Electron Flux Dropouts at L ∼ 4.2 From Global Positioning System Satellites: Occurrences, Magnitudes, and Main Driving Factors

Dropouts in electron fluxes at L ∼ 4.2 were investigated for a broad range of energies from 120 keV to 10 MeV, using 16 years of electron flux data from Combined X‐ray Dosimeter on board Global Positioning System (GPS) satellites. Dropouts were defined as flux decreases by at least a factor 4 in 12 h, or 24 h during which a decrease by at least a factor of 1.5 must occur during each 12 h time bin. Such fast and strong dropouts were automatically identified from the GPS electron flux data and statistics of dropout magnitudes, and occurrences were compiled as a function of electron energy. Moreover, the Error Reduction Ratio analysis was employed to search for nonlinear relationships between electron flux dropouts and various solar wind and geomagnetic activity indices, in order to identify potential external causes of dropouts. At L ∼ 4.2, the main driving factor for the more numerous and stronger 1–10 MeV electron dropouts turns out to be the southward interplanetary magnetic field Bs, suggesting an important effect from precipitation loss due to combined electromagnetic ion cyclotron and whistler mode waves in a significant fraction of these events, supplementing magnetopause shadowing and outward radial diffusion which are also effective at lower energies.


Introduction
The outer radiation belt environment of the Earth consists of energetic electrons from ∼100 keV to ∼10 MeV, with flux levels that can vary by several orders of magnitude within a few hours (e.g., see Baker et al., 1986;Li et al., 2017;Turner et al., 2013) and pose various threats to satellites (Welling, 2010;Wrenn, 1995). Large and fast decreases in the electron population, called dropouts, have been investigated over more than a decade now, but the actual causes of such strong and fast electron losses throughout the outer radiation belt are not yet fully understood, in spite of some important advances (e.g., Green et al., 2004;Turner et al., 2013). Dropouts could be produced by a number of mechanisms, such as magnetopause shadowing aided by outward radial diffusion (Kim & Lee, 2014;Shprits et al., 2006;Ukhorskiy et al., 2015), precipitation loss (Bailey, 1968;Bortnik et al., 2006;Li et al., 2007;Mourenas et al., 2016;Su et al., 2016), or reversible adiabatic effects (Kim & Chan, 1997;McIlwain, 1966), either separately or simultaneously.
Magnetopause shadowing is due to the compression of the magnetopause by the solar wind. As the magnetopause moves closer to the Earth, the electrons that were on closed drift shells will be able to escape to open space. Once the magnetopause recovers to the precompression shape, there will be a higher electron Phase Space Density (PSD) closer to the Earth than farther away, where the electrons have just been lost. This spatial gradient in PSD then leads to a fast outward radial diffusion of electrons from the region of high PSD to the region where electrons have just been lost. This also results in a loss of electrons coming progressively closer to the Earth as electrons diffuse radially toward higher Ls Turner et al., 2013).

10.1002/2017JA024523
The most rapid and important MeV electron dropouts of this kind are expected to be produced by simultaneous EMIC and whistler mode wave scattering Zhang et al., 2017) and can occur for the average EMIC wave upper frequency cutoffs observed for H-band and He-band waves Zhang et al., 2017), that is, such dropouts do not need EMIC waves very close to the helium gyrofrequency, contrary to dropouts due to EMIC waves alone. In the simultaneous presence of intense EMIC and chorus waves on the same L shell (possibly at different MLTs), whistler mode waves fill the trough in pitch angle diffusion at high equatorial pitch angles left by the sole EMIC wave diffusion. Moreover, EMIC wave scattering is so fast at low pitch angles that it creates a kind of effective loss cone for electrons at pitch angles much larger than the usual loss cone value, leading to a strong reduction of electron lifetimes as compared with a situation with whistler mode waves alone (without EMIC waves) Zhang et al., 2017). Simulations have demonstrated that such combined diffusion by EMIC and whistler mode waves can really produce fast (<0.5-1 day) dropouts of electrons above ∼2 MeV in realistic conditions, with MLT-and time-averaged EMIC wave amplitudes >50-100 pT and chorus amplitudes >50 pT Zhang et al., 2017), even during nonstorm times (one such observation is discussed by Su et al., 2016).
Adiabatic effects result in a reversible loss of electrons due to the conservation of the three adiabatic invariants (Dessler & Karplus, 1961). During the main phase of a geomagnetic storm, the intensity of the ring current increases, decreasing the strength of the magnetic field, leading to the deceleration of electrons to conserve the first adiabatic invariant and the outward movement of the drift path to conserve the third adiabatic invariant. This is reversed when the ring current decreases back to its prestorm level, increasing the magnetic field strength, accelerating the electrons and moving back their drift paths closer to the Earth. Since this phenomenon occurs during geomagnetic storms, it has often been referred to as the "Dst effect" (Kim & Chan, 1997). Adiabatic effects should generally occur at all energies simultaneously and with similar strength. However, many past works have pointed out the importance of net electron flux loss during dropouts, demonstrating that reversible effects often do not prevail, at least around geosynchronous orbit (e.g., Boynton, Mourenas, et al., 2016;Turner et al., 2013).
Electron dropouts have mainly been studied at Geosynchronous Earth Orbit (GEO) due to the large amount of electron flux data available from the corresponding satellites. Borovsky and Denton (2010) used a superposed epoch analysis during geomagnetic storms to investigate the dropouts at GEO. They observed that increases in dynamic pressure and a southward interplanetary magnetic field (IMF) coincided with the dropouts. A superposed epoch analysis was also employed by Yuan and Zong (2013) for dropouts occurring during geomagnetic storms. They investigated the effects of solar wind dynamic pressure and different orientations of the IMF on the dropouts at GEO, showing similar results to Borovsky and Denton (2010), with high pressure and southward IMF leading to larger dropouts. Gao et al. (2015) studied all dropouts occurring during storm and nonstorm periods and found that both dynamic pressure and southward IMF can separately influence relativistic electron dropouts. They concluded that magnetopause shadowing was not responsible for all the dropouts. Boynton, Mourenas, et al. (2016) compiled statistical data of dropouts for energies ranging from 24 keV to 2.7 MeV and further determined the main solar wind and geomagnetic conditions controlling the dropouts, using a Nonlinear AutoRegressive Moving Average eXogenous (NARMAX) Error Reduction Ratio (ERR) approach. A minimum dropout by at least a factor of 4 was selected to differentiate dropouts from the slower electron flux decay due to scattering by chorus waves, since Boynton et al. (2014) had found that GEO electron fluxes decay slower (have lifetimes that increase) with increasing energy in rough agreement with chorus-induced electron loss models from Mourenas et al. (2012) at low energies. The ERR results showed that the factors having the most important influence on the dropouts were the AE index at low energies (E ≤ 90 keV), dynamic pressure coupled with solar wind density at intermediate energies (128 ≤ E ≤ 925 keV), and dynamic pressure coupled with southward IMF at higher energies (1.3 ≤ E ≤ 2 MeV). They concluded that magnetopause shadowing coupled with outward radial diffusion is probably not the sole driving factor for all the dropouts, especially at MeV energies.
The aim of the present study is to investigate electron flux dropouts within the heart of the radiation belts at L ∼ 4.2, for energies ranging from 120 keV to 10 MeV, and to try to identify their possible causes. Similar to Gao et al. (2015) and Boynton, Mourenas, et al. (2016), we compile a statistics of all dropouts occurring during both storm and nonstorm periods, using here 16 years of nearly equatorial electron flux measured on board the U.S. Air Force's Global Positioning System (GPS) satellites at L ∼ 4.2. The electron flux data and the adopted criteria for dropout selection are discussed in section 2. The statistical analysis of the dropouts is provided in section 3 and focuses on waiting times between dropouts and dropout magnitudes. Section 4 is devoted to a search for possible relationships between dropout magnitude and external factors, such as solar wind parameters and geomagnetic indices, making use of the NARMAX ERR methodology, which is able to determine the main controlling factors among various potential nonlinear relations (Boynton, Balikhin, Billings, Wei, et al., 2011;Boynton et al., 2013). The statistical results at L ∼ 4.2 are then discussed in this light. Section 5 discusses the radial extension of dropouts of relativistic electrons, comparing the identified dropouts at L ∼ 4.2 to dropouts at GEO catalogued by Boynton, Mourenas, et al. (2016). Finally, section 6 investigates the relationship of GPS dropouts with plasmapause and magnetopause locations.

Electron Flux Data and Methodology
The electron flux data used in this study come from the Combined X-ray Dosimeter (CXD) carried on board nine GPS Block IIR and IIR-M satellites designated as SVN53-61. All these spacecraft have a nearly circular orbit at an altitude of ∼20,200 km with an inclination of 55 ∘ and, therefore, measure electron fluxes through a range of L shells at L ≥ 4.2. The CXD instruments were designed at Los Alamos National Laboratory (LANL) over the course of more than 20 years. The electron flux data are supplied by the National Oceanic and Atmospheric Administration (NOAA) (https://www.ngdc.noaa.gov/stp/space-weather/satellitedata/satellite-systems/gps/), which provides differential electron fluxes at 15 energies from 120 keV to 10 MeV. The data are available from satellite SVN54 from February 2001 onward, eight other satellites having been added on GPS orbit over the following 7 years. These GPS data were made freely available to the scientific community thanks to the Executive Order "Coordinating Efforts to Prepare the Nation for Space Weather Events" issued by the White House on 13 October 2016. The corresponding data have been discussed in details by Morley et al. (2017). GPS electron fluxes have been checked to be similar (within a factor 2) to fluxes measured by the Van Allen Probes between 140 keV and 4-5 MeV (Morley et al., 2016).
This study aims to investigate dropouts in whole populations of electrons up to high equatorial pitch angles at L ≈ 4.2 over a wide energy range. It is well known that all radiation belt electrons travel through the geomagnetic equator, whereas only part of them reach high geomagnetic latitudes. Therefore, for each energy range, the electron flux from each individual satellite was sampled when the spacecraft was at 4.1 < L < 4.3 measuring electron fluxes in the vicinity of the geomagnetic equator. The data from all the satellites were then averaged over each 12 h period (00-12 UTC and 12-24 UTC), resulting in an electron flux data set from 18 February 2001 to 31 December 2016 for 15 energies with a 12 h cadence.
As for the previous study by Boynton, Mourenas, et al. (2016), an electron flux dropout is defined here as a flux decrease by a factor of 4 occurring over 1 day or less. Since our present GPS data set has a 12 h resolution, the dropout can take place over one or two time steps. The selection criteria of a decrease by factor of 4 were chosen so that the slower decay of electrons due to scattering by chorus or hiss waves, which usually corresponds to lifetimes >1 day for >120 keV electrons at L ∼ 4.2 (e.g., Mourenas et al., 2014Mourenas et al., , 2016Orlova & Shprits, 2014), would not be considered as a dropout. Therefore, the dropouts were defined as follows: (1) A decrease by a factor of 4 in 12 h (the previous electron flux, J(t − 1), being 4 times greater than the current flux, J(t), 4J(t − 1) ≥ J(t)); (2) A decrease by a factor of 4 in 24 h (the electron flux measured 2 time steps before, J(t − 2), being 4 times greater than the current flux, J(t), 4J(t − 2) ≥ J(t)) where there is a decrease by at least a factor of 1.5 in 12 h (the electron flux measured 2 time steps before, J(t − 2), being 1.5 times greater than the previous flux, J(t − 1), 1.5J(t − 2) ≥ J(t − 1) and the previous electron flux, J(t − 1), being 1.5 times greater than the current flux, J(t), 1.5J(t − 1) ≥ J(t)).
The GPS electron flux data contain a number of spikes, or large and rapid oscillations, where the flux increases sharply before immediately strongly decreasing. Under the above-stated conditions, such peculiar oscillation events would have been counted as dropouts. However, the actual dropouts that we wish to study here rather correspond to periods of sudden, important loss occurring from an elevated, relatively stable level of electron flux, that is, not just rapid oscillations related, for instance, to narrow patches of high electron flux occasionally passing by the satellites. Therefore, two new conditions were added to remove such oscillation events. Such events were removed from the dropout list if (1) the electron flux 12 h before the start of the dropout, J(t B − 1), was at least 2.5 times smaller than the electron flux at the start of the dropout, (2) the electron flux 24 h before the start of the dropout, J(t B −2), was at least 4 times less than the electron flux at the start of the dropout,

Mean Waiting Time Between Consecutive Dropouts and Dropout Magnitudes
For each of the 15 energy channels, electron flux dropouts at L ≈ 4.2 were automatically identified and some of their statistical properties were evaluated. Table 1 shows the number of dropouts identified for each electron energy channel within the 16 year period. One finds a low number of dropouts between 300 keV and 1 MeV, with only 23 to 42 dropouts observed in each of these energy channels over 16 years. Above 800 keV, the number of dropouts increases strongly, peaking at 5 MeV with 195 observed dropouts, then weakly decreasing up to 10 MeV. The low number of dropouts between 300 keV and 800 keV could stem from smaller flux variations in this range compared to other (higher or lower) energies. However, the global variance of the logarithmic electron flux does not show any relationship with the number of dropouts (see Table 1). As an example, Figure 1 displays the variations of 800 keV and 8 MeV electron fluxes over 16 years, which correspond to similar logarithmic variances, and where identified dropouts are marked in red. The much more numerous dropouts identified at 8 MeV simply correspond to 1 day periods during which the electron flux decreases sensibly faster than at 0.8 MeV. It is also worth emphasizing that for 30% to 40% of the identified dropouts at all energies, the electron flux does not recover a level comparable to its initial level before the dropout until at least 2-3 days after the dropout. In addition, the most numerous multi-MeV electron dropouts often occur several days after an important flux increase (see Figure 1), which may be due to chorus-induced electron acceleration during the recovery phase of a previous geomagnetic storm (Horne et al., 2005). Previous studies have shown that most electron flux dropouts at 1-3 MeV near geostationary orbit likely correspond to real losses (Boynton, Mourenas, et al., 2016;Turner et al., 2013).
For each energy channel, the corresponding mean waiting time between two successive dropouts (an important quantity for the determination of time-integrated radiation doses on satellites) was calculated as well as the 10, 20, 30, 40, 50, 60, 70, 80, and 90 percentiles of the distribution. The mean and percentiles are displayed in Figure 2 and are listed in Table 2. The mean waiting time increases with energy from 120 keV up to 800 keV  and then decreases, being sensibly smaller at 2-10 MeV than at 0.2-1 MeV. The percentiles show a similar pattern to the mean, where the mean is usually located around the 60-70 percentiles.
The mean and 10, 20, 30, 40, 50, 60, 70, 80, and 90 percentiles of the magnitude of the dropouts were calculated for each energy channel. The dropout magnitude was defined as the magnitude of electron flux decrease, given by the ratio J(t B )∕J(t D ) of the flux at the time before the dropout, t B , divided by the flux at the time of the dropout, t D . The mean and percentiles are listed in Table 3 and shown in Figure 3. The mean dropout magnitude increases strongly with energy until 3 MeV and then oscillates. The median (50 %) dropout magnitude (as well as all percentiles above 30 %) exhibits a similar behavior as the mean, increasing with energy until 1 MeV and then remaining approximately constant, which implies that dropout magnitudes are globally increasing with energy. Both the 80 and 90 percentiles of dropout magnitudes are sensibly larger (by factors >2) at E ≥ 0.8 MeV than at 0.12-0.6 MeV. Moreover, the mean is larger than the 90 percentile above 1 MeV, indicating the presence of a small number of extremely large dropouts in each of these high energy channels.  10, 20, 30, 40, 50, 60, 70, 80, and 90  The above results demonstrate that there are consistently more frequent and stronger dropouts at high energy E > 0.8 − 1 MeV than at lower energy, suggesting either an energy-dependent efficiency of the loss processes or the presence of additional (or different) loss processes at higher energy. We shall now proceed in the next section to a NARMAX ERR analysis of potential governing factors for dropouts, with the hope that the additional insight gained from such an analysis will help us to identify the causes of the observed dependence of dropout magnitude and occurrences on electron energy, among a wealth of different possible mechanisms.

Solar Wind Data and ERR Analysis
The solar wind parameters and geomagnetic activity indices are supplied by the OMNI website (http:// omniweb.gsfc.nasa.gov). The upstream measurements of the solar wind are taken by the Advanced Composition Explorer situated at L1, which gives readings ∼30-90 min in advance. These data were further sampled at a 12 h cadence to match the electron flux data over the same period of time from 18 February 2001 to 31 December 2016.
To identify the main external factors that influence the electron flux dropouts, this study employed a methodology based on the NARMAX ERR analysis (Billings et al., 1988;Boynton, Balikhin, Billings, Wei, et al., 2011). The ERR is able to identify a set of nonlinear parameters that control most of the variance of the output signal from input-output data and has previously been employed to identify the solar wind control parameters for the Dst index (Balikhin et al., 2010) and GEO electron fluxes in the radiation belt (Balikhin et al., 2012;Boynton et al., 2013). These control parameters were then successfully implemented as inputs to model the respective systems (Boynton et al., 2015;Boynton, Balikhin, Billings, Sharma, et al., 2011;. The model structure used in this study can be represented mathematically as follows: where the output y at a time t is represented as a nonlinear function F, in the present case a polynomial, of m different inputs, each with a different maximum lag n u 1 , … , n u m . The terms with the highest ERR are more significantly contributing to the output variance. The advantage of the ERR analysis is that it is able to automatically identify and rank a wide class of nonlinear influences and separate out the contributions from the different governing factors.
For the ERR analysis, the output data were a time series of dropout magnitudes, defined as the electron flux before the dropout divided by the lower electron flux during the dropout. When no dropout was observed, dropout magnitudes were set to zero. The inputs were the solar wind velocity v, density n and dynamic pressure p, the southward IMF B s , the AE index, and the Dst index. The minimum and maximum lags for the inputs were, respectively, set to 0 and 4 data points, the latter corresponding to 2 days in the past, and the nonlinear function F was assumed to be a third-order polynomial.
The results of the ERR analysis are listed in Table 4, which show the top three terms identified by the ERR analysis with their respective ERR. For energies ≤300 keV, p(t − 2)Dst(t − 4)B s (t − 1) has the highest ERR, while between 425 keV and 600 keV, the term with the highest ERR is p(t − 0) 2 Dst(t − 0). One striking result of the analysis is that the term B s (t − 1) 3 turns out to have the highest ERR for all electron energies between 800 keV and 10 MeV. Moreover, the top three terms obtained from the ERR analysis are identical between 1 MeV and 10 MeV, with B s (t − 1) appearing as the lone or dominant factor in the top two terms, whereas p and Dst are conspicuously absent from these three dominant terms. These results suggest that B s is by far the main governing factor for E ≥ 1 MeV electron dropouts at L ∼ 4.2, with no significant influence from solar wind dynamic pressure p or Dst, while p does play a role roughly equivalent to B s or Dst in dropouts occurring at lower energy.

Discussion of Statistical Results in Light of the ERR Analysis
Below 700 keV, solar wind dynamic pressure p, Dst, and B s at E < 300 keV appear as the prevalent factors determining dropout magnitudes. Unfortunately, the fact that all these different factors are similarly significant does not allow to discriminate between possible physical mechanisms. However, one very neat and important additional result of the ERR analysis is the identification of B s (t − 1) 3 as the main governing factor for dropout magnitude at high electron energy >0.8 MeV. The contrast with lower energies is striking. Clearly, B s is considerably more important for dropouts at MeV and multi-MeV energy than it is at lower energy (compare the power of B s in the dominant term and the presence of not of other factors in Table 4). Interestingly, although the B s (t − 1) 3 factor starts to become important at 0.6 MeV before prevailing above 0.8 MeV, the influence of solar wind dynamic pressure (p(t − 0)) disappears only at slightly higher energy, for E ≥ 1 MeV. This highlights the progressively more (less) prominent role played by B s (p) as energy increases from 0.5 to 1 MeV.
Let us now reexamine our previous statistical results on dropout magnitudes and occurrences in light of the new information drawn from the ERR analysis. Figure 3 demonstrates that electron flux dropouts have a much stronger mean magnitude, and a sensibly higher median magnitude, at E > 0.8 MeV when the dominant driving term is B s (t−1) 3 than at 120-600 keV where p, Dst, and B s are similarly important. In contrast, the processes of magnetopause shadowing and subsequent outward radial diffusion are generally expected to be nearly independent of electron energy (e.g., Kim et al., 2008;Ozeke et al., 2014). Moreover, magnetopause shadowing can occur in the presence of either solar wind dynamic pressure impulses or strong B s , with some simulations even suggesting that an increase in dynamic pressure p should lead to a stronger magnetopause shadowing than an increase of B s (Kim & Lee, 2014;Kim et al., 2008). The fact that Dst has a significant impact on dropouts at 120-800 keV, but almost none at E ≥ 1 MeV, further suggests that some identified dropouts might be partly related to a reversible Dst effect, but only (or mainly) in the range E < 800 keV.
A dominant effect of magnetopause shadowing (and outward radial diffusion) would therefore be consistent with both the roughly similar dropout magnitudes and occurrences at 300-600 keV in Figures 2 and 3 and the corresponding main controlling factors p(t − 0) 2 Dst(t − 0) at 300-600 keV and p(t − 2)Dst(t − 4)B s (t − 1) at 120-300 keV. At E ≤ 300 keV, substorm-related electron injections can mitigate electron loss (Turner et al., 2017), probably explaining the weaker and less frequent dropouts in this low energy range. However, both the finding that the main (by far) governing factor at E > 0.8 MeV is B s (t − 1) 3 (i.e., with no dependence on p) and the sensibly larger magnitude and occurrence of dropouts in this high energy range do not seem to be consistent at all with a prevalence of magnetopause shadowing loss.
What could explain this apparent inconsistency? First, a dependence of the initial L distribution of the electron PSD on the first adiabatic invariant (i.e., on electron energy) could modulate the ultimate effects of magnetopause shadowing and outward radial diffusion on local flux variations. It is well known that important, localized PSD peaks usually form around L ∼ 5-5.5 in the 1-5 MeV energy range, due to electron acceleration by chorus waves or inward radial diffusion from an on-off source (e.g., see Horne et al., 2005;Mann et al., 2016;Turner, Angelopoulos, Morley, et al., 2014). As a result, the initial electron PSD is generally decreasing faster between L = 5-5.5 and L = 7 in the multi-MeV energy range than at lower energy (Turner et al., 2013;. The initial L ∼ 4.2 over L = 7 electron PSD ratio is then likely to be much higher at multi-MeV energies than at lower energy. A chorus-induced increase of electron PSD localized near L = 5 may therefore allow the formation of a steeper downward PSD gradient toward the magnetopause. Such a preconditioning can make the further development of a dropout via outward radial diffusion and magnetopause shadowing both easier and faster than for an initially null PSD gradient (Turner et al., 2013). All these facts could concur to produce stronger dropouts at multi-MeV energies than at 300-600 keV in the sole presence of significant magnetopause shadowing and outward radial diffusion. Deeper and more frequent dropouts at high energy could also occur due to drift shell bifurcation, which should lead to a larger spreading in L of particles and consequently a stronger loss at higher energy (e.g., Ozturk & Wolf, 2007;Ukhorskiy et al., 2015).
However, it is much more difficult to reconcile the assumption that magnetopause shadowing is the dominant cause of dropouts at MeV energies with the identification by the ERR analysis of B 3 s as the sole main controlling factor of the magnitude of such dropouts, without any significant influence of solar wind dynamic pressure p. In the presence of magnetopause shadowing during strong IMF B s , an increase of dropout efficiency might occur at high electron energy when there is an important B field gradient along the magnetopause, provided that there is no significant normal magnetic field component at the magnetopause, but this seems an infrequent situation (Kim & Lee, 2014). Moreover, it is unclear whether magnetopause shadowing, especially with a strong B s alone and no dynamic pressure increase, can really manage to produce a strong and rapid dropout down to L ∼ 4.2 (Gao et al., 2015;Kim & Lee, 2014;Kim et al., 2008;Turner, Angelopoulos, Morley, et al., 2014).
The preceding considerations suggest that fast dropouts of MeV electrons at L ∼ 4.2 should be at least partly ascribed to some other (additional) physical processes, rather than to magnetopause shadowing and radial diffusion alone. But which other processes? Geomagnetic field line stretching near local midnight can lead to anomalous electron scattering at high (MeV) energies only, but this should work only during very strong storms (e.g., Artemyev et al., 2013;Sergeev & Tsyganenko, 1982).
Alternatively, dropouts can become stronger at relativistic energies due to MeV electron precipitation induced by combined effects of EMIC and chorus or hiss wave scattering (Li et al., 2007;Mourenas et al., 2016;Su et al., 2016;Zhang et al., 2017). In fact, EMIC and whistler mode wave amplitudes are known to increase strongly with geomagnetic activity, especially with AE, that is, not necessarily during storms (e.g., Artemyev et al., 2016;Kersten et al., 2014;Meredith et al., 2007Meredith et al., , 2014Mourenas et al., 2014Mourenas et al., , 2017Orlova & Shprits, 2014;Zhang et al., 2016). Since AE is known to be influenced by the southward IMF B s (e.g., Arnoldy, 1971;Meng et al., 1973), a larger B s is expected to correspond to the presence of more intense EMIC and chorus waves. However, B s was selected by the ERR analysis as a much more important parameter than AE for MeV electron dropouts. This could stem from a better correlation of the simultaneous presence of EMIC and chorus waves with B s than with AE. Another explanation could be that most multi-MeV electron dropouts, being likely partly due to magnetopause shadowing, partly due to combined EMIC and chorus-induced loss, may better correlate with B s variations. This would be consistent with a previous statistics of relativistic electron dropouts during both storm and nonstorm periods, based on Geostationary Operational Environment Satellites (GOES) and NOAA Polar Orbiting Environmental Satellites, which has shown that increases of B s alone can indeed lead to strong dropouts coincident with intense MeV electron precipitation at L ∼ 3.5-5.5 apparently linked to EMIC waves (Gao et al., 2015).
Therefore, the presence of some important MeV electron precipitation induced by simultaneous EMIC and whistler mode waves could really account for both the stronger mean (and, to a lesser extent, median) magnitude of dropouts observed at L ∼ 4.2 for E > 0.8 MeV and the dominance of southward IMF B s in the governing factors for such dropouts. Wave-induced precipitation could be dominant during only a small 10-20% portion of the multi-MeV dropouts, consistent with the mean and 80-90 percentiles of the dropout magnitudes being much higher than the median, but they could also contribute to the remaining dropouts, modulating the final dropout magnitude and blurring the influence of magnetopause shadowing and dynamic pressure p.

Radial Extension of Dropouts of Relativistic Electrons
To better assess the respective roles of magnetopause shadowing and precipitation in relativistic electron dropouts at L ∼ 4.2, we can examine the radial extent of such dropouts. Are these GPS orbit dropouts extending up to GEO or not? Although precipitation loss related to EMIC waves may exist over a wide L range (e.g., Gao et al., 2015), wave statistics suggest its confinement to a domain of radial extension ΔL < 2 in general (Usanova & Mann, 2016). Besides, GEO dropouts at relativistic energies often correspond to true losses  (Boynton, Mourenas, et al., 2016;Turner et al., 2013). Thus, dropouts on GPS orbit extending up to GEO should likely correspond to true losses as well.
A data set of electron flux dropouts at GEO (L = 6.6) previously identified by Boynton, Mourenas, et al. (2016) based on LANL satellite measurements has been employed to first evaluate the inward radial extension of relativistic electron PSD dropouts occurring at GEO, at fixed first adiabatic invariant. For each of the GEO dropouts at each energy, the dropouts at L ∼ 4.2 were checked to identify any corresponding dropout occurring during the same time interval and with a similar first adiabatic invariant. Table 5 shows the energy channels for the GEO dropouts, together with the GPS energy channels at L ∼ 4.2 corresponding to a similar first adiabatic invariant. The percentage of GEO dropouts extending down to GPS orbit was calculated for each GEO energy and plotted in Figure 4a, demonstrating that the proportion of fast and deep relativistic electron dropouts extending from L ∼ 6.6 to L ∼ 4.2 increases significantly with electron energy, climbing from 12% for 0.4-0.6 MeV at GEO (i.e., for 1-1.6 MeV at L ∼ 4.2) to 20%-30% for 1-3 MeV at GEO (2-6 MeV at L ∼ 4.2). Similarly, the percentage of GPS (L ∼ 4.2) dropouts extending up to GEO was calculated for each GEO energy and plotted in Figure 4b, showing that 20% of the 1-1.6 MeV (energy at L ∼ 4.2) GPS dropouts extend up to GEO, while ∼60-70% of the 2-6 MeV (energy at L ∼ 4.2) GPS dropouts extend to GEO.
This means that 25-40% of the multi-MeV GPS dropouts are localized around L ∼ 4.2 and do not reach L = 6.6. Such dropouts (or at least a portion of them) might therefore correspond to fast precipitation induced by combined EMIC and whistler mode wave scattering localized in L. In addition, the 10 to 90 percentiles of the distribution of 3 MeV electron dropout magnitudes at L ∼ 4.2 are sensibly higher for the subset of dropouts that do not extend up to GEO than for all the dropouts: the median magnitude, 80 and 90 percentiles for dropouts that do not extend up to GEO are 31,489,946,versus 27,191, 664 for all the dropouts. Thus, multi-MeV dropouts localized around L ∼ 4.2 are often stronger than dropouts extending up to GEO.
Conversely, many of the 60-70% of multi-MeV dropouts that extend to GEO are likely related to magnetopause shadowing combined with outward radial diffusion-although precipitation loss may affect their total magnitude-explaining the prevalence of the sole B s as their main governing factor. Actually, the fact that B s is the sole main governing factor for MeV dropouts at L ∼ 4.2 stands in stark contrast with the results from a previous ERR analysis, which showed that both B s and p are among the main governing terms for such dropouts at GEO (Boynton, Mourenas, et al., 2016). This implies that dynamic pressure impulses have a definitely weaker impact on dropouts occurring closer to the Earth as compared with southward IMF.
The ratio of GEO to GPS orbit dropout magnitudes was also calculated for each of the wide (in L) relativistic electron dropouts. The mean and the 10, 20, 30, 40, 50, 60, 70, 80, and 90 percentiles of this ratio are plotted in Figure 5, showing that both the mean and median ratios increase up to a GEO energy of 2 MeV and then decrease at 2.65 MeV, being generally comprised between 0.6 and 2. Figure 5 further shows that 40% to 60% of the relativistic electron dropouts at L ∼ 4.2 are stronger than at L = 6.6 when they extend up to GEO. This could be due to either the presence of an additional loss process at GPS orbit compared with GEO, or to the initial L distribution of the PSD and the way the dropout develops from GEO, which may sometimes allow a stronger reduction at lower L.

GPS Dropout Occurrences Versus Plasmapause and Magnetopause Location
It is interesting to check the plasmapause position L pp with respect to the GPS satellite (i.e., L ∼ 4.2 here) during the dropouts, because of the known absence of hiss and chorus waves over a L range comprised between ∼ L pp −0.5 and ∼ L pp +0.1 (e.g., see Mourenas et al., 2017, and references therein). Strong precipitation-related dropouts should not occur there (in contrast, there is no such restriction concerning the presence of EMIC waves near L ∼ 4.2). Moreover, chorus-induced acceleration of electrons up to MeVs generally occurs just above the plasmapause (Horne et al., 2005) and may facilitate the subsequent occurrence of multi-MeV dropouts by substantially increasing the flux levels there. One therefore expects that precipitation-related dropouts at L ∼ 4.2 should correspond to L pp < 4.1 or L pp > 4.7. Figure 6 shows the position of the plasmapause calculated from the AE index based on the statistical plasmapause model from O'Brien and Moldwin (2003) versus L ∼ 4.2, during dropouts at 3 MeV. The median L pp location is also marked. During most 3 MeV electron dropouts, one indeed finds that L pp < 4. In such a case, precipitation-induced dropouts should generally be ascribed to combined effects of EMIC and chorus waves, although hiss waves could also be present in duskside high-density plumes.
Finally, the minimum magnetopause locations during each 3 MeV dropout, calculated using the model of Shue et al. (1998), have also been plotted in Figure 6. For nearly 50% of the dropouts, the magnetopause remained above L = 6.6, while for roughly 20% of the dropouts, the magnetopause never reached L shells smaller than 8. Consequently, magnetopause shadowing was likely significant in at least half of these dropouts. However, results in Figure 6 suggest again that magnetopause shadowing was probably not the main cause for ∼20% of the dropouts. This likely accounts, at least partially, for the weak dependence of MeV dropouts at L ∼ 4.2 on solar wind dynamic pressure.

Conclusions
High-quality data from GPS satellites have been used to perform a statistical study of fast and strong electron flux dropouts that have occurred at L ∼ 4.2 between 2001 and 2016. Such dropouts have been automatically selected and statistics of dropout magnitudes and occurrence rates as a function of electron energy (between 120 keV and 10 MeV) have been derived. The Error Reduction Ratio (ERR) analysis has been further used to identify possible linear and nonlinear relationships between dropouts and solar wind or geomagnetic activity indices.
The 1-10 MeV electron dropouts turn out to be both more frequent and stronger than dropouts at 120-800 keV. In particular, the mean magnitude of multi-MeV dropouts appears much larger than at lower energy. The median dropout magnitude also increases with energy, although sensibly less rapidly. The ERR analysis shows the presence of a similar threshold in the main factors governing GPS dropouts. While both the southward IMF B s , solar wind dynamic pressure p, and Dst index, can influence dropout magnitudes at low energy, B s becomes by far the most important controlling factor above ∼0.8-1 MeV, with no significant influence from dynamic pressure p or Dst. This contrasts with a previous ERR analysis at GEO, which showed that 1-3 MeV electron dropouts at L = 6.6 are controlled by both B s and p (Boynton, Mourenas, et al., 2016). Moreover, we found that for ∼20% of the multi-MeV electron dropouts at L ∼ 4.2, the magnetopause remained above L = 8, while during 25-40 % of these dropouts at L = 4.2, no similar dropout was recorded at geostationary orbit. Taken as a whole, all these results are consistent with the presence of some additional loss mechanism at multi-MeV energy as compared with lower energies during many dropouts at L ∼ 4.2, and they further indicate that this additional loss mechanism should depend principally on B s and that it should be relatively independent of magnetopause shadowing. It therefore suggests an important role of precipitation loss due to combined EMIC and whistler mode waves in a significant fraction of these events. Such occasional precipitation losses would increase the mean magnitude of multi-MeV dropouts and more generally modulate dropout strength, supplementing magnetopause shadowing and outward radial diffusion that also affect dropouts at lower energies.
We found also that almost all multi-MeV electron dropouts at L ∼ 4.2 occurred above the plasmapause. The present statistical results are therefore consistent with a significant contribution from precipitation induced by simultaneous EMIC and chorus waves in multi-MeV electron dropouts at L ∼ 4.2. In the future, it would be useful to examine in more details in GPS data the magnetic local time development of each of these dropouts, to study the radial progression of dropouts at L shells comprised between L ∼ 4.2 and L = 6.6, and to check the presence of EMIC and whistler mode waves from other available satellites: all this would help to confirm (or not) the proposed interpretation of the present results, but it is beyond the scope of the present paper. Finally, we note that a 12 h resolution data set was used in our analysis. This focus on dropouts lasting at least 12 h stems in part from our interest in time-integrated effects on satellites but also from the usefulness of averaging fluxes from various GPS satellites over half a day to get rid of spurious count variations. Moreover, dropouts of >1.1 MeV electrons driven by high-speed streams were found to last >18-24 h at geostationary orbit (Borovsky & Denton, 2009). Studies of other dropouts give similar time scales in the outer belt and show that it takes generally more time to recover initial flux levels for multi-MeV dropouts (e.g., . Nevertheless, dropouts of <500 keV electrons may last less than that, due to substorm-related injections (e.g., .Therefore, some fast and very short-lived dropouts, lasting less than 12 h due to a very fast recovery of electron flux levels in less than half a day, might not be identified. Such very short-lived dropouts would be worth examining too in future work.