USSR case study: catastrophic floods

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1 USSR case study: catastrophic floods A.N. KRENKE & V.M. KOTLYAKOV Institute of Geography Academy of Sciences Starmonetny per 29 Moscow , USSR This case study discusses models for two types of outburst: from glacier-dammed lakes and those from englacial cavities. those OUTBURSTS FROM GLACIER-DAMMED LAKES Lake volume reached 20 10^ m^ in Abdukagor Lake, dammed by the surging Medvezhiy Glacier (Pamirs); volume varied from ^ irr* to np in Mertsbakher Lake, between outbursts from the lake dammed by Yuzhniy Inulchek Glacier (Tienshan Mountains). Both the lakes are nourished by glaciers situated above them. Before the formation of the lakes their volume could be predicted with the help of the area-level curve of the lake basin f(h), where h is the altitude of the level over the lower mark of the ice dam. The maximum volume of the lake, V max, may be considered as where fynax V m ax= J f(h).dh (1) h=o hmax = 0.9 H d (2) and H<j is the altitude of the ice dam. The moment of the outburst is predicted from the water-balance of the lake as the moment when its volume reaches V max. In the USSR, several methods have been proposed for the computations of the outburst hydrograph and its maximum discharge. Computation method based on widening the channel and the equation of motion (Glazyrin & Sokolov, 1976) Development of the outburst channel (with the initial section S 0 at the moment of flotation at depth h under the surface of the lake) may be calculated by solving the system of three equations: Decrease of level f(h) ~ = -0(t) (3) where t is time, Q is discharge of the outflow. 115

2 116 A.N. Krenke & V.M. Kotlyakov Equation of flow Q = u-s = K-S 43 -(sln a + > y * (4) where u is the velocity of water flow in the channel, S is the section of the channel, a is the inclination of the channel,8. is the length of the channel, K is an empirical coefficient determined by comparison with actual floods. Equation of widening of the channel walls due to heat content of water and energy losses caused by resistance of the walls T = Q-(2.2.1(f 5 -sin a + 0, 014)^) (5) dt S. where Tf is the temperature of water in the lake. Equation (4) has been derived from the balance of gravitational forces, gradient of water pressure and friction resistance, neglecting the inertial force, with regard to the Chezy and Manning formula: u = ^- R 16 «R-a (6) K l where R is the hydraulic radius of the channel, and the assumption of uniform pressure drop in the channel from gph above the entry of the channel to 0 at the exit. Equation (5) has been derived with regard to numerical values of the share of energy losses on melting of the walls according to Rothlisberger (1972), thermal equivalent of mechanical energy, heat of ice melting and the assumption of the uniform widening of the channel. The system of equations (3), (4) and (5) contains three unknown variables h, S and Q and is solved numerically for Q (t) in finite differences under given initial conditions S. And -rr and h«dt dt are replaced by the differences hj + - hj and Sj + ] - Sj. The values of the other variables are taken at the moment i. Solutions are found for different values of K, which are collated by the best agreement with the measured hydrograph, and in predictions are taken by analogy with the previous floods. During the previous outburst, K equalled 6.1 and 5.5 at the Abdukagor Lake. The rising limb of the computed hydrograph is close to the actual limb (Fig. 1). However the computation hydrograph is very sensitive to the temperature of water (Fig. 2). Inaccuracies in its determination are compensated by the collation of K, which, however, lowers the quality of the prediction. The chosen length of the time step has insignificant influence on the computations. At the beginning of calculations it may be taken to be 1 to 2 h with successive reduction to 5 min by the period of maximum discharge. Initial data for predictions are: (1) the date when the volume of the lake reaches V max ; (2) function f(h); (3) the length of the Channel 1, approximately equal to the distance from the lake to the glacier terminus; (4) slope of the glacier a; (5) the temperature of water in the lake Tf; (6) the number K taken by analogy with previous or other outbursts.

3 USSR case study: catastrophic floods 117 i i i \ o.-rr-rrrf f ÇÇ... S -~Ita=R t 1600q 1 )0- ) "E 800- o - i _ 400- (b) oj ^J t FIG. 1 Computed hydrograph (dotted line) and that obtained from the emptying of Abdukagor Lake outburst on 19 to 20 June (a) and 3 July (b), Q is water discharge in m 3 1s, t is time in hours (according to Glazyrin & Sokolov, 1976). i id FIG. 2 Computed hydrographs of the Abdukagor Lake outburst on 19 to 20 June 1973, with the constant K, but different values of water temperature in the lake Tf. Q is water discharge in m^s^^, t is time in hours (according to Glazyrin, Sokolov, 1976).

4 118 A.N. Krenke & V.M. Kotlyakov Computation method based on widening the channel and outflow from a short tube Another modification of computations (Vinogradov, 1977) also takes into account (though in the altered form) the widening of the channel due to heat storage, the energy of the flow motion, and the time taken for lake drainage; the hydrodynamic equation of motion (4) is replaced by the hydraulic equation for the outflow from a short tube. It is assumed that the motion inside the channel is controlled, not by pressure, but by slope, as the pressure drops where the tunnels widen, and the tunnel is self-regulated to admit the discharges, which will be supplied by a "short tube". Then: Q = K 2 -S 54 -h 12 (7) where K 2 is an empirical coefficient, obtained in the same way as K by the best fit with the measured discharges. The function V(h) is given in this model in the form h = a'v or V = a m -h 1m = B-h 1m (8) where B is the parameter determined from the topographic plan. The expression p «g c a S = r- [( -T +AH)(V -V) + -TT (V -v""" 1 ) (9) p. T-8, lv g w max m+1 max where p and pj is the density of water and ice, r is the heat of ice melting, C 0 is heat capacity of ice, g is acceleration due to gravity, a and m are morphometric parameters from (8) and â H is the vertical distance between the ends of the outburst channel and is based on comparison of the thermal widening of the channel dsdt depending on Q with the water storage decrease of the lake ^V - q. Substitution of (9) by (7) provides the dt expression for Q (V), which is recalculated with the help of (3) and (8) into the usual hydrograph Q (T) by way of numerical or grapho-analytical differentiation. The maximum discharge will take place with the value of V, which turns into equality the relation: C a 2.5 C 2.5 V ( -t +AH+- -V ) = V«[( +1)( «t +AH) ( +3.5).^] max g w m+1 max m g w m+1 m With T f = 0 (7) and (8) will be simplified because of the C insignificance y of -T. g w The model has been implemented for the outburst lakes Abdukagor, Tal'sekva, Grimsvatn and Graenalon. The "best fit" coefficient K 2 applied to them, decreased together with the length of the tunnel from 0.07 with 1 = 50 km to 2.68 with S. = 1.9 km (Fig. 3). In hydraulics the limiting value of K 2 for the opening with a thin wall equals Thus K 2 can be determined without (10)

5 USSR case study: catastrophic floods 119 K 2 3 f \3 0.2 S« I km FIG. 3 Relationship between the K 2 coefficient and the length of the runoff tunnel (according to Vinogradov, 1977). 1. Abdukagor Lake. 2. Tal'sekva Lake. 3. Grimsvatn Lake. 4. Graenalon Lake. any analogies In Fig. 3. The model was tested for the independent data on the outburst of the Vatnedalur Lake, in Iceland, with the volume of m 3 in The computed maximum discharge appeared to be 2650 m 3 s with the actual discharge being about 3000 m 3 s. The model becomes inapplicable, if the computed diameter of the tunnel is commensurate with the dimensions of the dam. The walls of the tunnel may fall and further outflow of water will follow the open channel. OUTBURSTS FROM ENGLACIAL WATER RESERVOIRS Forecasts of englacial outburst are complicated by the impossibility of observing water accumulation. In this case the method of water balance can be applied. Lack of knowledge of the increase or decrease of the runoff accompanying liguid water input to the glacier may pose difficulties. Another method is based on sudden deviation of the glacial river discharge from the known correlation graphs with neighbouring glacial rivers (Fig. 4). Vinogradov (1977) proposed the following computation model of the outburst hydrograph for an englacial water reservoir, shown in Fig. 5. Melt and rain waters q coming to the glacier are subdivided by the Dj-operator into two capacities. The Wj-capacity corresponds to the direct income of water to the runoff, and (^-capacity - to its retention in the glacier. If we assume the decrease of S^-capacity together with the growth of the amounts of melt waters M, the D^-operator can be approximated as q x = q-e -K -M(t) -K»M(t) d ; q 2 = q [1-e ] (11)

6 120 A.N. Krenke & V.M. Kotlyakov r. Ala-Archa FIG. 4 Correlation graph of the water discharge of the rivers Aksau (mouth) and Ala-Archa (above the mouth of Dzhyndysu River) for 1961 (northern slope of the Kirgiz Range). The mud flow took place on 29 July (according to Vinogradov, 1977). FIG. 5 Scheme of the model of glacial runoff formation and outburst flood (according to Vinogradov, 1977). Symbols are given in the text.

7 USSR case study: catastrophic floods 121 where q. and q are the income of water to the capacities W. and W, JC. is a coefficient, H(t) are amounts of melt waters occurring from the beginning of the season. The normal work of the glacier drainage system is to supply the runoff with discharges Qi and Q2 from the capacities Wj and W2- In case of drainage violation, the D2 operator divides the discharge Qj + Q2 between open and closed systems of cavities and runoff channels. In a simple case, the Qj2 discharge then flows to the runoff and Q] 2 3 discharge to the dammed capacity W 3. Ql23 = a (Ql + Q2> ; Ô12 = d-a)-(q 1 +Q 2 ) (12) where a is a water accumulation coefficient. Filtration from the capacity W 3 is executed by the discharge Q 31. The rest of the discharge Q32 corresponds to the englacial outbursts when W 3 reaches the crucial volume W. The process of draining capacity is described by the equation: 32 = b 32 H 32 b 32~ q 32 ^32* b 32' T (P(W 3 -W 3 ) (13) where a 3 2. b 3 2 are empirical parameters in relation Q = b-(e a * w - 1) (14) determined experimentally for Q 32 and W32. determined from Qo32 ^s Qo32 = b 32 < ex P a32*"3 - D U5> For the outburst flood on the Tuyuksu Glacier, using the optimization method,we obtained a 32 = "^; bg2 = ^-7' W 3 = 2'106m3 i j -e. the outburst began with 2'l()6m3 of water in cavities. Extrapolation of these values to other situations would be premature. In particular, b 3 2 grows rapidly with the destruction of glacier ice where an outburst of accumulated volume of water occurs within a short period. This, evidently, took place with the surge of Kolka Glacier (Caucasus) in 1902, when the catastrophic water-ice flood moved down the Genaldon River, despite the absence of glacier-dammed lakes, but accompanied by rapid increase in the volume of cavities in the glacier. When the surge was repeated in autumn and winter 1969, the probability of such an outburst was taken into account for the next summer. Computations of its possible volume and hydrograph at different reaches of the river were undertaken (Krenke & Rototaev, 1972). Water-balance computations showed that, since the beginning of May and to the end of June, 5.5»10^m^ of water accumulated in the glacier. Then the water build-up was interrupted by the release of ^ m^, but by 20 July the volume of water concentrated in the glacier reached its maximum, ô-lo^m^. By

8 122 A.N. Krenke & V.M. Kotlyakov 1 September this water gradually drained and in September the runoff corresponded to the discharge. A large outburst did not take place, as the volume of accumulated water constituted only about one-sixth of the cavities occurring in the glacier as a result of the surge ( ^m3). This is explained by the development of the drainage network during the surge, before major melt water production differing from conditions of the summer surge in With the volume W3 constituting more than 810 of the volume of cavities, i.e. more than 30-10"m3, the catastrophic flotation of the glacier could take place, as it did in It is noteworthy that the total volume of melt- and rain-waters in the glacier basin is about 64 to m 3. The maximum water income in summer with the probability of 1% accounts for 100 to 110'10 6 m3, Filtration from the glacier constitutes no less than 25'lO^m 3. Consequently in a normal year the dangerous volume, W3, could be accumulated only by the end of ablation period, and in an abnormally warm year, by its middle. The volume of the outburst in case of catastrophic flotation would be 30-lO^m 3, but it is necessary to consider the possibility of lesser outbursts which could start before the crucial moment. The form of hydrograph was calculated on the basis of tunnel modification with the maximum discharge at the end, and by outburst hydrograph with the maximum discharge at the first moment and its successive fall. In the first case the hydrograph was described by the equation: -ajt»t = Q max * e ^ (16) where Q t is the water discharge at the moment t, Q^x is the maximum discharge at the beginning of the outburst, t* is the period of the outburst, equalling the time of the decrease in discharge down to 10% of the maximum value corresponded to the Q condition Qt ~ j-. Thus it was assumed that a = 2 in all modifications to computations with different volumes W3 and periods t*. In the second case the hydrograph was described by equation Q t =Q Q - ef (17) where the ordinary discharge of 10 m 3 s~l was taken for Q 0, and the duration of the outburst up to its complete stoppage for t* was determined for each combination of W3 and t* separately, proceeding from the condition: t * W 3 =Q 0 J ef dt- a J - (e a - 1) (18) o consequently W_«a e a = ç- + 1 (19) *o

9 USSR case study. catastrophic floods 123 Solutions can be obtained for the given W3 and t*. W3 was taken as 3, 5, 10, 20 and 30'10 6 m 3, t* varied from 1 to 24 h. Computations of the runoff transformation in the river valley were undertaken on the basis of the simultaneous solution of the water balance equation of the river reach and dependence Q(V) along this reach: dv. dt it ^i+1 i+l = f ( V <>i where Vj is the volume of water in the reach, i is the number of the reach. Examples of hydrograph computations are presented in Fig. 3. To evaluate the height of flooding H max we plotted the curves H^x ^ f(q), using the Chezy formula. (20) 7 t, hours FIG. 6 Computed hydrographs of the possible outburst of water from inside the Kolka Glacier during its surges. 1. At the exit from the glacier km below the glacier terminus km from the glacier terminus km from the glacier end. REFERENCES Glazyrin, G.E. & Sokolov, L.N. (1976) Vozmozhnost' prognoza kharakteristik pavodkov, vyzyvayemykh proryvami lednikovykh ozyer (Possibilities for predicting the properties of floods caused by the outbursts of glacier lakes). In: The Data of Glaciological Studies. Chronicle. Discussion, N 26, Moscow, Krenke, A.N. & Rototaev, K.P. (1972) A surge of the Kolka GLacier and hydrometeorological consequences of the surge. Preprint of

10 124 A.N. Krenke & V.H. Kotlyakov International Symposium on the Role of Snow and Ice in Hydrology. Banff, Alberta. Rothlisberger, H. (1972) Water pressure in intra- and subglacial channels. J. Glaciol. 11(62) Vinogradov, Yu.B. (1977) Glyatsial'niye proryvnie pavodki i selevyey potoki. (Glacial outburst floods and mudflows). Leningrad, ffydrometeoizdat, 155 p.

Assessment of possible jôkulhlaups from Lake Demmevatn in Norway

The Eslrciui's of flu' Extremes: Eflraortlinarv Floods (Proceedings of ;i svinposinm held ill Reykjavik. Iceland. July 2000). IAliSPubl.no. 271. 2002. 31 Assessment of possible jôkulhlaups from Lake Demmevatn