## 1 Introduction  
A natural threat, soil erosion is the removing and carrying of soil particles from their original position. Various factors including wind and water can transport particles over long distances. In addition to contributing to sedimentation and landscape altering, soil particles are frequently deposited in other places after being removed from their original location. Along with altering the physical characteristics of the land and perhaps leading to soil degradation, this process has an impact on agricultural productivity, ecosystem health, and water quality. Soil erosion is greatly exacerbated by the loss of natural environmental barriers, such as through overgrazing and uncontrolled deforestation. Unsustainable land management techniques, such as exposing bare soil to wind and rain, growing crops that hasten erosion, employing inappropriate cropping patterns, and utilizing inappropriate irrigation techniques, are additional factors. By removing protective plants from the soil, these methods expose it to wind and water erosion, which eventually degrades the soil and lowers land productivity. Drainage catchments and sub-catchments are crucial components for efficient land and water resource management [1, 2, 3]. Because they provide a targeted approach to addressing both land use and water distribution, these natural divisions of the landscape aid in organizing and directing resource management activities [4]. Furthermore, by offering a framework for risk assessment and preventive actions, these units are essential in lessening the effects of natural disasters like floods and soil erosion. Since it maintains ecosystem health, encourages water efficiency, and lessens sensitivity to environmental risks, proper management of these regions is essential for promoting sustainable development. Investigating the drainage networks provides significant insights in understanding and assessing the natural threats and hazards including seismic activity, flash flooding, soil erosion, etc. [5]. Management of the watershed highlights the connections between upland and downstream regions as well as the interdependencies among land use, soil health, and water resources [6; 7]. Morphometric analysis can be described as the mathematical calculations of the Earth's surface, focusing on its different topographic signatures [8]. Morphometric studies began in the mid-twentieth century, utilizing conventional methods based on the manual analysis of topographic maps [9; 10; 11; 12]. Analyzing drainage network morphometrics using traditional methods is a highly time-consuming and labor-intensive process. Innovations in computational and geospatial technologies now facilitate more accurate and efficient evaluations. In situations where topographic maps are not accessible, satellite-based terrain information, such as digital elevation models (DEMs), can be utilized to extract the morphometric characteristics of a watershed. These DEMs can be integrated smoothly into geographic information systems (GIS) and provide continuous data, unlike the segmented contours found in traditional topographic maps [4]. The recent scientific literature utilizing DEMs for morphometric analysis includes works by the authors in Refs. [13; 14; 15]. In addition, investigations leveraging satellite imagery and GIS technology for morphometric assessments in watershed management encompass the work of the authors referenced in [16; 17; 18; 19]. Therefore, the analysis of the morphometric parameters using GIS and remotely sensed data and techniques offers a significant quantitative description assessment of the major morphological and hydrological characteristics present in different landscapes and Earth surface landforms. The characteristics of drainage networks within catchments and sub-catchments can be effectively modeled through the detailed examination of significant morphometric parameters, including stream order, bifurcation ratio, and stream length ratio [9].