In the spectral analysis of time series, the necessity of a robust determination of the background power spectrum and identification of discrete power enhancements, due to the occurrence of periodic fluctuations, encompasses many research fields. Some application in geophysical and astrophysical observations are the identification of periodic density structures in the solar wind, the distinction between discrete and broadband Ultra Low frequency waves in Earth’s magnetospheric field, and the turbulent evolution of the solar wind. Here, we present a new method based on the adaptively weighted multitaper estimate of the power spectral density. Given the direct spectrum (raw) and its four different smoothed versions (med, mlog, bin, but) we obtain, via a maximum likelihood approach, robust background spectrum estimates according to four models (WHT, PL, AR(1), BPL). We select the best representation through statistical criteria and define the confidence levels of possible power spectrum enhancements. We identify periodicities in the time series by combining the discrete power enhancements identified in the spectrum with those identified in the multitaper harmonic F test. We demonstrate the algorithm on a case study of magnetospheric field fluctuations directly driven by periodic structures in the solar wind proton density. The method is robust and flexible, allowing for the characterization of the background spectrum in three distinct environments: the solar wind, magnetosphere, and ground observatories. Using our algorithm to identify background spectra and identify discrete periodicities, we show that there is a directly driven periodicity at f≈0.9 mHz and possibly at f≈0.2 and ≈0.4 mHz.

Identifying the nature and source of Ultra Low Frequencies (ULF) waves (f ≤ 4 mHz) at discrete frequencies in the Earth’s magnetosphere is a complex task. The challenge comes from the simultaneous occurrence of externally and internally generated waves, and the ability to robustly identify such perturbations. Using a recently developed robust spectral analysis procedure, we study an interval that exhibited in magnetic field measurements at geosynchronous orbit and in ground magnetic observatories both internally supported and externally generated ULF waves. The event occurred on November 9, 2002 during the interaction of the magnetosphere with two interplanetary shocks that were followed by a train of 90 min solar wind periodic density structures. Using the Wang-Sheeley-Arge model, we mapped the source of this solar wind stream to an active region and a mid-latitude coronal hole just prior to crossing the Heliospheric current sheet. In both the solar wind density and magnetospheric field fluctuations, we separated broad power increases from enhancements at specific frequencies. For the waves at discrete frequencies, we used the combination of satellite and ground magnetometer observations to identify differences in frequency, polarization, and observed magnetospheric locations. The magnetospheric response was characterized by: (i) forced breathing by periodic solar wind dynamic pressure variations below ≈ 1 mHz; (ii) a combination of directly driven oscillations and wave modes triggered by additional mechanisms (e.g., shock and interplanetary magnetic field discontinuity impact, and substorm activity) between ≈ 1 and ≈ 4 mHz; and (iii) largely triggered modes above ≈ 4 mHz.