A hybrid global optimization method: the one-dimensional case
Journal of Computational and Applied Mathematics
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In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, 驴), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of 驴 i = 2驴i are modulated with the annual signal harmonics of 驴 j = 2驴j/365.25 as 驴 ijM = 2驴i(1 卤 j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are 卤15 TECU and 卤6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.