# A New Parameter-Free Slope Unit Division Method That Integrates Terrain Factors
## 2 Methods and Study Area
### Specific Process  
The process of extracting slope units via the Terrain Factor Parameter-Free Slope Unit Division (TFPF-SU) method is shown in Figure 2.  
First, to ensure the accuracy and reliability of the slope unit division, it is necessary to check for NoData values in the DEM data. Furthermore, we implemented rigorous data preprocessing on the original DEM data by applying Gaussian filtering to effectively reduce noise and smooth out anomalies. The goal was to eliminate nontopographic factors that might affect subsequent analysis results and to enhance data quality. Second, using the processed DEM data with ArcGIS 10.7 software, we systematically calculated a series of key topographic parameters, such as slope, aspect, and curvature. These parameters comprehensively reflect the terrain undulations, surface directional characteristics, and local terrain curvature, providing a solid foundation for the precise division of slope units. The calculated slope, aspect, and curvature were then classified to obtain discrete label matrices. Next, an array of the same size as the DEM was initialized to record the unit affiliation ID of each pixel. With this information, unclassified pixels were identified through pixel-by-pixel traversal and selected as potential region-growing starting points, or seed points. Seed point selection is dynamic, with every unassigned pixel having the potential to become a new seed point, ensuring coverage of the entire DEM area. Starting from a selected seed point, slope units were gradually constructed through neighborhood expansion. Neighborhood expansion follows the principle of topographic similarity, ensuring that pixels newly added to the slope unit share similar topographic features with the seed point on the basis of the classified label matrices of slope, aspect, and curvature. Using a stacked structure, eligible pixels were recursively labeled to indicate that they are associated with the same slope unit. A seed point was first added to the stack, and its  
Figure 2: TFPF-SU method flowchart for extracting slope units. neighboring pixels were checked. If a neighboring pixel meets the topographic similarity criteria and is unassigned, it is labeled as part of the current slope unit and added to the stack. This process was repeated until all eligible neighboring pixels were assigned, completing the division of one slope unit. Then, the process returned to the previous step to select the next unclassified pixel as a new seed point, repeating the region-growing and recursive labeling processes until all the pixels in the DEM area were assigned to the corresponding slope units. Through the above steps, the scientific division of slope units was achieved. Each slope unit exhibits a high degree of consistency in terms of slope trends, aspect distributions, and topographic curvature characteristics, ensuring the accuracy and reliability of the division results. Finally, the entire result was optimized through postprocessing steps, such as splitting and merging, to generate the final slope units. The implementation of this process relies on the Python 3.9 programming language and ArcGIS software. Furthermore, we validated the effectiveness of this method by conducting a comparative analysis with traditional hydrological analysis methods. Aspect [34] is a fundamental topographic factor that describes the morphology of the Earth's surface. It refers to the orientation of a slope. The calculation formula is Equation (1):  
\[\theta=a\tan 2\left(\frac{\partial z}{\partial y},-\frac{\partial z}{\partial x }\right)\times\frac{180}{\pi} \tag{1}\]  
where \(\frac{\partial z}{\partial x}\) represents the slope variation in the x-direction, \(\frac{\partial z}{\partial y}\) represents the slope variation in the y-direction, and \(\theta\) denotes the aspect. The aspect significantly impacts the subdivision of slope units, primarily because it is related to variations in environmental factors such as solar radiation, the rainfall distribution, and temperature conditions.