## 2 Materials and Methods
### Numerical Methods
#### 2.4.1 Ramms  
RAMMS (Rapid Mass Movement Software) was specially developed (2005) from experts of Avalanche Research SLF and WSL Institute for Snow. The main development was made by researching a case study of Illgraben debris flow in Switzerland [14; 27; 28]. It is one-phase FVM (Finite Volume Method)-based, calculating displacement in a change in volume, pressure, and depth in time F(V, P, h, t).  
As the main input data, the DTM (Digital Terrain Model) was used as information of terrain using automatic extraction of the source material. The suggested resolution was from 5 m to 25 m. Here, a pre-event DTM was used on 5 m. The calculation was carried out in a Cartesian coordinate system.  
The mass balance equation incorporates the field variables flow height \(H\) (\(x\), \(y\), \(t\)) and flow velocity U (\(x\), \(y\), \(t\)) and is given by  
\[Q(x,y,t)\cdot=\partial tH+\partial x\ (H\ Ux)+\partial y\ (H\ Uy) \tag{1}\]  
where the earth pressure coefficient ka = p is normally set to 1 when running the standard Voellmy-Salm friction approach, \(cx\) and \(cy\) represent topographical coefficients determined from the digital elevation model, \(Sg\) is the effective gravitational acceleration, and \(S_{f}\) is the frictional deceleration in directions x and \(y\)[28].  
The frictional deceleration \(S_{f}\) of the flow is determined using the Voellmy friction relation and specifies the dry-Coulomb term (friction coefficient \(\mu\)) scaling with the normal stress and the viscous or turbulent friction (coefficient \(\xi\) depending on the flow velocity \(U\)[11; 29]:  
\[S_{f}=\mu pgH\cos\varphi+\left(\rho gu^{2}\right)/\xi \tag{2}\]  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Determination of Specific Weight of a Sample St1** \\ \hline ms (g) & 49.738 \\ mpvm (g) & 362.144 \\ mpv (g) & 331.554 \\ Gs & 2.60 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measurement results from the experiment determining the specific weight of sample St1.  
where \(\rho\) is the mass density, \(g\) is the gravitational acceleration, \(\varphi\) is the slope angle, and Hgcos \(\varphi\) is the normal stress on the overflowed surface. The tangent of the effective internal friction angle of the flow material can be defined for the resistance of the solid phase (the term containing \(\mu\) which extensively controls the deceleration behavior of a more slowly moving flow). The resistance of the viscous or turbulent fluid phase (the term including \(\xi\)) prevails for a more quickly moving flow [29].  
Entrainment Model  
The erosion algorithm in the RAMMS model is defined using the maximum potential erosion depth \(em\) and a specific erosion rate. The erosion algorithm predicts the maximum potential depth of erosion \(em\) as a function of the computed basal shear stress in each grid cell:  
\[em=0\ for\ \tau<\tau c \tag{3}\]  
\[em=\ dz/d\tau\ (\tau-\tau c)\text{for}\tau\geq\tau c \tag{4}\]  
and the shear stress \(\tau\) is approximated using the depth-slope product:  
\[\tau=\rho ghS \tag{5}\]  
The potential erosion depth (per kPa) \(dz/dt\) controls the rate of vertical erosion (in the z-direction) as a linear function of channel-bed shear stress.  
When the critical shear stress \(\tau c\) is exceeded, sediment can be entrained from the channel. Entrainment stops when the actual erosion depth \(et\) reaches the maximum potential erosion depth \(em\) (Equation (6)). Normally, the specific erosion rate is implemented using the default value \(dz/dt=-0.025\) m\({}^{-1}\).