Introduction
Kunmalike River is located at the head of the Tarim River on the southern side of the Tien Shan mountains on the border between China and the Soviet Union. Its annual runoff volume is 4.54 × 109 m3 measured at the stream gauge Xiehela in China. The basin area is 12 816 km2. Figure 1 shows the location of the river basin. Hydrological records indicate that jökulhlaups occur frequently in the river. The source of these jökulhlaups is Lake Mertsbakher (Ozero Mertsba-khera), which is dammed by the South Iniltchek Glacier, a 65 km long glacier on the southern side of the Tien Shan mountains in the Soviet Union. Many glaciologists and hydrologists, most of them Russian, have investigated this glacier-dammed lake since it was discovered by G. Mertsbacher in 1902.
Fig. 1. The location map of Kunmalike River and the glacier-dammed Lake Mertsbacher.
The volume of meltwater stored in the lake at the beginning of the jökulhlaups has ranged from 38.4 × 106 m3 to 327.4 × 106m3. The lake drains under the glacier for a distance of 14 km to the glacier terminus. From this point, the water flows into the Kunmalike River and thence to the stream gauge at Xiehela, a total distance of 203 km, where, since 1956, the Xingjiang Hydrological Service has recorded the jökulhlaups. The measured flood waves at this gauge are similar to the hydrographs measured near the glacier terminus in the Soviet Union.
The present paper describes the characteristics of the jökulhlaups from Lake Mertsbacher and discusses the twin problems of forecasting their discharges at the stream gauge and their volumes.
Characteristics of the Jökulhlaups and Their Influence
Table 1 lists some characteristics of the jökulhlaups recorded at Xiehela and Figure 2 shows three hydrographs in different seasons.
In general, the duration of the jökulhlaups is about one week, but the longest one was 18 days. They rise gradually to their peak and then drop abruptly in less than one day, and occasionally in less than 10 hours. The peak discharge of the largest jökulhlaup was 1.6 times larger than that of the maximum melt flood. The volume of water drained averages 1.64 × 108m3 for each jökulhlaup, which is 3.8% of the annual runoff at the Xiehela gauge. The maximum volume of a jökulhlaup was 3.275 × 108 m3, which is 7.2% of the annual runoff, and corresponds to the average total runoff for four months, from January to April. No systematic pattern can be found in the timing of the jökulhlaups although more than 80% of them occurred between July and September. The probability of a jökulhlaup occurring every year is over 90%, and in 1956, 1963, 1966, 1978 and 1980 two occurred. The shortest interval between jökulhlaups was only 60 days. There are no relationships between the peak discharge, volume of the jökulhlaup, and mean summer temperature.
Table 1. Characteristics of jökulhlaups at Xiehela stream gauge in Kunmalike River
* Inferred from 1 The Hydrology Yearbook published by Xingjiang Hydrological Service. Other figures are calculated by the author.
The occurrence of jökulhlaups has an important impact on the seasonal floods and runoff in Kunmalike River. In some years the ice-dammed lake stores meltwater during the summer and drains it in jökulhlaups later during the autumn or winter. More often, however, the jökulhlaups add to the normal melt floods in summer. Thus, 12 flood peaks have exceeded 1280 m3s−1, the maximum discharge of seasonal melt floods at the stream gauge.
Fig. 2. Hydrographs of jökulhlaups at the gauge Xiehela stream in Kunmalike River.
Fig. 3. Comparison of measured and simulated hydrographs by an exponential relationship (Q0 in m3 s−1):
A. 22 August 1984, Q0 = 543, b: 0.0103.
B. 18 August 1968, Q0 = 590, b: 0.012
C. 18 May 1978, Q0 = 139, b: 0.0166
D. 17 August 1983, Q0 = 366, b: 0.0178
E. 9 November 1958, Q0 = 38.9 b: 0.168.
Each division on the abcissa is 1 day for events A, B, C and D, and 2 days for event E. Symbols (x and ·) show measured hydrographs; lines (−) show simulated hydrographs.
The Release Mechanism And Forecasting of Jökulhlaups
The shapes of the hydrographs of the jökulhlaups indicate that the water drains out of the lake through gradually enlarging subglacial tunnels. This was verified by Reference GolubevGolubev (1977) after a jökulhlaup in 1971. The hydrographs are quite different from those of jökulhlaups in the Yarkant River on the northern side of the Karakoram mountains where a lake sometimes drains after a mechanical failure of a glacier dam.
Prediction of the timing of the jökulhlaups is difficult. The lake sometimes drains after its level has reached 0.9 of the height of the ice dam. However, jökulhlaups have been triggered at lower lake levels. Further, conditions of the glacier dam and the lake are different from year to year and they are difficult to survey.
Prediction of the hydrographs of the jökulhlaups is also difficult using theoretical models such as those derived from Reference NyeNye (1976), Reference MathewsMathews (1973), Reference Spring and HutterSpring and Hutter (1981), and Reference ClarkeClarke (1982). Such predictions would require data on the lake volume-distribution with elevation, and on temperature of the lake. These data are not readily available. Therefore, a forecasting method is advocated based on statistics and characteristics of their hydrographs.
If the mean diurnal discharge of the river increases at a rate of 200 m s−1 per 24 hours over two or three days, a jökulhlaup is probably in progress. Further, as the peak discharge only exceeds 1280 m3 s−1 in jökulhlaups in summer, a jökulhlaup can be expected if the discharge exceeds that value. The prediction is done by extrapolating the jökulhlaup component, Qj. This component is derived from the measured hydrograph, Q, by subtracting the base flow, Q0, and the diurnal meltwater component, Qm, from the recorded discharge.
Fig. 4. Comparison of measured and simulated hydrographs by a linear relationship.
The rise of the jökulhlaup component of a flood can be simulated by the exponential relationship
Qj = Q0 exp(bt)
where Q0 is a base value for the discharge at time t = o and b is a constant. Both Q0 and b are obtained by fitting an exponential curve to the hydrograph of the jökulhlaup. Reference MathewsFigure 3 shows the values obtained for b.
The peak discharge of the jökulhlaups cannot be predicted accurately becasue we cannot predict the timing of the peak. Table 1, however, shows that the development of a jökulhlaup takes at least 3.5 d and usually 5 d.
In most of the jökulhlaups (90%) the discharge increases approximately linearly with time after the first two days. Figure 4 compares a linear relationship with the measured hydrographs. The mean error of using the linear relationship is 10% of the measured discharge.
