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Long term prediction models

The ionospheric variability of the E and F1 layers can be adequately described by the Chapman theory. This means that the behaviour of these layers can be predicted through very simple formulas. For example, the historical series of measurements of the critical frequencies foE and foF1 collected at the Rome (Italy) observatory, have been used to conduct a statistical regression analysis from which the following two formulas have been devised: 

foE= 3.18[(1+8.83*10-3*R)cosχ]0.222   (1)
foF1 = 4.00[(1+1.36*10-2 R)cosχ]0.196 (2)
 The formulas (1) and (2) are valid in the Mediterranean area. They are directly derived from the Chapman theory and constitute an example of long-term prediction models. These formulas show that the critical frequencies depend on the solar activity (through the sunspots number R) and on the solar zenith angle χ that varies according to the formula
cosχ = senφsenδ + cosφcosδcosω
being φ the geographic latitude of the observation site, δ the solar declination (the height of the Sun over the celestial equator, ranging between around –22.27° in winter solstice and +22.27° in summer solstice) and ω the solar hourly angle in the location and at the time under consideration.
Since the F2 region does not follow the behaviour described by the Chapman theory, its variability cannot be predicted through simple formulas. Generally, the prediction models concerning the F region are developed by using parameters as R12 (a solar activity index defined as the twelve-month smoothed mean of sunspot number R; although other kinds of smoothed means could have been used) and the monthly median values of the ionospheric characteristics (foF2, MUF(3000)F2, M(3000)F2, h′F2, foF1, h′F1, foE, h′E) collected by a network of ground ionospheric stations over a long time interval.
Usually, a significant statistical regression analysis that takes into account the huge data records produced is carried out to find the “law” that fits better the measurements.
This “law” is used to predict the ionospheric parameter under consideration for a future period. The ionospheric parameters obtained in this way, are then interpolated to calculate the values in those areas where they cannot be directly measured (for example, deserts and oceans). This approach is used to produce local and regional prediction maps of all the ionospheric characteristics. These maps, usually obtained for a given value of R12, and for a given month and time, constitute the long term predictions, that are valid in the case of undisturbed ionospheric conditions, i.e. in the case of “quiet” ionosphere (figure 1).
Figura 1 Long term prediction map of the ionospheric characteristic foF2 obtained through the SIRM model over the European region in September 2008 at 14.00 UT.


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