A BSTRACT. W a ter flowing in tubul a r cha nn els in sid e a gl acier produces fri c tio na l hea t, w hi ch causes m elting o f the ice wa ll s. H owever the cha nn els a lso have a tend en cy to cl ose under the overburden pressure. Using the equilibrium equa tion that at every cross-sec tion as much ice is m el ted as flows in, d ifferentia l equa ti o ns a re g iven [or steady fl ow in horizonta l, inclined and verti cal channels a t va ria ble d epth a nd [or varia bl e discha rge, ice properties a nd cha nnel ro ughn ess . It is shown th a t the pressure d ecreases with in creas ing discha rge, whi ch p roves tha t wa ter must flo w in m a in a rteries. The sam e argum ent is used to show tha t certa in gl acier la kes a bove long fl a t va ll ey glaciers must form in tim es of low discha rge a nd empty when th e discha rge is hig h, i.e. when th e wa ter head in the subglacia l dra ina ge sys tem drops below th e la ke level. U nder th e conditio ns of th e mod el a n ice m ass o f uniform thickn ess d oes no t fl oa t, i. e. there is no wa ter layer a t the bo ttom , when the bed is inclined in th e d own -hill direction, but it ca n floa t o n a h orizon ta l bed if th e exponent n o[ the law [or the ice creep is small . It is furth er show n tha t basa l strea ms (bottom condui ts) a nd la tera l streams at the h ydra ulic g ra d e line (gra dient conduits) ca n coexist. Time-depend ent fl ow, local topogra phy, ice motio n, a nd sedi men t load a re no t accounted [or in th e theor y, althoug h they may strong ly influence the ac tua l course o[ the wa ter. Com puta ti ons have been ca rri ed out for the G orn ergl e tsche r w here the bed to pogra phy is known a nd where some d a ta a r c ava ila ble o n subgl ac ia l wa ter pressure. R ESUME. Pression de l'eau dans les condllites intra -et sous-glaciaires.La co ndition suivante est a d m ise: le re trecissem ent d e la conduite sous-gl acia ire d l! a la pression de la glace es t compe nse pa r la fusio n provoquee pa r la transform a ti on en c ha leur d es pertes d e c ha rge. D es equa tio ns differenti ell es pour I'eco ule ment stationna ire d a ns d es conduites horizon ta les, inclinees e t verti cales en fonc tion d e la profo ndeur e n d esso us d e la surface du glacier, du d ebit, d es proprie tes d e la glace et d e la rugosite d es p a ro is d e la conduite sont indi q uees. A insi, il s'es t avere que la press io n d ecroit lorsque le d e bit a ugm ente, ce qui prouvera it que I'ea u s'ecoul e d a ns des a rteres principa les. U ne a rgume nta tion a na logue montre que certa ins lacs d e ba rra ge gl acia ire situes a u-d essus d ' un e langue d e glacier e tendue d oivent se fo rm er lorsque le d ebit est fa ibl e e t se vid en t lo rsque le d ebit est e leve, c'est-a-dire lorsque la ligne d e cha rge du system e d e draina ge sous-gl acia ire d esce nd e n d essous d u ni veau du lac. Selon les hypotheses du m od ele, une masse d e glace d 'epaisseur uniform e ne fl otte pas, c'es ta-dire, il n ' y a pas d e couche d 'eau a u fond ...

Water flowing in tubular channels inside a glacier produces frictional heat, which causes melting of the ice walls. However the channels also have a tendency to close under the overburden pressure. Using the equilibrium equation that at every cross-section as much ice is melted as flows in, differential equations are given for steady flow in horizontal, inclined and vertical channels at variable depth and for variable discharge, ice properties and channel roughness. It is shown that the pressure decreases with increasing discharge, which proves that water must flow in main arteries. The same argument is used to show that certain glacier lakes above long flat valley glaciers must form in times of low discharge and empty when the discharge is high, i.e. when the water head in the subglacial drainage system drops below the lake level. Under the conditions of the model an ice mass of uniform thickness does not float, i.e. there is no water layer at the bottom, when the bed is inclined in the down-hill direction, but it can float on a horizontal bed if the exponent n of the law for the ice creep is small. It is further shown that basal streams (bottom conduits) and lateral streams at the hydraulic grade line (gradient conduits) can coexist. Time-dependent flow, local topography, ice motion, and sediment load are not accounted for in the theory, although they may strongly influence the actual course of the water. Computations have been carried out for the Gornergletscher where the bed topography is known and where some data are available on subglacial water pressure.

The results of systematic movement studies carried out by means of an automatic camera on the Unteraargletscher since 1969 (Flotron, 1973) are discussed together with more recent findings from theodolite measurements made at shorter intervals and over a longer section of the glacier.In addition to the typical spring/early-summer maximum of velocity known from other glaciers, an upward movement of up to 0.6 m has been recorded at the beginning of the melt season. It was followed, after various fluctuations of the vertical velocity, by a similar but slower downward movement which continued at an almost constant rate for about three months. The uplift was not confined to the section covered by the camera but occurred nearly simultaneously in profiles located 1 km below and 2 km above. The times of maximum upward velocity (increases of up to 140 mm/d) coincided approximately with periods of large horizontal velocity and occurred after increases of melt-rate.The following explanations for the variations of vertical velocity are considered: (1) Changes of longitudinal strain-rate. (2) Changes of the sliding velocity in a channel of variable width and with a bed slope deviating from horizontal. (3) Changes of volume due to opening or closing of crevasses. (4) Swelling or contraction of veins at the grain edges. (5) Growth (and closure) of cavities in the interior of the glacier. (6) Changes of large-scale water storage at the bed.Although all of the mechanisms (1)–(5) have some effect on the vertical ice movement, they cannot account for the observed variations of vertical velocity. We therefore conclude that large-scale water storage at the bed is the main cause of the uplift. Apparently the storage system is efficiently connected with the main subglacial drainage channels only during times of very high water pressure in the channels.The findings are of some interest to the concepts of glacier sliding: As mentioned above the maxima of horizontal velocity—and thus of the sliding velocity—have not been measured at the time when the storage had attained a maximum, but at the time of maximum vertical velocity, which we assume to be the time of most rapid growth of cavities at the bed. This behaviour of the sliding velocity agrees with that predicted by a simple finite-element model of the basal ice on a wavy bed with water-filled cavities. In particular, the model shows that the sliding velocity is larger during the process of cavity growth than at the final stage when the cavities have grown to the size which is stable for the applied water pressure.

Results of systematic movement studies carried out by means of an automatic camera on Unteraargletscher since 1969 are discussed together with supplementary theodolite measurements made at shorter intervals and over a longer section of the glacier. In addition to the typical spring/early summer maximum of velocity known from other glaciers, an upward movement of up to 0.6 m has been recorded at the beginning of the melt season. It was followed, after a few fluctuations of the vertical velocity, by an equal but slower downward movement which continued at an almost constant rate for about three months. Possible explanations of the uplift are discussed, the most satisfactory explanation being water storage at the bed. The observations then suggest that this storage system is efficiently connected with the main subglacial drainage channels only during times of very high water pressure in the channels. Detailed measurements showed that the times of maximum horizontal velocity coincided with the times of maximum upward velocity rather than with the times when the elevation of the surveyed poles had reached a maximum. On the basis of the hypothesis of water storage at the bed this finding means that the sliding velocity is influenced mainly by the subglacial water pressure and the actual, transient stage of cavity development, while the amount of stored water is of lesser influence.

In order to improve their hydro-electric power production in the Grimsel area, Kraftwerke Oberhasli (K WO) plan to construct a new reservoir with a storage leve l about 110 m high er than th e existing Grimselsee. This paper deals with the expected changes of Unteraargletscher after periodical contact with the resulting water body . Upon initial flooding, the lowe rmost section of Unteraargletscher, about 800 m long, will float , drift away, and melt. A rough estimate of the heat balance shows that the energy input into the lake would be sufficient to melt this ice within 2-3 years, so that calving and me lting will continue at a frontal ice cliff. The main effort of the study was aimed at forecas ting this retrea t. A pre-ex isting se ismic s urve y was supplemented by new so undings by radar and se ismic refl ec tion , resulting in re liabl e cross-sections and information about the sub-bottom material. The forecast is based on the existing mass flux and an empirica l calving rate relationship with water depth and predicts an equilibrium pos ition of the terminus so me 3-4 km further back than today, and a gain of water storage volume of 50 x 10 6 m 3 after 10 years.

A rapid displacement of glaciers occurs at times when the water supply from melting or lake drainage surmounts the capacity of the subglacial drainage system. It is explained by the hydraulic action of water at high pressure in cavities which open up on the lee side of undulations or steps of the glacier bed. It is suggested that, because of pressure-induced temperature fluctuations, rock fragments may freeze on to the glacier sole and be lifted out into an opening cavity. Laboratory experiments have shown that small pressure fluctuations of a few bars*only are sufficient for rock slabs of a considerable thickness to be moved in this way.

The results of systematic movement studies carried out by means of an automatic camera on the Unteraargletscher since 1969 (Flotron, 1973) are discussed together with more recent findings from theodolite measurements made at shorter intervals and over a longer section of the glacier. In addition to the typical spring/early-summer maximum of velocity known from other glaciers, an upward movement of up to 0.6 m has been recorded at the beginning of the melt season. It was followed, after various fluctuations of the vertical velocity, by a similar but slower downward movement which continued at an almost constant rate for about three months. The uplift was not confined to the section covered by the camera but occurred nearly simultaneously in profiles located 1 km below and 2 km above. The times of maximum upward velocity (increases of up to 140 mm/d) coincided approximately with periods of large horizontal velocity and occurred after increases of melt-rate. The following explanations for the variations of vertical velocity are considered: (1) Changes of longitudinal strain-rate. (2) Changes of the sliding velocity in a channel of variable width and with a bed slope deviating from horizontal. (3) Changes of volume due to opening or closing of crevasses. (4) Swelling or contraction of veins at the grain edges. (5) Growth (and closure) of cavities in the interior of the glacier. (6) Changes of large-scale water storage at the bed. Although all of the mechanisms (1)–(5) have some effect on the vertical ice movement, they cannot account for the observed variations of vertical velocity. We therefore conclude that large-scale water storage at the bed is the main cause of the uplift. Apparently the storage system is efficiently connected with the main subglacial drainage channels only during times of very high water pressure in the channels. The findings are of some interest to the concepts of glacier sliding: As mentioned above the maxima of horizontal velocity—and thus of the sliding velocity—have not been measured at the time when the storage had attained a maximum, but at the time of maximum vertical velocity, which we assume to be the time of most rapid growth of cavities at the bed. This behaviour of the sliding velocity agrees with that predicted by a simple finite-element model of the basal ice on a wavy bed with water-filled cavities. In particular, the model shows that the sliding velocity is larger during the process of cavity growth than at the final stage when the cavities have grown to the size which is stable for the applied water pressure.

ABSTRACT. A bri ef d escrip tion o f t he resistivity method is given , stressi ng the p oints wh ich a re of pa r ticu la r im po rta nce when working on g laciers. Th e literature is bri efl y reviewed . R EsUME. l\1esllre de la risistivite de la glace et sondages ilectriques: Remarqlles /Jreliminaires. La me th od e des resisti vites est d ecrite d e fa<;:on som m a ire et les points particu li ers it son a p pli cat ion su r les g laciers sont mi s en ev idence. U ne breve revue de la li ttera ture es t presentee. Z USAMMENFASSUNC . Elektrisclze Jl1iderstalldsmessllngen lInd Sondierllngen mifGletschern: Eirifiilmmg. Di e elektrisc he Widersta ndsmet hode w ird ku rz beschri eben , wob ei der Anwen dung a u f Gl etschern b esond ere Beachtu ng gesch enk t wird . Fern er wird ein kurzer Uberblick li ber di e L itera tur gegebe n. I NTR O D UCTI ONDuring th e Internationa l Association of Scientific H ydrology symposium a t Obergurgl on varia tions of the regime of existing glaciers in Septem ber 1962 three of the a u thors of pa pers to be published shortly in thi s J ournaL m et on the initiative of H ochstein to discuss th eir resistivity work and to agree tha t they would contribute their unpublished results to a j oint paper on th e subj ect, entitled " The electrical resistivity m ethod used in glaciological work " . The idea was to cover different as pects of recent resistivity work on ice a nd to compa re experience gained a nd results fr om various pa rts of th e world . Additional a uthors could be found who were willing to contribute to the j oin t efforts. The individu a l contributions, whi ch wer e collected by R othlisberger, varied so much in scope and size tha t it looked m ore appropriate to keep th em as a seri es of a rticles rather th a n to try to combin e them in a single pa per. Som e obvio us r epetitions of sta tem ents b y different a uthors ha ve been deleted , however, a nd an adjustment of no tations has been m a d e.By the electrical resistivity m ethod we understa nd prim a ril y geo physical prospecting techniques based on the m easurem ent of the po tential produced by a D .e. (or low frequency A. C .) current introduced into the g round . PRI NC IPL E O F RESISTIVITY S OUNDINGSAlthough it is no t th e purpose of this article to d escribe the resistivity m ethod as suchgeophysical textbooks m ay be consulted-a short note on the principles used seem s appropria te for those readers who are not a t a ll familiar with geoelectrical m ethod s. Th e obj ective of geoelectrical surveys is to investigate the sub-surface b y m eans of surface m easurem ents. A stand a rd technique consists of p roducing an electric curren t in the gro und between two electrodes, the current electrodes, and to m easure simultaneously the electric fi eld between two different electrodes, the po tential electrodes. ' I\fith the 4-electrod e m ethod the variable contact quality at the current electrodes does no t affect the result. Two electrod e configurations a re commonly used , bo th lin ear and symm e...