division of the drainage into two separate systems thus seems to have comprised (though p r o b ­ably not wholly) also the firn areas—and in the northern half the water drained from the firn area must also have passed through the lateral stream. As the period of comparison was shor t , this statement must be regarded as a preliminary one. However, the relative areal ablation of the northern half of the glacier above 1 425 m, — according to Schytt (1966, fig. 5), the height of the equilibrium line in a balanced year is just below 1 450 m, — was 20% of the ab la t ion of the whole — glacier, so wide margins of error must be exceeded, if my statement is to be questi­oned. Thus, it seems most probable that at least a large fraction of the melt water from the firn area is included in the divided drainage.

Conclusions

To sum up, as regards Storglaciâren, despite the fact that the frontal streams had markedly changed their mutual discharges as between the 2 years of investigation, the drainage model

Internal drainage of glaciers 125

was essentially the same, with the exception that the water from the northern half of the glacier above an anomalous topographical locality was drained indirectly to the southern main stream in one year and via a dammed water volume directly to the northern main stream in the other year of observation.

A basic two-drainage-system model seems to apply to both Mikkaglaciâren and Storgla-ciâren. It seems reasonable to assume that other glaciers with similar topographical, structural and thermal characteristics may also be represented by such an internal-drainage model. Applications to glaciomorphological problems may be fruitful (cf. examples in Stenborg 1969).

PHYSICAL POSSIBILITIES OF FORMATION OF INTERNAL

DRAINAGE COURSES

The drainage courses at Mikkaglaciâren and Storglaciâren have partly been surveyed in principle by investigations of glacier mills and related drainage structures, and studies of in­ternal drainage connections. The depth relationship between the deepest glacier mills and the ice in different parts of the tongue (Fig. 6) illustrates the geometrical conditions governing the possibilities of drainage penetration. The physical possibilities of drainage penetration below the depth of ordinary superficial crevasses will now be discussed.

A simple fact that is often overlooked must first be stressed. Explanations of the widening of existing drainage tubes which refer to flowing water are not applicable to the initial develop­ment of the tubes. The topog­raphical positions of the drain­age courses are determined pri­marily by their original estab­lishment.

For the initiation of inter­na] drainage courses, two pos­sibilities can be discussed. (1) Development of drainage cour­ses in connection with pre-ex­isting vents of glacier-tectonic origin or in connection with vents of that kind arising con­temporaneously or subsequent­ly. As already discussed, these vents are especially to be expec­ted in lateral positions, in view of the relatively high shear strain-rates, the thinner ice and the water supply through obli­que superficial crevasses. (2) Development of drainage cour­ses due to standing water.

The development of "a deep hole filled with water" by a pressure-melting mechanism,

Fig. 6. Cross-sections of Mikkaglaciâren and of the valley floor at the front. Sur­face topography measured; substratum topography approximated accor­ding to measured depths along the centre line of the glacier. The posi­tions of the frontal streams, W and P, and lateral stream, L, are also shown. The stippled zones of each section reach the depths of 20 and 40 m below the ice surface. 20 m is a frequent value of measured mil! depths, and this also corresponds to normal crevasse depths (observations and references can be found, for example, in Holdsworth 1969). 40 m is 1 m greater than the maximum miil depth ever observed on the glacier

126 Thorsten Stenborg

due to the pressure difference between ice and water, was once proposed by Werenskiold (1943). With regard to conservation of energy, this can be shown to be wholly unrealistic. The heat transfer necessary for the development of the hole, even at an infinitesimal rate, is greater than can be supplied by the extremely small gradients possibly existing betv/een ice and water or downwards in the hole itself. Besides, if convection took place in the water, the hole would probably develop at a comparatively higher rate in its uppermost part. The theoretical rejection of Werenskiold's hypothesis agrees with the facts on Mikkaglaciâren, where no deepening—or widening, except temporarily and locally—of water-filled mills was observed.

The mechanism of the ice-flow development of water-filled holes proposed by Glen (1954) is based on the postulate that the pressure difference between the water and the ice, from a certain depth and downwards, will bring about flowage of ice. In the application of this principle it is necessary to bear in mind some basic assumptions and this has often not been done by glacial geologists or geomorphologists who have made use of Glen's theory. Three main conditions may be observed: (1) the time necessary for the process, (2) the level difference between the ice and water surfaces and (3) the previous conditions that must have existed for the water to pene­trate down to the critical depth required to start the mechanism.

These conditions which restict the applicability of Glen's theory have been discussed in more detail by Stenborg (1969, p. 37). Here, two problems will be discussed:

(i) Glen stated a critical depth of about 150 m, pre-supposing that the ice and water sur­faces coincide in level. The critical depth increases rapidly with the lowering of the water surface and a relatively lower water surface is in fact the normal condition. Except in depressions, e.g. laterally, the water may be drained off by superficial crevasses. During most of the year the water supply is absent and the water surface cannot be restored to its maximum level during the possi­ble deepening of a water-filled hole.

(ii) For the release of the mechanism, the water-filled hole should reach a critical minimum depth, which varies with local and time-dependent conditions. With the exception of bore holes and ice-dammed lakes, this would pre-suppose the water-filling of "tectonic" vents existing down to the required depth or developing down to this depth due to the water pressure. There is little probability that the maximum depths of such openings would coincide with the tempo­rary and locally critical depth in the Glen mechanism. If the tectonic vents are shallower, the Glen mechanism will not operate, and if they are deeper, the Glen mechanism, as a contributary factor, will produce courses dictated by the tectonic openings and weaknesses, and the ice anisotropy. In both cases near-lateral positions of the developed drainage courses in glacier tongues seem probable.

Ice-dammed lakes

As regards ice-dammed lakes, the conditions are to some extent different. The very existence of a lake means that the normal tectonics do not allow draining. This fact may be ascribed to the topographical position of the lake and the special conditions of ice movement and differential stresses associated with this environnant. For the emptying of an ice-dammed lake—when not initiated supraglacially—there remain three possibilities, namely, initiation by "accidental crevassing", initiation due to buoyancy (Thorarinsson, 1939) or initiation by ice flow due to pressure difference (Glen, 1954). In this connection, only the Glen mechanism will be discussed, as its implications help to elucidate the conditions of normal glacier drainage, which is the subject primarily discussed in this paper.

In his paper, Glen (1954, p. 317) said that "the water will tend to spread equally in all directions along the bed". He also expressed the view that the emptying will take place under the ice "in the downhill direction", as enlargement in that direction yields "increased pressure

Internal drainage of glaciers 127

there relative to the other points". The conditions may be further elucidated by the following discussion.

The greatest pressure difference in a hole that is deeper than the critical depth is at its bot­tom. However, under purely hydrostatic conditions and with isotropic ice, the ice flow would at any moment occur in an arbitrary direction from the deepest part of the hole. In reality, the direction will thus be determined primarily by tectonic weaknesses and ice anisotropy and be local differences in ice pressure. It seems more probable that the extension of the hole will taky place more or less horizontally along the glacier bed than perpendicularly to the contours of the substratum. Besides the possible existence of tectonic weaknesses down-glacier in lateral positions and longitudinal ice anisotropy, the normal ice sur­face topography facilitates a down-glacier direction of lateral emptying (Fig. 7). By extension of the hole along the bottom transverse to the glacier direction, the critical depth for the Glen mechanism would gradually increase, as a glacier dam­ming a lake has a convex transverse surface profile; by extension down-glacier along the lateral bottom surface, the critical depth, regulated by the constant water level of the dammed lake, would instead diminish with the decreasing ice-surface level.

DRAINAGE OF FIRN AREAS

The present paper is not concerned with the conditions in true firn areas. However, some ideas from the present study may also be useful for the study of such areas. Direct tracing with radioactive substances may be possible, giving travel times and—if more than one frontal stream exists—giving indications of drainage-area separation. Many studies on the isotopic composition of firn on glaciers have been made during the last few years (e.g. Epstein and Sharp, 1959; Dansgaard, 1961; Ambach and others, 1968[a]). Ambach and others (1968[b], p . 134) have pointed out that the differences in tritium content in different parts of a glacier could be made the basis of a study of summer melt water in winter run-off. If such a study could be per­formed—preferably on different occasions during the whole recession period—at a glacier having two separate drainage systems in its tongue, this might give an indication of the corre­spondence between the drainage system of the firn area and that of the tongue.

Though the present study is not concerned with the conditions in true firn areas, it never­theless represents the main drainage of the two investigated glaciers, as the larger part of the melt water passes via the drainage systems studied. As regards Mikkaglaciâren, the above-mentioned determinations of areal ablation indicate that at least 60% of the melt water is concerned; as regards Storglaciaren, the corresponding percentage is even higher (cf. p. 124). In fact, the determination of the areal ablation and discharge relations of glaciers with two frontal streams and approximately equal areal ablation on the two halves of the glacier will form the basis for a survey of drainage areas also in the firn area.

Fig. 7. The local critical depth in the Glen mechanism along a transverse section (T) and a near-lateral section (L) from an ice-dammed lake at a hypothetical glacier. The dotted lines represent the local critical level in the Glen mechanism corresponding to a critical depth of 150 m when the water and ice surfaces coincide in level. (Buoyancy as a cause of emptying has not been discussed in this paper; for similar reasons, development due to buoyancy would also cause drainage in sub-lateral positions.)

128 Thorsten Stenborg

RUN-OFF, MOVEMENT AND DRAINAGE

A major lag between melting and discharge in early summer and an increased range of summer discharge, compared with non-glacierized areas, are some of the main characteristics of non-polar glacier run-off. The glacier characteristics primarily responsible for these condi­tions are: (1) the impermeable glacier surface, accentuated in early summer by snow and superimposed ice blocking most internal drainage intakes, and (2) the glacier movement and settling in deep firn, causing the destruction of drainage connections on both the macro- and the micro-scale.

In different investigations—e.g. Liitschg-Loetscher (1944) at Obérer Grindelwaldglet-scher; Elliston ([U.G.G.I.], 1963 p. 65-66) at Gornergletscher; Paterson (1964) at Athabasca Glacier; Oelsner (1967) in Spitsbergen — a correlation has been established between ice velocity and melting (air temperature) both for short periods and for the main seasons. The lag found be­tween glacier velocity and run-off is of especial interest. The most rapid ice velocity was found during late spring and early summer, followed by a velocity decrease in July and August. These and similar investigations have been concentrated on the effect of melting (or delayed run-off) on glacier movement by water supply to the inner and bottom parts of the glacier. The observa­tions are naturally of the greatest importance in connection with the glacier-sliding theories that have been developed during the last decade (e.g. Weertman, 1957, 1964; Lliboutry, 1959, 1968).

However, it should be noted that there is also a reverse effect—the influence of movement on the drainage conditions of the glacier and thereby on the run-off. As a consequence of the increased velocity during the first part of the summer, crevasse formation becomes more fre­quent. In connection with the opening of most of the earlier drainage connections by the gradual clearing from the ice surface of snow and superimposed ice, the increased crevassing subse­quently leads to the draining of stored and faster draining of delayed melt water and to an in­creased rate of recession of ordinary melt water run-off. With or without an increased rate of melting and rain, this explains the run-off maximum occurring after the period of greatest ice velocity.

In fact, the increase of drainage rates and the better possibilities of draining the water volumes, temporarily stored in the ice, that will follow the developing internal drainage connec­tions, may in their turn be the main reason for the decrease of ice velocity during the later part of the summer, which was observed in some of the investigations referred to above. This velocity decrease is otherwise difficult to explain, as it has already started during periods of the summer which have the highest rate of melting.

Thus a general model may be sketched, involving the mutual influences of superficial and internal drainage, glacier movement and run-off. The beginning of the summer will be cha­racterized by some melting, small amounts of run-off, a high ice velocity influenced by the in­creasing storage of water in and under the glacier. Then the internal drainage will develop under the influence of the frequent crevassing and wastage of the snow and superimposed ice that have blocked the old drainage courses superficially (cf. Stenborg, 1968, p. 27). Run-off will often reach its summer maximum at this time. From the further development of drainage courses, higher rates of run-off recession will follow, the temporarily stored water will be gradually drained and the ice velocity will thereby decrease during the rest of the summer.

Internal drainage of glaciers 129

ACKNOWLEDGEMENTS

Prof Â. Sundborg of Uppsala and Prof. V. Schytt of Stockholm made valuable comments on the manuscript. Prof Schytt also kindly provided the ablation data from Storglaciaren and discharge data from the high-water period in 1968. The maps and diagrams were drawn by Miss K. Andersson and Mr N. Tomkinson checked the English text.

Permission to reproduce and distribute the maps (Figs.3-5) was given by the Geographical Survey Office of Sweden on 2 March 1966 and 7 January 1969.

REFERENCES

AMBACH, W. and others. 1968 [a]. The altitude effect on the isotopic composition of precipitation and glacier ice in the Alps by W. Ambach, W. Dansgaard, H. Eisner and J. Moller. Tellus, Vol. 20, No. 4, p. 595-600.

AMBACH, W., and others. 1968 [b]. Tritium content in the firn layers of an alpine glacier, (by) W. Ambach, H. Eisner and L, L. Thatcher. Union de Géodésie et Géophysique Internationale. Association Internationale d'Hydrologie Scientifique. Assemblée générale de Berne, 25 sept.-7 oct. 1967. [Commission de Neiges et Glaces.] Rapports et discussions, p. 126-34.

DANSGAARD, W. 1961. The isotopic composition of natural waters with special reference to the Greenland ice cap. Meddeleher om Grantancl, Bd. 165, Nr. 2, p . 7-120.

EPSTEIN, S.,and SHARP, R. P. 1959. Oxygen-isotope variations in the Malaspina and Saskatchewan Glaciers. Journal of Geology, Vol. 67, No. l , p . 88-102.

GLEN, 3. W. 1954. The stability of ice-dammed lakes and other water-filled holes in glaciers. Journal of Glaciology, Vol. 2, No. 15, p. 316-18.

GLEN, J. W. 1958, Measurement of the slip of a glacier past its side wall. Journal of Glaciology, Vol. 3, No. 23, p. 188-93. HOLDSWORTH, G. 1969. Primary transverse crevasses. Journal of Glaciology, Vol. 8, No. 52, p . 107-29. LLIBOUTRY, L. 1959. Une théorie du frottement du glacier sur son lit. Annales de Géophysique, Tom. 15, No. 2, p. 250-65. LLIBOUTRY, L. 1968. General theorv of subglacial cavitation and sliding of temperate glaciers. Journal of Glaciology, Vol. 7,

No, 49, p. 21-58. LUTSCHG-LOETSCHER, O. 1944. Beobachtungen liber das Verhaiten des vorstossenden Obern Grmdenwaldgletschers im Berner

Oberland. Beiirage zur Géologie der Schweiz. Geotechnische Série. Hydrologie, Lief. 4, p. 75-101. NYE, J. F. 1952. The mechanics of glacier flow. Journal of Glaciology, Vol. 2, No. 12, p. 82-93. OELSNER, C. 1967. Seismoakustik, eine neue Messmethode fur die Gletschermechanik. Polarforschung, Bd. 6, Jahrg. 35. Ht. 1-2,

1965, p. 19-27. PATERSON, W. S. B. 1964. Variations in velocity of Athabasca Glacier with time. Journal of Glaciology, Vol. 5, No. 39, p. 277-85. SCHYTT. V. 1966. Notes on giacioiogical activities in Kebnekaise, Sweden, during 1965. Geografislca Annuler, Vol. 48A, No. 1,

p.' 43-50. STLNBORG, T. 1965. Problems concerning winter run-off from glaciers. Geografiska Annuler, Voi. 47À, No. 3, p. 141-84, STENBORG, T. 1968. Glacier drainage connected with ice structures. Geografiska Annaler, Vol. 50A, No. 1, p. 25-53. STENBORG, T. 1969. Studies of the internal drainage of glaciers. Geografiska Annaler, Vol. 51A, Nos. 1-2, p. 13-41. THORARINSSOM, S. 1939. The ice-dammed lakes of Iceland with particular reference to their values as indicators of glacier

oscillations. Geografiska Annaler, Ârg. 21, Ht. 3-4, p. 216-42. UNION GEODÉsiquE et GÉopmsiqUE INTERNATIONALE. (1963).

Colloque d'Obergurgl (suite). Bulletin de l'Association Internationale d'Hydrologie Scientifique, 8e An., No, 2, p. 50-142. WEERTMAN, J. 1957. On the sliding of glaciers. Journal of Glaciology, Voi. 3, No. 21, p. 33-38. WEERTMAN, J. 1964. The theory of glacier sliding. Journal of Glaciology, Vol. 5, No. 39, p. 287-303. WERENSKIOLD, W. 1943. Fysisk geografi. Bd. 2. Oslo.

9