## 4 Qualitative and Quantitative Analyses
### Quantitative Analysis
#### 4.2.1 Flow Direction  
The flow direction grid variety, defined as the count of distinct flow direction categories within a single slope unit, quantifies the spatial complexity of water flow patterns. As shown in Figure 7, SUD-CGHP-derived slope units generally exhibit higher frequency percentages of low variety levels (1-4) compared to HPAM-derived units, while the HPAM dominates higher variety categories (5-8). Cumulative frequency analysis further reveals  
Figure 6: Plane slope unit extraction comparison diagram. (**a**) Yanglousi Town corresponding area satellite map; (**b**) slope units extracted using HPAM; (**c**) slope units extracted using SUD-CGHP. that SUD-CGHP maintains superior cumulative values for variety levels 1-6, achieving comparable results with the HPAM only at extreme variety levels (7-8). These findings suggest that although SUD-CGHP produces simpler flow direction patterns (lower overall variety), its segmentation demonstrates significantly higher internal directional consistency. While both methods yield consistent mean flow directions across all slope units (Figure 7b), notable differences emerge in directional variety analysis (Figure 7c). SUD-CGHP-derived units exhibit substantially lower variety values in the northeast (NE), north (N), and northwest (NW) sectors compared to the HPAM. This directional selectivity indicates that SUD-CGHP achieves superior segmentation accuracy in northern-oriented terrains through its integrated hydro-mechanical framework, effectively capturing regional flow convergence patterns without introducing artificial complexity. This analysis highlights two critical advantages of the SUD-CGHP method: (1) homogeneity optimization achieved through balanced simplicity-complexity trade-offs via controlled variation in flow direction patterns, resulting in superior internal consistency indices compared to conventional approaches, and (2) enhanced directional discrimination capability, as evidenced by reduced directional variability in key mountainous regions (the northeastern, northern, and northwestern sectors). Such advancements enable SUD-CGHP to deliver geometrically coherent and hydrologically representative slope unit delineations, offering significant practical value for watershed management, landslide susceptibility mapping, and sustainable land planning through improved spatial accuracy and processing efficiency. Figure 8 provides the per-unit visualizations of the flow direction grid variety for slope units derived using SUD-CGHP and HPAM, accompanied by slope unit examples obtained using two methods and background flow direction grids of the same area which is conducted using D8 algorithms in selected regions. The D8 algorithm, widely recognized for its efficacy in surface water and groundwater hydrology [45; 46], constitutes a critical computational component within the HPAM flow direction framework. This methodological choice stems from its proven capacity to resolve flow direction uncertainties across diverse terrain morphologies, particularly in complex watershed systems where topographic anisotropy demands high-fidelity directional discretization. Regionally, SUD-CGHP-derived units (Figure 8a) exhibit an alternating pattern of high- and low-variety zones across the entire  
Figure 7: Variety of flow direction. (**a**) Flow direction variety frequency statistics; (**b**) flow direction distribution of slope unit; (**c**) average variety in all directions. study area, while HPAM-derived units (Figure 8c) display a pronounced east-west zonation, with western regions dominated by high variety and eastern areas characterized by low variety. This spatial distribution contrast highlights SUD-CGHP's ability to balance variety variation while maintaining natural flow patterns. At the intra-unit scale, SUD-CGHP demonstrates superior internal flow direction homogeneity (Figure 8b) compared to HPAM (Figure 8d), as evidenced by the more uniform distribution of flow direction grids within individual slope units.