The real height analysis of ionograms: A generalized formulation

Abstract

A new procedure is described for the calculation of real height profiles from ionospheric W(f) records. The equations are formulated in a way which can reproduce all current methods of analysis, and provide many powerful extensions. For general use a sixth-order overlapping polynomial analysis is recommended, with real height sections determined by a least squares fit to real and virtual height data. Coefficients can also be obtained for single polynomials fitted separately to each ionospheric layer. All methods include Chapman layer peaks, and a model valley between layers. High-order least squares calculations give greater accuracy and stability than any current procedures, and are particularly suitable for the analysis of high-density data from digital ionosondes. INTRODU CTIO NThe sweep frequency ionosonde is a basic tool for ionospheric research. It produces records which can, in theory, be analyzed to give the variation of electron density with height up to the peak of the ionosphere. Such electron density profiles provide most of the information required for studies of the ionosphere and its effect on radio communications. Only a minute fraction of the recorded ionograms are analyzed in this way, however, because of the effort required and the uncertain accuracy of many results. To improve this situation we must make better use of the computing power now available, to reduce the need for careful selection of data and checking of results.Current procedures for the real height analysis of ionograms fall into three basic classes. Lamination methods calculate the profile pointsstep by step, beginning from the lowest frequency. Each step begins from the last calculated real height and is determined to fit (exactly) the next virtual height. ling, 1965; Becker, 1967; Wright, 1967; Gulyaeva, 1973] the initial gradient is matched to the previous real height section, and the gradient changes linearly within the calculated interval so as to match the next virtual height. This curvature gives a considerable increase in accuracy over the linear lamination procedure, although a similar increase can be obtained more simply by modifying the endpoints of the linear sections [Titheridge, 1979]. 2. Single-polynomial or profile-fitting methods represent the entire real height curve, up to the peak of a layer, by a single mathematical expression [Titheridge, 1961, 1967b, 1969]. This expression is normally a polynomial in plasma frequency (or in electron density), with some modification to include a parabolic peak. All real height coefficients are determined in one step, by a single fit to all the virtual height data. When the number of coefficients is equal to the number of measured virtual heights, the calculated profile will correctly reproduce the data. If the number of real height coefficients is made less than the number of virtual height data points, the calculated profile gives virtual heights which are a best least squares fit to the data [Titheridge and Lobb, 1977; Huang and Reinisch, 1982; Reinisch and Huang, 1983]. ...

Retrieval of thermospheric parameters from routinely observed F2-layer Ne(h) profiles at the geomagnetic equator

“…All the above indicate that additional tests are required in order to extract safe conclusions on the potentiality of the proposed method in accommodating routine Digisonde profiles. These tests should include the assessment of the method with manually scaled Digisonde profiles and/or the implementation of alternative scaling techniques, as for example POLAN software (Titheridge 1988).…”

Ionogram inversion for MARSIS topside sounding

“…The EOF-based inversion is developed from the traditional polynomial analysis of Titheridge (1961Titheridge ( , 1967aTitheridge ( , b, 1969Titheridge ( , 1975Titheridge ( , 1988 and Huang and Reinisch (1982) where the prior polynomials, e.g., Taylor polynomials or shifted Chebyshev polynomials, have now been replaced with empirical orthogonal functions (EOFs). The new technique has been applied here to the data processing of the MARSIS ionograms, with EOFs retrieved from the MGS radio occultation measurements.…”

“…Therefore, the lamination methods are now rarely used in practice. Titheridge (1961Titheridge ( , 1967aTitheridge ( , b, 1969Titheridge ( , 1975Titheridge ( , 1988 proposed a model-fitting method, or polynomial analysis in which the curve of true height vs. plasma frequency, h( f p ), is represented as a single or overlap-ping polynomial(s). Huang and Reinisch (1982) further developed the polynomial analysis by replacing Titheridge's Taylor polynomials with shifted Chebyshev polynomials, and applied it to the data processing of ISIS topside ionograms.…”

Local ionospheric electron density profile reconstruction in real time from simultaneous ground-based GNSS and ionosonde measurements

“…For example, a premature truncation of the scaled F2 trace were made by earlier versions of the autoscaling software, caused by echo trace gaps due to restricted frequency bands and/or bands of strong interference (Reinisch et al, 2005). Also, a comparison of the true-height electron density profiles inverted from ionograms using the POLAN (Titheridge, 1988) and NHPC (Reinisch et al, 2005) methods showed significant systematic differences (Sauli et al, 2007). Such differences can be explained with the differences in the underlying ionospheric profilers that are used.…”