## 4 Results and Discussion
### Basic Geometries of the Wadi Haly Catchment  
Basic geometric parameters play a pivotal role in hydrological modeling, watershed management, and soil erosion studies, as they allow for the assessment of how water moves through the landscape and how different features influence this movement. For instance, parameters such as catchment area, perimeter, and length can help determine the drainage efficiency and potential runoff characteristics. Furthermore, the shape of a catchment can significantly impact erosion patterns and sediment transport, which are vital for maintaining ecosystem health and preventing land degradation. Ultimately, a thorough understanding of these basic geometric parameters is essential for effective catchment management and sustainable environmental practices. The Wadi Haly catchment is 14,793.81 km\({}^{2}\) in total area and has a circumference (perimeter) of 487.65 km. As illustrated in Figures 4 and 5b, the Wadi Haly sub-catchments have areas and perimeters that range from 40.06 to 691.93 km\({}^{2}\) and 30.82 to 211.23 km, respectively. High levels of soil erosion are typically detected in larger sub-watersheds (Table 2). This occurs due to extended overdland flow durations, which provide enough time for runoff to thoroughly wash away soil particles before they reach a stream. Therefore, the sub-catchments could be assigned from lowest perimeter to highest perimeter [40]. Due to the results of Refs. [40; 48], the region has higher values of characteristics that are significantly impacted by soil erosion. Nevertheless, this is not always the case for all watershed studies  
Figure 5: (**a**) Stream orders and (**b**) sub-catchments of the Wadi Haly catchment. in the different regions. The findings of this study indicate that sub-catchments 14 and 10 hold the first and last positions, respectively, when evaluated by their perimeter values. In contrast, these sub-catchments are categorized as having moderate and high risks of soil erosion, respectively, according to the overall average ranking of all defined characteristics. To prioritize sub-catchments, the authors in Refs. [24; 40] emphasized the importance of identifying additional effective elements that aid in soil erosion processing, such as land use actions, different soil types, slope, and climatic changes. This suggests that the area and perimeter by themselves are not capable enough of assessing soil erosion rates in sub-catchments since other factors could influence low or high classes of soil erosion process. As suggested by Refs. [40; 49; 50], several different effective morphometric parameters, including basic, relief, linear, and areal signatures, may be applied by specialists to compare different sub-watersheds. In addition to the previously mentioned factors, several essential parameters, including stream order index, stream number index, stream length index, and average elevation, play a crucial role in identifying catchments that are particularly susceptible to soil erosion. These parameters not only help evaluate how physical characteristics of the watershed influence erosion processes but also aid in pinpointing specific catchments that require targeted mitigation strategies. Stream order, which reflects the hierarchy and arrangement of major rivers and streams within the studied watershed, is a significant indicator of the complexity of different drainage systems. Regions of high stream order typically show steeper slopes, long streams, and dense drainage patterns all of which are characteristics that are associated with increased soil erosion potential. More intricate drainage systems can improve soil dissociation and enable quicker water flow. Faster water flow and better soil dissociation could be possible by more complex drainage networks. Workers and land leaders can more effectively manage to plan their soil conservation actions by defining these correlations, which will guarantee that the most susceptible sub-catchments receive the resources and attention they need for efficient soil erosion control techniques.