THE ELECTRON DENSITY PROFILE INVERSION FOR INCOMPLETELY DEVELOPED CASE OF F1 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 F₁ layer is common in vertical incidence ionograms, and it is usually expressed as smooth transition from F₁ layer to F₂ layer, not a cusp appeared at the critical frequency of F₁ layer. However, the existing ionospheric models and inversion algorithms are generally intended for the completely developed F₁ layer with the assumptions of a parabolic profile and an infinite slope at the peak of F₁ layer, which are not suitable for the profile of incompletely developed F₁ layer which achieves the maximum electron density of F₁ layer and enters F₂ layer at the peak of F₁ layer and has a finite slope. Consequently, an F₁ layer electron density profile model based on the shifted Chebyshev polynomial for incompletely developed case of F₁ 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 F₁ and F₂ 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.