This work designs a new model called PreMevE to predict storm time distributions of relativistic electrons within Earth's outer radiation belt. This model takes advantage of the cross-energy, cross-L-shell, and cross-pitch angle coherence associated with wave-electron resonant interactions, ingests observations from belt boundaries—mainly by a National Oceanic and Atmospheric Administration Polar Operational Environmental Satellite in low-Earth orbit, and provides high-fidelity nowcast (multiple-hour prediction) and forecast (>~1 day) of MeV electron fluxes over L-shells between 2.8 and 7 through linear prediction filters. PreMevE can not only reliably anticipate incoming enhancements of MeV electrons during storms with at least 1-day forewarning time but also accurately specify the evolving event-specific electron spatial distributions afterward. The performance of PreMevE is assessed against long-term in situ data from one Van Allen Probe and a Los Alamos National Laboratory geosynchronous satellite. This new model enhances our preparedness for severe MeV electron events in the future and further adds new science utility to existing and next-generation low-Earth orbit space infrastructure.

Key Points

Event-specific behaviors of MeV electrons in the outer belt can be reliably predicted from LEO and GEO inputs
Multiple kinds of cross-population coherence are utilized for predicting trapped MeV electrons
PreMevE forecasts the starting times of MeV electron events and also evolving distributions afterward with high fidelity

Plain Language Summary

Relativistic electrons in Earth's outer radiation belt present a hazardous radiation environment for spaceborne electronics. These electrons, with energies up to multiple megaelectron-volt (MeV), manifest a highly dynamic and event-specific nature due to the interplay of competing processes. Thus, developing a forecasting model for these electrons has long been a critical but challenging task for space community. Recent studies have demonstrated the vital roles of electron resonance with various wave modes; however, it remains difficult for diffusion radiation belt models to reproduce MeV electron behaviors during geomagnetic storms due to reasons such as large uncertainties in input parameters. This work designs a new model called PreMevE to reliably predict storm time changes of MeV electrons within the whole outer belt. Taking advantage of newly identified coherence caused by wave-electron resonance, this model ingests observations mainly from satellites in low-Earth orbits to provide high-fidelity forecasts. As a first-of-its-kind, PreMevE can not only accurately predict incoming enhancements of MeV electrons with 1-day forewarning time but also reliably specify evolving electron spatial distributions afterward. PreMevE's high performance is assessed against long-term in situ observations. This model enhances our preparedness for future severe MeV electron events and further the science usage of existing and future space infrastructure in low-Earth orbits.

1 Introduction

Growing reliance on modern-technology infrastructures makes our society prone to space weather threats. For instance, satellite-based global navigation and communication systems are known to be vulnerable to sudden increases in near-Earth space radiation, often caused by the arrival of solar-originated coronal mass ejections, corotating interaction regions, and solar energetic particle events. Other space weather-related risks include ground-induced currents that disrupt power grids, petroleum pipelines, and high-speed rail systems. For details about how space weather affects our society, readers are referred to reviews such as Pirjola et al. (2005) and Ferguson et al. (2015). Consequently, in the National Space Weather Strategy (National Science and Technology Council, 2015a) and the National Space Weather Action Plan (National Science and Technology Council, 2015b), for the first time, the U.S. government issued guideline principles to coordinate efforts to enhance national space weather preparedness. Among the list of strategic goals prioritized in those two documents is to advance understanding and predictions of energetic particles encountered by spacecraft within Earth's magnetosphere.

Aiming to address this high-priority goal, here we specifically target on the Megaelectron-volt (MeV) electrons trapped inside Earth's outer radiation belt, distributed between the slot region (~ 2.5 R_E) and magnetopause (up to ~10 R_E). MeV electrons, also called relativistic electrons due to their very high speeds, adversely affect satellites in two major ways. First, they are the main contributor to total ionizing dose on satellites operating in the outer belt (Daly et al., 1996). Using empirical models such as AE9 (Ginet et al., 2013), engineers can manage and reduce the total ionizing dose on satellite payloads with proper shielding designs, though. More dangerously, relativistic electrons are notorious for causing instrument malfunctions through the deep-dielectric charging and discharging phenomenon (Lai et al., 2018). Due to their high penetration capability, MeV electrons can travel through satellite's surface and deposit charges deeply inside internal dielectric materials. Those charges quickly accumulate with prolonged high levels of MeV electrons, and when the induced electric field exceeds the breakdown threshold of the insulator material, electrostatic discharge occurs and sometimes can be devastating to spaceborne electronics that are increasingly miniaturized nowadays. Indeed, model calculations have suggested the cause of deep-dielectric discharges by sudden increments of MeV electrons (Bodeau 2010). Also, there are a list of reported spacecraft anomalies or failures accounted by this phenomenon (e.g., Baker, 2000; Iucci et al., 2005; Koons et al., 1998 , and Ferguson et al., 2015). Hence, it will be of great practical benefit to be able to predict when the MeV electron population will start to rise significantly and how long high electron fluxes will sustain.

MeV electrons inside the Earth's outer radiation belt are well known to be highly dynamic when disturbed. As shown in Figure 1a, Van Allen Probes (also known as Radiation Belt Storm Probes [RBSP]; Mauk et al., 2013) observe that MeV electron fluxes vary by orders of magnitude during geomagnetic storms; for example, the wide red regions indicate flux increments, while blue for decays and fast dropouts. However, changes in MeV electron fluxes differ event by event and not simply determined by storm intensities (i.e., the minimum Dst values) as discovered previously (Reeves, 1998; Chen et al., 2007). This event-specific behavior suggests the governing physics for MeV electrons are very different from those experienced by newly injected ring-current particles (mainly tens to hundreds keV ions) during storms. Dynamics of outer belt electrons have intrigued the space research community throughout the past half century, and recently, substantial progress in both understanding the drivers and modeling the diffusive processes has been made. For example, it is now widely accepted that the ups and downs in MeV electrons reflect the various interplaying processes, including the local energization caused by the resonance of whistler mode chorus waves with injected seed populations, local precipitation losses due to hiss and electromagnetic ion cyclotron waves, magnetopause shadowing losses when drifting electrons encounter the high-altitude boundary, radial redistribution caused by ultralow frequency waves, and adiabatic effects due to the distorted global magnetic field induced by upstream solar wind structures. However, comprehensively understanding MeV electron dynamics demands much more efforts, and implementing all these entangled physics to make event-specific predictions of MeV electron behaviors is still challenging and ongoing.

Details are in the caption following the image — **Figure 1**
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Dynamics of different electron populations in the outer radiation belt. Here radial distributions of electrons are observed to vary dramatically during geomagnetic storms (*Dst* index not shown here), and coherent responses of all populations can be clearly seen. (a) Radial distributions of spin-averaged fluxes for 1-MeV electrons, measured by MagEIS on board RBSP-a, are plotted as a function of time. At L = 6.6 is plotted 1-MeV electron fluxes observed by SOPA on board LANL-01A GEO satellite. Fluxes at RBSP-GEO conjunctions (e.g., including on days ~90–180) are used for deriving an adjusting factor that is applied to SOPA fluxes. Count rates (CRs) for (b) >100-keV, (c) >300-keV, and (d) >1-MeV precipitating electrons; that is, measurements from the 90° telescopes of MEPED E2, E3, and P6 channels on board POES NOAA-15 are presented in the same format. All electron data are binned by 5 hr in time and 0.1 in L-shells. Data in this plot cover a 1,289-day interval ranging from 20 February 2013 to 31 August 2016.

Developing a reliable predictive model needs two essential steps: first, identifying proper informational trigger(s) as inputs; and second, building an appropriate triggering mechanism to generate predictions (outputs) quantitatively. Different approaches in these two steps lead to different kinds of models. For MeV electrons, first-principle models are the first kind, in which the informational trigger mostly includes upstream solar wind conditions and background parameters, while the triggering mechanism is implemented by simulating the related physical processes as described above (see Chen et al., 2016, for a brief review). Models of this kind are usually based on the diffusive framework and often face challenges such as the comprehensiveness of physics included and the accuracy of parameterized input parameters driven by forecasted geomagnetic index from other sources. Predictive models of the second kind are more or less based on empirical relations—often with unspecified physics—by directly relating solar wind conditions and/or geomagnetic indexes to MeV electrons in specific regions. These include the Relativistic Electron Forecast Model (REFM) operated by the National Oceanic and Atmospheric Administration (NOAA), which is confined to the geosynchronous (GEO) orbit (Baker et al., 1990). Recent new models also appear by applying data mining techniques, such as the neural network scheme using solar wind inputs to predict GEO electrons by Shin et al. (2016) and Kalman filter using in situ RBSP data to nowcast outer belt electrons by Coleman et al. (2018). Although outperforming persistence models, the latter model cannot reliably forecast the arrival of incoming MeV electron events due to the lack of a storm precursor in its inputs.

Following a different approach, this work develops a new model to predict the event-specific variance of relativistic electron fluxes within the whole outer radiation belt, by expanding our previous study of identifying and utilizing cross-population coherence in Chen et al. (2016). This new model aims to forecast MeV electron distributions even with no in situ measurements available, for example, during the post-RBSP era, and is designed to be driven by easily accessible inputs from long-standing space infrastructures including constellations in low-Earth orbit (LEO) and GEO. In section 2, instruments and data are to be described and we also explain how the model is constructed based upon identified coherence that is related to the governing physics. Model prediction results, quantitative verification, and validation are presented in section 3, followed by discussions for further improvements in section 4. The paper is summarized and concluded by section 5.

2 Model Construction Based Upon Multiple Cross-Population Coherence

Electron data used in this work come from measurements made by RBSP, one Los Alamos National Laboratory (LANL) GEO satellite, and one NOAA Polar Operational Environmental Satellite (POES) within a period ranging from February 2013 to August 2016. First, fluxes of trapped MeV electrons across a range of L-shells are in situ measured by the Magnetic Electron Ion Spectrometer (MagEIS) instruments (Blake et al., 2013) on board RBSP spacecraft, which operate in low-inclination and nearly GEO-transfer orbits with a period of ~9 hr. Original MagEIS level 2 spin-averaged fluxes were downloaded from RBSP's data portal (https://www.rbsp-ect.lanl.gov), and here we use McIlwain's L-shell (McIlwain, 1966) values calculated from the quiet Olson and Pfitzer magnetic field model (Olson & Pfitzer, 1977) together with the International Geomagnetic Reference Field model. Second, to expand the L-shell coverage, we also use observations from the Synchronous Orbit Particle Analyzer (SOPA; Belian et al., 1992) and Energy Spectrometer for Particles (ESP; Meier et al., 1996) instruments carried by one GEO satellite LANL-01A. Original GEO data are 10-s spin-averaged SOPA/ESP fluxes generated by the co-author Michael Henderson. Here, for simplicity, all GEO fluxes are placed on one fixed L = 6.6, and an adjusting factor is derived—by statistically matching RBSP 1-MeV electron fluxes to GEO fluxes when both are simultaneously located at L = 6.6—and applied to GEO fluxes aiming to have relatively smooth radial flux distributions at most times. This simplified treatment of GEO data should not cause significant issues at this model development stage, and we leave the effects of temporally varying L-shells of GEO satellites to the future. Last, precipitating electrons are monitored by the Space Environment Monitor 2 (SEM2) instruments on board NOAA POES satellites in LEO (Evans & Greer, 2000). Original 2-s count rates by NOAA-15 are level 2 data files downloaded from the NOAA website (http://www.ngdc.noaa.gov/), and their L values calculated from the International Geomagnetic Reference Field model are used for this study. Here we use POES data from the 90° telescopes that measure outer belt electrons near and/or cross the loss cone and thus register more dynamic features than those from the 0° (zenith-pointing) telescopes. For convenience and to distinguish from the “trapped” population measured by RBSP and GEO, hereinafter we use the term precipitation loosely to refer to the electron populations with small equatorial pitch angles measured by POES. All RBSP, LANL-01A, and POES-15 original fluxes have been cleaned for background removal and assumed to have high quality. Furthermore, following Rodger et al. (2010), we exclude POES electron data points with fluxes lower than 2 times of P3 (240–800 keV) proton fluxes to reduce the potential proton contamination. All electron data are binned by 5 hr to allow for RBSP's full coverage on the outer belt for each time bin.

We started with the visual resemblance between trapped MeV electrons and precipitating electrons. As mentioned, Figure 1a presents the fluxes of trapped 1-MeV electrons measured by RBSP-a and LANL-01A. One can clearly see that the responses of trapped MeV electrons to storms are typically in an event-specific but globally coherent manner. For practical purposes, here we ignore electron dropouts and only focus on MeV electron events—the half-raindrop-shaped (cut along the line of symmetry) features in the L-time plot—that are characterized by sudden significant enhancements over the core region (with L-shells ~3–6) followed by slow decays over days. During those events, fluxes over a wide range of L-shells vary L-dependently, while more intense storms tend to affect electrons closer to the Earth. Meanwhile, count rates of precipitating electrons observed by NOAA-15 in LEO are plotted in Figure 1b for >100-keV (E2 channel), Figure 1c for >300 keV (E3), and Figure 1d for >1 MeV (P6, see Appendix A for details). For MeV electron events, one can discern the one-to-one temporal relation existing across the outer belt between the increments of trapped population (Figure 1a) and intensifications of precipitating populations (Figures 1b, 1c and 1d), as discovered by Chen et al. (2016), but over a much longer interval here.

To quantify the cross-population coherence, we next proceeded to compute the time-shifted correlation between the simultaneous observations of trapped MeV and precipitating electrons. First is the cross-energy cross-pitch angle coherence for each L-shell. As in Figure 2, high correlation coefficient (CC) values are found between POES E2/E3 and RBSP 1-MeV data. For CC distributions in Figure 2a, the maximum value for each L-shell within ~3.6–5.0 is generally >0.7. More importantly, the significant and positive lead times of low-energy precipitating electrons ahead of 1-MeV trapped electrons can be found from the maximum CC locations (the black curve) in the plot. For example, at L = 4.0, CC values in Figure 2a have a maximum of 0.84, and the lead time for >100-keV precipitating electrons is ~20 hr ahead. In Figure 2b for >300-keV precipitating electrons, high maximum CC values (> 0.7) are seen to extend to L-shells as low as ~3.0, but the lead times at maximum CC are shortened to ~10–15 hr for low L-shells and even negative for L-shells larger than 4.6. Chen et al. (2016) suggest this coherence is a consequence of the dominance of local wave-particle interactions in the region, and the ~10- to 20-hr leading time in hundreds keV electron precipitation can be explained by different diffusion speeds in causing precipitation and energization. (Indeed, these 10- to 20-hr time difference is shorter than and thus consistent with the typical >~1-day timescales calculated for the electron energization caused by chorus waves; e.g., Li et al., 2007.) Therefore, following the success in Chen et al. (2016), the positive lead times at L ≤ 4.8 for E2 and E3 precipitating electrons will be used as the first partial informational trigger for predicting MeV electron events, specifically as precursors for event starting times.

For larger L-shells, significant coherence also exists for electron populations at different L-shells. As shown in Figure 2c, the three solid curves present the correlation between E2 electrons at L = 4.6 to 1-MeV trapped electrons at larger L-shells 5.0, 6.0, and 6.6, respectively. For instance, the red curve indicates a maximum CC between >100-keV precipitating electrons at L = 4.6 and 1-MeV trapped electrons at L = 6.0 is ~0.6 with a leading time >20 hr. We speculate this cross-L-shell coherence is due to the dominance of spatial redistribution process in the region, for example, the outward radial diffusion whose importance grows as a power function of L-shells (Schulz & Lanzerotti, 1974). This coherence will also be used for forecasting the start of incoming MeV electron events at L > 4.8.

The last coherence studied in this work is between the trapped and precipitating populations with the same energy at the same L-shell. First reported by Kanekal et al. (2001), this global coherence is confirmed to exist over a wide range of L-shells as the CC distributions shown in Figure 2d between precipitating (POES P6) and trapped 1-MeV electrons. Compared with those in Figures 2a and 2b, CC values in this panel are generally higher (e.g., the maximum CC is 0.75 at L = 6.0) though with negative lead times at maximums. It is understandable because this high cross-pitch angle coherence reflects the efficient local pitch angle diffusion, and time delay is expected for wave-particle interactions to diffuse electrons into the loss cone. The negative lead times indicate this coherence cannot be used for predicting the onsets of MeV electron events, but it still suits as an informational trigger for predicting and tracking electron flux values during steady, long-lasting decays following initial enhancements.

Finally, with above three informational triggers identified, we developed a new PREdictive models for MeV Electrons, that is, the PreMevE model, by implementing linear predictive filters (LPFs) as the main triggering mechanism. Using linear combination of past values as inputs, Chen et al. (2016) have proven that a simple LPF can forecast MeV electrons at a single L-shell with high fidelity. Therefore, here the application of LPFs is expanded to the core region in the outer belt. Figure 2e illustrates how the model is constructed: Within the gray-shaded L-shell region and in GEO, an individual LPF is trained for each L-shell, while for 6 < L < 7, interpolation and extrapolation over L-shells are used. We confine LPFs below L = 6 mainly due to the continuous RBSP data coverage in the area. For each LPF at individual L, MeV electron fluxes are predicted by the moving average linear filter (Detman & Vassiliadis, 1997) J = Aj, where J is the predicted MeV electron flux for n time steps ahead of the current time t; j are the model inputs, for example, LEO electron count rates, at times t, t − 1, …, t − m + 1 (m is the total number of data points needed by the filter); and the filter vector A is determined by applying the singular value decomposition algorithm to a training data set. An LPF is called static if the filter vector A is fixed after the initial training, and an LPF is called dynamic if A is updated over time with new (or the latest) data being available for training. Here the PreMevE model has an L-shell bin size of 0.1 and a time step of 5 hr.

It should be noted that as a simple but powerful analysis tool for linear time-varying systems, the LPF method has been applied for understanding and predicting radiation belt dynamics for decades. Pioneer forecasting works include predicting >2-MeV electrons at GEO using the Kp index as inputs by Nagai (1988) and the previously mentioned REFM model based on upstream solar wind conditions (Baker et al., 1990). Also, LPFs have been used to characterize the time-delayed responses of MeV electrons to upstream solar wind (Vassiliadis et al., 2002), and the combination of data assimilation with LPFs has been suggested to improve prediction performance by Rigler et al. (2004). The PreMevE model differs from previous ones by taking advantage of the newly discovered cross-population coherence to predict the onsets of MeV electron events as well the varying flux distributions in the outer belt, even with no in situ measurements of trapped MeV electrons.

The current version of PreMevE includes two submodels: Submodel 1 focuses on predicting arrival timings of MeV electron events, and submodel 2 specifies evolving flux levels afterward. For inputs, submodel 1 is driven by storm precursors POES E3 electrons for L < 3.6, E2 electrons for 3.6 ≤ L ≤ 4.8, and E2 fluxes fixed at L = 4.6 for larger L-shells. Submodel 2 is driven by both E2 and P6 data from LEO, except at GEO where LANL SOPA data replace P6 data. This arrangement is based on the fact that the correlations at GEO in Figures 2a, 2b, and 2d are not very high—with maximum CC < 0.55. As a special treatment, we decided to use the self-coherence for GEO, which has a high value of 0.8 even with a lag time of 25 hr as shown by the dashed curve in Figure 2c. Though this coherence is excellent for tracking steady decays, it cannot forecast the sudden enhancements due to the arrival of new MeV electrons, and thus, SOPA data are only used for submodel 2. All input choices are based on a trial-and-error method with the goal of optimizing model performance. For example, Figure 2e shows flux distributions predicted by submodels 1 and 2 for one time bin compared with observations. It is seen that submodel 1 captures the distribution shape but with flux values being too high, while submodel 2 reproduces observations precisely.

3 Prediction Results and Model Performance

As an overview, 25-hr (i.e., n = 5) predictions of 1-MeV electron fluxes by PreMevE are presented in Figures 3b and 3c for the whole ~1,300-day interval. Following Chen et al. (2016), observations (Figure 3a) in the first 2 months (300 time bins) are used as training data for deriving the filter vector at each L-shell, and the number of data points for LPF inputs is chosen to be m = 15 here. (Effects of different training period lengths and m values will be further discussed in the next section.) All LPFs used here are static; thus, predictions in the first 2 months verify the method, and rest of the results can validate the model performance as out-of-sample tests. First, from visual inspection, both submodels reproduce MeV electron fluxes reasonably well but with noticeable differences. For example, submodel 2 predictions in Figure 3c resemble observations more closely than those of submodel 1 in Figure 3b, particularly for those MeV electron events (the red-yellow areas in plots). Also, submodel 2 is able to predict most variations in GEO but not submodel 1 as shown in Figure 3d (and Figure 3i). To examine details, a 260-day period is selected for enlargement (Figures 3f–3j), which includes multiple intense storms (Figure 3j). For the 10 major MeV electron events during the period, submodel 1 (Figure 3g) seems to capture all arrival timings correctly in the core region but tends to overpredict fluxes afterward for most events (e.g., those between days 900 and 990). In comparison, submodel 2 cannot predict the start of events, but it does capture the evolving flux distributions, particularly during decays (Figure 3h). Factually, the performance of the two submodels differs by our design as discussed in section 2.

Closer inspection reveals more details when predictions are plotted against observations for multiple individual L-shells as in Figure 4. In Figure 4 (left column), submodel 1 successfully predicts the onsets of all major MeV electron events within the forecasting window for L-shells below 6, indicated by the vertical green boxes with a width of 25 hr (also called prediction windows), and most other lower-level events. The L-shell dependence is clear in model performance: The higher L-shells sees more MeV increments are not timely predicted by submodel 1 as indicated by the yellow and blue boxes; that is, the forecasted enhancements are not within prediction windows. Indeed, by visually examining the whole ~1,300-day interval, success percentages of submodel 1 capturing the starting of MeV electron enhancements within prediction windows are 92%, 95%, 88%, 67%, and 61% for L = 3.0, 4.0, 5.0, 6.0, and 6.6, respectively. It implies the effect of cross-L-shell coherence degrades quickly with increasing L values. When comparing Figures 4e1–4b1, one can see more apparent enhancements in electrons at GEO and many of them cannot be predicted by LEO electron intensifications, suggesting factors other than local wave-resonance energization may take over. On the other hand, although missing the starting phases, submodel 2 predicts fluxes at individual L-shells with high fidelity as shown by Figure 4 (right). Thus, submodel 2 can tell us for how long high electron fluxes above a given level will sustain. Note the usage of LANL GEO data as inputs leads to excellent predictions at GEO by submodel 2 (Figure 4e2), except for lagging behind at the starting of events.

We also calculate forecast skill scores to quantify the submodel 1 performance in forecasting onsets of MeV electron events in a more objective and rigorous way. Figure 5 (left column) compares 25-hr forecasts by submodel 1 (in red) for 1-MeV electrons with observed fluxes at a single L = 4.6 in the core of the outer belt over the whole interval. The forecasted starting times are automatically identified from submodel 1 forecasts when predicted fluxes increase consecutively and the accumulated increments in the logarithm of fluxes are beyond the threshold value of 0.35 (i.e., a ratio of linear flux values ≥2.24). Events in four categories are identified in the plot: A prediction is called successful (indicated by a green dot) when the forecast falls within the 25-hr prediction window compared with observations; when a starting is predicted but earlier than the observed one by more than 1 day, it is called a partial success, such as the one on day ~123 in Figure 5a1; when a predicted starting cannot find a correspondence from observations, it is called a false alarm indicated by a blue dot; and a prediction miss is called when the observed onset is not predicted at all, such as the one on day ~102 (red dot). As indicated in Figure 5, there are 105 successful events, 4 partial successes, 15 misses, and 34 false alarms. Following Mozer and Briggs (2003), we first calculate a contingency table with coefficients n₁₁ = (successes) + 0.5 * (partial successes) = 107, n₀₁ = false alarms = 34, and n₁₀ = (misses) + 0.5 * (partial successes) = 17. Then, a list of standard skill scores can be calculated: The hit rate (HR) can be calculated as n₁₁/(n₁₁ + n₀₁ + n₁₀), which expresses the ratio of events correctly forecasted to those either forecasted or observed, ranging from 0 (worst) to 1 (perfect); the probability of detection (POD) can be calculated as n₁₁/(n₁₁ + n₁₀), the ratio of successfully predicted events, ranging from 0 (worst) to 1 (perfect); the false alarm rates (FARs) can be calculated as n₀₁/(n₀₁ + n₁₁), ranging from 0 (perfect) to 1 (worst); and the bias ratio (BR) can be calculated as (n₁₁ + n₀₁)/(n₁₁ + n₁₀), which determines if the forecast system is consistently overforecasting or underforecasting events, and has an ideal value of 1. Therefore, for L = 4.6, skill scores are HR = 0.68, POD = 0.86, FAR = 0.24, and BR = 1.16. Figure 5 (right column) compares submodel 2 forecasts with observations that track each other closely over the whole period.

To further examine the submodel 1 performance dependence on L, predictions for the other two L-shells, 5.6 and 3.2, are also plotted in Figures 6 and 7, respectively. From Figure 6 (left column), the contingency table coefficients are n₁₁ = 112.5, n₀₁ = 12, and n₁₀ = 48.5, and therefore, skill scores at L = 5.6 are HR = 0.65, POD = 0.70, FAR = 0.10, and BR = 0.77. Similarly, from Figure 7 (left column), the contingency table coefficients are n₁₁ = 16.5, n₀₁ = 7, and n₁₀ = 2.5, and therefore, skill scores at L = 3.2 are HR = 0.63, POD = 0.87, FAR = 0.30, and BR = 1.24. Therefore, comparing above skill scores, we see HR does not change much over three L-shells, POD tends to decrease at large L-shells, and the model changes from overforecasting to underforecasting with increasing L-shell values. All these trends are basically consistent with what is shown in Figure 4. Finally, it is interesting to see that FAR tends to decrease with increasing L values.

With the same weight given to all flux values, the model performance is additionally quantified by calculating values of prediction efficiency (PE; e.g., Nash & Sutcliffe, 1970) defined as $urn:x-wiley:15427390:media:swe20839:swe20839-math-0001$ , where subscripts p and o for flux j indicate predicted and observed values, respectively, and $urn:x-wiley:15427390:media:swe20839:swe20839-math-0002$ is the mean of the observations. PE = 1 indicates that event-specific changes in fluxes are predicted perfectly point to point. PE = 0 means predictions fit observations with the same average and same variation; for example, an empirical distribution averaged from all observations will have PE = 0. And PE < 0 means predictions perform worse than using the average of observations. Figure 8a plots submodel 1 PE values for the whole interval as a function of L-shell for different prediction lead times: current, 5 hr (1 time step, n = 1), 25 hr (n = 5, also called 1 day here), and 50 hr (n = 10, also called 2 days). As PE values are not expected to be high for submodel 1 per design, we still see values of >0.2 for L-shells below 5. The double peaks at L ~ 3.4 and 4.0 are due to switching filter inputs from POES E2 to E3 electron count rates at low L-shells, and the local peak at L ~ 4.8 is caused by changing to cross-L coherence at large L-shells. Differences between PE curves are not significant for submodel 1 since it aims at predicting the correct onset times (which have much limited data points compared with data set over the whole interval) but not statistically matching observations. In Figure 8b, submodel 2 has relatively high PE values for even 2-day predictions. For example, PE values at L ~ 4 are all above 0.8 for all four curves. Also, PE values at GEO increase from 0.45 for 2-day predictions to 0.70 for 1-day predictions and to 0.93 for 5-hr predictions. To put these PE values into context, REFM has slightly higher values of 0.71 (0.49) for 1-day (2-day) predictions for daily averaged fluence of >2-MeV electrons at GEO, and Shin et al. (2016) appear to have PE values of ~0.6 for 24-hr predictions on ~1-MeV electron hourly fluxes. Besides, the performance of submodel 2 gets better with shorter lead times. This indicates the reliability of submodel 2 improves as we get closer to the real time, and thus, flux distributions in MeV electron events can be predicted in the same way as terrestrial weather by gaining accuracy from long-term to short-term forecasts.

4 Discussions

Currently, PreMevE is designed to be driven by inputs from long-standing satellite constellations in LEO and GEO, assuming no in situ MeV electron measurements are available. This arrangement targets at the future but realistic scenario after the RBSP mission being ended. Indeed, a persistence forecasting model driven by in situ measurements can statistically outperform our current PreMevE submodel 2, as shown by the purple and blue curves in Figure 8c. It is not surprising because the information from in situ data is expected to improve predictions on a persistent system like the outer radiation belt. Nevertheless, using only in situ MeV electron data is still unable to forecast the occurrence of MeV electron events due to the lack of related informational trigger. If including RBSP data to drive PreMevE by replacing POES P6 data (but keeping E2), submodel 2 PE values can be the highest as shown by the green curve in Figure 8c. This again supports the fact that the addition of electron data from LEO does help improve the model's performance. Thus, in term of predicting both the starting times and evolving flux levels of MeV electron events, a combination of in situ MeV and LEO one and multiple hundreds keV electron data will be ideal for model inputs if possible.

In addition, it is useful to examine how the PreMevE model performance depends on different model parameters, such as the length of training data set and the number of input data points m needed by LPFs. Results that have shown so far use observations in the first 2 months, that is, data points in the first 300 time bins, as training data and the number of data points for LPF inputs has m = 15. These numbers are chosen based on two reasons. First, from Figure 2, it can be seen that CC values on the right side of maximum values monotonically decrease with increasing lag times and their values get significantly lower over a 75-hr interval; meanwhile, as in Figure 3a, in the first 2 months, MeV electrons exhibit several major MeV electron events during multiple geomagnetic storms and thus should provide adequate dynamic information for LPF training. Second, results justify the means: Examples in our previous study by Chen et al. (2016) and the predictions in this work have demonstrated those numbers will work reasonably well. Still, the effects of different training data lengths and m values are tested and their PE values are compared in Figure 9. As shown in Figure 9a1, longer training data sets can increase PE values of submodel 1 by ~0.07–0.3 at L > 5, while longer training data sets have no obvious effects on submodel 2 performance as in Figure 9b1. Increasing m values from 15 to 25 shows no noticeable difference for both submodels as in Figure 9 (right). Nevertheless, results in Figure 9 are still preliminary, and more detailed analyses of wider parameter ranges are left for future work.

We also extend the model for electrons with higher energy. Following the same approach as described in section 2, forecasts for 2-MeV electron fluxes are presented for the same 260-day period in Figure 10b and 10c. In general, 2-MeV electron flux distributions are reasonably well predicted but not as accurate as those for 1-MeV electrons. For example, both submodels overestimate the dynamics at L-shells < ~3.5 during days 900–990. One possible explanation can be the lack of 2-MeV precipitating electron measurements from POES. We also found the use of dynamic LPFs improves predictions for 2-MeV electrons statistically (not shown here). Figure 10d plots PE values for submodel 1 as a function of L-shell for current and three different prediction lead times. The maximum PE values are not very high (~0.3) for L-shells close to 4, and it is interesting to see PE values for 2-day predictions are higher than the others in the area. In Figure 10e, as expected, submodel 2 has statistically better performance than submodel 1, and PE values for all four cases are relatively high (with maximum values >~0.75) for the high-flux region with L < 4.5. In general, PreMevE submodel 2 predictions for 2-MeV electrons are comparable but not as good as those for 1-MeV electrons. Systematically extending PreMevE to higher energy will be one of our future goals.

The performance of PreMevE has demonstrated that LEO electron data, as internal constraining conditions for recurring local wave-particle interactions, are the critical information trigger for predicting storm-specific MeV electron events in the core region; however, the relatively low PE values at larger L-shells indicates other inputs may also be needed. For example, adiabatic effects and varying radial diffusion rates can play significant roles in modulating MeV electron fluxes at large L-shells, to which LEO data simply bear no adequate information for reliable predictions (e.g., as shown by Figure 4e1). Whereas being the external driver, upstream solar wind conditions have been successfully used for predictions at GEO as discussed in section 1, and thus, they should be added to the input list to improve PreMevE performance. Besides, our current model only exploits simple linear relations but no nonlinear ones. Therefore, another future direction is to employ deep neural network (NN) tools (e.g., LeCun et al., 2015) and take advantage of NN's ability to auto-analyze the relationship—linear or nonlinear—between multisource inputs through self-learning and thus produce results without any hypothesis of predictive function forms. It is also possible to merge the two submodels into a single one through employing NN algorithms in future work.

As a first-of-its-kind predictive model for outer belt energetic electrons, PreMevE can have a unique role in space weather forecasting and satellite-operating communities. This model is simple and lightweight but also powerful. Once put into operation, it will be an invaluable tool for satellite operators to make decisions by providing early warnings of when MeV electron events are incoming and also for how long the high flux levels of electrons will sustain—both critical for preventing severe internal dialectic charging/discharging and thus for preparing us for future severe space weather situations. Additionally, PreMevE is specifically designed to only rely upon inputs from long-standing space infrastructures (POES satellites in LEO and other satellites in GEO), and the easy data availability also makes it feasible for PreMevE to operate in real time. Indeed, inputs for PreMevE are not necessarily confined to POES and LANL GEO data; electron data sets from other satellites in alike orbits are expected to work similarly. For example, LANL GEO data used here may be replaced by measurements from NOAA GOES satellites, and hopefully some future LEO missions equipped with electron instruments can be put into operation before the retirement of current NOAA POES fleet. Furthermore, the coherence study here and others in Chen et al. (2014) have suggested that particle observations in LEO can be highly useful for remote sensing and predicting the radiation dynamics in the near-Earth space and thus assign new science utilities to existing and next-generation LEO space missions (e.g., particle instruments with high energy resolution and wide energy range on board smallsates or even cubesats).

5 Conclusions

In this work, we have (1) identified the informational triggers needed for predictions, by expanding our previous study of the coherence between electron populations inside the Earth's outer radiation belt and (2) implemented LPFs and developed a reliable model to forecast storm time changes of relativistic electrons within the region. This PreMevE model, taking advantage of the multiple coherence caused by local wave-electron resonant interactions, ingests observations at outer belt boundaries, specifically from NOAA POES in LEO and LANL GEO, to provide high-fidelity nowcast (multiple-hour prediction) and forecast (>~1 day) of MeV electron fluxes over L-shells between 2.8 and 7. PreMevE can not only reliably predict the start of enhancements in MeV electrons during storms with at least 1-day forewarning time but also accurately specify the evolving electron spatial distributions afterward. High performance of PreMevE is assessed against long-term in situ data from one Van Allen Probe and a LANL GEO satellite. With possible further improvements, this new model enhances our preparedness for severe MeV electron events in the future and also adds new science significance to existing and next-generation LEO space infrastructure.

Acknowledgments

We gratefully acknowledge the support of the U.S. Department of Energy through the LANL Center of Space and Earth Science (CSES) Program (special large project 2015-007) and LANL internal funding, the NASA Heliophysics Guest Investigators Program (14-GIVABR14_2-0028), NASA Heliophysics Space Weather Operations to Research Program (18-HSWO2R18-0006), NASA's Prime contract no. NAS5–01072, and RBSP funding contract NNG13PJ05I. We want to acknowledge the PIs and instrument teams of NOAA POES SEM2, and RBSP EMFISIS and MagEIS for providing measurements and allowing us to use their data. Thanks to CDAWeb for providing OMNI data. We are grateful for the use of IRBEM-LIB codes for calculating magnetic coordinates. RBSP and POES data used in this work were downloadable from the missions' public websites (https://www.rbsp-ect.lanl.gov and http://www.ngdc.noaa.gov), while LANL GEO data are provided as supporting information.

Appendix A: Can NOAA POES P6 Data Be Used for >1-MeV Electron Precipitation Quantitatively?

The P6 channel of SEM2 proton detectors on board POES satellites was designed to detect multiple-MeV protons but has been reported to essentially measure >1-MeV electrons in the outer belt region (Sandanger et al., 2009). To quantify the P6 measurements on >1-MeV electrons, we use the independent electron data set from Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions (DEMETER) for interinstrument calibration. DEMETER has operated from 2004 to 2010 into a circular polar Sun-synchronous orbit at an altitude of ~700 km—slightly lower than the POES altitude of ~750 km—with an inclination of 98°. The Instrument for the Detection of Particle (IDP) on board measures locally mirrored electrons ranging from 70 keV up to ~2.5 MeV with well-resolved energy spectra for L-shells up to ~7 (Sauvaud et al., 2006).

Here we compare IDP measurements of >1-MeV electrons to P6 fluxes from NOAA-17 within 40 days in 2008, as shown in Figure A1. During the period, DEMETER and NOAA-17 simultaneously operate in the same local time sectors and have very similar orbits (Figure A1c). In Figures A1a and A1b, fluxes from both instruments exhibit similar dynamics during the stormy intervals (e.g., days 2–7, 11–15, and 27–34) as well as on quiet days, suggesting the P6 channel does effectively respond to MeV electrons. In addition, the correlation between IDP and P6 fluxes is quantified to be significant with a CC value of 0.68, and ~85% of flux ratios between the two instruments fall within the factor of 3 (Figure A1d). Finally, periodical assessment reports issued by David Evans from NOAA, available from http://ngdc.noaa.gov/stp/satellite/poes/documentation.html, have addressed the intercalibration between SEM2 suites on difference POES satellites and suggested their similar performance in general. Therefore, we believe it is reasonable to use NOAA-15 P6 fluxes quantitatively for the dynamics of precipitating >1-MeV electrons.

Supporting Information

References

Baker, D. N. (2000). The occurrence of operational anomalies in spacecraft and their relationship to space weather. IEEE Transactions on Plasma Science, 28(6), 2007–2016.
Baker, D. N., McPherron, R. L., Cayton, T. E., & Kebesadel, R. W. (1990). Linear prediction filter analysis of relativistic electron properties at 6.6 R_E. Journal of Geophysical Research, 95(A9), 15,133–15,140.
Belian, R. G. G., CAyton, T., & Christensen, R. (1992). High-Z energetic particles at geosynchronous orbit during the Great Solar Proton Event Series of October 1989. Journal of Geophysical Research, 97(A11), 16,897–16,906.
Blake, J. B., Carranza, P. A., Claudepierre, S. G., Clemmons, J. H., Crain, W. R., Dotan, Y., Fennell, J. F., Fuentes, F. H., Galvan, R. M., George, J. S., Henderson, M. G., Lalic, M., Lin, A. Y., Looper, M. D., Mabry, D. J., Mazur, J. E., McCarthy, B., Nguyen, C. Q., O'Brien, T. P., Perez, M. A., Redding, M. T., Roeder, J. L., Salvaggio, D. J., Sorensen, G. A., Spence, H. E., Yi, S., & Zakrzewski, M. P. (2013). The Magnetic Electron Ion Spectrometer (MagEIS) instruments aboard the Radiation Belt Storm Probes (RBSP) spacecraft. Space Science Reviews, 179(1-4), 383–421. https://doi.org/10.1007/s11214-013-9991-8
Bodeau, M. (2010). High energy electron climatology that supports deep charging risk assessment in GEO, in Proc. 48th AIAA Aerosp. Sci. Meeting, Orlando, FL, USA, Jan. 2010, paper AIAA 2010-1608, pp. 1–13
Chen, Y., Fridel, R. H. W., Reeves, G. D., Cayton, T. E., & Christensen, R. (2007). Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: An integrated investigation during geomagnetic storm times. Journal of Geophysical Research, 112, A11214. https://doi.org/10.1029/2007JA012314
Chen, Y., Reeves, G. D., Cunningham, G. S., Redmon, R. J., & Hendersion, M. G. (2016). Forecasting and remote sensing outer belt relativistic electrons form low Earth orbit. Geophysical Research Letters, 43, 1031–1038. https://doi.org/10.1002/2015GL067481
Chen, Y., Reeves, G. D., Friedel, R. H. W., & Cunningham, G. S. (2014). Global time-dependent chorus maps from low-Earth-orbit electron precipitation and Van Allen Probes data. Geophysical Research Letters, 41, 755–761. https://doi.org/10.1002/2013GL059181
Coleman, T., cCollough, M., P, J., Young, S., & Rigler, E. J. (2018). Operational nowcasting of electron flux levels in the outer zone of Earth's radiation belt. Space Weather, 16, 501–518. https://doi.org/10.1029/2017SW001788
Daly, E. J., Hilgers, A., Drolshagen, G., & Evans, H. D. R. (1996). Space environment analysis: Experience and trends, Environment Modelling for Space-based Applications, Symposium Proceedings (ESA SP-392), ed. By W. Burke and T.-D. Guyenne, p. 15, ESTEC, Noordwijk
Detman, T., & Vassiliadis, D. (1997). Review of techniques for magnetic storm forecasting. In Magnetic Storms, Geophysical Monograph (Vol. 98, pp. 253–265). Washington, DC: American Geophysical Union.
Evans, D. S., & 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, CO
Ferguson, D. C., Worden, S. P., & Hastings, D. E. (2015). The space weather threat to situational awareness, communications, and positioning systems. IEEE Transactions on Plasma Science, 43(9), 3086–3098.
Ginet, G. P., O'Brien, T. P., Huston, S. L., Johnston, W. R., Guild, T. B., Friedel, R., Lindstrom, C. D., Roth, C. J., Whelan, P., Quinn, R. A., Madden, D., Morley, S., & Su, Y. J. (2013). AE9, AP9 and SPM: New models for specifying the trapped energetic particles and space plasma environment. In N. Fox & J. L. Burch (Eds.), The Van Allen Probes mission (pp. 579–616). Boston, MA: Springer.
Iucci, N., Levitin, A. E., Belov, A. V., Eroshenko, E. A., Ptitsyna, N. G., Villoresi, G., Chizhenkov, G. V., Dorman, L. I., Gromova, L. I., Parisi, M., Tyasto, M. I., & Yanke, V. G. (2005). Space weather conditions and spacecraft anomalies in different orbits. Space Weather, 3, S01001. https://doi.org/10.1029/2003SW000056
Kanekal, S. G., Baker, D. N., & Blake, J. B. (2001). Multisatellite measurements of relativistic electrons: Global coherence. Journal of Geophysical Research, 106(A12), 29,721–29,732.
Koons, H. C., Mazur, J. E., Selesnick, R. S., Blake, J. B., Fennel, J. F., Roeder, J. L., & Anderson, P. C. (1998). Proceed. 6^th Spacecraft Charging Tech. Conf., 7–11, Nov. 2–6, 1998, AFRL Sci. Cent., Hanscom AFB, MA, USA
Lai, S.T., Cahoy, K., Lohmeyer, W., Carlton, A., Aniceto, R., & Minow, J. (2018). Deep dielectric charging and spacecraft anomalies. In N. Buzulukova (Ed.), Extreme events in geospace: Origins, predictability, and consequences (pp. 419-432). Amsterdam, Netherlands: Elsevier Inc.
LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444.
Li, W., Shprits, Y. Y., & Thorne, R. M. (2007). Dynamics evolution of energetic outer zone electrons due to wave-particle interactions during storms. Journal of Geophysical Research, 112, A10220. https://doi.org/10.1029/2007JA012368
Mauk, B. H., Fox, N. J., Kanekal, S. G., Kessel, R. L., Sibeck, D. G., & Ukhorskiy, A. (2013). Science objectives and rationale for the Radiation Belt Storm Probes mission. Space Science Reviews, 179(1-4), 3–27. https://doi.org/10.1007/s11214-012-9908-y
McIlwain, C. E. (1966). Magnetic coordinates. Space Science Reviews, 5(5), 585–598.
Meier, M. M., Belian, R. D., Cayton, T. E., Christensen, R. A., Garcia, B., Grace, K. M., Ingraham, J. C., Laros, J. G., & Reeves, G. D. (1996). The energy spectrometer for particles (ESP): Instrument description and orbital performance. In Workshop on the Earth's trapped particle environment (Vol. 383, pp. 203–210). New York: Am. Inst. Phys. Conf. ROC.
Mozer, J. B., & Briggs, W. M. (2003). Skill in real-time solar wind shock forecasts. Journal of Geophysical Research, 108(A6), 1262. https://doi.org/10.1029/2003JA009827
Nagai, T. (1988). Space weather forecast: Prediction of relativistic electron intensity at synchronous orbit. Geophysical Research Letters, 15(5), 425–428.
Nash, J. E., & Sutcliffe, J. V. (1970). River flow forecasting through conceptual models part I—A discussion of principles. Journal of Hydrology, 10(3), 282–290. https://doi.org/10.1016/0022-1694(70)90255-6
National Science and Technology Council (2015a). National Space Weather Strategy, https://www.sworm.gov/publications/2015/nsws_final_20151028.pdf
National Science and Technology Council (2015b). National Space Weather Action Plan, https://www.sworm.gov/publications/2015/swap_final_20151028.pdf
Olson, W., & K. Pfitzer (1977). Magnetospheric magnetic field modeling, Tech. Rep., McDonnell Douglas Astronaut. Co., Huntington Beach, Calif.
Pirjola, R., Kauristie, K., Lappalainen, H., Viljanen, A., & Pulkkinen, A. (2005). Space weather risk. Space Weather, 3, S02A02. https://doi.org/10.1029/2004SW000112
Reeves, G. D. (1998). Relativistic electrons and magnetic storms: 1992–1995. Geophysical Research Letters, 25(11), 1817–1820.
Rigler, E. J., Baker, D. N., Weigel, R. S., Vassiliadis, D., & Klimas, A. J. (2004). Adaptive linear prediction of radiation belt electrons using the Kalman filter. Space Weather, 2, S03003. https://doi.org/10.1029/2003SW000036
Rodger, C. J., Clilverd, M. A., Green, J. C., & Lam, M. M. (2010). Use of POES SEM-2 observations to examine radiation belt dynamics and energetic electron precipitation into the atmosphere. Journal of Geophysical Research, 115, A04202. https://doi.org/10.1029/2008JA014023
Sandanger, M. I., Søraas, F., Sørbø, M., Aarsnes, K., Oksavik, K., & Evans, D. S. (2009). Relativistic electron losses related to EMIC waves during CIR and CME storms. Journal of Atmospheric and Solar - Terrestrial Physics, 71(10-11), 1126–1144.
Sauvaud, J. A., Moreau, T., Maggiolo, R., Treilhou, J.-P., Jacquey, C., Cros, A., Coutelier, J., Rouzaud, J., Penou, E., & Gangloff, M. (2006). High-energy electron detection onboard DEMETER: The IDP spectrometer, description and first results on the inner belt. Planetary and Space Science, 54(5), 502–511. https://doi.org/10.1016/j.pss.2005.10.019
Schulz, M., & Lanzerotti, L. (1974). Particle diffusion in the radiation belts. New York: Springer.
Shin, D.-K., Lee, D.-Y., Kim, K.-C., Hwang, J., & Kim, J. (2016). Artificial neural network prediction model for geosynchronous electron fluxes: Dependence on satellite position and particle energy. Space Weather, 14, 313–321. https://doi.org/10.1002/2015SW001359
Vassiliadis, D., Klimas, A. J., Kanekal, S. G., Baker, D. N., & Weigel, R. S. (2002). Long-term-average, solar cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research, 107(A11), 1383. https://doi.org/10.1029/2001JA000506

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Volume17, Issue3

March 2019

Pages 438-454

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PreMevE: New Predictive Model for Megaelectron-Volt Electrons Inside Earth's Outer Radiation Belt

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Model Construction Based Upon Multiple Cross-Population Coherence

3 Prediction Results and Model Performance

4 Discussions

5 Conclusions

Acknowledgments

Appendix A: Can NOAA POES P6 Data Be Used for >1-MeV Electron Precipitation Quantitatively?

Supporting Information

References

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PreMevE: New Predictive Model for Megaelectron-Volt Electrons Inside Earth's Outer Radiation Belt

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Model Construction Based Upon Multiple Cross-Population Coherence

3 Prediction Results and Model Performance

4 Discussions

5 Conclusions

Acknowledgments

Appendix A: Can NOAA POES P6 Data Be Used for >1-MeV Electron Precipitation Quantitatively?

Supporting Information

References

Citing Literature

Figures

References

Related

Information

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