## 2 Methodology
### Modeling Approach and Analysis Criteria  
The study's modeling approach and analysis criteria can be categorized into two distinct methodologies: quantitative analysis and qualitative analysis. The study employed quantitative analysis to transcribed workplane illuminance (WPI) values onto a tabulated format, focusing on the central grid positioned between bilateral windows on the south-north axis. Simulations were conducted for summer and winter solstices, as well as mid-season dates (21 June, 21 December), specifically at 12:30 p.m. and  
Figure 5: (a) Spherical annual sun path (map location of the case study); (b) 3D sun position at solstice winter midday time in Dammam city in Saudi Arabia. 3:30 p.m., coinciding with Duher and Aser prayer times. These periods were chosen to assess annual variations and critical times. Simulation points (grids) within the prayer halls were arranged according to the layout of work planes, with a minimum of 225 points in the men's hall and 60 in the women's hall, all at a height of 0.30 m suitable for reading the holy Quran. The spacing between these points was maintained at 1.8 m for precision, as shown in Figure 6. A hemispherical fisheye camera (180\({}^{\circ}\)) was strategically placed at the center of each hall. The rendered images were presented in false color using a logarithmic scale for clarity. The study also incorporated an evaluation of indoor visual comfort using the green building rating system, Leadership in Energy and Environmental Design (LEED v4.1). This standard focuses on two main metrics: spacial daylight autonomy (sDA\({}_{300\text{lux}}\)) and annual sun exposure (ASE > 1000 lux, 250 h). The sDA\({}_{300\text{lux}}\) metric assesses the percentage of an often-occupied floor area achieving the desired illumination levels (300 lux) under varying sky conditions throughout the year. The ASE\({}_{>1000\text{lux},250\text{h}}\) metric quantifies the proportion of regularly used floor space receiving direct sunlight (>1000 lux) for over 250 h annually Additionally, the useful daylight illuminance (UDI) metric, with thresholds ranging from 300 lux to 3000 lux, was employed to effectively indicate high illumination levels that may cause discomfort gl  
Figure 6: **(a)** Photograph of the indoor prayer zone in Alshagroud Mosque. (**b1**) Plan view and (**b2**) section view of grid arrangement and camera positioning for the men’s prayer zone. (**c1**) Plan view and (**c2**) section view of grid arrangement and camera positioning for the women’s prayer zone simulation setup. To further enhance the study, a modeling approach, qualitative analysis, and analysis criteria were introduced, focusing on an additional daylighting metric: daylight glare probability (DGP) [50; 57]. DGP is a critical metric for assessing visual comfort in indoor environments, as it quantifies the likelihood of occupants experiencing glare due to high luminance ratios or bright light sources within their field of view. This metric is particularly relevant in spaces with large window areas or direct sunlight exposure. Incorporating DGP into the analysis provides a more comprehensive understanding of the daylighting quality, ensuring not just adequate illumination, but also comfort and wellbeing of the occupants. It is important to note that a comprehensive understanding of glare throughout the year can provide a more holistic view of the building's performance. However, prioritizing summer analysis is a strategic decision that aligns with the peak conditions for sunlight exposure, ensuring occupant comfort and spiritual engagement during these significant times. This holistic approach to daylighting analysis, encompassing both quantitative and qualitative measures, aligns with the evolving standards of sustainable and human-centric design practices. Additionally, daylight distribution quality was measured using the uniformity index (Ui), a ratio of average to maximum illumination on the work plane, adhering to the NBN L13-001 code and international standards [35].