## 4 Results and Discussion
### Relief Characteristics of the Wadi Haly Catchment  
Catchment reliefs and topographic signatures are very important morphometric features that impact watershed drainage systems and reflect the topographical structure of the catchment. For the purpose of predicting water movement and controlling soil erosion in a catchment area, these features provide information on changes in elevations, slopes, and potential flow pathways. According to the soil erosion process assessment that was performed by the authors of Refs. [3; 48; 61; 62], defining and assigning relief parameters allows for the exact definition of different locations that are vulnerable to the soil erosion \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Sub-Catchments**} & **Form** & \multirow{2}{*}{**Circularity Ratio (Rc)**} & **Elongation** \\  & **Factor (Ff)** & & **Ratio (Re)** \\ \hline Sub-C1 & 0.35 & 0.32 & 0.67 \\ Sub-C2 & 0.88 & 0.46 & 1.05 \\ Sub-C3 & 0.67 & 0.35 & 0.93 \\ Sub-C4 & 0.77 & 0.34 & 0.99 \\ Sub-C5 & 0.54 & 0.47 & 0.83 \\ Sub-C6 & 0.55 & 0.40 & 0.84 \\ Sub-C7 & 0.44 & 0.45 & 0.75 \\ Sub-C8 & 0.61 & 0.52 & 0.88 \\ Sub-C9 & 0.17 & 0.34 & 0.47 \\ Sub-C10 & 0.71 & 0.35 & 0.95 \\ Sub-C11 & 0.18 & 0.25 & 0.48 \\ Sub-C12 & 0.48 & 0.28 & 0.78 \\ Sub-C13 & 0.38 & 0.56 & 0.69 \\ Sub-C14 & 0.20 & 0.19 & 0.50 \\ Sub-C15 & 0.34 & 0.38 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Areal morphometric measurements of the analyzed sub-catchments. process. The effective physical characteristics of different watersheds that help in assigning their erosion risks include the following: general channel gradient, roughness, Melton ruggedness number, relief ratio, basin relief, and catchment form [24; 62]. Defining and understanding the relationship between the soil erosion process and different relief features is very valuable for environmental workers, agricultural producers, and watershed management planners. Having this comprehensive and complete data is very valuable for building both structural and non-structural models that successfully prevent and/or minimize soil erosion risk effects. The link between soil erosion process, basin relief, and topographic signatures in a watershed is very complex and depends on several factors [16]. Sub-catchment 14 indicates considerable basin relief, which reflects the differential between a catchment's highest and lowest elevations (Figure 7). This high basin relief may worsen the soil erosion process when linked with slope, topography, and drainage density factors. It could be necessary to apply target management plans in this area to assign the soil erosion process and protect different soil sources. This is according to the possibility that faster surface runoff from steeper slopes related to higher relief signatures may exacerbate soil erosion and sediment transportation [51]. The link of basin topography to the longest assigned dimension (R) is an important metric for comprehending the different topographic signatures of the study catchment, reflecting that sub-catchments 7 and 14 in southeastern parts exhibit the highest R values, which indicate an obvious vertical drop relative to their horizontal extent. On the other hand, sub-catchment 2 indicates the lowest Rr, suggesting gentle topography signatures. High Rr index values confirm steep slopes that could be the result of the higher runoff velocity and a greater possibility of soil being dislodged and movement. Additionally, this metric not only assigns the overall steepness of a catchment but also directly links with the watershed's vulnerability to soil erosion process. As a result, catchments and sub-catchments with high Rr index values are more vulnerable to soil erosion action than those with lower Rr index values, assigning the higher needs of focused soil erosion management plans in these susceptible areas. Complementing this investigation is the basin slope parameter, which represents the average slope across the entire sub-catchment.