Assessment of possible jôkulhlaups from Lake Demmevatn in Norway

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1 The Eslrciui's of flu' Extremes: Eflraortlinarv Floods (Proceedings of ;i svinposinm held ill Reykjavik. Iceland. July 2000). IAliSPubl.no Assessment of possible jôkulhlaups from Lake Demmevatn in Norway HALLGEIR ELVEH0Y, RUNE V. ENGESET, LISS M. ANDREASSEN Norwegian Water Resources and Energy Directorate (NVE), PO Box 5091 Majorstua, N-0301 Oslo, Norway JACK KOHLER Norwegian Polar Research Institute, Norway YNGVAR GJESSING Geophysical Institute, University of Bergen, Norway HELGI BJÔRNSSON1 Science Institute, University of Iceland, Iceland Abstract Artificial drainage tunnels were constructed after repeated catastrophic jôkulhlaups from the glacier-dammed Lake Demmevatn. Models of glacier change and jôkulhlaup discharge were used to develop scenarios in which the rock tunnels were blocked. The results show how the maximum jôkulhlaup discharge depends on the volume of water in the lake and on the drainage mechanism. The discharge depends on the thickness of the glacier and thus on its response to a possible future climate change. Key words jôkulhlaup; outburst discharge model; Glacier Hardangerjokulen; Norway INTRODUCTION The Sima Hydropower Plant in southwestern Norway uses most of the runoff from the ice cap (73 km 2, 61 30'N and 7 30'E). One of the reservoirs, Lake Rembesdalsvatn, is situated downstream from the outlet Glacier Rembesdalskâka (17 km") which dams the Lake Demmevatn (Fig. 1). Written sources describe late-summer jôkulhlaups from Lake Demmevatn back to the eighteenth century. After a catastrophic jôkulhlaup in 1893, a rock tunnel was constructed to drain the lake artificially. However, a further decrease in glacier volume inflicted another two serious floods in 1937 and 1938, and a second, lower tunnel was opened. The tunnels keep the lake level m lower than the glacier surface in the threshold area. Here we assess the magnitude of possible jôkulhlaups should the rock tunnels become blocked. METHOD The following approach was adopted to assess the impact of possible jôkulhlaups: - Establish a relationship between lake volume and level to estimate water volumes that could drain for any given glacier thickness in the threshold area.

2 32 Hallgeir Elvehoy et al. - Map potential subglacial drainage paths and drainage basins using surface and bottom topography from topographical maps and low-frequency radar observations. - Model discharge as a function of time through a subglacial channel to estimate duration and maximum discharge of jôkulhlaups using the length and slope of the drainage tunnel. Model calibration should be based on historic observations. - Establish glacier geometry scenarios using a glacier dynamics model and mass balance scenarios to assess possible jôkulhlaup volumes/discharge using the discharge model. Subglacial drainage A network of water-filled channels and cavities exist beneath a glacier, in which the direction of water movement is controlled by the gradient in hydraulic head, Z/ given by: Z =Z h +^- (1) P w -g (Shreve, 1972), where Z/, is glacier bed elevation, P w is water pressure, p. is water density and g is the acceleration due to gravity. Subglacial drainage divides are located along "highs" in the hydraulic head, and do not necessarily coincide with glacier surface maxima. Unlinked cavities at the glacier bed are at a water pressure, which may be expected to be close or equal to the ice pressure. In a channel, the water pressure decreases relative to ice pressure with increasing discharge Q and channel slope (Rôthlisberger, 1972). Near the drainage divides, the channels are small and the discharge is low. Thus water pressure may be assumed to equal the ice pressure (Bjôrnsson, 1992). The glacier can dam a marginal lake when the ice pressure at the glacier bed is high enough to force water to flow towards the lake and not towards the

3 Assessment ofpossible jôkulhlaups from Lake Demmevatn in Norway 33 glacier terminus. If the lake level rises or the glacier thins the resulting difference between subglacial water pressure and the ice pressure is reduced, possibly leading to a removal of the barrier and a jôkulhlaup. Models for simulating outburst discharge and glacier dynamics To model the jôkulhlaups from Lake Demmevatn a simple outburst model was used (Kennett et al, 1997). The model consists of a cylindrical tunnel with a single straight section. Discharge Q through the tunnel with cross-section area A is given by: Q = 0A3-A 4 ' 3 -(3 1/2 «-' (2) where (3 is the gradient in hydraulic potential between the lake and the outlet of the glacier river, and n is the Manning roughness coefficient (Clarke, 1982). All thermal and potential energy in the water is assumed used to melt tunnel walls so that the crosssectional area of the circular tunnel is enlarged at a rate: da = Q-p w -g-h + Q-T-C-p w ( 3 ) dt Pi-s-L where p,-, p >, g, h, T, C, s and L are ice and water densities, acceleration due to gravity, lake surface elevation above the glacier river outlet, lake temperature, specific heat capacity of water, length of the tunnel and latent heat of melting for ice, respectively. Furthermore, the closure rate of the tunnel was assumed negligible compared to melt rates, which is reasonable since the jôkulhlaups are observed to have lasted less than a day and the tunnel remained open for 2 months. The lake level is related to discharge from the lake by: K*=\-^T (4) where h, and h t +& are lake levels at time steps t and t + At, Q = (Q, + g/+a,)/2, and A, is lake surface area at time t. Assuming a constant melt rate over the tunnel segment, a jôkulhlaup could be simulated using equations (2)-(4). To investigate future changes to the glacier geometry a time-dependent one-dimensional finite-difference model with a simple glacier shape representation (Bindschadler, 1982), modified for plateau glaciers (Laumann, 1987) was used. DATA Lake bathymetry was constructed from surveys in the 1890s (Rosendahl, 1938), maps from the 1920s and soundings from Comparison between maps from 1925 and 1995 showed only minor front position changes in Lake Demmevatn. Ice thickness was mapped using ice-penetrating radar (Gjessing & Bjôrnsson, unpublished; Elvehoy et al, 1997), seismic profiling (Sellevold & Kloster, 1964) and hot water drilling (NVE, unpublished). Grids (30 m * 30 m horizontal resolution) of

4 34 Hallgeir Elvehoy et al. ice surface elevation and ice thickness were constructed by interpolation photogrammetric elevation data (1995) and the thickness data, respectively. from CURRENT PHYSICAL CONDITIONS FOR RELEASE OF JÔKULHLAUPS During the 1937 and 1938 jôkulhlaups, the lake level was 1286ma.s.l. and the estimated glacier surface and bottom elevation in the threshold area were and 1180 m a.s.l., respectively. Analogously, the lake level and the estimated glacier surface elevation for the 1893 jôkulhlaup were 1310 and m a.s.l. These figures suggest that the water pressure was 83-93% and % of the ice pressure in and Apparently jôkulhlaups can be expected when the lake level is more than 80% of the theoretical minimum hydraulic head elevation, which is in accordance with studies in Iceland (Bjôrnsson, 1992). Figure 2 shows the expected lake levels and corresponding lake volumes associated with a jôkulhlaup as a function of glacier surface elevation in the threshold area. In theory, jôkulhlaups from Lake Demmevatn are released when the lake level is equivalent to the minimum hydraulic head elevation in the area damming the lake. Thus the hydraulic head elevation of the critical area was calculated for the present glacier geometry (Fig. 3). Since the glacier surface slopes towards the northwest part of the glacier, the lake will probably drain along the edge of the glacier if the lake level rises to m a.s.l., which is m above the present level. However, if the glacier surface becomes more horizontal, the minimum in hydraulic head will coincide with the thickest part of the glacier, and thereby favouring subglacial drainage. This suggests preference to subglacial drainage in periods when the glacier is larger and the surface slope towards the northwest is less than at present.

5 Assessment of possible jôkulhlaups from Lake Demmevatn in Norway 35 Hydraulic head elevation Fig. 3 Present glacier surface (black) and bottom (grey) topography (left) and hydraulic head elevation (right) in the area close to Lake Demmevatn. JÔKULHLAUP DISCHARGE AND VOLUME Two release scenarios of jôkulhlaups from Lake Demmevatn were identified: (1) the glacier thins so much that it no longer dams the lake, and (2) the artificial drainage tunnels are blocked, causing the lake level to rise above the critical level. To investigate geometrical glacier change scenarios, the dynamic glacier model was calibrated using data on glacier geometry, mass balance ( ) and front position change ( ). The dynamic model was run for 50 years ahead with three different mass balance scenarios: specific net balance equal to -0.5, 0 and +0.5 m year"'. Climate change scenarios for western Norway (Sasltun et al., 1998) applied to a simple mass balance model which estimated specific net balance of Glacier Rembesdalskâka from winter precipitation and summer air temperature in Bergen, favoured the in-balance scenario. The +0.5 m year"' scenarios provide an envelope of possible change. A positive net balance gave a 700 m front advance and a 40 m thickening of the glacier in the Lake Demmevatn area, while a negative balance gave a 200 m front retreat and a 40 m reduction in ice thickness. Discharge calculations The 1938 event is the best4cnown jôkulhlaup from Lake Demmevatn and was used to test the discharge model. The tunnel length was estimated to be 1800 m, and the

6 36 Hallgeir Elvehoy et al. Manning roughness coefficient n was set to m" l/j s" 1 (Clarke, 1982), leaving water temperature as the only independent parameter. We adjusted the water temperature to make the modelled lake level fit with two observations of lake level during the jôkulhlaup. The best fit was achieved with a mean water temperature of 1.5 C, in good agreement with observed lake surface temperatures of C in 1897 and 1898 (Liestol, 1956). The modelled peak discharge was nr's" 1, and a volume of 10 x 10 6 m J was released during 7 h between the first and the last observation. The glacier geometry scenarios for the next 50 years were used to calculate the lake levels most prone to release a jôkulhlaup. The jôkulhlaup discharge simulation model produced corresponding peak discharge of between 100 and 8500 m J s _1. The worst-case scenario corresponds to a water volume of 41 x 10 6 m J (Fig. 3). With the present glacier geometry, a subglacial drainage of Lake Demmevatn could be expected if the lake level rises more than 30 m above the present level, producing a peak discharge of between 500 and 1200 m 3 s" 1 and a volume of 11 x 10 6 m 3. CONCLUSIONS A simple method for assessing jôkulhlaups was applied to the glacier-dammed Lake Demmevatn in western Norway. The results showed that modest flood volumes can be expected under present glacier conditions. Nevertheless, a glacier change scenario based on a positive mass balance suggests possible jôkulhlaups in the order of 40 x 10 6 m J (8500 m J s" 1 ) during the next 50 years. However, this could only occur if the rock tunnels were blocked. An alternative scenario based on a negative mass balance leads to much smaller potential floods. Acknowledgement Statkraft Engineering AS financed these investigations. REFERENCES Bindschadler, R. (1982) A numerical model of temperate glacier flow applied to the quiescent phase of a surge-type glacier. J. Glacial. 28(99), Bjôrnsson, H. (1992) Jôkulhlaups in Iceland: prediction, characteristics and simulation. Ann. Glacial. 16, Clarke, G. K. C. (1982) Glacier outburst Hoods from "Hazard Lake", Yukon Territory, and the problem of Hood magnitude prediction. J. Glacial. 28(98), Elvehoy, H., Kohler, J., Engeset, R. & Andreassen, L. M. (1997) Jôkulhlaup fra Demmevatn. Report no. 17/1997. Norwegian Water Resources and Energy Administration, Oslo. Kennett, M., Laumann, T. & Kjollmoen, B. (1997) Predicted response of the calving glacier Svartisheibreen, Norway, and outbursts from it, to future changes in climate and lake level. Ann. Glaciol. 46, Laumann, T. (1987) En Dynamisk Modell for Isbreers Bevegelse. V-Pitbt. no. S/I9S7, Norwegian Water Resources and Energy Administration, Oslo. Liestol, O. (1956) Glacier dammed lakes in Norway. Norsk Geogr. Tidsskt: 15(3-4), Rosendahl, II. (1938) Rembesdalsskâka og Demmevatn pâ Hardangerjokulen. Natural 62, Rôthlisberger, II. (1972) Water pressures in intra- and subglacial channels. J. Glaciol. 11(62), Sellevold, M. A. & Kloster, K. (1964) Seismic measurements on the glacier Hardangerjokulen, Western Norway. Polarinslitutt Arbok 1964, Shreve, R. L. (1972) Movement of water in glaciers. J. Glaciol. 11(62), Sœlthun, N. R., Ailtoniemi, P., Bergstom, S., Einarsson, K., Jôhannesson, T., Lindstom, G., Ohlsson, P.-E., Thomsen, T., Vehviliiinen, B. & Aamodt, K. O. (1998) Climate change impacts on runoff and hydropower in the Nordic countries. TemaNord 552, Nordic Council of Ministers, Copenhagen. Norsk