## 2 Materials and Methods
### Revised Universal Soil Loss Equation (RUSLE)  
The Revised Universal Soil Loss Equation (RUSLE) is a widely adopted empirical model for predicting long-term average annual soil loss from specific field slopes in specified cropping and management systems [40]. A critical component of this model is the soil erodibility factor (K), which quantifies a soil's inherent susceptibility to erosion. The K factor is computed using Equation (1), developed and refined through extensive field studies as part of the USLE and RUSLE projects [41; 42]. \[K=\frac{\left[2.1\times 10^{-4}\times(12-P_{om})\times(M)^{1.14}+0.0325\times(S_{ Struc}-2)+0.025\times(F_{perm}-3)\right]}{100} \tag{1}\]  
where  
K = soil erodibility factor (ton-acre-hr / hundreds of acre-ft-tonf-in)  
\(M=\) particle size parameter, computed as [(%silt + %very fine sand) \(\times\) (100 - %clay)]  
\(P_{om}=\) percentage of organic matter  
\(S_{struc}=\) soil structure index  
\(F_{perm}=\) profile-permeability class factor  
The constants in this equation (\(2.1\times 10^{-4},\ 0.0325,\ \text{and}\ 0.025\)) were empirically derived from comprehensive soil erosion studies conducted by [PERSON], [PERSON], and others [41; 42]. These values have been widely validated and are considered standard in applying RUSLE across various geographical and climatic conditions. The particle size  
Figure 3: (**a**) Demonstration of the jagged and uneven edges of the land due to the erosion process. (**b**) Depiction of a steep earthen cliff with a significant crack and mass soil fall due to erosion processes. (**c**) Shows clear signs of erosion, with a visible water channel filled with muddy water and vegetation. parameter (M) reflects the soil's textural characteristics, particularly emphasizing the role of silt, very fine sand, and clay. High M values, indicative of soils rich in silt and very fine sand but low in clay, suggest greater erodibility. This is because silt and very fine sand particles are easily detached and transported by runoff, while clay provides cohesive strength, resisting erosion. Organic matter (OM) is a critical soil property that enhances aggregate stability, improves water retention, and increases infiltration, reducing runoff and soil loss. In Equation (1), as OM increases, the K factor decreases, reflecting organic matter's protective role against erosion. Soil structure (s) significantly influences infiltration, runoff, and erosion dynamics. The RUSLE categorizes soil structure into four classes:  
1. Very fine granular soil: Highly resistant to erosion
2. Fine granular soil: Good resistance
3. Medium or coarse granular soil: Moderate resistance
4. Blocky, platy, or massive soil: Least resistant  
These classifications reflect the soil's aggregation patterns. Granular structures, especially fine ones, promote water infiltration and resist detachment, whereas blocky or massive structures are more prone to erosion due to reduced infiltration and weaker inter-particle bonds. Soil permeability class factor \((F_{perm})\) governs water movement through the soil profile, affecting runoff generation. The RUSLE defines six permeability classes:  
1. Very slow infiltration: Highest erosion risk
2. Slow infiltration: High risk
3. Slow to moderate infiltration: Moderate to high risk
4. Moderate infiltration: Moderate risk
5. Moderate to rapid infiltration: Low to moderate risk
6. Rapid infiltration: Lowest risk  
Soils with rapid infiltration rates allow more water to enter the profile, reducing surface runoff and erosion. Conversely, soils with slow infiltration rates generate more runoff, leading to higher erosion potential. The downstream area, subject to increased water flow during rainfall events, is particularly vulnerable to erosion. A high K factor in this region suggests the soil is more susceptible to detachment and transport, potentially leading to accelerated expansion rates.