THE ELECTRON DENSITY PROFILE INVERSION FOR INCOMPLETELY DEVELOPED CASE OF F sub(1) LAYER

The electron density profile inversion from vertical incidence ionograms is essential for research in ionospheric structures and movements, wave propagation and space weather applications, hence has gathered very wide attention. The echo trace of incompletely developed F sub(1) layer is common in vertical incidence ionograms, and it is usually expressed as smooth transition from F sub(1) layer to F sub(2) layer, not a cusp appeared at the critical frequency of F sub(1) layer. However, the existing ionospheric models and inversion algorithms are generally intended for the completely developed F sub(1) layer with the assumptions of a parabolic profile and an infinite slope at the peak of F sub(1) layer, which are not suitable for the profile of incompletely developed F sub(1) layer which achieves the maximum electron density of F sub(1) layer and enters F sub(2) layer at the peak of F sub(1) layer and has a finite slope. Consequently, an F sub(1) layer electron density profile model based on the shifted Chebyshev polynomial for incompletely developed case of F sub(1) layer is introduced with a parameter named as the model setting critical frequency. Taking into account the profile smoothness, an electron density profile inversion algorithm with constrained optimization F sub(1) and F sub(2) layer parameters based on the model mentioned above is proposed. The validity of the model and the inversion algorithm is analyzed through the simulation, and the effectivity of the proposed algorithm is further verified by the comparison between the synthesized vertical sounding & oblique sounding traces and the measured data.