Parameterized Procedure for Determining Real Height from Ionograms by Use of Generalized Parabolic Profiles

摘要

In previous reports an analytic procedure was developed for determining real heights from ionograms by directly solving the integral relation between real height and virtual height. The real height could then be obtained by a direct integration of the virtual height over the range of frequencies encountered. In a later report the method was applied to typical ionograms; the required integration being performed numerically. In addition, a simplified procedure was developed in which and ionogram could be fitted to a parametric series of polynomials and the integration required for determination of real height performed analytically. This report generalizes this procedure by modeling electron density provides in terms of a parameterized series of generalized parabolic profiles. The profiles are then converted to virtual height or ionogram form. The real height corresponding to a given ionogram is obtained by comparison of the ionogram with the parameterized profiles. Since the real height for a given paramterized profile is related in a very simple way to its virtual height, the integration process required for the previous polynominal method is hereby avoided. In additions, since the parabolic profile has a vertical slope at the maximum electron density, it provides a better fit to ionospheric data than a polynomial.