## 1 Introduction
The advancement of physiographic quantitative methods and the description of the history and behavior of drainage networks have received significant attention in the field of geomorphology [9; 20; 21]. The authors in Ref. [22] suggested that the physiographic features of the various watersheds could be connected to several hydrological phenomena. Furthermore, morphometric analysis improves our comprehension of hydrologic responses, such as groundwater potential, infiltration capacity, and surface runoff generation. More precise and insightful forecasts of other catchment characteristics, like travel duration, period to peak, and the intensity of erosion processes, are additionally made possible by this approach [23]. It is thus an effective method in ungauged watersheds where information on soil, hydrology, geology, and geomorphology are insufficient [24; 25]. Furthermore, conserving and controlling different natural resources, assessing drainage catchments, determining the frequency of flash floods, and preserving soil erosion controls may all benefit greatly from morphometric analysis research [15; 26]. Effective water resource management, landslide risk assessment, groundwater potential evaluation, soil erosion mitigation, and watershed activity prioritization all depend on the data acquired from the morphometric evaluation of watersheds [15; 27; 28; 29]. Many mountainous catchments and sub-catchments are experiencing degradation and are in a significantly threatened condition due to factors such as deforestation, urban expansion, and jhum cultivation. Comprehensive management plans are essential for achieving sustainable development for these degraded watersheds [19; 29]. Identifying priority watersheds is vital for effective management, as it informs the project costs, types, and the ranking of development initiatives. Recently, morphometric analysis has become an important area of study for policy makers and researchers, particularly in watershed management. The assessment of sub-watersheds can be directed by various goals, such as managing runoff, controllingfloods, enhancing groundwater resources, and evaluating soil erosion levels. The authors in Ref. [30] defined sub-watershed prioritization as a method for ranking sub-watersheds due to the intensity of soil erosion and the critical condition of drainage areas. When prioritizing sub-watersheds, various factors can be considered, including soil loss, land use and land cover, morphometric characteristics, and the socio-economic conditions of the local population. A wealth of scientific studies have investigated the influence of morphometry on watershed prioritization. For instance, the authors in Ref. [31] focused on positioning check dams by prioritizing sub-watersheds using the sediment yield index (SYI) model index. The authors in Ref. [32] conducted research in the Guhiya basin due to the sediment yield index; additionally, the authors in Ref. [33] examined the Nagmati river watershed for soil and water conservation activities. The authors in Ref. [15] developed a GIS-based tool for catchment prioritization to minimize potential uncertainties. The study referenced as [34] employed morphometric analysis to determine management priorities for nine sub-watersheds of the Piperiya primary watershed. Meanwhile, the authors in [35] utilized morphometric techniques and watershed prioritization as strategic tools for improving management planning in the Gidabo basin, Ethiopia. By using in-depth morphometric analysis unique to the Wadi Haly watershed, which has not been thoroughly examined in the previous literature, in this study, a substantial contribution is made to the field of soil erosion research. While previous studies, such as Ref. [24], have utilized comparable techniques, our study sets itself apart by incorporating a wider variety of morphometric parameters and a more detailed prioritization approach tailored to local hydrological and environmental factors.