Signal decomposition techniques for foF2 long-term ionospheric trend analysis

Four signal decomposition techniques were applied to the problem of estimating ionospheric long-term trends: a variant of Empirical Mode Decomposition (EMD), Seasonal and Trend decomposition using Loess (STL), Singular Spectrum Analysis (SSA), and Fourier Transform (FT). This is the first time these techniques have been used to estimate ionospheric trends. The results were compared with the classic double-step linear regression method, the most used method to filter the solar influence from the ionospheric foF2, and with atmospheric general circulation models. Since yearly average ionospheric data exhibit strong linear correlation with solar EUV proxies, we analyze five solar flux indices at radio wavelengths alongside ionospheric data from 9 stations covering the period 1976–2022. The decomposition models can be used independently on every time series to filter periodicities and trends. The proxies are scaled to ionospheric data range using a linear regression, and the residuals are subtracted in order to estimate trends. The results using solar flux F15 are in good agreement with trends predicted by atmospheric circulation models of 0.7 %/decade, STL and SSA result in −0.8 %/decade, and FT in −0.5 %/decade; most models and proxies result in a negative averaged trend. F10.7 trends are lower than expected, about −0.2 %/decade for SSA and STL, and − 0.1 %/decade using FT. Among the tested methods, the FT provides the most consistent results. CEEMDAN can also estimate reliable results, but only when solar and ionospheric data are filtered in the same number of steps. This work demonstrates how novel techniques can complement the study of long-term trends in the upper atmosphere. While recent studies have identified the F30 solar flux as the most suitable proxy for trend estimation, our analysis reveals that it consistently produces stronger negative trends than expected. In contrast, the F15 solar flux, an index that is rarely used, emerges as the most reliable proxy using the methodology presented in this work.