## 2 Materials and Methods
### Sample Representation Forms and Conditioning Factors
#### 2.2.2 Conditioning Factors  
There has never been a consensus on the selection of debris flow conditioning factors [20], but the following conditions should be met: (1) The accessibility of the conditioning factors is the first factor to be considered, and when the relevant data resources are scarce and extremely difficult to obtain, the corresponding factors should not be considered; (2) The selected conditioning factors should be able to be transformed into various types of data for computation; and (3) The combination of the selected conditioning factors should be a reflection of the possible influences controlling the triggering mechanism of debris flows. Finally, a total of 9 conditioning factors was collected. Figure 3 shows the  
Figure 1: The debris flow inventory map of Fangshan District.  
Figure 2: Schematic of the sample representation forms: (**a**) single grid; (**b**) multi-grid; (**c**) watershed unit.  
conditioning factor based on grids, and Figure 4 demonstrates the conditioning factor based on watershed units.  
Rainfall plays an important role in the formation of most debris flows. A large number of unstable bodies are destabilized and washed out under rainfall conditions [21]. The average annual rainfall was therefore applied as a conditioning factor. The related data were obtained from a climate website (Worldclim.Org, accessed on 1 August 2024).  
Figure 3: Conditioning factors based on grids: (a) rainfall; (b) altitude; (c) slope; (d) plane curvature; (e) profile curvature; (f) TWI; (g) NDVI; (h) DTF; (i) DTR.  
Topographic factors are never absent from DFSM studies. Altitude, slope, plane curvature, profile curvature, and topographic wetness index (TWI) were considered in the present study. Based on a 30 m digital elevation model, all these factors could be obtained based on some calculations and transformations. Altitude can be regarded as an indirect influence on debris flow formation since characteristics such as temperature, rainfall, and vegetation usually exhibit distributional differences for different altitude ranges [22]. Slope is closely related to debris flow formation, circulation, and accumulation processes, and is therefore one of the most commonly used conditioning factors in DFSM studies [9]. Plane curvature and profile curvature are two factors that can determine the flow process of surface runoff movement [23]. The TWI is normally associated with soil moisture. As the soil moisture increases, so does the potential for unstable slopes to provide a source of material for debris flows [24].  
Figure 4: Conditioning factors based on watershed unit: (**a**) rainfall; (**b**) altitude; (**c**) slope; (**d**) plane curvature; (**e**) profile curvature; (**f**) TWI; (**g**) NDVI; (**h**) DTF; (**i**) DTR.  
Surface vegetation cover is recognized to play an important role in debris flow formation [25]. Areas with less vegetation cover have more potential to provide material sources for debris flows. The normalized difference vegetation index (NDVI) was therefore chosen to describe the vegetation conditions in the present study.  
The distance to a particular target is often used as a measure of the extent to which that target influences debris flow formation. The development of faults and the construction of roads could provide material sources for debris flows [26]. Accordingly, distance to faults (DTFs) and distance to roads (DTRs) were considered as two important conditioning factors.