Introduction

Movement and ablation studies on Miar Glacier are part of the Snow and Ice Hydrology Project, a comprehensive research effort in the Karakoram Himalaya, the prime aim of which is to elucidate the interplay between the rainfall, snow-melt, and ice-melt components of the hydrology of the Upper Indus basin. Detailed descriptions of the project, conducted on a bilateral basis between the Water and Power Development Authority (WAPDA) in Pakistan and several Canadian universities, have been given by Reference HewittHewitt (1985) and Snow and Ice Hydrology Project (Reference HewittHewitt, 1986, 1987).

Measurement of glacier mass balance by monitoring accumulation and ablation over an annual, or even a summer, period at sta locations is difficult in the Himalayan environment. is usually almost impossible to reach elevations above the equilibrium line without major effort, and always very difficult once there to make meaningful measurements. The ablation areas are often heavily crevassed and/or debris-covered, and this poses difficult sampling problems. The method used in this study is to monitor annual surface movement on a cross-profile as near as possible to the equilibrium line. The measurements obtained, in conjunction with depth soundings made on the same profile, allow the annual ice flux through the cross-profile to be calculated (Reference Reid and PatersonReid and Paterson, 1973). If an approximately steady-state glacier is assumed, this flux would be expected to be roughly equivalent to the rate of ice loss below the profile. If the cross-profile is coincident with e equilibrium line, then the flux would also be expected to be approximately the same as the accumulation rate above the profile.

The Field Area

Miar Glacier lies within the drainage system of the Barpu River, a tributary of the Hunza River in the central Karakoram of northern Pakistan. It is approximately 28 km in length and has an area of 53 km². Its equilibrium line at approximately 4100 m roughly coincides with the top of a steep ice fall (Fig. 1). It ranges in elevation from 2850 m at its snout to about 7000 m at the highest parts of its accumulation area (Table I). The accumulation area is mainly avalanche-fed and the ablation area is remarkably debris-free. In places there is evidence of small rockfalls on to the glacier surface but these are far smaller than the immense collections of rockfall debris found on the adjacent Sumaiyarbar and Bualtar Glaciers. Neither major medial moraines nor extensive crevasse fields are found in the ablation area below the ice fall. There is a series of very obvious wave ogives below the ice fall, and it is these features which make the ablation area of Miar Glacier accessible and almost ideal for field study (Fig. 2).

Methods and Instruments

The instrument system used to sound glacier thickness is a monopulse radar similar to that described by Reference Rose and VickersRose and Vickers (1974), Reference Watts and EnglandWatts and England (1976), Clarke (1977). and Reference Watts and WrightWatts and Wright (1981). The system is easily carried by a group of three people and consists of a transmitter and antenna which together generate a very short-duration pulse centred at between 1 and 5 MHz, and a receiving antenna plugged into the high-impedance input of an oscilliscope. Most soundings were made at about 1 MHz using 40 m antenna half-lengths, but in addition a few shallow soundings were made with shorter antennae.

The receiver is a small, portable oscilloscope Tektronix 221, having a band width of 5 MHz, high input impedence, and 1 μs per division horizontal sweep rate. This instrument provides a visual display of the signal, and the timing can be read directly. The oscilloscope has been modified to accept an external 12 V d.c. power supply; the receiver antenna is identical to that used with the transmitter. No problems with radio-frequency interference were encountered; local ambient radio-frequency noise was not a problem because of the remoteness of the study area.

Fig. 1.

Map of the Miar Glacier basin.

Table I.

Area—elevation relationship within the miar glacier basin

For the determination of ice thickness, the value for the radio-wave speed in ice is taken from Reference PatersonPaterson (1981) to be v_i = 168 m μs⁻¹. To convert the time-amplitude scale into a depth scale, the following equation is used:

where d is the ice thickness in m, t is the time in us from arrival of air wave to arrival of secondary pulse, t₀ = s/v_a, where v_a is 300m μs⁻¹ and is the speed of light in air, and s is antenna spacing. The margin of error in the time measurement from the oscilloscope is about 0.2 divisions so, with 0.1 μs per division, this represents about 20 m of ice. The sensitivity of the trigger setting is thought to introduce another error in the receiving unit of about 0.1 division, or 10 m of ice.

The uncertainty associated with a spatially sparse data set is an insidious problem throughout the Earth sciences. In this case, it is difficult to know from what direction the reflection is coming, and thus what part of the subglacial topography is actually being sampled.

Field Measurements

Analyses

The results of glacier-depth soundings are shown in Figures 4 and 5. The seven depths taken along the central axis of the glacier (Fig. 4) are consistent and fall mostly in the range 453–487 m. The greater depth of 555 m at M12, is probably because this point is furthest towards the glacier right bank, and also because, as indicated in the transverse profile (Fig. 5), the deepest part of the glacier is slightly to the right of centre; it is also a reading which was subjectively rated poor, indicating concern over interpretation of the signal.

The crests of 20 successive ogives were surveyed along a line running down the approximate centre of the glacier. The mean distance between ogives on this line was 166 m. Above the transverse profile, the mean distance apart was 143 m and the mean surface slope was 1.9°. It was always a subjective judgement as to what exactly constituted the crest of an ogive, so that quoted widths of individual ogives may well be inaccurate by up to 10 m. However, by measuring the distances between many successive crests, average widths become more meaningful. If there is any consistent bias in these measurements it will have been towards slightly exaggerating the ogive spacing, as some slight deviations were taken from the centre line of the glacier.

Surface movement of the glacier was monitored during the summers of 1986 and 1987 on the transverse profiles shown in Figures 3 and 5. Table II summarizes these movement data. There are three points to note. First, the glacier is exhibiting blockschollen flow. Velocities increase rapidly from the edges of the glacier, and over most of its width the glacier is moving at a fairly constant velocity. Secondly, as shown in Table II, velocities during the summer can vary while, on the evidence from one stake only, summer and winter velocities are not markedly different. No attempt has yet been made to correlate these different velocities with availability of melt water. Thirdly, annual surface movement at point M4, measured as 164.7 m between 14 May 1986 and 18 May 1987, is very similar both to the mean spacing of all 20 ogives of 166 m, and also to the spacing of the two ogives nearest to M4 which was 158.5 m. Using a distance-weighted average, the mean annual surface velocity is calculated as 148.5 m a⁻¹. Following Reference NyeNye (1965), this is the figure taken as the mean annual velocity through the transverse section.

Fig. 2.

Miar Glacier trom Rosh Phari showing wave ogives (photograph by k. Hewitt).

The base of the glacier shown in Figure 5 has been depicted as a series of straight lines joining adjacent depth soundings; no attempt has been made to fit a smooth curve through these points. The resulting cross-sectional area is 3.82 × 10⁵ m². Average ice flux through the section is calculated as the product of cross-sectional area and mean annual movement, and is 5.67 × 10⁷ m³ a⁻¹, or 5.10 × 10⁷ m³ a⁻¹ water equivalent.

Hydrological Implications

Care must be taken in interpreting the figure of 5.10 × 10⁷ m³ a⁻¹ water equivalent. It is only a first approximation of water loss from the glacier below the transverse profile and it does not therefore represent total annual water yield from the area below the profile. Ice loss will be augmented by precipitation falling on that part of the glacier as either rainfall or snowfall with subsequent melt. There are also other assumptions related to glacier dynamics and glacier/climate equilibrium. Velocities may not be the same each year; the glacier may speed up in particularly warm years and the flux of ice through a cross-section may be affected by the passage of a kinematic wave. It is known that Miar Glacier has been in recession in the past few decades and the quantity of ice loss represented by glacier thinning or retreat would be additional to that passing through the transverse profile. Lastly, ice loss must be subdivided into evaporation and melt-water formation. Evaporation rates have not been measured accurately for this glacier, but in such a hot dry environment they are certainly high. The area of Miar Glacier below the transverse profile is approximately 7 km². If the ice flux through the profile is assumed to represent ice loss equally over this area, then mean ice loss producing run-off and evaporation, but discounting loss due to glacier thinning, is 8.10 m a⁻¹.

Fig. 3.

Map of echo-sounding locations and positions of stakes surveyed for movement.

Fig. 4.

Long profile from M12 to BL10.

Fig. 5.

Transverse profile M1 to M7.

Future Work

It is intended that additional work be undertaken on Miar Glacier in the near future. This will consist of a more comprehensive study of glacier movement for all areas below the ice fall, and the establishment of a network of ablation stakes monitored throughout the summer melt season. Such measurements, tied in with climatic observations at local meteorological stations, are expected greatly to help in the interpretation of the 1987 findings. Mapping of the glacier ablation area at successive intervals in the future will also help in the estimation of ice loss due to glacier retreat.

It is hoped that this method of estimating water yield from the ablation areas of major glaciers in the Karakoram will be applied to a number of other glaciers in the same general region in order to make possible an estimate of the differences between glaciers.

Table II.

Surface movement on transverse profile

Acknowledgements

This work was carried out as part of the work of the Snow and Ice Hydrology Project, jointly funded by the Water and Power Development Authority in Pakistan and the International Development Research Centre in Canada. Funding support from these organizations is gratefully acknowledged.