## Numerical Simulation of Lake Currents Preparation

In order to quantitatively certify the hydrodynamic system in Tsho Rolpa (Fig. 6), lake currents were three-dimensionally simulated by making a three-dimensional figure of the Tsho Rolpa lake basin in the calculation domain (Fig. 11). The lake basin of actual size was made up by referring to the bathymetric map of 1992 (Fig. 1) . The new version of the CFD program for the airflow simulation, "PHOENICS 2006", was used for the lake current simulation. Considering spatial distributions of ice mass below the lake bottom , the calculation domain of x x y x z = 3,249m x 760m x 130m was set to be occupied by a solid block (0°C) of Ax x Ay x Az = 200m x 760m x 130m at x = 0 to 200m and a solid block (adiabatic) of Ax x Ay x Az = 3,049m x 760m x 130m at x = 200 to 3,249m, which uniformly contain stone-chippings inside. Corresponding to the outflow observed in Tsho Rolpa , the glacier-melt water inflow of 3 to 15m3/s was given constant at the inlet of Ay x Az =20m x 5m at x = 0. The outlet was set at the place corresponding to its actual location on the lake surface (Fig. 1A). Considering the grain size distributions of suspended sediment , the meltwater (0°C) was mixed with sediment (particle density, ps = 2,730kg/m3) consisting of particles of 250pm (2%), 62.5pm (3%), 16.25pm (15%), 3.91pm (40%) and 0.977pm (40%) in diameter. The mixture was given the bulk density, pc = 1,003kg/m3 (C = 5.0g/L). Flow velocity (m/s) at the lake surface was changed from (u, v) = (-0.05, -0.01) to (0, 0) as a wind-driven current, where u and v are the x and y components of flow velocity.

As initial conditions, the whole lake water was set to be uniformly at 3.5°C, and the blocks around the lake basin were given at 0°C. Considering the net radiation observed at site AWS , the heat flux at the lake surface was given constant at 130 W/m2. The Coriolis effect on the lake currents was taken into account by giving the Coriolis parameter f = 2Qsin0 =6.813 x 10-5 s-1, where Q is the angular speed of the earth (=7.29 x

10-5 rad/s) and 9 is the latitude (=27°51' for Tsho Rolpa). The islets near the end moraine were set as ice mass of 0°C. As in the airflow simulation, the completely implicit and hybrid methods were used to resolve discrete types of integral equations of continuity and motion (Navier-Stokes) for incompressible fluids. The eddy viscosity in the Navier-Stokes equation was calculated by using the standard k - e model. The following advective diffusion equation, Eq. (1), of suspended sediment concentration, C, was resolved by using the flow velocity field calculated and assuming the eddy diffusivity to be equal to the turbulent diffusivity of suspended sediment.

Meltwater inflow (itSfe)

Meltwater inflow (itSfe) Figure 11. Tsho Rolpa lake basin of actual size built up in the calculation domain. The basin shape is made by referring to the bathymetric map in Fig. 1.

-+ u\-1 + v - +(w - w,)-1 = —I Kx-1 + — K - +—\Kz-I (1)

dt ^Sx ) ) " \dz ) dx ^ x dx ) dy ^ y dy ) dz ^ z dz )

where w is the z component of flow velocity, ws is the settling velocity of suspended sediment in still water, and Kx, Ky and Kz are the turbulent diffusivity of sediment. The suspended sediment concentration, C, was given as the volume fraction in water, where numerical values of near unit mean sediment deposition. The molecular diffusion is neglected, since the turbulent diffusion is relatively very large.