## 2 Materials and Methods
### Integrated Model Construction  
The most important data of this model are the terrain data (digital elevation model, DEM), and the grid used for the model calculation is the structural grid obtained directly from the DEM. The advantage of the model is that no preprocessing step is required to generate the computational grid, which improves the running efficiency of the model. The DEM data used in this integrated model include the underwater topography of the reservoir area, the elevation of the dam, and the terrain of the downstream insulation area.  
Figure 4 shows the schematic diagram of the integrated simulation. As shown in Figure 4, the orange grid is the dam area, the red grid is the initial breach, the two-dimensional calculation area I is the upstream reservoir area, and the underwater terrain of the reservoir area is used, and the two-dimensional calculation area II is the downstream flood propagation area. The location of the dam and the initial breach are located according to the latitude and longitude. The DEM value in each time step is updated according to  
Figure 3: Schematic diagram of the collapse and expansion process of the dam breach.  
the scour depth of the breach, and then the water depth and current velocity value of each grid are updated through the flood propagation model. The new water depth and current velocity values at the breach grid are used to calculate the breach evolution model in the next time step.  
Figure 5 shows the flow chart of the model. The most important feature of this coupled model is that the iteration of each time step is realized by directly updating the DEM of the computational grid, and the regional grid of the dam is involved in the model calculation instead of only describing the shape of the dam. The driving water depth and current velocity values of the breach evolution are directly calculated by the corresponding water depth and current velocity values of the breach at the previous time step. This avoids the process of using the weir flow formula to calculate the flow out of the breach. At the same time, through the water depth in each time step rather than using the reservoir capacity curve to reflect the changes in the water volume of the reservoir area, the strong coupling of the upstream reservoir area, the dam, and the downstream propagation area is realized.  
Figure 4: The schematic diagram of the integrated model.  
Figure 5: The flow chart of the model.  
The coupled models input data by writing files in a specific format and output the result data in a specific format. The necessary input data of the model are configuration file and terrain file (DEM). Additional data include roughness coefficient, source boundary information, streamflow hydrograph, runoff hydrograph, etc. The roughness can be provided either as a constant number or in the form of a matrix raster map matching the number of DEM grid cells. The output of the model includes water depth and unit discharge data. Two types of output data (spatial and temporal) are generated in a separate folder, each user-specified: one is that the water depth and unit discharge are written in the form of a matrix type file, and the other is that the water depth and unit discharge at the specified point locations (defined in the input files) can be output in a single file for each variable. The resulting data can be post-processed and displayed by a variety of tools, which provides great flexibility.