measuring glacier-motion fluctuations using a computer-controlled survey system

NOTES

Measuring glacier-motion fluctuations using a computer-controlled survey system

GARRY K. C. CLARKE AND ROBERT D. MELDRUM Department of Geophysics and Astronomy, The University of British Columbia, Vancouver, B. C . , Canada V6T 1 WS

AND

SAM G. COLLINS 7 Tenley Drive, West Lebanon, NH 03784, U.S.A.

Received June 5, 1985

Revision accepted November 20, 1985

We describe a computer-controlled, distance-measuring system designed for glacier-motion surveys. A Sharp PC-1500 pocket computer is used to control an AGA Geodimeter 122 infrared laser ranger. Slope distance and vertical angle are automatically measured and plotted at preselected time intervals and recorded on magnetic tape. As a demonstration, three field experiments were performed on Trapridge Glacier, Yukon Territory. In the first experiment the position of a glacier flow marker was measured at 1 min intervals for 39 h. The average velocity (toward the instrument) was found to be 2.99 mm h-'. Subglacial water pressure was simultaneously measured at the flow marker site. For the duration of the survey, water pressure was low, and there is no clear relationship between pressure variations and glacier motion. In the second experiment the distance to a stationary target was measured at 1 min intervals for 9 h. The calculated motion of this target was -0.149 mm h-', giving an indication of the magnitude of uncorrected distance errors. The third experiment lasted 35 h and again involved measurements of glacier flow. The calculated target motion was 1.80 mm h-' toward the instrument.

Nous dtcrivons un systkme de mesure a distance, assist6 d'un petit ordinateur, conGu pour enregistrer les mouvements des glaciers. Un ordinateur de poche, Sharp PC-1500, a CtC utilisC pour contrbler un Geodimeter AGA 122 a laser infrarouge. La distance de pente et l'angle vertical sont mesurks a,utomatiquement et portCs en graphique a des intervalles de temps prtsClectionnCs et enregistrts sur bande magnCtique. A titre de dCmonstration, trois essais de terrain ont kt6 kalists sur le glacier Trapridge, dans le Temtoire du Yukon. Dans la premikre exptrience, la position du marqueur du mouvement du glacier a kt6 mesurCe a des intervalles d ' l min durant 39 h. La vitesse moyenne (en direction de l'instrument) a kt6 CvaluCe a 2,99 mm h-I. La pression de l'eau sous-glaciaire a t t t mesun5 simultanCment a l'emplacement du marqueur. La pression de l'eau Ctait faible durant toute la duke de l'expCrience et il n'y a aucun indice Cvident d'un lien entre les variations de pression et le mouvement de la glace. Dans la deux2me expkrience, la distance a une cible stationnaire a t t t mesurte des intervalles d ' l min durant 9 h. Le dCplacement calcult de cette cible Ctait de -0,149 mm h-', ce qui atteste la magnitude des erreurs de distance noncomgCes. La troisikme expCrience a d u d 35 h, et elle comprenait tgalement des mesures de l'tcoulement du glacier. Le mouvement calculC de la cible a ttC de 1,80 mm h'l en direction de l'instrument.

[Traduit par la revue] Can. J. Earth Sci. 23, 727-733 (1986)

Introduction The discovery that glacier flow can be irregular over short

time scales (Meier 1960; Goldthwait 1973; Iken 1973, 1977; McSaveney and Gage 1968; Miiller and Iken 1973) has led to increased interest in taking frequently repeated position measurements of glacier flow markers. The earliest measurements of velocity fluctuations (e.g., Meier 1960) were made using conventional optical surveying equipment, and the typical interval between measurements was 1-24 h. In recent years, time-lapse cameras (Krimmel and Rasmussen 1986; Harrison et al. 1986) and electronic survey systems have been em- ployed. As the time interval between observations is decreased it becomes tedious to take measurements manually. For this reason we have developed a computer-controlled survey system (Fig. 1) that allows automatic measurement of both changes in the distance from the survey instrument to a target and changes in vertical angle that result from repointing the instrument. (Vertical angle changes that result from target motion cannot be automatically detected.) The time interval is selected by the operator. Measurements are plotted as they are taken and stored on magnetic tape for subsequent analysis.

Instrumentation The survey equipment we use is a Wild T2g theodolite and

Printed in Canada / lmprime au Canada

an AGA Geodimeter 122 infrared (910 nm wavelength) laser ranger. When operated manually the Geodimeter measures slope distance to a precision of 1 mrn and vertical angle to a precision of 0.002g. Horizontal angles are measured optically using the theodolite.

The introduction of an RS-232C serial interface (AGA part No. 571134290) allows the Geodimeter to be placed under computer control so that measurements can be taken automatically. AGA Geodimeter manufactures a controller under the trade name Geodat, but this unit is costly and inflexible. Mea- surements taken using the Geodat are readily stored on magnetic tape but must be manually initiated, so operator attention is constantly demanded. We therefore rejected this choice.

The computer used to control the Geodimeter is a Sharp PC-1500 pocket computer. It is inexpensive, compact (195 mm x 86 rnm x 25.5 mm), lightweight (375 g), and program- mable in BASIC. Because it is virtually identical to the Radio Shack PC-2 computer, pens and printer paper are widely avail- able. To increase the power of the PC-1500 we added the Sharp CE-155 8 kbyte RAM (random access memory) expan- sion module, giving a total of about 12 kbyte of memory for program and data storage. The Sharp CE-158 RS-232C interface provides the communication link between the Geodimeter and the computer.

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728 CAN. J. EARTH SCI. VOL. 23, 1986

FIG. 1. The computer-controlled survey system. A Geodimeter 122 is mounted on a Wild T2g theodolite. The Geodimeter is under the control of a Sharp PC-1500 pocket computer. Measurements of slope distance and vertical angle are taken automatically at a time interval selected by the operator. Data are plotted as measurements are taken and stored on magnetic tape for subsequent analysis.

A minor modification was performed on the RS-232C interface of the Geodimeter to allow computer-initiated measurements. Without this modification the Geodimeter must be operated in the "tracking" mode. Ordinarily this mode is used for tracking the approximate location of a rodman walking with the survey target; measurements are taken continuously, and there is no averaging of successive values. Thus distance and vertical angle measurements taken in the tracking mode are less accurate than those obtained when the Geodimeter is operated normally, automatically averaging successive measurements before completing a measurement cycle.

The Sharp PC-1500 computer has an internal clock that is used to control the interval between successive measurements. (The minimum interval between measurements is approximately 5 s and is limited by the Geodimeter.) As measure-

ments are taken, the slope distance variations are plotted using the Sharp CE-150 graphing printer (with cassette interface) and stored in the memory. Periodically the computer writes the data on a Sharp CE-152 audio cassette tape recorder for storage. Data are recorded on cassettes using a frequency-shift- keyed format and can be reloaded into the computer for subsequent analysis or transfer to a larger machine. Power to the cassette tape recorder is turned on and off by the computer as required, so that magnetic tape and battery power are not wasted. We can record 1500 measurements on one track of a standard C-60 audio cassette (more than 24 h of measurements at one sample per minute). Although a digital tape recorder would provide far greater storage capacity, it would greatly increase the cost.

While automatic measurements are being taken the survey

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NOTES 729

TABLE 1. Summary of experiments

Experiment 1 Instrument position Target Nominal distance (m) Angle, 0 (") Start time Stop time Sampling interval (min) Apparent target velocity, v, (mm h-') Glacier flow rate, Ivl (mm h-l) Measured annual flow rate, I VI (mm h-l) Correction factor, A Pressure sensor location Ice thickness, hi (m) Start time for pressure Stop time for pressure Sampling interval for pressure (rnin)

Experiment 2 Instrument position Target Nominal distance (m) Start time Stop time Sampling interval (min) Apparent target velocity, v, (mm h-I) Correction factor, A

Experiment 3 Instrument position Target Nominal distance (m) Angle, 0 (") Start time Stop time Sampling interval (min) Apparent target velocity, v, (mm h-l) Glacier flow rate, Ivl (mrn h-l) Measured annual flow rate, I VI (mm h") Correction factor, A

LN 14

948 53.8

2323 22 July 1983 151 1 24 July 1983

1 2.99 5.06 4.48

-0.261 14

63.4 1346 16 July 1983 1630 24 July 1983

4

LN TN 1433

1606 24 July 1983

MK 8

345 52.7

2237 19 July 1984 0943 21 July 1984

1 1.80 2.97 3.93

-0.507

instrument must occasionally be relevelled and repointed. Vari- ations in vertical angle that result from changes in the instrument orientation are automatically sensed by the Geodimeter and recorded by the computer whenever the angle changes. (As previously noted, the Geodimeter cannot automatically sense vertical angle changes that result from motion of the survey marker. If these are significant over a short time scale, then frequent repointing of the instrument is necessary.) Hori- zontal angle changes are entered manually via the Sharp PC- 1500 keyboard, and these are keyed in under program control whenever changes occur. For sampling intervals exceeding 30 s, new values of horizontal angle can easily be entered without displacing an automatic measurement operation. Obvi- ously the survey instrument should be placed so that horizontal angle changes are small and the main variation with time is in slope distance. Measurements of atmospheric pressure and temperature are also taken at regular intervals and added to the data stream via the Sharp PC-1500 keyboard.

A 12 V automobile battery provides power to the system. The Geodimeter requires 1 A of 12 VDC power, while the computer and its peripheral devices require 6 VDC. A 12 V to 6 V converter delivers power to the 6 V computer components. With this arrangement, 36 h of continuous operation is possible before the 12 V battery must be replaced or re- charged.

Field experiments Three field tests were conducted on Trapridge Glacier,

Yukon Temtory: two in the summer of 1983 and one in summer 1984 (Table 1). In the first experiment, a reflecting prism was attached to flow marker 14, located near the centreline of the glacier. (For further information on this glacier and a com- plete set of references see Clarke et al. (1984).) The distance between the target and the fixed instrument position at site LN was 948 m. The angle between the optical path from site 14 to LN and the known flow direction of marker 14 was approximately 13 = 53.8", so the measured changes represent only 59.1 % of the total target motion. The experiment com- menced at 2323 on 22 July 1983 and was continued for 39 h; measurements were taken at 1 rnin intervals, although several interruptions occurred during the course of the experiment. Atmospheric pressure and temperature were measured at the Geodimeter site at intervals of roughly 20 rnin throughout the experiment. Subglacial water pressure beneath site 14 was simultaneously measured so that any observed fluctuations in glacier flow might be correlated with changes in basal water pressure. To measure basal water pressure we mounted an automobile oil-pressure sensor (VDO part No. 0-360-003) in a Plexiglas housing and placed the unit at the bottom of a hole drilled to the glacier bed. The sensor is mechanical, varying resistance as pressure changes. These resistance variations were converted to voltage variations and recorded on a Date1 DL2 data logger. Pressure measurements were taken every 4 min.

The second experiment involved measurements of distance between the Geodimeter at station LN and a nonmoving target placed at station TN, a distance of 1433 m. The objectives of this experiment were to test the reliability of the correction for atmospheric variability and to determine the magnitude of the remaining error in distance measurements. The experiment was started at 1606 on 24 July 1983 and continued for 9 h.

The third experiment was performed in July 1984 and incor- porated several improvements to the measuring system. A reflecting target was attached to marker pole 8 along the glacier centreline and immediately upstream from a pronounced wavelike bulge in the glacier surface (Clarke et al. 1984). The distance between the target and the fixed instrument position at site MK was 345 m. The angle between the optical path from site 8 to MK and the known flow direction of marker 8 was approximately 52.7", so the measured distance changes represent 60.6% of the total target motion. The experiment was started at 2237 on 19 July 1984 and continued for 35 h. On several occasions fog, rain, and snow blocked the optical path, so there are data gaps and irregularities in the distance measurements. The system restarts from these interruptions without operator intervention.

Analysis of results The recorded measurements of time, slope distance, vertical

angle, horizontal angle, pressure, and temperature were subse- quently transcribed to nine-track digital magnetic tape. The data were then analyzed using an Amdahl470 V/8 computer. The analysis procedures are described below.

Atmospheric variability Atmospheric variability contributes two sources of error to

distance measurements: a rapidly varying noise contribution n(t) from atmospheric turbulence; and a slowly varying contribution d*(t) from density changes caused by meteorological

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CAN. J. EARTH SCI. VOL. 23. 1986

July 1 9 8 3 21 24

1 1 ' , n " I ~ L k , ' l i L 1 L r 1 t r ~ l J 1 ~ L 6 n r n i r ~ i h 1 . 1 5

July 1 9 8 3 25

July 1 9 8 4

- (-7

Elapsed Time (h)

FIG. 2. (a) Target motion of Trapridge Glacier survey marker 14 measured from site LN at a distance of 948 m. The measurements started at 2323 on 22 July 1983 and continued for approximately 39 h. The interval between successive distance measurements was 1 min, although occasional data gaps exist. Atmospheric pressure P and temperature T were measured at approximately 20 min intervals, and from this the meteorological contribution d*(t) to optical path length variability was calculated using a standard formula. Comparison of the graphs of P(t) and T(t) with that for d*(t) shows that temperature variation is the main source of meteorological error in the path length measurements. The steady component of glacier motion was found to be 2.99 mm h" (26.2 m year-'), and the residual r(t) + n(t) was obtained by removing this component and applying a meteorological correction described in the text. The residual time series was smoothed using a moving average filter to obtain < r(t) > . The graph of < r(t) > shows little evidence of fluctuating glacier flow. The noise component of the residual is taken as n(t) = [r(t) + n(t)] - < r(t) > . The smoothed root-mean-square noise power a(t) = <n2(t) > " is an indication of the amount of atmospheric turbulence and shows a marked diurnal variability. The measured variation in optical path length A D(t) and the smoothed variation Ad@) are also plotted. (The two curves have been vertically displaced to facilitate comparison.) Arrow annotations 1 and 2 on the graph of r(t) + n(t) indicate noise spikes arising from instrumentation problems. (b) Apparent motion of fixed target at site TN measured from site LN, a distance of 1433 m. The measurements were started at 1606 on 24 July 1983 and continued for approximately 9 h. The interval between successive distance measurements was 1 min. The measurements were analyzed by the same procedures that were used for the moving-target experiment. The apparent rate of target motion was found to be -0.149 mm h-' and gives an indication of the magnitude of the uncorrected errors in the data. (c) Target motion of Trapridge Glacier survey marker 8 measured from site MK at a distance of 345 m from the target. Measurements were started at 2237 on 19 July 1984 and continued for approximately 35 h. The interval between successive distance measurements was 1 min. The steady component of glacier flow in the direction of the instrument station was 1.80 mm h-' (15.8 m year-'). Fog, rain, and snow produced data gaps and irregularities in the distance measurements. The system is able to restart from these interruptions without operator intervention. Arrow annotations 3 and 4 on the graph of r(t) + n(t) indicate measurement disturbances arising from meteorological interference.

variations in pressure P and temperature T, We assume that = 275 79 . 55P n(t) is a zero-mean random variable and that d*( t ) can be 273 + T adequately estimated from P and T measurements at the instrument site. where C is the correction factor (mm km-I), P is the atmos-

The Geodimeter 122 operating manual (Anonymous 1981) pheric pressure (mbar), and T is the atmospheric temperature proposes the correction ("C). (Other more accurate formulas involving additional vari-

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NOTES

July 1983

1 om

Elapsed Time (day) FIG. 3. Variation of subglacial water pressure at Trapridge Glacier site 14, 16-24 July 1983. Pressure is expressed as percentage of the ice

overburden pressure at site 14; thus, 100% pressure corresponds to ice flotation. (Ice thickness at this site is 63.4 m, and the density of ice is taken as 900 kg m-3.) During event E, water pressure increased from 21.5% to 82.9% over the time interval 1640- 1728 on 17 July 1983. During event E, water pressure increased from 8.5 % to 41.5 % over the time interval 0306 -0354 on 20 July 1983. The flow measurements on marker 14 were started at 2323 on 22 July and ended at 2327 on 24 July; this observation interval is indicated on the figure as "Exp. No. 1 ." Basal water pressure was low and relatively constant throughout experiment 1.

ables such as partial pressures of water vapour and COz have been proposed (EdlCn 1966; Owens 1967).) The path length correction (rnrn) is therefore d*(t ) = D(t )C [P(t ) , T(t) ] / 1000 where D(t) is the measured path length (m).

When this correction was calculated, we found that its magnitude exceeded the magnitude of the apparent meteorological effect in the data. We compared the corrections obtained using the Geodimeter formula with those obtained using the EdlCn (1966) and Owens (1967) formulas and found no significant difference. The most probable explanation for the discrepancy is that temperature measurements taken at the instrument sites were not typical of the average value over the optical path. Thus, instead of applying the calculated correction directly to our measurements, we followed a somewhat different approach.

The meteorologically induced distance error d*( t ) that is estimated by [ I ] will include a nonvarying component that is the mean of d*(t) over the observation period; we denote this - d*( t ) , where overlines will be used to indicate averaging over the entire time series. The residual d" = d*( t ) - d*(t) is the fluctuating component of d*( t ) . We assume that the true am- plitude of the meteorologically induced fluctuations is given by d r ( t ) = Adrr ( t ) , where A is an unknown constant. The value of A was determined by least-squares fitting and effectively re- moves the component of the distance measurements D(t ) that is correlated with d r r ( t ) . Further details of the least-squares fitting procedure are given in the following section.

Estimating the steady and fluctuating components of target motion

We assume that target motion consists of a steady component at velocity vo and a fluctuating component r( t ) . Thus, the variation of true target distance with time is given by

where do is a constant displacement. The sign of vo has been chosen so that target motion toward the instrument yields a positive velocity. Optical measurement of d ( t ) introduces error due to meteorological variability, so that the measured distance is

- where Do = do + d*(t) is a constant displacement. The values of Do, vo and A were found by least-squares fitting to minimize [r ( t ) + n(t)12. The residual time series r( t ) + n(t) is assumed to contain a slowly varying contribution r ( t ) , from glacier- motion fluctuations, and rapidly varying zero-mean measurement noise n( t ) . To estimate r ( t ) we smoothed the residual time series using an 11-point moving-average filter. If < n(t) > = 0, as assumed, then < r ( t ) + n(t ) > = < r( t ) > . (Angular brackets are used to denote smoothing using a moving average filter.) Any low-frequency sources of error such as

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CAN. J. EARTH SCI. VOL. 23. 1986

July 1983 23 24

- -5 E E V

C = A Q ) , E E o

b t Q - n V) .- a +5 4 E

Elapsed Time (h)

FIG. 4. Comparison of the smoothed residual distance <r ( t ) > and the basal water pressure at site 14. Note that for the graph of pressure variation, increasing pressure corresponds to downward deflections. This sign change has been made to facilitate comparison with the displacement measurements; high subglacial pressure might be expected to increase the glacier flow rate and thus decrease the distance between the target and the instrument. The water pressure p* is expressed as a percentage of the ice overburden pressure and has been smoothed using a three-point filter. There appears to be no clear relationship between the small fluctuations in water pressure and the displacement of marker 14.

incompletely corrected meteorological variations and tripod perfectly calculated atmospheric correction. In every case the drift would also contribute to < r(t) > . The noise contribution magnitude of the actual meteorological influence is less than n(t) is estimated by subtracting < r(t) > from the residual time series r(t) + n(t). As an indication of atmospheric turbulence we also calculated the smoothed root-mean-square power of n(t) to obtain the time series a(t) = <n2(t) > %; again an 11- point moving average filter was used.

The steady component of target velocity estimated from 131 is a projection of the true velocity vector v . If n is a unit vector pointing from the target to the survey instrument then v, = n . v = Ivlcos 8 where 8 is the angle between the vectors v and n. The annually averaged velocity V of flow markers on Trapridge Glacier is known from annual surveys. Using n . V to determine cos 0 allows Ivl to be calculated and compared with the annual velocity 1 VI .

thepredicted variation. This couldbe readily explained if the temperature variations at the measurement site exceeded the temperature variations averaged along the optical path, as we suspect they do.

In Fig. 2, the smoothed residuals <r(t) > show no clear evidence for jerky or fluctuating glacier flow: a(t) has a pronounced diurnal variation, being largest near mid-day when viewing conditions are most disturbed by turbulence. Occa- sional spikes in the unsmoothed residuals r(t) + n(t) (e.g., annotations 1 and 2 in Fig. 2a) are from uncorrectable data errors. A ground loop in the system caused the audio tape to be contaminated by noise from the Geodimeter; we corrected this problem before the 1984 experiment. Annotations 3 and 4 in Fig. 2c show the effect of interference and interruptions from

Results fog, rain, and snow. Curiously, this type of atmospheric dis- Table 1 and Fig. 2 summarize the survey results. The turbance appears to lead to errors that decrease the apparent

measured variation of target distance with time is plotted as distance to the target. AD(t), and the smoothed and corrected distance variation as In experiment 1 the steady component of target velocity for Ad(t). (The vertical displacement between the two curves has marker 14 was estimated as vo = 2.99 mm h-', corresponding been introduced to facilitate comparison and has no signifi- cance.) Comparison of the graphs for P(t) and T(t) with that for d*(t), the meteorological correction calculated using 111, shows that temperature variation is the main source of meteorological variability in the distance measurements. The best-fit values for the meteorological correction factor A were -0.261 for the target 14, -0.084 for fixed target TN, and -0.507 for target 8. The negative sign follows from the defini- tion of A and is consistent with the fact that C in [I] increases with increasing temperature; A = - 1 would correspond to a

to a glacier flow velocity of I vl = 5.06 mm h-' . The annually averaged flow velocity (July 1983 - July 1984) for marker 14 was 4.48 mm h-'. We consider the indicated difference to be real. Throughout experiment 1, subglacial water pressure was measured at site 14. In Fig. 3 we plot the dimensionless pressure p* = plp,, where p is water pressure and pi = pighi is ice overburden pressure; pi = 900 kg m-3 is the density of ice; g = 9.8 m s - ~ is the gravity acceleration; and hi = 63.4 m is the ice thickness at site 14. The conditionp* = 1 corresponds to the ice flotation pressure. Subglacial water pressure can

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I NOTES 733

fluctuate dramatically, and two pressure events can be seen in Fig. 3. Event El began at 1640 on 17 July 1983 and within 48 min resulted in a pressure increase from 2 1.5 % to 82.9 % of the flotation pressure. Event E, began at 0306 on 20 July 1983 and increased pressure from 8.5% to 41.5% in 48 min. It is interesting that the rise time for both events is identical and that E, occurs at a time when the surface melt contribution to the subglacial drainage system is low. Water pressure remained low and relatively constant during experiment 1 (Fig. 3), and examination of Fig. 4 suggests no clear relationship between pressure variations and glacier motion. We have used power spectral analysis to estimate the transfer function H(w) that relates fluctuations of p*(t) to < r(t) > . The results were in- conclusive.

In experiment 2 the apparent motion of a fixed target at site TN was measured from site LN. The purpose of this experiment was to estimate the magnitude of the uncorrected atmospheric contribution to apparent target distance variations. Comparison of <r(t) > in Fig. 2 a and b shows that fluctuations in <r(t) > for the fixed target TN are comparable to those for the moving target 14. Thus the apparent motion fluctuations for marker 14 are probably not associated with glacier flow variations. The apparent motion of TN is v, = -0.149 mm h-', a further indication of the magnitude of incompletely corrected distance errors.

Experiment 3 was similar to experiment 1 except that im- proved equipment was used and subglacial water pressure was not simultaneously measured. The steady component of target velocity was estimated as 1.80 mm h-I and corresponds to a glacier flow velocity of Ivl = 2.97 mm h-' compared with the measured annual flow velocity (July 1983 - July 1984) of I VI = 3.93 mm h-I. Again we consider these velocity differences to be real.

In its present form the computer-controlled survey system should prove an invaluable component in our ongoing studies of Trapridge and other surge-type glaciers. A final improve- ment that we plan to make to the system is to automate, under the direction of the Sharp PC-1500 computer, the acquisition of the meteorological data.

Acknowledgments Funds for this project were provided by the Natural Sciences

and Engineering Research Council of Canada and the Univer-

sity of British Columbia Committee on Arctic and Alpine Re- search. Parks Canada kindly gave permission for the field testing to be done in Kluane National Park. We thank Almut Iken for her advice on the design of water-pressure sensors and Peter Whaite for help with computing. Marc GCrin, Francis Jones, Paul Langevin, Terry Ridings, and Jeff Schmok as- sisted with the fieldwork.

ANONYMOUS. 1981. AGA geodimeter 122 operating manual. Holmer and Holmerlab acoprint Lidingo, Publication No. 571.133.801, 50 p.

CLARKE, G. K. C., COLLINS, S. G., and THOMPSON, D. E. 1984. Flow, thermal structure, and subglacial conditions of a surge-type glacier. Canadian Journal of Earth Sciences, 21, pp. 232-240.

EDLBN, B. 1966. The refractive index of air. Metrologia, 2, pp. 71 -80.

GOLDTHWAIT, R. P. 1973. Jerky glacier motion and melt water. Intemational Association of Scientific Hydrology, Publication 95, pp. 183-188.

HARRISON, W. D., RAYMOND, C. F., and MACKEITH, P. 1986. A time-lapse photographic system and its application to the pre- and post-surge dynamics of Variegated Glacier, Alaska. Annals of Glaciology, 8. (In press.)

IKEN, A . 1973. Schwankungen der Oberflachengeschwindigkeit des White Glacier, Axel Heiberg Island. Zeitschrift f i r Gletscherkunde und Glazialgeologie, 9, pp. 207 -219.

IKEN, A. 1977. Variations of surface velocities of some alpine glaciers measured at intervals of a few hours. Comparison with arctic glaciers. Zeitschrift fbr Gletscherkunde und Glazialgeologie, 13, pp. 23-35.

KRIMMEL, R. M., and RASMUSSEN, L. A. 1986. Using sequential photography to estimate ice velocity at the terminus of Columbia Glacier, Alaska. Annals of Glaciology, 8. (In press.)

MCSAVENEY, M. J., and GAGE, M. 1968. Ice flow measurements on Franz Josef Glacier, New Zealand, in 1966. New Zealand Journal of Geology and Geophysics, 11, pp. 564-592.

MEIER, M. F. 1960. Mode of flow of Saskatchewan Glacier, Alberta, Canada. United States Geological Survey, Professional Paper 35 1, 70 p.

MULLER, F., and IKEN, A. 1973. Velocity fluctuations and water regime of arctic valley glaciers. Intemational Association of Scien- tific Hydrology, Publication 95, pp. 165 - 182.

OWENS, J. C. 1967. Optical refractive index of air: dependence on pressure, temperature and composition. Applied Optics, 6 , pp. 51 -59.

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