Ice melt under a debris layer

Ice melt under a debris layer is calculated using the degree-day method as explained in Kayastha et al. (2000b). The method needs positive degree-day factor for ice ablation and a relation between degree-day factor and debris properties, namely, relation between ratio of degree-day factor for given debris thickness kd to the factor for ice ablation kb and ratio of thermal resistance of debris R to thermal resistance for critical debris thickness Rc (Figure 6 in Kayastha et al. 2000b). A critical debris thickness is the thickness at which the ablation rate for debris-covered glacier ice is the same as for debris-free ice. In this study, the relation between degree-day factor and debris properties is used that was obtained from field observation carried out on debris-covered part of Lirung Glacier for a short period in June 1995 (Rana et al. 1996). Figure 2.3 shows the relation between degree-day factor and debris properties obtained from the observed data at debris thickness from 5 to 13 cm on Lirung Glacier. The critical debris thickness was 9.0 cm and mean thermal conductivity for the debris thickness from 5 to 13 cm was 1.4Wm-1 °C-1. Since the observations were only on up to 13-cm thick debris layers, which is not representative to whole debris-covered area because there are much thicker parts too and the exact thickness of the debris layer is not known, the thermal resistance was extrapolated up to 50 cm debris layer and its mean value 0.19m2 ° CW-1 is used to get kd /kb from the relation in Figure 2.3.

The calculated value of kd/kb is 0.54. Since the thickness of debris is thicker on the lower part of glacier than on the higher part, two values of kd/kb are used for lower and higher parts, namely, 0.50 for the lower two altitude bands 4125 m and 4375 m a.s.l. in Langtang Khola Basin and 4100m and 4300m a.s.l. in Lirung Khola Basins, and 0.58 for the rest of the higher altitude

R/Rc

Figure 2.3 Ratio of kd to kb versus ratio of R to Rc on Lirung Glacier in June 1995

bands on both basins. Monthly ice melt under a debris layer is calculated by multiplying the monthly PDD by the kd/kb and degree-day factor for ice ablation. If snow is present on the debris, the available degree-day sum is used first to melt snow and the remaining is used to melt ice under the debris layer.

Rana et al. (1997) mentioned that the average thermal resistance derived from satellite data for the debris-covered part of the Lirung Glacier was 0.14 m2 °CW-1, which is lower than the value derived from field observation. This could be due to the effect of low thermal resistance of supraglacial ponds and exposed ice cliffs on them. However, reasonable value of kd/kb can be obtained by changing the value of thermal conductivity. In the case of Lirung Glacier, the thermal conductivity should be 1.35 times larger than the observed thermal conductivity. In this way, if a relation between debris properties and degree-day factors is established for the debris-covered part of a glacier, ice melt under the debris layer can be estimated from the thermal resistance of debris layer derived from satellite data, provided the degree-day factor is known.

2.5 RESULTS AND DISCUSSION

Monthly specific snow and ice melt and rainfall are calculated at the mean altitude of each altitude bands in both basins. The area-averaged snow and ice melt and rainfall is calculated on each altitude bands, and their sum gives the discharge from the whole basin. The total discharge from the basin consists of melting from bare ice, ice melt under debris, snow melt above debris, melting of snow on rock and rainfall.

Variation in observed and calculated monthly discharges in Langtang and Lirung Khola Basins is shown in Figures 2.4 and 2.5, respectively. Figure 2.4

J-85 A-85 S-85 O-85 N-85 D-85 J-86 F-86 M-86 A-86 M-86 J-! Figure 2.4 Observed and calculated monthly discharges in Langtang Khola Basin from June 1985 to July

300 200 100 -00

J-96 F-96 M-96 A-96 M-96 J-96 J-96 A-96 S-96 O-96 N-96 D-96 Figure 2.5 Observed and calculated monthly discharges in Lirung Khola Basin in 1996

1986

Figure 2.6 Variation in observed annual mean air temperature, total precipitation, and calculated discharges in Langtang and Lirung Khola Basins from July 1985 to June 1986 and from 1988 to 1999. The values plotted in 1985 represent from July 1985 to June 1986

1980 1985 1990 1995 2000

Figure 2.6 Variation in observed annual mean air temperature, total precipitation, and calculated discharges in Langtang and Lirung Khola Basins from July 1985 to June 1986 and from 1988 to 1999. The values plotted in 1985 represent from July 1985 to June 1986

shows the observed and calculated monthly discharges in Langtang Khola Basin from July 1985 to June 1986. Similarly, Figure 2.5 shows the observed and calculated monthly discharges in Lirung Khola Basin in 1996. Data were not available for a few days from May to July (May - 8 days, June - 2 days and July - 5 days) in the observed discharge. Figures 2.4 and 2.5 show that the calculated monthly discharges are quite reasonable compared to observed discharge. The total observed discharge in Langtang Khola Basin was 1357 mm from June 1985 to July 1986, whereas the calculated discharge is 1365 mm. Therefore, the degree-day method using monthly mean air temperature and total precipitation can be a useful tool to estimate discharge from glacierized Himalayan basins where daily hydrometeorological parameters are not available.

Variation in observed annual mean air temperature, total precipitation, and calculated discharges from July 1985 to June 1986 and from 1988 to 1999 in Langtang and Lirung Khola Basins are shown in Figure 2.6. The values from July 1985 to June 1986 are plotted in 1985. The remaining snowfall amount in certain altitude band and year is added to the snowfall amount in January in the next year. Since precipitation data for a few months in 1994 are not available, discharge and precipitation data are not plotted in Figure 2.6. In general, the discharge from both basins is increasing, as temperature increases although the precipitation amount did not change much. It implies that the mass of snow and ice in both basins is depleting. The large discharge from Lirung Khola Basin nearly two times that of Langtang Khola Basin is mainly due to snow and ice melt from comparatively larger glacier-covered area in the basin (67%) than in Langtang Khola Basin (38%).

2.6 CONCLUDING REMARKS

Degree-day method is used to estimate snow and ice melt and discharge using monthly mean air temperature and total precipitation in two glacierized basins viz., Langtang and Lirung Khola Basins in the Langtang valley, Nepal. Lower parts of glaciers in both basins are covered with debris and hence a relation between degree-day factor and debris properties obtained on Lirung Glacier of Lirung Khola Basin is used to estimate ice melt under debris layers. Compared to the simplicity of the method, results are very encouraging. The annual total observed and calculated discharges from Langtang Khola Basin are similar, namely, 1357 mm and 1365 mm, respectively, and for the Lirung Khola Basin as well. Therefore, the current degree-day method can be taken as a useful tool for estimating discharge from glacierized basin in the Himalayas where hydropower and other socioeconomic activities are speeding up but glaciohydrological data are still very scarce. This study shows that the mass of snow and ice in Langtang and Lirung Khola Basins is depleting and hence such changes should be taken into account while formulating any water project in such region. It would be better to have representative degree-day factors for snow and ice ablation and the relation between degree-day factor and debris properties in other glacierized basins so that the method can be used to estimate discharge from the glacierized basins.

2.7 ACKNOWLEDGMENTS

This study was carried out under the Postdoctoral Fellowship Program for Foreign Researchers by the Japan Society for the Promotion of Science (JSPS). We are thankful to Dr. Roberto Ranzi for his constructive review of our paper. We wish to thank

Dr. A. B. Shrestha of Department of Hydrology and

Meteorology, Ministry of Science and Technology,

His Majesty's Government of Nepal for providing meteorological data of Langtang hydrometeorological

Station in the Langtang valley, Nepal.

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