Comparative Observations of the Outer Belt Electron Fluxes and Precipitated Relativistic Electrons

Relativistic electron precipitation (REP) refers to the release of high‐energy electrons initially trapped in the outer radiation belt, which then precipitate into Earth's upper atmosphere, contributing significantly to the rapid depletion of radiation belt electron flux. This study presents a statistical analysis of REP observations collected by the Calorimetric Electron Telescope (CALET) experiment aboard the International Space Station from 2015 to the present day. Specifically, the analysis utilizes count rates acquired from the two top scintillators constituting the top charge detector, each sensitive to electrons with energies above 1.5 and 3.4 MeV, respectively. Analysis of CALET data reveals a previously unreported semi‐annual variation in the occurrence of REP events. REP periodicities resemble those observed for trapped electron fluxes in the outer belt. Furthermore, their amplitude follows the overall trend of solar wind high‐speed streams and the solar activity.

REP can be categorized into two groups based on the driving mechanisms.The first group corresponds to scattering resulting from wave-particle interaction (Blum & Breneman, 2020;Kataoka et al., 2020;Loto'Aniu et al., 2006;Omura & Zhao, 2012).These interactions have been observed at all magnetic local times (MLTs), but they are concentrated at specific regions depending of the wave acting with the electrons.Microbursts are a type of rapid precipitation, typically lasting ∼100 milliseconds, and are more frequently observed in the morning sector (Blake et al., 1996;Blum, Li, & Denton, 2015).Meanwhile, precipitation bands are a type of precipitation observed at low-Earth-orbit (LEO) over several seconds and have been seen at all MLTs, but they seem to concentrate in the same regions where electromagnetic ion cyclotron (EMIC) waves near the dusk and pre-midnight sectors are commonly observed (Blum, Li, & Denton, 2015;Dachev, 2018).Plasmapheric hiss waves are also believed to contribute to the REP registered at all MLTs (Ma et al., 2021;Yahnin et al., 2016).The second group correspond to scattering that originates from the breaking of the first adiabatic invariant in regions where the curvature of the magnetic field is similar to the electron gyroradius.This process frequently occurs in the current sheet, hence the name CSS, and it is typically observed around midnight [22-02 MLT] (Capannolo et al., 2022;Smith et al., 2016).
Temporal periodicities associated with the magnetosphere were first reported by Sabine (1851), who noticed a semi-annual variation of the number of disturbances as described by the local magnetic field declination in two mid-latitude stations during the years 1843-1845.The number of disturbances during boreal fall equinox was found to be larger than the number of disturbances during the boreal spring equinox.Since then, multiple studies have shown a semi-annual variation of different physical quantities in multiples regions of the magnetosphere.Cliver et al. (2000Cliver et al. ( , 2002) ) and Lockwood et al. (2020) observed a semi-annual variation in the using geomagnetic activity indices (aa, aa H , AL, D ST ).In addition, Baker et al. (1999) used the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) relativistic electron observations at LEO to show a semi-annual variation of electrons in the outer belt, which is consistent with the observations made by POLAR spacecraft.In the case of SAMPEX, the observations were obtained for high energy electrons (2 < E < 6 MeV) throughout the entire outer belt (2.5 < L < 6.5), mostly associated with the trapped population and quasi-trapped electrons, allowing an estimation of the entire outer radiation belt electron flux (Baker et al., 1997;Katsavrias et al., 2021;Lyons et al., 2009).
A semi-annual variation has also been observed in the occurrence of Pc1 geomagnetic micropulsations at middle latitudes in an inverse relation with the solar cycle and the semi-annual period of hydromagnetic emissions (Fraser-Smith, 1970).In addition, Bravo et al. (2011) showed a semi-annual variation of the maximum electron density of the F2 layer in the ionosphere.In all cases, the peaks of the variation were observed around 1-month after the equinoxes, suggesting a underlying mechanism.While the reason for these delayed peaks is unknown, a significant role might be played by the electron intensity periodicities associated with the 27-day solar rotation period (Lam, 2004;Nakamura et al., 1995;Paulikas & Blake, 1979;Williams, 1966).
The drivers of the semi-annual variation are currently a topic of discussion, with three proposed mechanisms (Cliver et al., 2000;Katsavrias et al., 2021): 1.The axial hypothesis (Bohlin, 1977;Cortie, 1912;Svalgaard, 1977): it is based on the heliographic latitude of Earth during the year.When Earth is above or below the heliographic equator, it is better aligned with solar active regions, increasing the magnetospheric coupling of the magnetosphere with the solar wind.2. The equinoctial hypothesis (Cliver et al., 2000(Cliver et al., , 2002;;Yoshida, 2009): it is based on the seasonal variation of the Earth's dipole with respect to the solar wind flow.In this case the dipole inclination reduces the coupling of the magnetosphere with the solar wind near the solstices rather than increase it during equinoxes.3. The Russell-McPherron (RM) effect (Russell & McPherron, 1973): It is based on the larger negative z component of the interplanetary magnetic field with respect to the dipole which increases the solar wind coupling with the magnetosphere when Earth is at equinox.

Katsavrias et al. (2021) performed a superimposed epoch analysis on Van
Allen probes data to test the relevance of the three effects on outer belt electrons, determining that the RM effect is the main contributor.However, none of these mechanisms fully explains the nearly 1-month delay with respect to the equinox, nor the peak asymmetry of the semi-annual variation of both geomagnetic variation and relativistic trapped population.Despite these advances, more evidence and analysis is required to unveil the drivers of these periodicities.
It has also been observed that solar wind structures, such as coronal mass ejections, corotating interaction regions, and high-speed streams (HSSs), play a significant role in modulating the intensity of relativistic electrons (Miyoshi & Kataoka, 2011).In the case of HSS, they more frequently occur during the declining phase of the solar cycle.Elevated levels of geomagnetic activity often coincide with the presence of HSS, leading to a notable increase in relativistic electron fluxes detected at geosynchronous orbit and the outer belt (Borovsky & Denton, 2010;Lyons et al., 2005;Miyoshi et al., 2013).
This letter presents the first observation of the semi-annual variation of REP.Section 2 outlines the data sets and methods utilized in this study.Section 3, provides a description of the observations.Section 4 is dedicated to the

Geophysical Research Letters
10.1029/2024GL109673 discussion, while Section 5 summarizes the conclusions drawn from the findings.Finally, Data Availability Statement, detailing the sources of the data used.

Data Sets and Analysis Methods
This study utilizes a catalog of REP events observed between October 2015 and October 2021 by the Calorimetric Electron Telescope (CALET) instrument on board the International Space Station (ISS) (Brogi et al., 2020;Torii et al., 2019).The catalog was generated by Vidal-Luengo et al. ( 2024) through an unsupervised machine learning technique known as Self-Organizing-Map (SOM).CALET measurements are made from the ISS at an altitude of approximately 400 km, with an orbit inclination of 51.6°and a temporal resolution of 1 s.CALET comprises two scintillator arrays (CHDX and CHDY) placed at the top of the instrument.These detectors were designed to provide cosmic-ray charge discrimination, and are also sensitive to electrons with energies >1.5 MeV and >3.4 MeV, respectively (Bruno et al., 2022).This characteristic makes them suitable for the detection of REP events (Kataoka et al., 2016).After visual inspection of the sample, 87 events were identified as false REP events and discarded, the remaining 1361 REP events are used for analysis.
The capabilities of CALET are particularly useful for the study of REP as it has been operative simultaneously with the Van Allen Probes (2012-2019) and Arase (2016-present) missions.The Van Allen Probes were two spacecraft at a nearly equatorial (∼10.2°) and highly elliptical orbit that crossed the radiation belts.They had an approximate orbit with an apogee of 30,600 km and a perigee of 618 km (Fox & Burch, 2014).The Arase (formerly ERG) mission consists of a single spacecraft crossing the belts with a moderately inclined orbit of approximately ∼31°and a highly elliptical trajectory.Its orbit has an approximate apogee of 32,110 km and a perigee of 460 km (Miyoshi, Shinohara, & Jun, 2018;Miyoshi, Shinohara, Takashima, et al., 2018).Figure 1 shows an example of a typical REP event observed by CALET.These events are characterized by an increase in the CHDX count rate, especially in the CHDX channel; they have a time extension of a few minutes, and they are typically observed at L > 3.
The Energetic particle, Composition and Thermal plasma suite (ECT) aboard the Van Allen probes provided relativistic electron fluxes (Spence et al., 2013) and it was processed by Boyd et al. (2021).Similarly, the Highenergy electron experiment (HEP) aboard the Arase spacecraft provides pitch angle sorted electron flux data (Hori et al., 2020;Matsuoka et al., 2018;Mitani et al., 2018).The relativistic electron fluxes data set used in this study covers the period with common spacecraft coverage, from October 2015 to December 2019 for VAP-A/B and from March 2017 to October 2021 for Arase.In both cases, the pitch-angle resolved data was combined in order to obtain the omnidirectional relativistic electron fluxes data set used in the analysis.
In addition to the relativistic electron data, 1-min solar wind from OMNI data (Papitashvili & King, 2020a), and 1hr F10.7 OMNI data (Papitashvili & King, 2020b) is used to asses the solar activity conditions.To facilitate comparison with VAP-A/B, Arase, and CALET observations, the solar wind data was 28-days averaged.
This study considers all REP in the catalog (selected after having removed false events based on visual inspection).However, it presents only REP events and electron fluxes measured near the center of the outer belt (4 < L < 5) where electron scattering due to plasma waves is more likely to occur.For this region, CALET observed 554 REP events.Further characterization of the data involves spectral analysis techniques, as detailed in Section 3. Specifically, the monthly count of REP events and the monthly median electron fluxes from VAP-A/B and Arase were subjected to fast-Fourier-transform (FFT) and continuous-wavelet-transform (CWT) analysis.

Observations
Figure 2a presents a histogram depicting the number of REP events (binned by month) observed by CALET.Figures 2b and 2c illustrate 1.44-1.87MeV and 1.50-1.70MeV electron fluxes observed during the selected time interval by VAP/ECT and Arase/HEP-H, respectively.Figure 2d shows the binned number of REP events on top of the median value of VAP-A/B electron fluxes, and the median of Arase electron fluxes.Due to the slightly different energy and orbit inclination the fluxes observed by Arase, they were numerically adjusted by calculating a scaling factor that minimizes discrepancy during the common observation time period between VAP-A/B and Arase.The similarity between the number of REP events and the outer belt electron intensities is quantified using the Pearson correlation coefficient.A statistically significant value (0.91) was obtained for the 4 < L < 5 region.Figure 2e displays the solar wind speed and the F10.7 index (both 28-day averaged) to compare fluxes and REP with HSS and solar activity.
The occurrence of the REP events exhibits a semi-annual variation, with a maximum after the boreal fall equinox and a secondary peak after the boreal spring equinox.The amplitude of this semi-annual variation of REP decreases in agreement with the decrease of the solar activity at the end of solar cycle 24 and beginning of cycle 25, but also with the solar wind speed.This is expected due to the reduction of the magnitude and number of solar wind structures impacting the magnetosphere that contribute to the acceleration and loss of relativistic electrons in the outer belt.Figure 2e shows that the number of REP events overall trend better follows the solar wind speed rather than the solar activity described by the F10.7 cm index.
To better compare the periodicities in REP occurrence and trapped radiation belt fluxes, the CWT was calculated for the monthly count of REP events to characterize the semi-annual variation and its evolution over time.
Figure 3a shows a FFT of the monthly REP event count and relativistic electron fluxes combined (VAP-A/B and Arase).Figure 3b displays the CWT of the monthly REP event count.Figure 3c shows the CWT of the combined (VAP-A/B and Arase) omnidirectional electron fluxes.There is a strong agreement between the relativistic precipitation and outer belt fluxes observations.Both show a semi-annual variation during the same period of time that decreases in amplitude.In addition, in both cases there is also an annual variation.The annual variation is, at least partially, a representation of the asymmetry observed in the semi-annual variation, which is most noticeable by peak asymmetries between boreal fall and boreal spring equinoxes, however other factors cannot be discarded.
There is also present a peak during 2017 with a period of 2.4 months (∼73.2days).This periodicity is just slightly above the Nyquist period (T Ny = 1/f Ny ) for the monthly binned data, then it may have been affected by aliasing.However, it is consistent with periodicities observed VAP/MagEIS for 1.575 MeV at L = 4.75 as shown in Figure 4c of Katsavrias et al. (2021).While the origin of the 2.4 months periodicity in relativistic fluxes is still unknown, it is relevant that is also observed in REP.The cone-of-influence (COI) is marked with a dashed line.Above the COI, the wavelet may have been influenced by edge effects, making those regions less reliable for analysis.
One question that arises is whether the REP semi-annual variation is a result of the change in the number or the magnitude (i.e., count rates) of REP events.Figure 4 displays the monthly average of the maximum count rates of each REP event observed by CALET.This value does not exhibit a particular pattern that could assist in its association with any magnetospheric process; instead, it remains above 10 4 counts/s and relatively constant over time, with some exceptions.It only changes when the number of REP events is very small or nonexistent (see Figure 2).This result suggests that the amount of precipitation deposited in the atmosphere is mainly driven by the number of REP events rather than by the magnitude of them.

Discussion
This study reveals a semi-annual variation in REP events occurrence, which closely mirrors the periodic fluctuations observed in relativistic electron fluxes by the Van Allen Probes and Arase satellites.Additionally, both phenomena exhibit a decrease in amplitude during the declining phase of the solar cycle 25, as described by the F10.7 cm index and the solar wind speed.In addition to the observed semi-annual variation in REP event occurrence and their correlation with solar activity indicators, the analysis also reveals an interesting observation regarding the magnitude of REP events.Despite the clear periodic fluctuations in event occurrence, the magnitude of REP event count rates does not exhibit similar periodicity.This suggests that the amount of relativistic electrons lost from the outer belt due to REP is driven by the number of REP events rather than by their magnitude.However, more studies are necessary to verify the role of the REP magnitude for the semi-annual variation.
The strong relationship between outer belt electron fluxes and REP suggests that the semi-annual variation of REP may be driven by either the number of electrons present in the outer belt, the variation of plasma wave occurrence, or a combination of both.In the first scenario, plasma waves responsible for electron scattering occur at a constant rate over time, but the acceleration and the other loss mechanisms (e.g., radial diffusion, magnetopause shadowing) would have a semi-annual variation that drives the number of electrons that can be potentially scattered.In the second scenario, the semi-annual variation of REP is driven by the semi-annual variation of the occurrence of plasma waves (and in consequence electron scattering) independently of the number of electrons present in the outer belt.The third scenario, is a combination of the first two.The number of electrons in the magnetosphere could influence the magnitude or rate occurrence of wave activity responsible of REP.
These results are also important for modeling and prediction of space weather given that high energy electrons pose a hazard to space assets and astronauts.Future studies analyzing the statistical occurrence of plasma waves would contribute to a better understanding of this semi-annual variation and help to identify the underlying mechanism.

Conclusions
This study has revealed the existence of a semi-annual variation of precipitated relativistic electrons.The results are summarized as follows: • The occurrence variability of REP observed by CALET between 2015 and 2021 has been studied.• The REP event counts have been compared with omnidirectional electron fluxes measured by the VAP-A/B (2015-2019), and Arase spacecraft (2017-2021).• The semi-annual variation of REP is in strong correlation with the monthly averaged relativistic electron fluxes measured by VAP-A/B and Arase • The amount of precipitation seems to be driven by the number of REP events rather than by the magnitude of them.
• Future studies analyzing the temporal evolution of magnetospheric plasma waves will help clarifying whether the semi-annual variation of REP is driven by the quantity of electron fluxes in the outer belt, the temporal variation of scattering mechanisms, or a combination of both.

Figure 3 .
Figure 3. (a) FFT of the relativistic electron precipitation (REP) event counts (blue) and FFT of VAP-A/B and Arase omnidirectional electron fluxes (red).(b) Continuous wavelet transform (CWT) of the REP event counts.(c) CWT of the combined (VAP-A/B and Arase) omnidirectional electron fluxes.Dashed lines mark the cone of influence.Observations are for 4 < L < 5.

Figure 4 .
Figure 4. Average of the maximum count rate (CHDX; counts/s) observed when events are binned by month for 4 < L < 5. Error bars calculated to the 68.27% of confidence using Poisson statistics (Feldman & Cousins, 1998).