On the long-term stability of the association between foF2 and EUV solar proxies

Solar extreme ultraviolet (EUV) radiation is the main source of heating and ionization of the Earth's upper atmosphere, forcing most of this system's time variability, which in annual scales corresponds to the solar activity ∼11-year cycle. Due to the difficulties in obtaining solar EUV time series covering extended periods of time or during periods without measurements available, the use of solar EUV proxies became a solution. In the case of the ionosphere, and in particular the F2-layer critical frequency (foF2), in addition to the solar activity cycle variation, it may also exhibit the effect of long-term trend forcings, like the monotonous increasing greenhouse gas concentration since the industrial revolution. To accurately detect and measure this weak trend against the solar activity variability, it is crucial to account for the solar forced variation. Traditionally, it is modeled as a linear association between foF2 and a given solar EUV proxy. However, the stability of this association has become a controversial issue. It would be reasonable to assume, in turn, that if the ionospheric environment is undergoing a trend forced by a non-solar diver, like the greenhouse gas concentration increase, the relationship between foF2 and solar proxies may be affected, ceasing to be stable if this additional driver is not introduced in the modeled association. Using rolling regressions over the period 1960–2023 to analyze this stability, our results suggest that the issue may not only lie in the steady trend expected in foF2 from a non-solar source or the need to include terms in the simple linear regression commonly used, but also in the possible deviation of the different proxies from the 'true' EUV solar flux, which is the ultimate main driver of F2 region ionization, a deviation that has been intensifying over the last two decades. We assert that it is a deviation from the actual EUV behavior because the indices diverge from one another, something that should not occur if they all reflect the same solar EUV.