# A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory
## 1 Introduction  
The ionosphere is a crucial component of the Sun-Earth space environment, affecting the performance of various radio information systems such as satellite navigation, communication, and radar due to its refraction, reflection, scattering, and absorption effects on radio waves passing through it. Therefore, studying the ionosphere's characteristic parameters and understanding its spatiotemporal variations are of significant practical value for high-frequency communications, terrestrial and space radio links, and other applications [1]. The ionosphere, characterized by complex and variable plasma activities, functions as a nonlinear system with random temporal and spatial fluctuations. Notably,the F2 layer within the ionosphere harbors the highest electron concentration, significantly influencing different radio propagation modes [2]. The critical frequency of the F2 layer (foF2) is a key parameter for ionospheric research and a primary focus for studying ionospheric plasma disturbances. In addition, foF2 is extensively utilized in space weather [3] and high-frequency communications [4], among other applications. Accurate forecasting of the foF2 is crucial for these applications. The foF2 varies with diurnal and seasonal cycles and solar activity, and it is strongly correlated with spatial latitude and longitude [5]. Accurate reconstruction of the foF2 is thus critical for understanding and utilizing the ionosphere [6]. The foF2 can be directly or indirectly observed by vertical and oblique ionospheric detectors [7]. If no ionospheric detection station exists, then these parameters can be obtained by reconstructing the spatial reconstruction model.  
For a long time, ionospheric reconstruction has been a major focus of ionospheric research. Scholars worldwide have continuously studied ionospheric regional reconstruction technology to improve the accuracy of ionospheric parameter predictions. In recent years, researchers have gradually established models in localized regions such as China [8], Europe [9], and Oceania [10]. Typical examples include inverse distance weighted interpolation [11], thin-plate spline interpolation [12], spherical harmonics [13; 14], and Kriging interpolation [15]. These methods have demonstrated good performance in reflecting the global or local spatial distribution characteristics of the foF2. On one hand, based on the coverage of models, foF2 spatial reconstruction can be divided into global and regional types. Models like IRI [16] and ITU-R [17] span large spatial scales, offering more generalized predictions by considering the overall features of the global ionosphere and focusing on large-scale spatial structures. On the other hand, regional models, which require higher real-time performance, can accurately predict small- and medium-scale changes in the foF2 within localized areas. Therefore, regional models are mainstream in current research and are essential for future communication system applications [18].  
To enhance the accuracy of spatial reconstruction of the ionospheric foF2, we adopted the HAS modeling theory. This method typically produces optimal results in spatial data interpolation [19]. One key advantage is that the coefficient matrix of the linear algebraic equations remains constant in each iteration [20], necessitating only a single inverse calculation, which significantly lowers the computational burden [21]. After years of iteration, the HAS method has achieved excellent results in many fields [22; 23]. This paper is structured as follows. First, we introduce the background and significance of ionospheric research and foF2 parameter studies. Second, we sequentially introduce the data, concepts, methods, and specific modeling processes used. Then, we compare the proposed model with IRI and Kriging to verify the method's correctness and effectiveness. Finally, we summarize the effects of reconstruction of the ionospheric foF2 parameter.