## 1 Introduction

[2] The formation of equatorial irregularities in the ionosphere can cause communications outages by disrupting waveforms as a signal travels through the irregularity. Sharp changes in ion density within and around an irregularity cause communication signals to refract as they travel through the ionosphere, distorting the waveform recorded by an observer. The Communications/Navigation Outage Forecasting System (C/NOFS) satellite carries a suite of instruments to measure a number of expected drivers for irregularity formation.

[3] The purpose of this paper is to establish a methodology for detecting plasma irregularities from in situ satellite data which will reveal instability regions that coincide with the observations of scintillation on the ground. For this purpose, we have calculated a “quasi *S*_{4} index” for which the appearance above a given threshold can be compared with the true *S*_{4} index measured by a ground station. The *S*_{4} index [*Briggs and Parkin*, 1963] measures the root mean square fluctuations in signal intensity, normalized by the average signal intensity:

It is not our intent here to compare the absolute magnitude of the derived *S*_{4} index with true values observed on the ground. Rather, we seek to establish that irregularity occurrence regions identified with an elevated “quasi *S*_{4} index” coincide with those observed on the ground.

[4] Perturbations to in situ measurements of total ion density by the Coupled Ion and Neutral Dynamics Investigation (CINDI) along the satellite track are extracted using wavelets. Wavelets are a time-domain technique useful for signal analysis and many other applications. Wavelets have been used to analyze amplitude scintillation measurements by *Wernik* [1997] and *Materassi and Mitchell* [2007] as well as to study turbulence in the high latitude ionosphere [*Lagoutte et al.*, 1992]. A review of wavelets for geophysical applications can be found in *Kumar and Foufoula-Georgiou*.

[5] The Morlet wavelet is chosen here due to its construction using the sines and cosines present in Fourier analysis. This construction gives the Morlet wavelet a limited bandwidth that can be used to isolate variations at a particular scale size. Further, the power spectrum as well as the waveforms isolated for a particular scale size may be interpreted similarly to those produced by Fourier analysis. Thus, the results from the Morlet wavelet may be compatible with analyses and intuition based upon Fourier analysis of ionospheric irregularities.

[6] An advantage of wavelets over the Fourier method is that time information is retained, providing greater specificity on when irregularities occur. The retained time information also offers some practical benefits in producing an accurate characterization of density variations in a long satellite data set. Using wavelets, density measurements may be analyzed using very short segments of the data set in real time but produce the same result as if the whole data set was analyzed at once. While the frequency resolution of the Fourier transform is dependent upon the overall length of the data set analyzed, this does not apply to wavelets. Wavelets are time-limited signals thus the convolution of a wavelet and a signal that comprises the wavelet transform is only nonzero within the wavelet. Data sets longer than the wavelet thus have no impact on the quality of the results. While the use of a short data segment will introduce errors in the wavelet transform near the edges of the segment, these locations are known and may be ignored. By using a series of overlapping segments along the satellite track, a complete analysis of the data set may be constructed using only wavelet transforms unaffected by edge effects, producing an accurate power spectrum for all density measurements.

[7] To validate the wavelet-extracted density perturbations along the satellite track, the perturbations are used to estimate *S*_{4} following the in situ analysis performed by *Basu et al.* [1976] for the equatorial OGO-6 satellite. *Basu et al.* [1976] implements the phase screen analysis by *Rufenach*[1975, 1976] which presumes that the irregularity follows a power law with scale size. This power law is used to relate the magnitude of irregularities at sizes measurable by the satellite to scale sizes that impact radio waves of interest. *Wernik et al.* [2007] use *Rino* [1979a] and incorporates the International Reference Ionosphere (IRI) model to account for the location of the peak in ion density relative to the satellite to identify polar scintillation using Dynamics Explorer data. The work by *Rino* [1979a] requires a turbulence parameter which may be determined using the measured spectral index as well as the power within the irregularity at one scale size. These parameters may also be determined using the presented method.

[8] Scaling the observed densities to those observed at the *F* peak is not attempted here and is reserved for future work. Without knowledge of the full density altitude profile, the presented in situ-estimated *S*_{4} index is expected to under report the scintillation intensity and should not be used in an absolute sense. Further, in situ measurements reported by *Singh and Szuszczewicz* [1984] also demonstrate deviations from a power law in the spectral index based upon scale size, which are not included here. Using a single power law scaling may overestimate scintillation at smaller length scales [*Retterer*, 2010]. For this paper, a constant spectral index is assumed.

[9] The in situ estimate is compared against measurements of *S*_{4} performed by the Scintillation Network and Decision Aid (SCINDA) [*Groves et al.*, 1997; *Carrano and Groves*, 2006], a network of ground-based receivers that monitor scintillations at the UHF and L-Band frequencies caused by electron density irregularities in the equatorial ionosphere. A comparison of the in situ *S*_{4} and SCINDA 5 min averages of *S*_{4} at 250 MHz is presented and used to establish that wavelets are effective at identifying irregularities from total ion density measurements and that the wavelet-determined variance associated with the irregularity may be used as input for scintillation estimation methods.