LEEM: A new empirical model of radiation-belt electrons in the low-earth-orbit region

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012ja017941, 2012 LEEM: A new empirical model of radiation-belt electrons in the low-earth-orbit region Yue Chen, 1 Geoffrey Reeves, 1 Reiner H. W. Friedel, 1 Michelle F. Thomsen, 1 Mark Looper, 2 David Evans, 3,4 and Jean-Andre Sauvaud 5 Received 13 May 2012; revised 13 August 2012; accepted 27 September 2012; published 8 November [1] A new empirical model of radiation-belt electrons in the low-earth-orbit region has been developed based upon decade-long in situ observations from several low-altitudeorbiting satellites. This model LEEM aims to provide the electron environment conditions that a satellite would encounter in a given low Earth orbit. This model presents electron flux values for five energy ranges ( MeV, MeV, MeV, MeV, and MeV) within the space below an altitude of 600 km. Compared to the de-facto standard empirical model of AE-8, this model not only has a better data coverage in this specific region, but also can provide statistical information on flux levels such as worst cases and occurrence percentiles instead of solely mean values. The comparison indicates that the AE-8 model not only highly overpredicts the fluxes in the inner belt region in most cases, especially for the MeV electrons, which cannot be accounted for by the widely quoted error factor of 2 for AE-8, but also is unable to reflect the observed orders of magnitude variations in electron intensities. The LEEM model is carefully validated with both in-sample and out-of-sample tests. The characteristic electron environments along the International Space Station track and other virtual orbits are given as examples and as a demonstration of the use of the model. Citation: Chen, Y., G. Reeves, R. H. W. Friedel, M. F. Thomsen, M. Looper, D. Evans, and J.-A. Sauvaud (2012), LEEM: A new empirical model of radiation-belt electrons in the low-earth-orbit region, J. Geophys. Res., 117,, doi: /2012ja Introduction [2] The Low-Earth-Orbit (LEO) region, a region usually defined with the altitude range between 350 km (the top of the atmosphere) and 2000 km, is popular due to its easy accessibility and the short orbiting period and thus hosts a large number of satellites serving various purposes. Depending on the inclination of an orbit, the radiation received by the electronics and hardware onboard a LEO satellite can be from the proton dominated inner radiation belt (low inclination orbit) as well as from the energeticelectron dominated outer radiation belt (high inclination orbit). From either the measuring or the protecting perspective, it is important for us to have a reliable picture of the radiation specification in this region. This paper presents our updated knowledge of energetic electron distributions in the LEO region. 1 Los Alamos National Laboratory, Los Alamos, New Mexico, USA. 2 Aerospace Corporation, Los Angeles, California, USA. 3 Formerly at NOAA, Boulder, Colorado, USA. 4 Retired. 5 IRAP, CNRS-University of Toulouse, Toulouse, France. Corresponding author: Y. Chen, Los Alamos National Laboratory, PO Box 1663, MS D466, Los Alamos, NM 87545, USA. (cheny@lanl.gov) American Geophysical Union. All Rights Reserved /12/2012JA [3] From the practical perspective, a reliable radiation-belt model provides the designers of radiation-sensitive instruments and other equipment a critical tool to set the proper instrumental specifics so as to balance the cost and performance. Today the de-facto standard empirical model for trapped electrons is still the AE-8 model [Vette, 1991]. This model is based on data from the early years of space environment measurements (1960s and 70s) with limited coverage in the LEO region. Therefore, predictions from the AE-8 at LEOs are more likely extrapolated from higher altitude data and thus have a questionable accuracy. Another shortcoming of the AE-8 is the lack of statistical description accounting for the dynamic nature of the radiation belts, except for the commonly accepted error factor of 2 (e.g., modelweb.gsfc. nasa.gov/magnetos/aeap.html). Consequently, development of a new generation of space particle detectors and the continuing importance of valid design of radiation shielding for LEO spacecraft raise an urgent need for a new empirical model for this low altitude region. [4] Here we present a new empirical model for the radiation-belt electrons, which was recently developed based upon long-term in situ observations from several LEO satellites. This new Low-Earth-Orbit Electron Environment Model, hereinafter called LEEM, aims to provide the range of electron environment conditions that a satellite would encounter in a given low Earth orbit. This model provides electron flux values for five energy ranges (from 30 kev up to greater than 2.5 MeV) at altitudes less than 600 km as 1of14

2 Figure 1. LEO satellite data sampling positions and flux variations during a full orbital period on February 18, (a) L-shell and equatorial pitch angle values sampled by NOAA-16 and flux variations (color-coded) for the E1 channel (>30 kev). Data points with gray color indicate positions with no valid flux values available. (b) Data in the same format for SAMPEX ELO channel (>1.5 MeV). Gray grids in the background are model grids used by LEEM. The thick dashed black curve in each panel presents the loss cone size for reference, calculated at 150 km altitude in a dipole geomagnetic field. In Figure 1a, in the outer belt region, the SEM2 90 telescope measures electrons outside of loss cones while the 0 telescope measures inside. The letter M indicate the region where the maximum local pitch angles measured are smaller than at nearby L-shells and thus smaller fluxes are observed. Note that the color bar represents different flux ranges for two panels. a function of L-shell and equatorial pitch angle. Compared to the de facto standard empirical model of AE 8, this innovative model not only has a better data coverage in this specific region, but also can provide statistical information on flux values such as occurrence percentiles instead of only mean values. LEEM presents electron distributions with large variations, which are quite different from those provided by AE 8, and third-party observations in LEO are used for model validation. Characteristic electron environments along the International Space Station track and several other virtual orbits are given as example applications. [5] A description of instruments, data and preprocessing is presented in section 2. Section 3 describes the model formalism and presents LEEM flux distributions. Section 4 explains how to understand those distributions qualitatively, and section 5 shows the quantitative validation and application examples of the model. Caveats of the model are also discussed in section 5. This paper is concluded by a summary in section Instruments and Data Used by LEEM [6] Long-term electron observations used by LEEM come from four NOAA Polar Orbiting Environment Satellites (POES) spacecraft and one NASA Small Explorer, the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) spacecraft. The four POES spacecraft include NOAA-15 (with measurements from July 1998 to July 2007), NOAA-16 (October 2000 to July 2007), NOAA-17 (July 2002 to July 2007), and NOAA-18 (June 2005 to July 2007). SAMPEX measurements range from July 1992 to June In total there are about 35 satellite-year observations available. [7] POES satellites have circular sun-synchronous orbits (altitude km, inclination 98 ) with a period of 102 min. This constellation of four spacecraft together provides good local-time coverage. The Space Environment Monitor 2 (SEM2) on board each POES spacecraft contains two solid-state detector telescopes to detect electrons one oriented to view in the anti-earth-center direction on the 3-axis stabilized spacecraft (i.e., the 0 telescope) and the other to view at about 90 to the first (the 90 telescope) and therefore provides two uni-directional flux measurements at one instant. All of the electron telescopes measure electron flux in three energy ranges: Nominally, MeV (the E1 channel), MeV (E2), and MeV (E3) [Evans and Greer, 2000]. SEM2 data used for LEEM are averaged over 8 s, which is longer than the instrumental count-accumulating time of 1 s. The flux unit in SEM2 electron data sets is #/cm 2 /s/sr and LEEM follows it. The IGRF internal magnetic field model with secular variation coefficients is used for calculating the L-shell and local and equatorial magnetic field values along each POES satellite trajectory. As an example, Figure 1a illustrates data from the NOAA-16 E1 channel during one full orbital period, i.e., 4 crossings of radiation belts. The plot shows that the 0 (90 ) telescope measures 90 (20 40 ) equatorial pitch angles at equatorial crossings, and small pitch angles inside (outside) the loss cone at large L-shells. This reflects that the local pitch angle measured by the 0 (90 ) telescope decreases (increases) monotonically with increasing L-shell, determined by the configuration of telescopes. For most L-shells, 2of14

3 one of the telescopes can measure locally mirroring electrons, except for a region with L centered at 1.5 where both telescopes measure small local pitch angles, with the lowest at 60, thus forming a local minimum in fluxes along the satellite trace, as indicated by the letter M in the plot. (Further discussion on the M region can be found in auxiliary material Text S1, and in Figure S1, which shows the small local pitch angles. 1 ) [8] SAMPEX also has a low-altitude (520x670km) and polar-orbiting (inclination 82 ) orbit [Baker et al., 1993]. Its period is 96 min. The orbital plane of SAMPEX has a precession period 183 days and therefore sweeps all local times at the same L-shell every 3 months. The Proton/ Electron Telescope (PET) [Cook et al., 1993] on SAMPEX is designed to provide measurements of energetic electrons and light nuclei from solar, galactic, and magnetospheric sources. The PET is an all solid-state system that measures the uni-directional electron fluxes in two energy channels: MeV (the ELO channel), and MeV (EHI). PET data used here have a time resolution of 6 s. The flux unit in original data sets is #/cm 2 /s/sr/mev and LEEM follows it. The same IGRF internal magnetic field model is used in the calculation of the L-shell and local and equatorial magnetic field values along the SAMPEX trajectory. As an example, Figure 1b plots the data from the SAMPEX ELO channel during one full orbital period. [9] Measures are taken to reduce the potential proton contamination on electron data to the lowest level. For the SAMPEX PET instrument, the coincidence and rangeenergy technique applied [Cook et al., 1993] can effectively remove proton effects on electron data in most circumstances. Furthermore, periods with Solar Proton Events (SPEs) are excluded from this work since the proton contamination is statistically significant for MeV electrons. For the POES SEM2 data, it is well known that 100 s kev protons contribute to the SEM2 electron channels [Evans and Greer, 2000]. Following the method used by Rodger et al. [2010], we exclude E1 data points with electron fluxes lower than 2 times of SEM2 P2 ( kev) proton fluxes, and exclude E2 and E3 data points with electron fluxes lower than 2 times of P3 ( kev) proton fluxes. [10] Extensive work has been conducted on instrument in-orbit calibration as well as to address the potential aging issue for detectors over long-term performance period. Here is the summary of results and more details are in the auxiliary material. For SEM2, the inter-calibration factor between each pair of telescopes is generally under 1.6 (auxiliary material Figure S1), which is good enough for this work. Periodical assessment reports issued by the co-author David Evans assure the inter-calibration between NOAA spacecraft and rule out the possibility of any significant damage to SEM2 electron detectors over time. As for SAMPEX, indirect methods suggest that the error factor caused by aging is most likely under 2.5 (auxiliary material Figure S2), which is also acceptable compared to other error sources. [11] There are several limitations on the data that affect our way of developing LEEM: First, due to the instrument limitation on energy spectra (only 3 points from the POES SEM2 and 2 points from the SAMPEX PET, and usually POES 1 Auxiliary materials are available in the HTML. doi: / 2012JA and SAMPEX are at different locations), no attempt was made to interpolate flux over energy. This determines that the model is developed separately for each individual energy channel (or range). Second, since POES spacecraft and, usually, SAMPEX are 3-axis stabilized (SAMPEX is in spin mode occasionally), no attempt has been made to fit the local pitch angle distribution in LEEM as presented here. We take the instrument s central looking direction as the pitch angle for the measured flux, on which the error caused by the instrument opening angle is discussed in the Appendix A. Finally, the low altitudes of the satellite orbits and the bounce motion of electrons constrain this model to be applicable (without extrapolation) only to altitudes of 600 km or below. 3. Model Development and Results [12] We first present the formalism of the model. The current version of LEEM ignores any local-time dependence for simplicity. Thus, the physical space of the radiation belts is collapsed to 2 dimensions and is divided into many spatial bins of unequal size. The center of each bin has the coordinates of (L, a), where L is the L-shell and a is the equatorial pitch angle as the gray grids plotted in Figure 1. The values of L and a grid points can be found in Table 1. Specifying the equatorial pitch angle is equivalent to specifying the mirror latitude, so any point of (L, a) can be transformed to the mirror point of (x, z) in the X Z plane of a dipole magnetic field with the dipole pointing to the z direction. Hence contours of L and a are shown as a polar plot in Figure 2a. For one energy range, the uni-directional flux values observed in one spatial bin are further constructed as an occurrence distribution of flux levels, as in the example shown in Figure 2b for the ELO channel. This flux level distribution enables one to calculate statistically the flux value at any percentile. For example, in Figure 2c, the flux value of /cm 2 /s/sr/ MeV in the 90th percentile indicates an observer has a 90% chance of seeing flux levels at or below this value in this specified spatial bin and energy channel. In the case that the number of data points in one grid bin is below 100, all data in this bin are discarded so as to keep the distributions statistically meaningful. [13] Figure 3 presents examples of LEEM flux distributions. Panels in Row A show the uni-directional flux values for the five energy ranges at the 50th percentile on the (L, a) grids, and panels in Row B are fluxes at the 90th percentile. As mentioned in Section 2, the low-earth orbits of the satellites determine that only spatial bins with low-altitude mirror points are filled. Therefore, here uni-directional flux values along one L contour provide the equatorial-pitch angle distribution of flux close to the loss cone for one L-shell. Naturally, the flux levels at the 90th percentile are higher than those at the 50th. As a comparison, uni-directional fluxes derived from the AE-8Min model [Hess, 1968] are also plotted in Row C panels. (Uni-directional fluxes from AE-8Max are also calculated (not shown here) and the values are slightly higher than those from AE-8Min in the LEO region.) Figure 3c clearly shows the two-belt structure separated by the slot region at L approximately between , while a similar feature is also present in the LEEM flux distributions, particularly those for the two high-energy (MeV) ranges. Slot region positions for the first three LEEM 3of14

4 Table 1. Summary of Grid Points in the LEEM a Grid Points L-shell grid points (total number 44) 1.1, 1.2, 1.25, 1.3, 1.35, 1.4, 1.45, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.25, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.5, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0 Equatorial pitch angle grid points 90.00, 80.43, 71.70, 63.74, 50.51, 49.94, 44.01, 38.65, 33.82, 29.49, 25.62, 22.16, 19.09, 16.35, (in degree, total number 30) 13.96, 11.85, 10.00, 8.394, 6.998, 5.795, 4.763, 3.884, 3.139, 2.513, 1.993, 1.561, 1.208, 9.21e-1, 6.92e-1, 5.11e-1, Energy ranges (total number 5) MeV (corresponding to the lowest channel of POES SEM2), MeV (POES SEM2), MeV (POES SEM2), MeV (SAMPEX PET ELO), MeV (SAMPEX PET EHI) a Flux units: #/cm 2 /s/sr for the first three energy ranges and #/cm 2 /s/sr/mev for the last two MeV energy ranges. channels are higher with L at 3 4, and this is to be further discussed in the next section. Figures 3a and 3b highlight LEEM fluxes in the inner-belt region while bins for the outer belt region are compressed in polar plots and difficult to see. Therefore, Figures 3e and 3f replot LEEM fluxes for the same two percentiles but in different formats so as to show more details in the outer belt region. Figure 3d presents the numbers of data points used for the model for each of five energy channels. [14] For each of the first three LEEM channels, along the outer boundary of the flux-filled model domain as shown in Figure 3 (A1 A3, B1 B3), there appears to be another minimum region in the flux distributions with L at 1.5. In fact, this region corresponds to the M region as pointed out in Figure 1a, where SEM2 measures much smaller local pitch angles and thus smaller flux values comparing to neighboring regions along the POES trajectory. Note that this minimum would not exist when one traces the radial profile of fluxes measured by one specific telescope. In other words, this misleading minimum feature reflects the irregularity of SEM2 measurement coverage in the model s domain and this feature would disappear if the pitch angles measured by POES changed more smoothly, as in the case of SAMPEX. [15] From Figure 3, it can be seen that the AE-8 flux values (i.e., the mean values) are much higher than the LEEM flux values at the 50th percentile (i.e., the median values), particularly in the inner belt region by orders of magnitude. Comparing to the LEEM values at the 90th percentile, the AE-8 values are lower at large L-shells but still comparable or even larger at low L-shells, especially for the two highenergy (MeV) ranges. This suggests that the AE 8 model over-predicts the fluxes significantly in most cases, which may be because the AE 8 predictions in this region are extrapolated from higher altitude data due to the limited data coverage at low altitude. This result is also consistent with the result of Bühler et al. [1996] who compared AE 8 to the dose observed on board the Russian MIR space station. It should be noted that the mean and median values can be quite different for a non-normal distribution, especially a distribution with a long tail such as the one shown in Figure 2b. From the statistical sense, the mean value provides an over simplified and skewed reflection of a non normal distribution. It is from this sense that the LEEM is more advantageous than AE 8 by providing the flux occurrence distributions. Obviously, mean flux values from AE-8 with the widely quoted error factor of 2 can neither correctly Figure 2. Formalism of LEEM. (a) Contours of L and equatorial pitch angle (p/a) in the XZ plane with a dipole in z-direction. The curve for L = 2 is highlighted in red as one example and the curve for the equatorial pitch angle of 25.6 is in blue. The black square indicates the spatial bin whose contents are shown Figures 2b and 2c. (b) The flux statistical distribution (occurrence percentages normalized to the total number of flux data points in this bin) for the ELO channel in the specified bin. The vertical gray lines indicate flux levels for 10 percentiles (from the 10th to the 100th with an increment of 10). (c) Flux levels versus percentiles for the same bin. 4of14

5 Figure 3. Flux distributions from LEEM and AE-8 for all five energy ranges. (a) LEEM uni-directional flux distributions at the 50th percentile in polar plots. The integral L-shells from 2 to 8 are plotted in thick lines in each panel. (b) LEEM uni-directional fluxes at the 90th percentile in polar plots. (c) AE-8 unidirectional fluxes in polar plots. (d) Numbers of data points used in constructing LEEM for all five energy ranges in the L-p/a coordinate system. (e) LEEM uni-directional fluxes at the 50th percentile replotted in the L-a coordinate system. (f) LEEM uni-directional fluxes at the 90th percentile replotted. Fluxes for the first three energy ranges (columns) share the same color bar in the bottom and have the unit of #/cm 2 /s/sr. Fluxes in the other two channels are in the unit of #/cm 2 /s/sr/mev. 5of14

6 Figure 4. Distributions of uni-directional flux and pitch angle averaged flux from LEEM. (a) Unidirectional fluxes at the 50th percentile for the energy range of MeV. (b) Pitch angle averaged fluxes at the 50th percentile for the same energy range. Omni-directional flux can be obtained by applying a multiply factor of 4p to the pitch angle averaged flux. represent the average distributions nor appropriately represent the large variations in LEEM fluxes as shown at the two percentiles in Figure 3. In summary, for the LEO electron environment in the given energy ranges, LEEM paints an updated and more complete picture than AE-8 does, and the reliability of this picture will be discussed and tested in the next two sections. [16] LEEM can also provide omni directional fluxes, defined as the number of particles which arrive from all directions and traverse a test sphere with a unit crosssectional area. Since at a given position one can only observe electrons mirrored locally and with smaller pitch angles, the omni-directional flux at one point can be calculated by integrating uni directional fluxes over mirror altitudes at or below that point along the same field line. One such example is given in Figure 4 for the energy range of MeV: Figure 4a shows the uni directional fluxes from the LEEM and Figure 4b shows the pitch angle averaged fluxes from which omni directional flux can be obtained by multiplying by 4p. 4. Qualitative Discussions of LEEM Results [17] Before moving to the quantitative validation step, it would be beneficial to have some qualitative discussions of LEEM results so that we can have a better physical understanding of the model s statistical electron distributions. Through discussions, this section aims to address several questions that readers may have. [18] The first question is regarding the flux variations, such as where, how often, and when high-intensity fluxes occur. Variations in LEEM flux distributions mainly come from the changing geomagnetic activity in the region, and reflect the consequences of combined processes such as injection and diffusive transport. Distributions shown in Figure 3 already answer the where and how often questions, but to address the when question we need to look into the temporally evolving fluxes. Figure 5 presents the time history of L-sorted electron fluxes in LEO during 2001, when moderate activities occurred in radiation belts. As shown in Figure 5a, in the outer belt region, low-energy (>30 kev) electrons experience many enhancement events, which should be caused by injections from the plasma sheet during substorms indicated by high AE values (Figure 5e). Most of those enhancement events are confined to L-shells larger than 4 except for the large and sustained events occurring after the two equinoctial points. It is during these large events that new low-energy electrons can reach L-shells as low as 2 and the flux level stays high there for 10s of days. Figure 5b highlights low-energy electron fluxes at or higher than the 95th percentile given by LEEM, which are clearly associated with strong substorms. Comparatively, as shown in Figure 5c, high-energy (>1.5 MeV) electron enhancements occur less often and are more associated with geomagnetic storms indicated by the Dst index (Figure 5e). High-energy electron enhancements last longer and are confined to a narrower L range within 3 6 with the same exception during major storms after the two equinoctial points, when MeV electrons can reach lower L-shells. Figure 5d highlights the high-energy electron fluxes at or higher than the 95th percentile given by LEEM, which appear highly correlated to strong and prolonged enhancements in low-energy electron levels as suggested by Meredith et al. [2002]. The inner belt region (L < 2) is generally stable for both low- and highenergy electrons with no significant enhancement during The repetitive feature seen for MeV electrons in the inner belt region (Figure 5c) is due to the precession of SAMPEX orbit and has the period of 91 days, i.e., half of the orbital precession period, which actually reflects the stability of the inner belt. Enhancements of electrons at low L-shells occur only during extreme events, such as in 2003 when violent storms affected the whole radiation belts, and high flux levels can often be sustained over months, as shown in auxiliary material Figure S4. [19] Second, based on Figure 5 and the above discussion on enhancements, we can further answer the question of why spatial distributions are significantly different for lowand high-energy electrons, as shown in Figure 3. For highenergy electrons, most variations are in the outer belt and strong enhancements generally occur at L-shells of 3 6 (Figure 5c), which can be explained by the location of the strongest resonance with chorus waves as predicted by in situ wave acceleration theory. LEO MeV electrons have the slot region located at L of 2 (Figure 3), which is consistent with the classic theory that hiss waves quickly deplete highenergy electrons in the slot region [Lyons and Thorne, 1973]. MeV electrons are transported into the inner belt only during superstorms (e.g., auxiliary material Figure S4D) and it can 6of14

7 Figure 5. Electron enhancements observed by LEO satellites during Half-daily binned >30 kev (>1.5 MeV) electron fluxes observed by (a) NOAA-16 and (c) SAMPEX are shown as a function of L-shell and time. (b and d) Spatial and temporal positions of electron enhancement events, with flux values equal to or larger than the LEEM flux values at the 95th percentile. Here flux data have the same time resolutions used by LEEM. (e) The AE (black) and Dst (gray) indices. Vertical gaps in fluxes are due to the exclusion of data during SPEs. For >30 kev electrons, observations in the M region (with L at 1.4) are also excluded. take up to months for them to decay significantly [Abel and Thorne, 1998]. Therefore, the low level of MeV electrons in the inner belt (Figure 3) should reflect the relatively shorter time scale of the loss process than of the source process. By contrast, the minimum flux location for the first two energy channels is at L 4 as in Figure 3. This is consistent with the minimum L that can be reached by most injections as shown in Figure 5a, which may reflect the average size of the Alfven layer [Kivelson et al., 1979]. Injected electrons have much less chance to travel across the Alfven layer, but once they do, they can stay there for a long time. Therefore, the minimum flux location for low-energy electrons is the boundary that separates electron with closed drift shell (i.e., the inner belt) from those with open drift path (the outer belt). Of course, another contributing factor to this boundary may still be the hiss waves, whose resonance position is known to increase with decreasing energy and may be as large as 4 for 50 kev electrons as shown by Lyons and Thorne [1973]. However, which factor dominates the formation of this minimum flux position for low-energy electrons is definitely outside the scope of this work and we will leave it for the future. Again, the high level of low-energy electrons in the inner belt (Figure 3) should indicate stronger source processes than for MeV electrons. [20] Finally, LEEM electron intensities from the two MeV channels are orders of magnitude lower than those for the first three channels (Figure 3), therefore how realistic is it and how to understand such large differences? Though no single instrument used for LEEM covers the whole energy spectrum, we can explain and demonstrate the large differences from several directions. First, we want to point out that the energy-integral flux is used for the first three channels while the energy-differential flux is used for the MeV channels (Table 1). The latter brings MeV electron flux values numerically lower by up to one order of magnitude than if using energy-integral flux units uniformly. Second, distributions from AE-8 demonstrate the existence of large differences between the five channels, as shown in Figure 3. Intensities have similar orders of magnitude difference between channels when comparing AE-8 results (Figure 3c) to LEEM median distributions (Figure 3a), at least for L > 4. In addition, we also use observations from the Comprehensive Energetic Particle and Pitch Angle Distribution (CEPPAD) experiment [Blake et al., 1995] aboard Polar spacecraft, which are pitch angle resolved measurements from low- to mid-latitude regions, to map down to compare with LEO in situ measurements. Figure 6 compares the average radial profiles for the five channels during of14

8 Figure 6. Separations between fluxes for the five LEEM energy channels, derived from LEO and Polar CEPPAD observations during For the five LEEM energy ranges, (a) yearly averaged flux radial profiles measured in situ by NOAA-16 and SAMPEX are plotted, and (b) yearly averaged flux radial profiles mapped down to NOAA-16 and SAMPEX orbits from Polar positions are plotted. To compare to the trapped population, in Figure 6b the thin dashed lines are radial profiles for electrons with the 80 equatorial pitch angle measured in situ by Polar. Figure 6a presents curves averaged from in situ data from NOAA-16 and SAMPEX. Figure 6b presents fluxes mapped down to the same LEO locations (solid curves) derived from CEPPAD measurements, comparing to the fluxes at nearequatorial positions with 80 equatorial pitch angle (dashedlines). Considering the uncertainties in mapping and the coarse resolution in pitch angle distributions, we do not expect curves in both panels to have exactly the same flux values. However, it is clear that curves for LEO positions in both panels have similar shapes, and more importantly, there are similar large separations between the first three channels and the two MeV channels. For the first three channels in Figure 6b, the high intensities at L < 4 may be explained by the background contamination of CEPPAD s low-energy channels [Friedel et al., 2005]. Therefore, with high confidence we assert that the large differences between channels are real and are the combined results of the energy spectrum and energy-dependent pitch angle distributions. 5. Model Validation, Applications, and Caveats [21] We validate the model using both in-sample and outof-sample tests. The in-sample tests can demonstrate that there are no significant algorithm and coding errors in the model development steps. For this purpose, we validate the model by comparing individual POES and SAMPEX data to the statistical results. In Figure 7a, A1 and A2 compare in situ observations (black) for two energy ranges with the model flux values at five percentiles: 5th, 10th, 50th, 90th, and 100th (color coded differently), as functions of the L-shell during a 4 h period on one geomagnetically quiet day. It can be seen that most E2 data points are distributed around model fluxes at the 50th percentile while the ELO data points have high values between model fluxes at the 50th and 90th percentiles. In Figure 7b, B1 and B2 further compare flux data to the model on another 4 h period but on a geomagnetically disturbed day. During this 4 h period a moderate storm reached the end of its main phase. This time the E2 fluxes are high and close to the LEEM fluxes at the 90th percentile with the slot region almost filled, while the ELO fluxes are low and comparable to the 50th percentile level. (Here the quiet and disturbed days are picked from the ISGI monthly bulletin Since the flux is a function of both L and a, the curves in each panel can have multiple values at one specific L shell. Specifically in the inner belt with L 2.5, high (low) flux data points reflect times when the satellite was traveling inside (outside) of the South Atlantic Anomaly (SAA) region. Repetition of the above on other days has yielded similar results (not shown here). Therefore, through in-sample tests, we are confident that no artifacts are present in LEEM. [22] For the out-of-sample test, we use the independent electron data set from DEMETER (Detection of Electro- Magnetic Emissions Transmitted from Earthquake Regions). DEMETER was launched on June 29, 2004 into a circular polar sun-synchronous orbit at an altitude of 730 km with an inclination of 98. The IDP (Instrument for the Detection of Particle) on board measures locally mirroring electrons ranging from 70 kev up to 0.8 MeV with well resolved energy spectra for L-shells up to 7 [Sauvaud et al., 2006]. Therefore, we are able to compare IDP measurements over the POES E2 energy range against LEEM fluxes, with examples shown in Figure 8. In Figure 8a, A1 compares the time series of in situ observations (black) on one quiet day with the model flux values at five percentiles: 5th, 10th, 50th, 90th, and 100th (color coded differently). It can be seen that most data points fall in between the flux values at the 10th and 90th percentiles. In Figure 8b, B1 further shows the flux values as functions of the L-shell, in the same format as Figure 7. Clearly, for L-shells larger than 3, IDP fluxes are around the LEEM fluxes at the 50th percentile. Then, in Figure 8, A2 and B2 show the comparison on a disturbed day, with flux enhancement similar to what we see in POES data. Unusually high IDP fluxes are measured for L < 2, where saturation rates ( ) of IDP are observed as in both B1 and B2 in Figure 8b. This is probably caused by proton contamination in the region, as suggested by the calibration to POES SEM2 measurements (auxiliary material Figure S3). In addition, in the inner belt region, B1 and B2 of Figure 8 show no low IDP flux data points as SEM2 does in Figure 7, which is because IDP only provides enough valid data points covering the whole E2 energy range inside of the SAA. Repetition of the above on other days has yielded similar results (not shown here). Therefore, through out-ofsample tests, we are highly confident about the LEEM s validity. [23] One use of LEEM is to fly a LEO satellite through and see what flux levels will be expected by an electron detector 8of14

9 Figure 7. In-sample model validation. (a) A1 is NOAA-17 fluxes for the E2 channel ( MeV, black symbols) versus L-shell during a 4-h period on a geomagnetic quiet day (March 05, 2004), compared to the LEEM flux levels at five percentiles (5th (purple), 10th (blue), 50th (green), 90th (yellow) and 100th (red)); A2 is SAMPEX PET ELO fluxes (1.5 6 MeV, black symbols) during the same quiet period compared to the LEEM flux levels at the same five percentiles. (b) B1 is NOAA-17 fluxes for the E2 channel during another 4-h period on a geomagnetically disturbed day (March 10, 2004), compared to the LEEM fluxes; B2 is SAMPEX PET ELO fluxes during the same disturbed period. 9of14

10 Figure 8. Out-of-sample model validation. (a) Time series of DEMETER IDP electron fluxes in the SEM2 E2 energy range of MeV (black symbols) on a geomagnetic quiet (disturbed) period on Sep. 12, 2004 in A1 and Sep. 16, 2004 in A2, compared to the LEEM flux levels at five percentiles: 5th (purple), 10th (blue), 50th (green), 90th (yellow) and 100th (red). (b) The same flux data and model results versus L-shell during the same quiet (B1) and disturbed (B2) period. 10 of 14

11 Figure 9. Characteristic fluxes along the International Space Station orbit. (left) Flux levels from the 10th to the 100th versus L-shell for the five energy ranges. (right) Flux occurrence distributions (normalized as percentages for each L bin) for the same energy ranges. on board. Here we use the International Space Station (ISS) as an example. The ISS has an orbit of km and inclination of 51.6 deg, which is inside the LEEM region of validity. We downloaded the orbit data of ISS from the SSCWeb ( and fed these orbits to the model, with the results shown in Figure 9. A1 to E1 in Figure 9 show the fluxes in 10 percentiles (from the 10th to the 100th with an increment of 10) for five energy ranges, while A2 to E2 show the flux occurrence percentages. Curves in Panels in the left column can be very useful for designing an electron-detector on board the ISS. For example, in Figure 9, D1, it is shown that for the energy range of MeV the maximum flux level in the 100th percentile is /cm 2 /s/sr/mev, while the minimum flux in the 10th is /cm 2 /s/sr/mev. With the consideration of balancing performance and costs, a detector designer can 11 of 14

12 Figure 10. Characteristic fluxes at three orbits. (a) Pitch angle averaged flux levels versus percentiles for five energy ranges for a LEO orbit with a low inclination angle (0 ). Note that the flux unit for the first three energy range is #/cm 2 /s/sr, and the unit for the two MeV ranges is #/cm 2 /s/sr/mev. (b) Distributions for a LEO orbit with a moderate inclination (52 ). (c) Distributions for a LEO orbit with a high inclination (82 ). The yellow box in each panel highlights the ELO flux range from the 10th to the 90th percentiles. use these numbers to determine the geometric factor of the detector and the complexity of electronics, and a designer for other sensors will also know how much shielding is needed to prevent radiation damages. Flux values can be obtained for other LEO orbits in the same manner. [24] In addition, Figure 10 shows the effects of the orbit inclination. A LEO satellite with a low inclination (Figure 10a) stays in the inner radiation belt where 100 s of kev electrons have high intensities, while satellites with high inclinations (Figures 10b and 10c) travel through both belts and thus experience much higher fluxes of MeV electrons from the outer radiation belt. In this way, the LEEM can help customize instrument radiation design and/or radiation shielding for various satellite orbits. [25] There are several caveats that one should be aware of when using LEEM. As mentioned in Section 2, data used in this model have their own limitations, which are passed on to this model. For example, LEEM can only give out flux levels for five energy ranges and no attempt was made to provide fluxes at any given intermediate energy point (though it can be done with an assumed energy spectral shape.). In addition, since the statistical distributions for each energy range come from measurements from one sole kind of instrument, this model heavily relies on the capabilities of SEM2 and PET. For instance, for the energy range of MeV, the maximum flux level in the 100th may only reflect the saturated flux level measurable by the SAMPEX PET ELO channel. The real maximum flux level may be even higher. Furthermore, the wide opening angles for SEM2 (30 ) and PET (58 ) introduce an additional error factor to LEEM, which is further discussed in the Appendix. Finally, the LEEM uses POES and SAMPEX data sets as they are. Any further improvement of data quality will lead to updates of the LEEM in the future. Including more high-quality data sets from other missions is another future direction for LEEM improvement. 6. Summary [26] A new empirical model of radiation-belt electrons in the low-earth-orbit region (LEEM) has been developed based upon long-term in situ observations from NOAA POES and SAMPEX spacecraft. LEEM is able to provide reliable electron environment conditions that a particle instrument would encounter in a given low Earth orbit. LEEM presents electron flux values for five energy ranges ( MeV, MeV, MeV, MeV, and MeV) within the space with at altitudes 600 km. Comparing to the de-facto standard empirical model of AE-8, LEEM not only has better data coverage in this specific region but also, as the first publicly available model of this kind, can provide statistical information on flux values such as worst cases and occurrence percentiles instead of solely mean values. The comparison also indicates that the AE-8 model highly overpredicts the flux levels for the five energy ranges in the inner-belt region, especially for the MeV electrons, which cannot be accounted for by the widely quoted error factor of 2 for AE-8. Meanwhile, mean flux values by AE8 cannot reflect the orders of magnitude variations in electron intensities as shown by LEEM. After thorough validation tests, the characteristic electron environments along the International Space Station and other virtual orbits are given as examples and as a demonstration of the use of the model. This model, resulting from independent research efforts, should work complementarily with other models such as AE9 in the future. Appendix A: Evaluating the Averaging Effect of Instrument s Large Field-of-View on Electron Pitch Angle Distributions [27] The wide opening angle of a particle telescope degrades the instrument s directional resolving capability by averaging fluxes over a range of pitch angles. In the LEO region, particle flux levels are comparatively low and satellites cross L-shells with a very high speed. This situation 12 of 14

13 Figure A1. Effects of instrument s 30 FOV on the determination of pitch angle distributions. Here the loss cone size is 15. (a) Telescope s central looking directions, i.e., the values taken as measured pitch angles, compared to the real pitch angles for assumed local pitch angle distributions sin n (a); here n has six different values from 0 to 15. Points on the diagonal line indicate a perfect match. (b) Given assumed pitch angle distributions, ratios between observed fluxes and real fluxes at the measured pitch angles (i. e., telescope central looking directions). forces instrument designers to choose particle detectors with large geometric factors so as to optimize the balance between improving spatial/temporal resolution and obtaining a good statistics of event counts. It usually leads to a large field-of-view (FOV), or opening angle, for a LEO particle telescope, which thus raises this question: How much does the instrumental FOV bias the pitch angle distributions (PADs) and eventually affect LEEM? Here we attempt to address this question quantitatively. [28] First, we start from a hypothetical problem by testing the distortion on PADs by a SEM2-like virtual telescope. In reality, besides the telescope s wide FOV, other instrumental factors can also contribute to the PAD distortion, such as the angular response and the cross-section shape of the detector. For simplicity, here we assume the virtual telescope has a circular cross-section shape and isotropic angular response. For the shape of a real flux PAD, we assume it have the form of sin n (a), a popular functional form used to fit PADs by, e.g., Vampola [1998], where the exponent n determines the steepness of the distribution. In addition, we also assume a loss cone with a finite size and fluxes inside decreasing with the exponent n being 10. We have two options on how to use the telescope s measurements: Either taking the measured flux as true and finding out the correct corresponding pitch angle, which may be quite different from the central looking direction of the telescope; or taking the telescope s direction as true and finding out the correct corresponding flux, which may be quite different from the measured one. As an example, Figure A1 shows results for both options with assumptions of a30 FOV for the telescope and a loss cone size of 15. For the first option, Figure A1a presents comparisons between measured pitch angles, i.e., the central looking directions of the virtual telescope, to real pitch angles obtained by matching measured fluxes to the known PADs, for six different exponent n values. Obviously, measured pitch angles are more deviated for more anisotropic distributions, and how large the deviation can be depends on the telescope s looking directions, too. For each given PAD, there exists a turning point of pitch angle at 70, above which the real pitch angle is smaller than the measured one and below which the real pitch angle is larger. This can be explained by considering a pancake PAD and the averaging effect of the 30 FOV. Another turning point is the wedge feature at low pitch angles when the telescope measures electrons both inside and outside of the loss cone. How sharp the wedge is reflects the different PAD shapes inside and outside of the loss cone. For LEEM development, we have selected the second option, that is, assuming that the telescope s central looking direction is the true pitch angle. Thus, Figure A1b evaluates the error from this assumption. For the same six assumed PADs, the observed fluxes at given telescope directions are compared to real fluxes calculated from PADs, as shown in Figure A1b. For the curve withn=1,atthe90 pitch angle, the ratio between observed flux and real is slightly smaller than unity. With decreasing Figure A2. Comparison of LEEM fluxes to the model for the POES E2 channel based upon pitch angle fitting of observed fluxes. 13 of 14

14 pitch angles, the ratio increases slowly until the telescope covers both inside and outside the loss cone, where real fluxes are lower than the measured and thus form a dip in the ratio curve. For even smaller pitch angles, the flux ratio grows up quickly. Other curves have similar trends except that the size of the dip depends on the value of exponent n. Ratios at the dip can be much smaller for butterfly distributions with the exponent n being negative (not shown here). We repeat the above steps for a PET-like telescope with 58 FOV and the results are similar except that the bias gets more severe. (However, the nonuniform angular response of PET [Selesnick et al., 2003] should help alleviate the situation to some degree.) For a single telescope, measuring the medium local pitch angles at 70 appears to be able to minimize FOV effects without extra costs. [29] Thus far we have used assumed PAD shapes. Next, with SEM2 s two looking directions, we are able to evaluate the bias effects using more realistic PADs. LEEM, as presented in the main text, is based upon original measured fluxes without considering the telescope s averaging effects. Here, having two directional fluxes available and also considering the FOV effects, we are able to fit the true pitch angle distribution using the assumed PAD form of j 0 *sin n (a) with a steep decreasing function inside the loss cone, where j 0 is the flux level at 90 pitch angle. Then, using these fitted fluxes, we have another version of LEEM for the first three channels. We compare the two versions of LEEM, and results for the E2 channel are shown in Figure A2. It can be seen that ratios between original fluxes and fitted fluxes are around or slightly smaller than unity at local 90 pitch angles (i.e., along the upper boundary of the model s domain), are much higher than 1 for deep inside the loss cone (i.e., along the lower boundary), and can be lower than 1 for across the loss cone. This is consistent with results shown in Figure A1b. The averaged ratio for the whole model domain is 0.74 and other two channels have similar values. In this step, we do not discuss SAMPEX data since PET has only one looking direction. [30] For conclusions, we have demonstrated that the wide FOV of a particle telescope indeed makes the measured PADs more isotropic than the true ones. Particularly, measured fluxes inside the loss cone are often larger than they should be, and those for locally mirroring electrons are lower. However, on average, the current version of LEEM only underestimates fluxes by a factor of 0.74 due to the telescopes FOV effects, which is acceptable considering other error sources and thus justifies the usage of original SEM2 fluxes in LEEM without fitting. In addition, fitting by only two fluxes can add more uncertainties to the model since the true PAD form may be very different from the assumption. We realize that ideally all data going for empirical model development can be processed to be instrument independent. Unfortunately, it is not the case for the current version of LEEM. We look forward to seeing future LEO missions to provide measurements with better energy- and directionresolution, which not only will help improve LEEM but also are critical for understanding the electron precipitation phenomenon. [31] Acknowledgments. This work was supported by the DOE office of Nuclear and Non-proliferation, Los Alamos National Laboratory LDRD ER program, and NASA Living With a Star Program (07-LWS ). We are also grateful for the use of IRBEM-LIB codes for calculating magnetic coordinates. [32] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper. References Abel, B., and R. M. Thorne (1998), Electron scattering los in Earth s inner magnetosphere: 1. Dominant physical processes, J. Geophys. Res., 103, , doi: /97ja Baker, D. N., G. M. Mason, O. Figueroa, G. Colon, J. G. Watzin, and R. M. Aleman (1993), An overview of the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) mission, IEEE Trans. Geosci. Remote Sens., 31, , doi: / Blake, J. B., et al. (1995), CEPPAD: Comprehensive energetic particle and pitch angle distribution experiment on Polar, Space Sci. Rev., 71, , doi: /bf Bühler, P., L. Desorgher, A. Zehnder, E. Daly, and L. Adams (1996), Observations of the low Earth orbit radiation environment from MIR, Radiat. Meas., 26(6), , doi: /s (96) Cook, W. R., et al. (1993), PET: A proton/electron telescope for studies of magnetospheric, solar, and galactic particles, IEEE Trans. Geosci. Remote Sens., 31, , doi: / Evans, D. S., and M. S. Greer (2000), Polar orbiting environmental satellite space environment monitor: 2. Instrument descriptions and archive data documentation, NOAA Tech. Memo. OAR SEC-91, SEC, NOAA, Boulder, Colo. Friedel, R. H. W., S. Bourdarie, and T. E. Cayton (2005), Intercalibration of magnetospheric energetic electron data, Space Weather, 3, S09B04, doi: /2005sw Hess, N. W. (1968), The Radiation Belt and Magnetosphere, Blaisdell, Waltham, Mass. Kivelson, M. G., S. M. Kaye, and D. J. Southwood (1979), The physics of plasma injection events, in Dynamics of the Magnetosphere, edited by B. S. I. Akasofu, pp , D. Reidel, Norwell, Mass., doi: / _20. Lyons, L. R., and R. M. Thorne (1973), Equilibrium structure of radiation belt electrons, J. Geophys. Res., 78, , doi: / JA078i013p Meredith, N. P., R. B. Horne, D. Summers, R. M. Thorne, R. H. A. Iles, D. Heynderickx, and R. R. Anderson (2002), Evidence for acceleration of outer zone electrons to relativistic energies by whistler mode chorus, Ann. Geophys., 20, , doi: /angeo Rodger, C. J., M. A. Clilverd, J. C. Green, and M. M. Lam (2010), Use of POES SEM-2 observations to examine radiation belt dynamics and energetic electron precipitation into the atmosphere, J. Geophys. Res., 115, A04202, doi: /2008ja Sauvaud, J. A., T. Moreau, R. Maggiolo, J.-P. Treilhou, C. Jacquey, A. Cros, J. Coutelier, J. Rouzaud, E. Penou, and M. Gangloff (2006), High-energy electron detection onboard DEMETER: The IDP spectrometer, description and first results on the inner belt, Planet. Space Sci., 54, , doi: /j.pss Selesnick, R. S., J. B. Blake, and R. A. Mewaldt (2003), Atmospheric losses of radiation belt electrons, J. Geophys. Res., 108(A12), 1468, doi: /2003ja Vampola, A. L. (1998), Outer zone energetic electron environment update, paper presented at 1997 Conference on the High Energy Radiation Background in Space, IEEE, Snowmass, Colo. Vette, J. I. (1991), The AE-8 Trapped Electron Model environment, Tech. Rep. NSSDC/WDC-A-R&S91 24, NASA Goddard Space Flight Cent., Greenbelt, Md. 14 of 14