# Hazard Assessment for a Glacier Lake Outburst Flood in the Mo Chu River Basin, Bhutan
## 3 Materials and Methods
### Hydrodynamic Modelling Using HEC-RAS 5.0.7  
We used the software package, Hydrologic Engineering Center's River Analysis System (HEC-RAS), to simulate the flooding scenarios. In addition to other features, this model can simulate two-dimensional unsteady river hydraulics. HEC-RAS was chosen, because it is freely available and has already delivered realistic results in other studies [18; 22; 23; 25; 26]. A full model description can be found in [27]. HEC-RAS is capable of simulating multidirectional flows and super-elevation of flow around channel bends, which are typical features of sudden-onset floods such as GLOFs [28]. We used the Saint-Venant equations, a system of partial differential equations implemented in HEC-RAS, which describe incompressible flow in an open channel. We made use of an implicit finite volume algorithm to simulate the flood as an unsteady clear water flow. In reality, sediment might be entrained into the flow, changing its rheology and shortening the travel distance. For this reason, assuming a clear water flow limits the validity of our results, which is a common problem in GLOF studies [26]. However, this simplification had to be accepted, because the simulation of erosion, transport, and deposition requires extensive field data which are not available. The model set-up starts with the definition of the spatial domain. The overall size of our simulated flow area is 260 km\({}^{2}\). HEC-RAS has the capability to capture sub-grid dynamics. For this reason, we have chosen a 20-m resolution for the computational grid. Combining the area with the mesh width results in 644,892 computational cells that have been modelled with a temporal resolution of one second. The next steps are the preparation of the elevation data (DEM), the selection of upstream and downstream boundary conditions, and the selection of the channel roughness (Manning coefficient or \(n\)-value). A dam breach hydrograph served as an upper boundary condition and input for the hydrodynamic model routine. This hydrograph was simulated by the equations of Frohlich [29], which are derived empirically from dam failures. The volume of the lake only equals the outburst volume in case of a 100% outburst. The bathymetric survey of Sintaphu Tsho [13] clearly shows that the lake is overdeepened by glacial erosion, which makes a complete drainage highly unlikely. For this reason and considering the topographic situation, we define the maximum possible outburst as 90% of the lake volume. Medium and small outburst scenarios are set to 70% and 40%, respectively. The absolute volumes and other dam breach parameters are presented in Table 1.  
Dam breaches are usually modelled as incisions which form in a certain time, releasing the flood wave known as breach hydrograph. The cross-section of the breach can be simplified as a trapezoid, which is defined by its depth, mean width, and side slopes (Figure 3). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **90\% Outburst** & **70\% Outburst** & **40\% Outburst** \\ \hline V\({}_{\text{w}}\): outburst volume (10\({}^{6}\) m\({}^{3}\)) & 5.58 & 4.34 & 2.48 \\ H\({}_{\text{b}}\): breach depth (m) & 43 & 30.2 & 17.2 \\ t\({}_{\text{f}}\): breach formation time (h) & 0.31 & 0.39 & 0.51 \\ B: mean breach width (m) & 45.3 & 41.2 & 33.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Anticipated outburst volumes, corresponding breach depths and dam breach parameters calculated by the equations of [PERSON] [29]. Figure 2: The region around Punakha, represented by the STRM 30-m DEM (**a**) and by the EM3D 5-m DEM (**b**). The anticipated outburst volumes define the breach depths \(\rm H_{b}\) for the given topography, which in our case range between 17 and 43 m (Table 1). The side slopes were set to a ratio of z = 0.7 (or 35\({}^{\circ}\)), which is the value proposed by [29] for failure modes other than overtopping. Since Sintaphu Tsho is not connected to its mother glacier and not threatened by ice avalanches from hanging glaciers, this choice seemed to be justified.