As mentioned in Fig. 2, AE8 and SPM are used by default. This is the case for the SPM model at low energy (< 30 keV) except in geostationary orbit when IGE-2006 is preferred and for AE8 at higher energy (> 30 keV) outside the coverage of the SLOT model, OZONE and IGE-2006. SPM is a model with no solar cycle dependence; thus electron fluxes resulting from this model are considered constant throughout the solar cycle. For AE8, two versions exist: AE8 MAX for the solar maximum and AE8 MIN for the solar minimum. It is common to consider a full solar cycle of 11 years with 4 years of solar minimum (2 years before the minimum and 2 years after) and 7 years of solar maximum. Thus, in GREEN, when AE8 is the preferred model, the appropriate version of AE8 (MIN or MAX) is taken according to the year chosen by the user.

The inner zone of electron radiation belts is a region in which interest has grown in recent years thanks to data from the Van Allen Probes (Li et al., 2015; Claudepierre et al., 2017). As mentioned in this figure, for L < 2.5 and energy greater than a few hundred kiloelectron volts, we choose to use a corrected version of AE8. Indeed, in a previous study, Boscher at al. (2018) showed that high-energy electron fluxes (greater than a few hundred kiloelectron volts) predicted by AE8 are overestimated in the region for L∗ < 2.5. It is difficult to estimate the error made by AE8, but this study aims at showing that in this region and for high energy the physical model Salammbô provides electron fluxes in agreement with in situ measurements. Thus, in this version of GREEN-e model, AE8 fluxes have been corrected, that is to say, divided by a given factor, calculated using the Salammbô model. The Salammbô model is not perfect everywhere, but it has been proven that the decrease of electron flux with energy is good (Boscher et al., 2018). Thus, when electron fluxes from AE8 are higher than those provided by Salammbô, they are divided by the ratio between the both, up to a factor 100, in order to limit the correction (Fig. 3). This correction is not perfect but does allow better estimation of high-energy electron flux in the region L∗ < 2.5.

Figure 2 shows also that the SLOT model is available from L∗= 2.5 to L∗= 5 and for energies from 100 keV to 3 MeV. The SLOT model developed in 2013 (Sicard-Piet et al., 2014) was a model that reflects the mean flux at each point along the magnetic field lines. This first version has been updated in 2017 and is described here. As explained in a previous paper (Sicard-Piet et al., 2014), the SLOT model is based on the correlation between the flux dynamics in LEO orbit with NOAA-POES (Polar Operational Environmental Satellites) data and the flux all along the magnetic field line. The first change in the model is its spatial extension: the upper spatial limit of the SLOT model is now L∗= 5 as opposed to L∗= 4 before. Then, taking into account new measurements such as those from the Van Allen Probes (MagEIS), correlation factors all along the magnetic field line have been recalculated, between L∗= 2.5 and L∗= 5. An example of the correlation between NOAA-POES data and Van Allen Probe-A measurements is plotted in Fig. 4 for electrons with energy > 0.3 MeV and for L∗ between 3.7 and 3.8. This kind of correlation is made with all data used in the model and listed in Sicard-Piet et al. (2014) plus the Van Allen Probes. As explained by Sicard-Piet et al. (2014), these correlation factors are multiplied with the NOAA-POES data in order to obtain mean electron fluxes between > 0.1 and > 3 MeV along all magnetic field lines between L∗= 2.5 and L∗= 5 (Fig. 5). An equatorial pitch angle distribution shape based on a sine function is assumed and constrained by data all along the magnetic field lines between L∗= 2.5 and L∗= 5 (Fig. 5).

The most significant change in this new version of the SLOT model is the dependence of fluxes on the solar cycle. In order to have dependence on the solar cycle in GREEN-e, we have to study in detail the dynamics of the measurements from all NOAA-POES spacecraft. As an example of this solar cycle dependence, > 300 keV electron fluxes vs. time from all NOAA-POES data is plotted in Fig. 6. This figure shows clearly a correlation between the dynamics of NOAA-POES electron fluxes and the solar cycle (F10.7). The dynamics have been studied for four energy channels: > 0.1, > 0.3, > 1 and > 3 MeV.

Then, the flux dynamics over time between 1978 and 2015 have been represented in the 11 years of the solar cycle, from year -6 to year 4, with year 0 being the solar minimum. The fluxes vs. year of the solar cycle in NOAA-POES orbit for electrons > 1 MeV and for each L∗ interval is plotted in Fig. 7. This modulation with the solar cycle has been defined in LEO orbit for the four energy channels of the SLOT model and has been applied to the mean flux all along the magnetic field lines, from low altitude to the Equator.

Finally, in order to take into account the modulation of flux from one solar cycle to another, this new version of the SLOT model provides mean flux for a given year of the solar cycle as well as the maximum flux of the three solar cycles used in the model for this given year.

Thus, the new version of the SLOT model provides electron fluxes from 0.1 to 3 MeV for all altitudes with L∗ between 2.5 and 5 with a dependence on the solar cycle.

OZONE is valid for L∗ > 4 and for energies greater than 300 keV. In geostationary orbit, OZONE agrees with IGE-2006 results; consequently OZONE will be used for energies > 300 keV in GEO orbit. The version of OZONE developed in 2009 (Bourdarie et al., 2009) was already dependent on the solar cycle, so the model was not modified before integration in GREEN-e.

IGE-2006 is a specification model developed exclusively for geostationary orbit (Sicard-Piet et al., 2008). This orbit is at a fixed altitude but is represented by a large L∗ range, between 5.7 and 7.1. As explained in Sicard-Piet et al. (2008), fluxes provided by IGE-2006 come from averaged fluxes measured by all available Los Alamos National Laboratory (LANL) spacecraft. In this version of GREEN-e, fluxes will be considered as a constant in this L∗ range. IGE-2006 is solar cycle dependent, so the model was not modified before integration in GREEN-e.

The first version of OPAL was a model valid for protons > 80 MeV and for altitude lower than 800 km, depending on the solar cycle (Boscher et al., 2014). This year, a new version of OPAL has been developed at ONERA, using ICARE-NG measurements on board Jason-2 and Jason-3 (Boscher et al., 2011). Now OPAL-v2 provides proton fluxes for energy between 80 and 800 MeV up to the orbit of Jason spacecraft (1336 km). It is important to keep in mind that input parameters of OPAL are the radio flux F10.7 of the Sun and the magnetic field of the given year. As OPAL depends on the radio flux F10.7, an input of OPAL is the date. So, for a given date chosen by the user in the past, the real F10.7 value is used to calculate proton fluxes. But for a given date in the future, it is not so easy because the F10.7 value is unknown. Consequently, a statistical study has been done on F10.7 values from 1947 to now in order to define a mean F10.7 value for each of the 11 years of a solar cycle. Thus, for a given date chosen by the user in the future, the year of the solar cycle is predicted (from year -6 to year +4, with 0 being the year of the minimum), according to which the corresponding mean F10.7 value is used in OPAL to calculate proton fluxes. Moreover, added to the mean proton fluxes, OPAL provides an upper envelope considering the variation from one solar cycle to another. Taking into account that high-energy proton fluxes are anticorrelated with F10.7 values, this upper envelope is calculated using the minimum F10.7 value measured since 1947 for each year of the solar cycle.

Figure 9 represents an example of a proton flux spectrum (cm-2 s-1 sr-1) at L∗= 1.3 near the magnetic equator (αeq= 85.125∘) resulting from OPAL-V2 (in blue) and AP8 MIN (in green). We can observe that, for this L∗ value, fluxes from OPAL-V2 are slightly higher than those from AP8 MIN. This new version of OPAL has been integrated in GREEN-p.

On board the Los Alamos National Laboratory satellites, from July 1976 (launch of the satellite: 1976-059) to June 1995 (end of the measurements on board: 1984-129 and 1987-097), there was a detector named CPA (Charged Particle Analyzer), which covered the energy range 80 keV–300 MeV (Higbie et al., 1978; Baker et al., 1979). To cover a larger energy range, we also used the measurements of the MPA (Magnetospheric Plasma Analyzer) detector on board LANL satellites being launched between September 1989 (launch of the satellite: 1989-046) and November 1995 (McComas et al., 1993). These measurements cover roughly the energy range, 0.1–38 keV.

MPA measurements are globally of good quality. The temporal resolution is 86 s most of the time, but it can be doubled (172 s) for short periods of time. The detector aged with time; it drifted. This drift is compensated for over time, but after several years it is impossible to measure the highest energies anymore (typically after 10 years, it is impossible to obtain measurements above 10 keV). For the development of a proton specification model, data between 1 and 32 keV have been used. Fluxes below 1 keV have not been used, due to uncertainties in the spacecraft potential determination. Thus, we determined monthly averages of the proton flux for each satellite. These monthly averages were made in order to analyze possible solar cycle or seasonal effects (linked to the magnetic field or to its activity). An example is given for the 1 keV protons in Fig. 10. Some points as high as 2.3 × 109 MeV-1 cm-2 s-1 sr-1 observed in June 1991 could be due to the effect of magnetic activity, a particular contamination during that period or a (or several) bad point(s). Apart from these, no seasonal effect is observed in the flux curve; if there is a solar cycle effect, it is very low. As the flux does not vary with time, an average spectrum was deduced from all the measurements, taking into account the number of points for each satellite.

The CPA instrument is in fact made of two different instruments: CPA-LoP and CPA-HiP, which respond respectively to protons in the range 73–512 keV and 400 keV–300 MeV. The measurements are also globally of high quality. The time resolution of the instrument is 10 s, which means that the number of points is much higher. A monthly average for each channel was produced. An example of this average is plotted in Fig. 11 for 80 keV protons for each available LANL spacecraft. From that figure, it appears that there is no seasonal variation in the 80 keV proton flux; if there is a solar cycle one, it should be small in the range covered by CPA-LoP (less than a factor of 2). We must note in this figure a few low flux values which lie below the general tendency of the curve; it is suspected that they are due to gain switches for that particular channel and that satellite. We have not removed them, as the total average is not affected by these points.

As for MPA, a global average of all the points was performed, in order to obtain a global spectrum of protons from 1 keV up to 1 MeV in geostationary orbit. Above 1 MeV, data were not used because of the contamination by protons from solar flares.

Combining the part of the spectrum from MPA and CPA up to around 1 MeV leads to Fig. 12. The average fluxes are plotted, together with an error bar which corresponds to the maximum and minimum values obtained in the monthly averages from the full time period and all spacecraft. Though a gap exists between the two instruments, it appears that both parts of the spectrum are consistent: at low energy the spectrum is very flat; it falls very quickly for energies greater than 50 keV. We also compared in this figure the obtained spectrum with AP8 (for longitude 0∘, AP8 MAX and MIN being equal in this region) (Sawyer and Vette, 1976). For unidirectional flux comparison, we divided the AP8 flux by 4π, the environment being nearly isotropic in geosynchronous orbit for trapped particles. We can see that the obtained spectrum is nearly consistent with AP8. In fact, near 1MeV, the main problem is distinguishing trapped particles from untrapped ones (solar protons and cosmic rays). That may explain part of the difference. Globally, while the obtained spectrum is nearly a power law, AP8 is more an exponential law, with characteristic energy around 100 keV.

We tried to determine an empirical formula with all the average flux values. For the high-energy part, we used a kappa function with 9 keV characteristic energy and = 5.45, not far from what was obtained by Christon et al. (1991) in the plasma sheet. An exponential part (with 2 keV characteristic energy) was added at low energy to fit the total spectrum: flux=4×108exp⁡(-E/0.002)+7×1010E1+E5.45x0.009-6.45, where E is the energy in megaelectron volts (MeV) and the flux in MeV-1 cm-2 s-1 sr-1.

The model result is compared to the average spectrum in Fig. 12. This spectrum is very useful for deducing surface material degradation for satellites in geostationary orbit. It also can be used for dynamic physical modeling of the radiation belt proton to set a boundary condition.

This model is compared to the NASA AP9-SPM one (Ginet et al., 2013; Roth et al., 2014) also in Fig. 12. The NASA AP8 model was limited to energies greater than 100 keV. In geostationary orbit, the low-energy part comes from the same measurements we used: the MPA detector on board the LANL spacecraft and the two models are very close (the difference can be due to the interpolation used between channels). In AP9-SPM, the obtained spectrum is extrapolated to around 100 keV, but it is possible that our way to connect the two parts of the model has to be improved. With AP9-SPM, the two parts of the spectrum do not match. Obviously, there is a discontinuity at around 100 keV. At higher energy levels, the spectra from AP8 and AP9 are not too different, up to around 500 keV. Above this value, AP9 exceeds AP8 by a growing factor. The main problem for such energies is distinguishing trapped and untrapped particles in the measurements. We know from magnetospheric shielding calculations that for this energy range both particles can be observed depending on the viewing direction. Looking to the east, trapped particles from the radiation belts are observed; looking to the west, only cosmic rays and solar protons coming from outside the magnetosphere are observed. That is why in our analysis no points were extracted for E > 1.14 MeV. The model just gives an extrapolation (reasonable as a power law). It is really difficult to validate the IGP model with other data, because good proton data are extremely rare in GEO orbit, due to contamination by electrons measurements and solar protons.