## 1 Introduction
The use of 5G-satellite networks in IoT applications, especially within smart cities, introduces unique challenges that necessitate further research. [PERSON] et al. [1] argue that integrating satellite connectivity in urban IoT frameworks requires careful planning to address interference from dense infrastructure, high device density, and environmental variability. [PERSON] et al. [2] discuss the technical implications of IoT applications in 5G-satellite integrated networks, focusing on stringent latency and reliability requirements for real-time applications like traffic monitoring, public safety, and energy management. Recent studies highlight the need for adaptive network control mechanisms to dynamically manage resource allocation and optimize connectivity. [PERSON] et al. [16] and [PERSON] et al. [17] suggest that 5G-satellite integrated networks for IoT in smart cities can benefit from algorithms for dynamic power adjustment, interference cancellation, and multipath routing, aiming to optimize network efficiency and resilience, especially where terrestrial support is limited. Advanced AI-driven approaches, as discussed by [PERSON] et al. [11], show promise for managing complex, real-time network adjustments, enhancing system adaptability to fluctuating environmental and traffic conditions. Building upon the established foundation of 5G-satellite convergence research, this study enhances the two-ray propagation model to incorporate complex environmental attenuation factors, such as rain and atmospheric absorption, that significantly impact high-frequency signals typical of 5G and satellite communications [18]. These factors are critical in modelling real-world scenarios accurately, especially at millimetre-wave (mmWave) frequencies, where propagation losses due to rain and atmospheric gases become pronounced [19; 20; 21]. We integrate the ITU-R rain attenuation model, which provides frequency-dependent attenuation based on the rain rate and path length, significantly affecting the signal strength under high rain conditions [22]. Additionally, we incorporate atmospheric absorption for oxygen and water vapour, critical for high-frequency bands in 5G and satellite communications, calculated based on ITU-R recommendations to account for temperature, humidity, and pressure variations along the path. Unlike previous studies focusing on terrestrial or satellite-only propagation, our work delves into how altitude, distance, and environmental reflections impact signal quality in 5G-satellite networks. These novel components enable a more comprehensive analysis of real-world signal behaviour, offering valuable insights for designing and optimizing robust hybrid communication networks for IoT applications in urban smart cities and remote regions. This paper extends the application of the two-ray model to 5G-satellite convergence, with a specific focus on its implications for signal strength and quality under realistic environmental conditions. Section 2 provides a review on 5G and satellite network convergence, summarizing existing studies and the literature. In Section 3, we introduce the enhanced two-ray model that includes rain attenuation and atmospheric absorption. We analyse the model's predictive capability in identifying areas of constructive and destructive interference, crucial for designing resilient hybrid systems. Section 4 presents the results, offering insights into optimizing 5G-satellite integrated networks capable of supporting diverse IoT applications in a 5G-satellite smart city. Section 5 shows analytical validation of our proposed framework and Section 6 gives the conclusions from our findings.