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Scale analysis of equatorial plasma irregularities derived from Swarm constellation
© The Author(s) 2016
- Received: 11 December 2015
- Accepted: 28 June 2016
- Published: 15 July 2016
In this study, we investigated the scale sizes of equatorial plasma irregularities (EPIs) using measurements from the Swarm satellites during its early mission and final constellation phases. We found that with longitudinal separation between Swarm satellites larger than 0.4°, no significant correlation was found any more. This result suggests that EPI structures include plasma density scale sizes less than 44 km in the zonal direction. During the Swarm earlier mission phase, clearly better EPI correlations are obtained in the northern hemisphere, implying more fragmented irregularities in the southern hemisphere where the ambient magnetic field is low. The previously reported inverted-C shell structure of EPIs is generally confirmed by the Swarm observations in the northern hemisphere, but with various tilt angles. From the Swarm spacecrafts with zonal separations of about 150 km, we conclude that larger zonal scale sizes of irregularities exist during the early evening hours (around 1900 LT).
- Equatorial plasma irregularities
- Ionospheric scale lengths
- Swarm constellation
At the low-latitude ionosphere, the equatorial plasma irregularities (EPIs), also often called equatorial plasma bubbles (EPBs) or equatorial spread-F (ESF), have been a subject of intense research for several decades. Their morphology, including the generation and evolution processes, spatial structures, global distribution, as well as their effects on the global navigation satellite system (GNSS) have widely been investigated by ground-based radars and in situ satellite observations (Tsunoda 1980; Huang et al. 2001; Burke et al. 2004; Kil et al. 2004; Su et al. 2006; Stolle et al. 2006; Yokoyama et al. 2007; Xiong et al. 2010, 2012; Huang et al. 2014; Park et al. 2015a). These plasma irregularities usually cover a range of scale sizes, from thousands of kilometers to a few meters (e.g., Zargham and Seyler 1989; Hysell and Seyler 1998). EPIs with scale sizes larger than about 100 km, between 10 and 100 m, and smaller than 100 m have been classified as large-, intermediate-, and small-scale structures, respectively (Lühr et al. 2014).
Singh et al. (1997) presented some examples of EPIs from the Atmosphere Explorer E (AE-E) satellite observations showing that EPIs can develop from wavy density structures in the bottom side F-layer around sunset. These wavy structures with zonal (east–west) wavelengths of about 150–880 km evolved later into either large-scale depletions or multiple depleted patches. In a fully developed EPI event, structures with wavelengths from 690 km down to about 0.5 km were simultaneously present. Plasma density measurements with high sampling rates (up to 1024 Hz) on board the ROCSAT-1 satellite have provided a comprehensive view of the spectral characteristics of EPIs (Su et al. 2001). They also showed that the plasma irregularity spectrum can be approximated by a power law with piecewise constant spectral indices. In the meridional (north–south) direction, the 50-Hz magnetic field data from the CHAMP satellite revealed EPI structures with scale size as small as 50 m (Stolle et al. 2006).
In situ satellite measurements mainly detect EPI structures along the satellite track. For a single spacecraft mission, the plasma irregularities can only be sampled either in the zonal direction (for low-inclination satellites, such as AE-E, ROCSAT-1, and C/NOFS) or in the meridional direction (for near-polar orbiting satellites, such as CHAMP and GRACE). ESA’s newly launched Swarm constellation comprised of three spacecrafts (with the lower pair flying side-by-side) providing now the opportunity for investigating EPIs in both meridional and zonal directions. Related case studies from Swarm observations focusing on a dayside plasma depletion (Park et al. 2015b) and its relation to GNSS signal losses (Buchert et al. 2015) have already been reported.
In this paper, we present a statistical study of EPI scale sizes, as derived from the Swarm constellation measurements. We aim to reveal the typical scale sizes of EPIs in both the meridional and zonal directions. In the section to follow, we first introduce the data set. Examples and statistical results of EPIs are presented in section “Results.” In section “Discussion and summary,” we will discuss our observations in the context of earlier reports and summarize our findings.
The Swarm fleet, comprising three spacecrafts, was launched on November 22, 2013, into a near-polar (87.5° inclination) orbit with initial altitude of about 500 km. From January 2014 onward, the three spacecrafts were maneuvered apart and achieved their final constellation on April 17, 2014. From then on, the lower pair, Swarm A and C, are flying side-by-side at an altitude of about 470 km, separated by about 1.4° in longitude. The third spacecraft, Swarm B, orbits the Earth at about 520 km with a somewhat higher inclination. The plasma density data set measured by the electric field instrument (EFI) onboard Swarm is available at http://earth.esa.int/swarm, including the Langmuir probe (LP)-derived plasma density data with a time resolution of 2 Hz.
After the final constellation has been completed on April 17, 2014, Swarm A and C started flying side-by-side at an altitude of about 470 km, separated by about 1.4° in longitude, with Swarm C a few seconds ahead of Swarm A. The evolutions of their longitudinal and temporal separations are presented in Fig. 1c, d. For the second period, we used data from April 17, 2014 to September 27, 2015, and consider only observations from the lower spacecraft pair, Swarm C/A.
For detecting EPI events from the Swarm electron density measurements, we used the same approach as described by (Xiong et al. 2010). Electron density (Ne) time series from each equatorial orbital segment (within ±40° magnetic latitude, MLAT) are first high-pass filtered with a cutoff period of 40 s, corresponding to an along-track wavelength of about 300 km. The magnetic latitude we used is calculated by the Apex or Quasi-Dipole magnetic field model, which has been defined by Richmond (1995) and updated by Emmert et al. (2010). Subsequently, the filtered signal is rectified. Values exceeding an upper limit (UL) are identified as an EPI event. For each event, the rectified signal should have multi-peaked values above UL, and this event is limited along the orbit, by rectified signals below a lower limit (LL) for at least 3° north and south of the event. Otherwise, the fluctuations of rectified signal are attributed to enhanced noise and are considered as not significant. The thresholds of UL and LL are set here to 3 × 1010 m−3 and 1.5 × 1010 m−3, respectively, which are mainly estimated from the level of quiet-time Ne variations at Swarm altitudes. Using such a method for detecting plasma irregularities, we focus on EPIs with plasma structures scale lengths less than 300 km.
For deriving EPI scale sizes, we determine their correlation from the electron density recordings between two Swarm spacecrafts. For the early mission phase, we divided the spacecraft into three pairs: Swarm B/A, A/C and B/C. As we are interested in plasma irregularities, the background density of each EPI event has been subtracted to reduce the effect of non-depleted variations on the correlation analysis. For each equatorial orbital segment with EPI, the Ne time series with 2 Hz resolution were first projected onto MLAT, then a multi-wavelet method has been applied to the MLAT profile of Ne. The wavelet function we used is “coiflets,” which is discrete, near symmetric and has scaling functions with vanishing moments (Beylkin et al. 1991). The wavelet coefficients with wavelengths between 240 and 960 km were used to reconstruct the background Ne profile. As reported in previous studies, EPIs exhibit inverted-C shell structures when projected onto the horizontal plane. In case of a westward-tilted inverted-C shell structure, more poleward EPI parts appear further westward (Kelley et al. 2003; Kil et al. 2004; Huba et al. 2009; Park et al. 2015a). This means that the Swarm spacecraft on the westside is expected to observe depletions at higher latitude than the spacecraft on the eastside. We examined such expected feature further by using a cross-correlation analysis. We treated separately the data from the two hemispheric parts (0° to ±20° MLAT). For each hemisphere, the electron density recording of the eastside spacecraft was taken as reference and the other one was time-shifted from −100 to 100 s. The maximum value of the correlation coefficients (R max) and the corresponding time shifts (Δt) were recorded for following statistical analysis. To keep consistency, a positive value of Δt means that the electron density from the westside spacecraft had to be shifted equatorward to get R max in both hemispheres.
Examples of EPIs observed by Swarm
Figure 2b, c presents two examples of EPIs observed by Swarm during the first study period. For both events, the top panel presents the latitudinal profiles of the original electron density time series (Ne, 2 Hz resolution) with different colors for different spacecrafts. The epochs, altitudes and longitudes when the spacecraft passed the geographic equator are listed in the topside. The middle panel shows the reconstructed background Ne and the bottom panel presents ΔNe with background variations subtracted. For the first event observed on December 10, 2013, the three spacecrafts flew at an altitude of about 501 km. Swarm B was the leading spacecraft, crossing the geographic equator 1 min earlier than A and C. In this case, Swarm A was 0.1° (about 11 km) westward of B and 0.2° (about 22 km) eastward of C, respectively. As the three spacecrafts were so close in time and space, they observed similar plasma density irregularities in both hemispheres. In the northern hemisphere, the correlations of the density depletions, R max, attained values of 0.91, 0.83 and 0.76 for the pairs Swarm B/A, A/C and B/C, respectively. As Swarm B/A were most closely spaced, R max is largest, as expected. Furthermore, a correlation less than 1.0 between Swarm B/A also reveals that the EPI had fine structure with zonal extent less than 0.1° (about 11 km) or that the plasma density structure did change within the 27 s leading time between Swarm B/A. As described in section “Processing approach,” to calculate the correlations, for each Swarm pair, we took the ΔNe series from the eastside spacecraft as reference and time-shifted the other one. In the northern hemisphere, we found Δt is about 2.0, 3.5 and 5.0 s for the three pairs, respectively. The positive values of Δt result from the EPI inverted-C shell structure. In fact, from the latitudinal profiles of electron density, we can also see that Swarm C observed the density depletion at highest latitudes, as expected for the most westerly spacecraft.
However, the correlations are significantly reduced in the southern hemisphere with R max of 0.56, 0.55 and 0.42 for the three pairs, compared to the northern hemisphere. The corresponding Δt with values of −10.0, −14.5 and −24.0 s are also somewhat larger in absolute value than those in the northern hemisphere. And we found the electron density latitudinal profiles show much finer structures between 6° and 12°S MLAT, which might contribute to the lower correlations in the southern hemisphere. In addition, the negative values of Δt in the southern hemisphere seem not support the westward-tilted inverted-C shell structure of EPI.
Figure 2c presents another example of EPI on December 19, 2013. The electron densities measured by Swarm also show similar depletions in both hemispheres. In this case, the three spacecrafts were practically at the same altitude of about 501 km, and Swarm B was 1 and 2 min ahead of Swarm A and C, respectively. The longitudinal separation between Swarm B/A increased to 0.2° (about 22 km), and 0.3° (about 33 km) between Swarm A/C. In the northern hemisphere, R max was larger than 0.7 for all the three pairs and again was largest for Swarm B/A. In the southern hemisphere, R max is somewhat smaller but still around 0.7. The time shifts (Δt) were again mainly positive in the northern and negative in the southern hemisphere.
In this study, we analyze the scale sizes of equatorial plasma irregularities based on observations from the Swarm constellation.
The examples of EPIs presented in Fig. 2 show that the plasma irregularities usually have various scale sizes in the meridional direction, and these structures sometimes are not well correlated in the zonal direction. As shown in Fig. 5, the correlation rapidly decreases between neighboring measurements over tenths of a degree in longitude. With longitudinal separations larger than 0.4° (about 44 km), no significant correlation was found any more. This result suggests that small-scale structures within EPIs have short correlation lengths in longitude. Numerical model studies also report typical density depletion diameters of 20–30 km (e.g., Huba and Joyce 2007; Retterer 2010; Yokoyama et al. 2015). Swarm observational results can help to constrain the range of EPIs sizes in simulation studies.
From the two examples presented in Fig. 2, we found Swarm C observed density depletions at highest latitude in the northern hemisphere. Considering the spatial formation of Swarm during the early mission phase (Swarm C is on the most westward), this result is consistent with the positive value of Δt for cross-correlation in the northern hemisphere and supports a westward-tilted inverted-C shell structure of EPIs, which is believed to be present for most of observed irregularity structures. However, the negative values of Δt in the southern hemisphere seem not to support such a simple model. Huba et al. (2009) showed that the shell structure of EPIs strongly depends on the vertical profile of zonal wind. For different zonal wind conditions, this shell structure can be westward tilted with different angles and sometimes is even eastwardly tilted (see their Fig. 4). Figure 5a, b illustrates this range of variations. In general, for other examples (not shown here), most of the EPI events presented positive Δt in the northern hemisphere (corresponding to westward tilt), but there were also some events of negative Δt in the northern hemisphere with R max larger than 0.6. The Δt in the southern hemisphere is more scattered toward both positive and negative values. For the interpretation of the observed latitude shift, we may have to consider also the magnetic field declination and meridional drifts, and dedicated study may be needed.
Another point to be considered here is the southern location of the geomagnetic equator. During December solstice month, being local summer in the southern hemisphere, larger electron densities are expected in the regions south of the geographic equator that has the potential to develop steeper ∇n, and thus enhance the EPI growth rate. We therefore explain the observed lower correlations of EPIs between Swarm A and C in the southern than those in the northern hemisphere by these two effects, low geomagnetic field and southern location of the magnetic equator.
In summary, the Swarm constellation mission provides us with the opportunity to study the scale sizes of equatorial plasma irregularities simultaneously in the meridional and zonal directions. We found that with longitudinal separations between Swarm satellites larger than 0.4° no significant correlation was found any more. This result suggests that EPI structures include plasma density scale sizes less than 44 km in the zonal direction. During the earlier mission period, clearly better correlations of EPIs are obtained in the northern hemisphere, implying more fragmented irregularities in the southern hemisphere where the ambient magnetic field is low. The previously reported inverted-C shell structure of EPIs is generally confirmed by the Swarm observations in the northern hemisphere, but with various tilt angles. From the Swarm spacecraft with zonal separations of about 150 km, we conclude that larger zonal scale sizes of irregularities exist in the early evening hours (around 1900 LT) that are interpreted as larger scale lengths, initial perturbations of post-sunset ionospheric plasma irregularities.
CX designed the MATLAB program for finding the equatorial plasma irregularity (EPI) events from Swarm electron density observations, performed the statistical analysis, and drafted the manuscript. CS provided fruitful discussion of the results and drafted the manuscript. HL, JP, BGF, GNK gave constructive suggestions for improving the text. All authors read and approved the final manuscript.
The authors thank J. Rauberg and I. Michaelis for their valuable comments on Swarm data processing. The European Space Agency (ESA) is acknowledged for providing the Swarm data. The official Swarm website is http://earth.esa.int/swarm, and the server for Swarm data distribution is ftp://swarm-diss.eo.esa.int.
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