Seppyo, 1976 H. Kodama and S. Mae 31

The Flow of Glaciers in the Region*

Hideo Kodama** and Shinji Mae***

Abstract

The results of measurements of the surface velocity of the glaciers in the Khumbu region

showed that the surface velocity underwent a seasonal variation in the upper parts of the ablation

area of the Khumbu and the glaciers, that is, the velocity from May to August was higher than that of the rest of the year. It was found that the surface of the Kongma Glacier

moved upward and this strange motion of the ice was discussed. The thickness of the Khumbu

and the Nuptse glaciers was estimated using the theory of glacier flow to be 110 m and 70 m, respectively. The discharge of the was also estimated to be 7.5 •~ 106, 3.4 •~ 106,

1.6 •~ 106 and approximately 0 •~ 106 tons/year at the elevations of 5340 m, 5280 m, 5140 m and

4960 m, respectively. Using these values and measured ablation rate, the increasing rate of the thickness of the Khumbu Glacier was obtained as follows, 1 m/year between 5340 m and 5280 m,

0.3 m/year between 5280 m and 5140 m, and -1.5 m/year between 5140 m and 4960 m. These

results indicated that the Khumbu Glacier was not in equilibrium.

basis of them the glacier flow is discussed. The 1. Introduction thickness and discharge of glaciers are estimated In 1956 Mailer (1968) carried out the first and the thickness change of the Khumbu Glacier measurements of flow velocity in the Khumbu is obtained. Glacier and found that the flow velocity increased in the premonsoon season, especially in May. 2. Measurements of flow velocity From his observation he concluded that the 2.1. Measured glaciers increase in the flow velocity was caused by the The measurements were carried out in the enhancement of basal sliding due to the percola- Khumbu, the Nuptse, the Kongma, and the tion of melt water stored as glacier ponds down Kongma-Tikpe glaciers which are shown in Fig. to the glacier bed. However, Muller measured 1. The morphology of the glaciers where the the flow velocity in only the Khumbu Glacier, measurements were performed are described as though there are various and complicated types follows. of glaciers in the , even in the 2.1.1. The Khumbu Glacier Khumbu region. The glacier is 18 km long and 1 km wide. The In the spring of 1973 the Glaciological Expedi- accumulation basin of the glacier is called the tion to Nepal (GEN) started measurements of West Cwm which is separated by a big ice fall flow velocity in many glaciers of the Khumbu from the ablation area. From 1 km down-glacier and the Dhaulagiri regions in order to determine of the ice fall to the glacier terminus the glacier the mechanism of glacier flow and the effect of is covered with a debris. climate on glaciers. In this paper the results of The velocity measurements were made at 4 the measurements are summarized and on the stake lines called the Everest Base camp line * Glaciological Expedition to Nepal (5340 m), the Pumo Ri line (5280 m), the Gorak , Contribution Shep line (5140 m) and the Lobuche line (4960 m) No. 10 as shown in Fig. 1. At each stake line which was ** Water Research Institute , Nagoya University (present address, Chubu Region Development located in the ablation area, 5 to 7 stakes were Research Center, Sakae 2, Naka-ku, Nagoya) set. Near the Everest Base Camp line ogives of *** Water Research Institute , Nagoya University, which the height and wave length are about 5 m Chikusa-ku, Nagoya 464 and 10 m were observed. At other lines no 32 The Flow of Glaciers in the Khumbu Region

Fig. 1. Glaciers in the Khumbu region.

ogive was observed but irregular undulations were were set at each stair of this stair-type glacier. observed. Below the Lobuche line the glacier is 2.1.4. The Kongma-Tykpe Glacier covered with a thick debris. This glacier is the smallest among the measured 2.1.2. The Nuptse Glacier glaciers and the surface is smooth. The stakes The Nuptse Glacier is a valley glacier. It is were set along the center line of the glacier from covered with a debris, as is the Khumbu Glacier, the highest point to the terminus including the but there are no big ice fall and no ogives. The ablation and accumulation areas. altitude of its terminus is the same as that of 2.2. Method of measurement the Khumbu Glacier and is 4900 m. The Nuptse Using a Sokkisha's No. 10 theodolite or Wild Glacier is 6 km long and 500 m wide. The ac- T-2 theodolite, the position of stakes were cumulation area is very steep, but in the ablation measured by triangulation method from fixed area the surface gradient is about 5 degrees. points located usually on a side moraine. The Two stake lines for the velocity measurments positions of the lines were determined on a were set and are called the upper (5380 m) and topographical map from the photographs near lower (5210 m) lines as shown in Fig. 1. At the lines. The directions of the lines were deter- each line 4 or 5 stakes were set. The upper line mined from measurements of the angles between is located just below the accumulation area and the lines and magnetic north using a Sokkisha's the surface gradient is 5 degrees, and the lower No. 10 theodolite. line is located near the terminus and the gradient Bamboo and alminium poles were used as is 8 degrees. stakes in the measurements. Bamboo stakes 2.1.3. The Kongma Glacier were successfull, but alminium stakes were a The Kongma Glacier is very small and com- little bit weak and sometimes bended strongly as pletely different from the Khumbu and the a consequence of some accidents. Therefore, the Nuptse glaciers. The morphology and the strati- position of the stakes were measured at their graphy of the Kongma Glacier were investigated foot. Errors in the stake position are caused in detail (Wushiki, unpublished). A few stakes by uncertainties in the setting of the theodolite, Seppyo, 1976 H. Kodama and S. Mae 33 in measuring the base line length, in reading the surveying instrument and by the effect of refrac- tion of light. These uncertainties are independent but their contribution to the error of the stake position is not independent. The error was, therefore, estimated using the law of propagation of errors. The flow velocity was calculated from the displacement of the stake position and the time interval between the measurements.

3. Results of measurements The flow velocities were represented in the Data Report of 1973 and 1974 GEN and in this section simple features of the glacier flow is described. 3.1. The Khumbu Glacier The directions of the flow are almost parallel to the center line of the glacier except at the Lobuche line where the directions deviate to left side of to glacier. At the Lobuche line, however, the error of the velocity magunitude is slightly larger than the calculated velocity. Therefore, it is concluded that at least the part below the Lobuche line is stagnant. The flow velocity at the Everest Base Camp line and the Pumo Ri line show a remarkable Fig. 2. Seasonal variation of surface velocity in seasonal variation consistent with Mailer's results. the Khumbu Glacier. Though Mailer (1968) reported that the velociey in 1956 increased only in May, the velocity in 1973 was large in May, June and July as shown in Fig. 2. This difference may be caused by the difference of ablation in 1956 and 1973. The difference between the velocities at the Everest Base Camp line in May, June, July and August and in winter is almost the same as that at the Pumo Ri line or a little smaller than it. This is consistent with Mailer's results. It is very interesting that such a seasonal varia- tion of the velocity as those at the Everest Base Camp line and the Pumo Ri line is not observed at the Gorak Shep line. This indicates that the flow mechanism at the former lines is not com- pletely the same as that at the latter line. 3.2. The Nuptse Clacier

In this glacier, the directions of the flow Fig. 3. Seasonal variation of surface velocity velocity is parallel to the center line at both the in the Nuptse Glacier. upper and the lower lines. From the measure- ments a stagnant part is not observed in the Therefore, near the terminus a stagnant part glacier, but the velocity at the lower line contains might be observed. a stagnant component as will be discussed later. The velocity at the upper line indicates a 34 The Flow of Glaciers in the Khumbu Region seasonal variation which is smaller than that at paratively large seasonal variation of the velocity the Everest Base Camp and the Pumo Ri lines is derived by the basal sliding. Theoretical work in the Khumbu Glacier as shown in Fig. 3. A on the basal sliding was begun by Weertman seasonal variation was not detected at the lower (1957), but the observations of it were not enough line. to obtain a relation between h and Vb until 3.3. The kongma Glacier Paterson (1970) obtained a following relation The Kongma Glacier has a flow completely different from that of the Khumbu and the (3) Nuptse glaciers. It was observed tht the surface with Vb in m/year and h in m. In the above of the glacier moved upward at its center. This equation Vb is the annual mean velocity of the strange phenomenon meight be caused by the basal sliding. stair-like morphology of the glacier. In order to The above discussion is applied to a valley understand this type of flow it is necessary to glacier like the Khumbu and the Nuptse glaciers. consider rotational motionof ice slabs as well as On the other hand, the discussion cannot be ap- its translational motion. plied to the Kongma and the Kongma Tihpe 3.4. The Kongma-Tikpe Glacier glaciers. In the Kongma Glacier, the rotational The velocity of this glacier is nearly the same motion of the ice slabs takes place. This rota- as that of the Kongma Glacier and at the lower tional motion suggests that basal sliding of the line of the Nuptse Glacier even though this ice on the glacier bed and sliding of ice slabs glacier is very small. A reason for this is that on the adjacent slabs occur. Therefore, in this the surface gradient is very large and so the glacier a strong and concentrated plastic defor- velocity of the Kongma-Tikpe Glacier is con- mation occurs at the boundaries between the sidered to be large. slabs as well as at the base. This is a new and 4. Analysis of results important type of glacier flow. 4.2. Seasonal variation of flow velocity 4.1. Flow mechanism The seasonal variation of flow velocity was A detailed analysis on the flow mechanism of observed at the Everest Base Camp and the glaciers in the Khumbu region will be given in Pumo Ri lines of the Khumbu Glacier and at the other paper. Only a simple discussion of the upper line of the Nuptse Glacier. As descrived the mechanism is given here. in 4.1., the increase in water amount at the The velocity, V, of the glacier flow consists of two velocity components due to plastic deforma- glacier bed enhances lubrication between the ice and the bed and the flow velocity increases. tion and due to basal sliding. Therefore, V is Therefore, Milner (1968) considered that melt given by water stored as glacier ponds on the surface (1) percolated down to the bed when water channels were open and then the velocity increased. Accord- where the suffixes p and b mean plastic deforma- ing to his explanation the increase takes place in tion and basal sliding. Assuming that the ice May. On the other hand, our observations show motion is laminar and the temperature at the that the increase takes place in May, June, July depth where the plastic deformation is significant and August. This means that in 1973 and 1974 is at the melting point (Mae, 1976), Vp is given the water supply continued until the end of the by summer. Therefore, it is not possible to apply Milller's explanation to our observations. (2) There are a big ice fall and a small one in

where ƒ¿ is the slope of the glacier surface, h is the Khumbu and the Nuptse glaciers, respectively.

the ice thickness, ƒÏ is the density of ice and q It is conceivable that there are open channels

is the gravitational acceleration. n and A are for water percolation in the ice falls in the spring

constants which determine the creep rate of ice. and summer seasons. The ice fall in the Nuptse

The increase in Vb is caused by the enhance- Glacier is very small compared with that in the

ment of basal sliding due to water supply to the Khumbu Glacier, so the water percolation in the

glacier bed. It is generally accepted that a com- ice fall in the Nuptse Glacier may be small. Seppyo, 1976 H. Kodama and S. Mae 35

Therefore, the water percolation through the ice 140 m. Since the is larger than fall may explain the large difference of the the Khumbu Glacier, the thickness of the Khumbu magnitude of the seasonal variation of these Glacier is smaller than 140 m. Therefore, from glaciers. The seasonal variation was not observed Table 2 it can be seen that h of the Khumbu at the Gorak Shep line and the lower line. This Glacier is approximately 110 m and its flow is indicates that the thickness of the water film is very similar to that of the Blue Glacier, a tem-

kept constant at these lines. However, at present perate glacie in the U.S.A.. Since the Nuptse the reason for this is not clear. Glacier is smaller than the Khumbu Glacier, the 4.3. Estimation of thichness estimated thickness at the upper line is over- If V can be obtained, h is estimated, using estimated because of longitudinal stress, as at the equations, (1), (2) and (3). Since the ice tem- Everest Base Camp line. The thickness at the perature is at the melting point as describe in lower line is under-estimated due to the stagnant 4.1., we can adopt as A a value for temperate component. Therefore, h of the Nuptse Glacier glaciers shown in Table 1. The results of the is as follows; estimation of h is shown in Table 2. Table 2 20 m•ƒh•ƒ100 m indicates that h at the Pumo Ri line is the same as h at the Gorak Shep line. This means that and h is expected to be about 70 m. the laminar flow assumption is valid at these The above estimate of h in the Khumbu Glacier places and the ice thickness of the Khumbu and the Nuptse Glacier can be confirmed in the glacier is nearly equal to h at these places. The following way. The shape of the glaciated open estimated thickness at the Everest Base Camp valley below the terminus is considered to be line is too large because the longitudinal stress similar to the bed rock shape under the glacier. due to the ice fall was ignored in this estima- The thickness described above satisfies this con- tion. The thickness at the Lobuche line is too dition. small because the ice at this line is almost It is impossible to estimate h of the Kongma stagnant. and the Kongma Tikpe glaciers because their Hsich Tzu-ch'u et al. (1975) measured the ice morphology is very complicated and the laminar thickness at 5400 m above sea-level in the flow assumption can not be applied. Rongbuk Glacier at the north slope of Mt. 4.4. Estimation of discharge and thickness Sagarmatha (Mt. Everest) and found that it was change of the Khumbu Glacier

Table 1. Values of A and n for various temperate glaciers.

Table 2. Calculated thickness of the Khumbu and Nuptse Glaciers. 36 The Flow of Glaciers in the Khumbu Region

Table 3. Amout of discharge of the Khumbu Glacier. Unit is 106 ton/year.

Table 4. Increasing rate of ice thickness of the Khumbu Glacier. Unit is m/year.

Using equations (2) and (3), we can estimate represented in Table 4. This result leads us to the discharge at the Pumo Ri and the Gorak a conclusion that the Khumbu glacier is growing Shep lines where the laminar flow assumption is thicker between the Everest Base Camp line and satisfied. The discharge, q, is given by the Pumo Ri line, it is almost in equilibrium between the Pumo Ri line and the Gorak Shep line and it is thinning between the Gorak Shep (4) line and the Lobuche line. with q in kg/year, where w is the width of the

glacier (m) and the values of A and n obtained References from the Blue Glacier (Shreve and Sharp, 1970) Hsieh Tzu-ch'u et al. (1975): Basic features of the are used. Substituting h and ƒ¿ at the lines, we glaciers of the Mt. Jolmo Lungma Region, obtain q as shown in Table 3. The discharge at southern part of the Autonomous Region , the Everest Base Camp line was estimated by China. Scientia Sinica, Vol. 18, 106-130. Mae, S. (1976): Ice temperature of Khumbu glacier following equation because the laminar flow as- , in this issue. sumption was not applicable. Muller, F. (1968): Mittelfristige Schwankungen der (5) Oberflachengeschwindingkeit des Khumbugletshers am . Schweizerische Bauzeitung, If the glacier is in a steady state, the following Jahrg., 86, Ht. 31, 569-574. equation must be satisfied. Nye, J.F. (1953): The flow of ice from measurements in glacier tunnels, laboratory experiment and the (6) Jungfraufirn borehole experiment. Proceedings of the Royal Society, Ser. A, Vol. 219, 477-489. where ƒ¢q is the discharge difference between the Paterson, W.S.B. and Savage, J.C. (1963): Measure-

points separated by a distance Ģ l, Ab and M ments on Athabasca Glacier relating to the flow are the rate of ablation and melting at the bed, law of ice. Journal of Geophysical Research, Vol.

and l is measured along the glacier. When 68, 4537-4543. Paterson, W.S.B. (1970): The sliding velocity of equation (7) is not satisfied, the glacier is not in Athabasca glacier, Canada, Journal of Glaciology, equilibrium. For continuity of the ice mass in Vol. 9, 35-63. the glacier, the local time derivative of h is given Shreve, R.L. and Sharp, R.P. (1970): Internal deforma- by tion and thermal anomalies in lower Blue Glacier, Mount Olympus, Washington, U.S.A., Journal of Glaciology, Vol. 9, 65-86. (7) Weertman, J. (1957): On the sliding of glaciers, Journal of Glaciology, Vol. 3, 33-38. As a detailed calculation will be published in Wushiki, H. unpublished. the other paper, only the results of •Ýh/•Ýt are