Numerical methods are developed for producing worldwide, long-term predictions of ionospheric characteristics. The methods are based on analyses of series of coefficients defining numerical maps, which take into account both annual and solar cycle variations of the ionosphere. The end product is a five-dimensional numerical map depending on two geographic coordinates, time of day (universal time), time of year, and solar index. Predicted numerical maps in geographical and universal time coordinates are obtained by specifying the month and a predicted value of solar index. The methods are applied to foF2 monthly medians, using for the analysis a series of 60 numerical maps from January 1954 through December 1958, Predicted and observed values of the characteristics are compared for a large sample of data.

The ionosphere of the Earth has been actively studied since the 1920's, following the discovery of ground radio-sounding. By means of this method results were ohtained by an international network of ionospheric stations, in particular, by the successful implementation of a number of rigorously planned international scientific research programs,'" enabling the collection of extensive experimental material on some of the most important parameters of the ionosphere - the critical freLjuencies of E-, Fl and F2-layers. Comprehensive analyses of these observation data give a fairly complete picture of the various changes taking place in the principal ionospheric layers at different points on our globe. Another important aspect of the study of the ionosphere, which has been in progress for the past three decades, is an extensive program of in situ determinations of the various physical parameters - first using rockets, and subsequently artificial satellites. The data thus obtained on the principal ionizing agent - short-wave solar radiation - and on the physical conditions prevailing in the upper atmosphere and in the ionosphere at different altitudes, allow the proposal of a self-consistent mechanism of ionosphere formation. A general outline of the theory of ionosphere formation at different altitudes is now complete. Its application to specific cases, dependent on a more accurate determination of input parameters to give solutions valid for a definite set of conditions etc., is yet to be accomplished. The use of artificial satellites in cosmic research yielded abundant scientific data.

Hourly values of ground-based ionosonde data have been subjected to a detailed statistical analysis in order to determine the day-to-day variability displayed by various ionospheric regions. It is found that the standard deviation about the observed F2 region monthly median critical frequency is two to three times that observed in the E and F1 regions at mid-latitudes. The day- to-day variability of foE and foF1 is such that monthly median values of those parameters can be used to represent the daily variation in the E and F1 region. This would imply that HF prediction programs which rely on median data for specification of the ionosphere yield results that can be used in day-to-day operations for those propagation modes that are controlled by the E and F1 region. As the F2 region is highly variable, a method of using timely observations of foF2 to predict the expected values of the F2 region critical frequency has been developed. The method has the advantage that errors in predicting the monthly median foF2 can be averted and the predicted values are generally closer to the actual observations than the observed monthly median.