## 1 Introduction  
The ionosphere, situated in the upper region of Earth's atmosphere, maintains a continuous state of ionization primarily caused by solar radiation. This layer spans from approximately 60 km to 1000 km above the Earth's surface [1]. The Earth's ionosphere plays a crucial role in facilitating high-frequency communication and navigation systems, serving as a critical medium for the propagation of radio waves. It exhibits complicated spatial and temporal changes that can disrupt the transmission of radio signals, adversely impacting satellites, communication, navigation, and geographic location [2; 3; 4; 5; 6]. The ionosphere's Total Electron Content (TEC) is a key parameter that characterizes the integrated electron density along the signal's path. The TEC is the total number of electrons in the path from the satellite to the receiver, in a column with a 1 m\({}^{2}\) cross-section. Its unit is the TECU, where \(1 TECU=10^{16}\) e/m\({}^{-2}\) is a parameter that describes the behavior of the ionosphere [7]. During radio wave propagation, the electron density in the Earth's atmosphere is expected to vary over a nominal range of \(10^{16}\) e/m\({}^{-2}\) to \(10^{19}\) e/m\({}^{-2}\), being the minimum and maximum values reached around midnight and mid-afternoon, respectively [8], and is obtained from the signals L1 (1.57542 GHz) and L2 (1.2276 GHz) of the Global Positioning Systems [9]. However, this region is not impervious to the influence of solar activity, particularly solar flares--intense bursts of radiation and energy released from the Sun's surface. Solar flares can lead to significant disturbances in the ionosphere, impacting TEC and affecting the reliability and performance of high-frequency communication and navigation systems. A solar flare, also referred to as a chromospheric burst, is a significant release of high-energy radiation frequently observed from the Sun. It holds immense importance in the realm of space weather due to its powerful and energetic nature [10; 11]. Solarflares stem from the active region of the Sun, typically near a cluster of sunspots, and can endure anywhere from minutes to hours. These solar flares represent the most powerful and abrupt explosive events during which a substantial number of high-energy protons, electrons, and intense radiation spanning the entire electromagnetic spectrum are emitted. Consequently, there is a notable surge in extreme ultraviolet (EUV) and X-ray emissions, leading to additional ionization in the dayside ionosphere [12]. Numerous studies have indicated a complex relationship between solar flares and ionospheric perturbations, with the potential to cause disruptions in TEC. Variations in electron density during solar flares can affect the phase and amplitude of radio signals propagating through the ionosphere, leading to signal fading, scintillation, and navigation inaccuracies [13; 14; 15; 16; 17]. Such effects can have substantial consequences for global navigation satellite systems (GNSS), satellite-based communication links, and other applications that rely on ionospheric propagation. [PERSON] et al. [13] investigated the influence of X-class solar flares on GNSS signals during the solar maximum of Cycle 24. Their study utilized GNSS data to analyze the TEC variations caused by solar flares and assess the impact on positioning accuracy. [PERSON] [14] reviewed the space weather effects on high-accuracy GNSS-based navigation, discussing the implications of solar flares on GNSS signal propagation, TEC estimation, and navigation performance. [PERSON] et al. [15] analyzed the impacts of the St. Patrick's Day storm on the high-latitude ionosphere using GPS and CHAMP data. Their study investigated the TEC variations induced by solar flares during this geomagnetic storm. [PERSON] et al. [16] examined the ionospheric response to the solar flare of 10 September 2017 and its impact on GNSS positioning in the Asia-Oceania region. Their research highlighted the regional variability of TEC disturbances caused by solar flares.