The accuracy of simple methods for determining the height of the maximum electron concentration of the F2-layer from scaled ionospheric characteristics

The techniques for estimating hmF2 from M(3000)F2 are reviewed with particular stress put upon those in which the effects of underlying ionization are accounted for by a correction (ΔM) to M(3000)F2, formulated in terms of the ratio foF2/foE(=xE). The simplifying assumptions involved in the three practical implementations (Bradley and Dudeney, 1973; Dudeney, 1974; Bilitza et al., 1979) are emphasised and their consequences investigated quantitatively using a numerical simulation. The factors considered are the dependence upon ymF2, the importance of the underlying layer shape (in particular the significance of the F1-ledge), and the influence of the geomagnetic field. It is demonstrated that the correction technique relies upon ymF2 being a direct polynomial function of hmF2. Analysis of observational data suggests that this relationship holds in practice. Fluctuations in ymF2 about this mean variation are shown to produce only small effects which decrease in magnitude as the amount of underlying ionization increases. The results indicate that underlying layer shape becomes very important when a large amount of underlying ionization is present (xE<2.5). However, the global morphology of the occurrence of the F1-ledge is such that it is invariably present in such circumstances (ignoring the polar regions). Hence, the ionosphere tends to assume a specific profile form for low xE cases. The three implementations are shown all to fortuitously incorporate this behaviour. It is demonstrated that exclusion of the geomagnetic field introduces a very small extra uncertainty dependent upon gyrofrequency and geomagnetic latitude, which decreases as the amount of underlying ionization increases. The three implementations are compared and it is concluded that the Dudeney (1974) scheme gives the best overall performance. The more modern and complex Bilitza et al. (1979) scheme appears to have no performance advantages, whilst containing a sunspot number dependent geomagnetic term whose behaviour is irreconcilible with the numerical simulation. The Dudeney (1974) equation is shown to be accurate to between 4 and 5% at magnetic mid-latitudes. The scope for further refinement is considered but rejected as being unlikely to produce an increase in accuracy commensurate with the effort required.