By the Fourier series expanding method, the observed F2 layer critical frequencies (foF2) globally over 70 station in a high solar activity year of 1958, are used to analyze the annual and semi-annual variations of foF2, and the world wide distribution features of their amplitude and phase in daytime and nighttime are studied in detail. The results for foF2 annual and semi-annual variation are summarized as follows. The midnight (2:00 LT) foF2 annual variations are noticeable in both hemipheres at mid-high latitudes, and their amplitudes are slightly larger in far pole regions than in near pole regions. Generally, at most stations, the midnight foF2 reach the maximum in summer, and no winter anomaly can be discerned. While in daytime (14:00 LT), there are pronounced annual variations with large amplitude in both hemispheres at mid-high latitudes. After carefully studying their phases, we find that these annual variations usually peak in winter, which indicate all the variations are classic winter anomaly. However, the winter anomaly is very weak in the equatorial zone and not even perceivable in South America. Moreover, the amplitude of daytime foF2 semi-annual variation is generally small in near pole regions and large in far poles region of both hemispheres. Compared with their annual component, the semi-annual variations in the tropical region are significant. Their phase distributions reveal that the semi-annual variation usually peaks in March and April.

In order to explain the results mentioned above, we studied the atomid molecular ratio [O/N₂] and confirmed that the noon foF2 annual variations prevailing in mid-high latitudes are caused largely by the annual variation of [O/N₂]. As the noon foF2 semi-annual variations pronounced in far pole regions, we should consider the contribution of [O/N₂], the solar zenith angle, the solar-driven low/mid-latitude thermospheric circulation and the magnetospherically driven high-latitude circulation. Moreover, we suggest that foF2 semi-annual variations appearing in the equatorial zone are closely related to other semi-annual variations in the upper atmosphere, such as the semi-annual variation of [O/N₂], the thermospheric circulation, the geomagnetic activities and even the ionospheric electrical field.