## 3 Results and Discussion
### Model Validation  
To evaluate the efficacy of the FR model, ROC was employed to corroborate the predictions' correctness [77,78]. The vertical axis shows sensitivity, whereas the horizontal axis displays specificity [79]. The estimated models have been graded as poor, medium, good, very good, or outstanding in AUC-ROC ranges of 0.5-0.6, 0.6-0.7, 0.7-0.8, 0.8-0.9, and 0.9-1, respectively. [PERSON] [80] classified models as poor, fair, good, very good, or exceptional based on the AUC-ROC ranges. The calculated area under the curve (AUC) for Figure 8 was found to be 90.11%, indicating a very good, effective model that may produce trustworthy results. The role of geological formations (Figure 3) is considered the basis of hydrological studies, and an important factor to consider is a formation's connection with the water-bearing layers and the ability of rocks to permeate water to feed the aquifer. In addition, the relationship between the surface characteristics and their influence on the degree of slope on the intensity of runoff is also important, as it turns out that there are interchangeable layers of soft rocks. The process of sculpting by flowing runoff on rocks with greater resistance, such as limestone rocks, indicates that the region was affected by erosion factors  
Figure 8: AUC-ROC rate calculated for the created FR model. Figure 7: The flood susceptibility map (FSM) produced by FR models. resulting from water runoff and then the phenomenon of undermining the bottom of the slopes, which led to rockslides in the region and increased rates of retreat of rocky edges. The city of New Cairo has a dense network of roads of all degrees and road widths that, in general, vary with location in the region and the degree of connection to neighborhoods. It is noted that the periodic paving operations, which result in an explicit change and transformation of the land surface from just a natural surface permeable to water in varying proportions to a solid artificial surface that prevents the natural drainage of falling rainwater, increase the rates of runoff risk in urban areas if the slope factor and its direct impact participate with it. The velocity of runoff indicates the ability of water to carry rock and soil materials. In this study, we analyzed the spatial relationships between all inputs using a process of digital conversion of the surface water drainage network that threatens the region. Additionally, we utilized spatial analysis to determine the areas threatened by the danger of surface runoff on all types of land use in the region. This is also due to the uncalculated encroachments on the old valleys' streams, changes in land uses, the lack of avoidance of the main valleys' streams, the general slope trends, and the inclinations of the earth's surface in different neighborhoods of the city that vary in their geographical distribution and degree of their danger. Flash floods pose a significant threat to the safety and well-being of communities around the world, including in New Cairo, Egypt. A growing body of research has sought to understand the causes and impacts of flash floods in this region, as well as to develop effective mitigation strategies to reduce their frequency and severity. Several recent studies have shed light on the factors contributing to flash floods in New Cairo. For example, [PERSON] and [PERSON] (2018) used GIS-based multi-criteria decision analysis to create a flash flood susceptibility map for the city, identifying areas at high risk for flooding. Similarly, [PERSON] and [PERSON] (2018) assessed the flash flood hazard and risk in the Wadi Degla Protectorate area of New Cairo, finding that the main factors contributing to flash floods were land use change, urbanization, and climate change. Other studies have focused on the impacts of flash floods in New Cairo and potential mitigation strategies. [PERSON] and [PERSON] (2018) developed a flash flood risk map for the city, highlighting the importance of improved drainage systems and land use management to reduce the risk of flooding.