Solar Proton Events: Risks and Modeling

• Solar Proton Events are transient, high-energy proton bursts triggered by solar eruptions that pose risks to space weather, satellite operations, and aviation.
• Research combines direct particle measurements, cosmogenic proxies, and advanced modeling to quantify SPE fluences, spectral features, and geophysical impacts.
• SPE impacts are assessed through atmospheric chemistry models and forecasting techniques to inform risk mitigation for technology and human exploration.

Solar Proton Events (SPEs) are transient, intense episodes of solar energetic proton acceleration and interplanetary transport, with major impacts in heliospheric physics, planetary atmospheric chemistry, space weather, and astrophysical risk modeling. SPEs are the dominant astrophysical source of hazardous proton irradiation for near-Earth space, planetary surfaces, and aviation, and also provide a critical forensic archive of extreme solar activity via geophysical and cosmogenic signatures. The following sections provide a technical synthesis of current understanding, methodologies, major open questions, and operational implications for SPEs, drawing upon recent research and data-driven modeling.

1. Physical Definition, Classification, and Plasma Sources

SPEs are defined as abrupt, sustained enhancements in the differential or integral flux of protons (and, by extension, heavier ions) in the near-Earth/heliospheric environment, with energies typically $E \gtrsim 10$ MeV, following major solar eruptive activity. A canonical threshold for event detection is a $>10$ MeV proton flux exceeding $10$ pfu ($1$ pfu $= 1$ cm$^{-2}$ s$^{-1}$ sr$^{-1}$); this forms the basis of both NOAA's operational event catalogs and empirical/statistical studies (He et al., 2015, Li et al., 2014).

Proton acceleration in SPEs is ascribed to two principal mechanisms: (1) impulsive acceleration in solar flare reconnection regions, generally producing short duration, soft-spectrum events, and (2) gradual acceleration at CME-driven shocks, yielding spectrally hard, GeV-extended particle populations often responsible for ground-level enhancements (GLEs) (Li et al., 2014, Atri, 2019). Empirical time-of-maximum and event-integrated spectra are characterized by power-law or Band-function parameterizations,

$$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$

where $\gamma_1$ (soft tail) and $>10$0 (hard tail) exponents, along with roll-over or cutoff energies, define the event's penetration and radiative hazard profile (Melott et al., 2016, Li et al., 2014). Notably, the 23 Feb 1956 SPE exemplifies the hard-spectrum class, reaching $>10$1 protons/cm$>10$2, while events such as 3–4 Aug 1972 are soft-spectrum dominated (Melott et al., 2016, Usoskin et al., 2020).

2. Statistical Occurrence, Proxy Signatures, and Extreme Event Constraints

Direct SPE measurements span only the space age and capture a limited range of fluence. For centennial to millennial constraints on the occurrence of extreme events, geophysical proxies are required. Cosmogenic radionuclide production, notably $>10$3Be and $>10$4C, is the most robust method, as SPE-induced secondary cascades yield time-correlated isotopic anomalies in ice cores and tree rings (Usoskin et al., 2012, Usoskin et al., 2020). The relevant detection thresholds are set by the event-integrated fluence $>10$5, with $>10$6 cm$>10$7 defining an "extreme" SPE.

Statistical analyses find no events exceeding $>10$8 cm$>10$9 in the last $10$0 kyr, constraining occurrence probabilities to $10$1 yr$10$2 ($10$3 cm$10$4), $10$5 yr$10$6 ($10$7), and $10$8 yr$10$9 ($1$0) (Usoskin et al., 2012). The primary limitation is proxy sensitivity: the reference 1956 SPE produces, at most, a $1$1 excursion in a single $1$2Be/ice-core record; only by stacking 5–8 independent records can events $1$3 times more intense become detectable at $1$4 (Usoskin et al., 2020). This constrains space weather risk: decadal-to-century spacecraft operations must plan for fluences up to $1$5 cm$1$6 (Usoskin et al., 2012, Usoskin et al., 2020).

Nitrate spikes in ice cores, formerly proposed as high-resolution SPE proxies (Melott et al., 2016), have been shown through chemistry–climate modeling to yield $1$7 column HNO$1$8 enhancement for the 1956 event compared to a $1$9–$= 1$0 ng cm$= 1$1 background, rendering them unreliable as unique SPE signatures given confounding tropospheric sources (Duderstadt et al., 2016).

3. Solar–Heliospheric and Magnetospheric Transport Phenomenology

The propagation of SPE protons from the solar corona to 1 AU is governed by interplanetary magnetic field (IMF) topology and particle transport processes. The Parker spiral configuration introduces a pronounced longitudinal bias: for any given angular separation between the observer's IMF footpoint and the solar source, eastern sources yield systematically higher observed fluxes due to shorter virtual path length and reduced perpendicular dilution (He et al., 2015). Focused transport equations of the form

$= 1$2

incorporate pitch-angle and perpendicular diffusion ($= 1$3), adiabatic deceleration, and magnetic focusing (He et al., 2015). This leads to a longitudinally asymmetric probability of SPE detection, with a typical east/west event ratio of $= 1$4 for $= 1$5 bins.

Magnetospheric shielding imposes additional complexity. During geomagnetic storms, medium-energy (1–20 MeV) proton cutoff latitudes display a strong local time response: storm-enhanced magnetopause currents push dayside cutoffs poleward (up to $= 1$6), while simultaneously cross-tail currents shift nightside cutoffs equatorward (up to $= 1$7) (Tyssøy et al., 2016). Empirical parameterizations for the cutoff latitude $= 1$8 as a function of Dst and IMF $= 1$9 (dayside) or solar wind pressure $^{-2}$0 (nightside) improve the fidelity of modelled atmospheric energy deposition, reducing $^{-2}$1–$^{-2}$2 overestimation to $^{-2}$3 (Tyssøy et al., 2016).

4. SPE Impact on Planetary and Atmospheric Chemistry

SPE-induced atmospheric ionization, via direct proton and secondary particle interaction, is a dominant source of energetic particle precipitation (EPP) in the polar D-region (50–100 km) and mesosphere. Ion pair production rates $^{-2}$4 [cm$^{-2}$5 s$^{-2}$6] are given by

$^{-2}$7

where $^{-2}$8 eV is the mean ion-pair energy and $^{-2}$9 is the stopping power. The resulting electron density profiles modulate radiowave absorption (CNA) and drive HO$^{-1}$0/NO$^{-1}$1 enhancement, which catalyzes O$^{-1}$2 depletion in the mesosphere/stratosphere (Heino et al., 2019, Tyssøy et al., 2016).

Observationally, D-region CNA during large SPEs is reproduced within $^{-1}$3 dB poleward of $^{-1}$4 geomagnetic latitude by coupled WACCM-D and riometer measurements, though model errors are amplified by the use of static cutoff latitudes and inadequate twilight transition representation (Heino et al., 2019). Ozone depletion of $^{-1}$5 tens of percent (mesosphere) and a few percent (stratosphere, post-winter descent) is implicated in radiative and circulation variability on timescales of weeks to months.

For non-terrestrial atmospheres, comprehensive GEANT4-based modeling shows that both the spectral hardness and fluence of a SPE jointly determine surface radiation dose. In Martian and exoplanetary contexts, a power-law scaling $^{-1}$6 (for doses in Gy, $^{-1}$7 in protons cm$^{-1}$8) emerges, with short atmospheric pathlengths ($^{-1}$916 g cm$^{-1}$0 for Mars) rendering even background GCR doses potentially mission-limiting (Atri, 2019, Atri et al., 2020). Minimal planetary shielding ($^{-1}$1 g cm$^{-1}$2) is required to avoid acute, lethal doses in hypothetical extreme events.

5. Timing, Observational Signatures, and Instrumental Systematics

SPE detection and classification rely on high-cadence, multi-channel particle measurements from geostationary (GOES, integral flux) and L1 (SOHO/EPHIN, differential flux) platforms. Comparative analysis of 83 10–50 MeV SPEs reveals that, for minor (S1) and moderate (S2–S3) events, L1 detects earlier onsets by $^{-1}$320 min and longer durations (with median peak flux ratios EPHIN/GOES $^{-1}$4). For severe (S4) events, GOES channels over-report flux by factors up to $^{-1}$5 due to high-energy contamination (Ali et al., 6 Nov 2025).

This implies that operational forecasts and cislunar mission risk models must account for instrument-specific biases and timing uncertainty ($^{-1}$630 min in onset, $^{-1}$71 hr in peak prediction) (Ali et al., 6 Nov 2025).

6. Event Statistics, Forecasting Methodologies, and Predictive Modeling

The temporal occurrence of SPEs exhibits a power-law waiting time distribution (WTD) with index $^{-1}$8 for large intervals ($^{-1}$9), consistent with a non-stationary Poisson process driven by clustering in the solar event rate (Li et al., 2014). The clustering parameter $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$0 determines the WTD tail, and the close match with type II radio burst statistics supports a CME-driven shock origin for most high-fluence events.

Recent advances in operational and research SPE forecasting increasingly leverage ML and deep learning (DL) on direct GOES proton and SXR features. Neural networks, SVMs, XGBoost, and sequence-to-sequence LSTM architectures have been benchmarked against NOAA operational forecasts. Key findings:

• Daily ML models, using only prior-day proton and SXR statistics, achieve true skill statistics (TSS) $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$10.7–0.8, outperforming both persistence and SWPC probabilistic products, especially in low-miss ("all-clear") regimes (Sadykov et al., 2021, Ali et al., 2023).
• Feature attribution studies show that the prior day's $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$2 MeV proton flux is the single most informative predictor, with marginal gains from SXR and active region (AR) inputs. Solar radio bursts and AR magnetic complexity can be excluded with negligible impact on TSS (Sadykov et al., 2021).
• Sequence-to-sequence LSTMs for 24 h profile prediction demonstrate that one-shot decoders minimize error accumulation (RMSE, normalized, $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$30.30 log-flux units for best models), and trend-smoothing X-ray data aids multi-input model performance (Yi et al., 6 Oct 2025).
• Cross-cycle ML generalization requires multi-decade training sets for robustness: models trained only on recent, SPE-sparse cycles (e.g., SC 24) transfer poorly in both TSS and HSS2 metrics (Ali et al., 2023).

These results indicate a mature transition to data-driven operational forecasting pipelines for SPE risk, provided data continuity and feature selection are managed appropriately (Sadykov et al., 2021, Ali et al., 2023, Yi et al., 6 Oct 2025).

7. Risk, Hazard, and Mitigation for Technology and Human Exploration

SPEs pose quantifiable hazards to satellites (single-event upsets, solar panel degradation), astronauts, aviation, and power systems. Observational upper limits on SPE fluence ($$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$4 cm$$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$5 in the last 11,400 yr) define probabilistic risk baselines for hardware design and mission planning (Usoskin et al., 2012, Usoskin et al., 2020).

Aviation-specific studies show that, for decadal-maximum SPEs, polar route cruise at $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$6 km leads to effective doses $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$7 mSv ($$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$8ICRP public limit); rapid descent to $$F(E) = F_0 E^{-\gamma}\,\,\,\text{(power-law)}, \qquad F(E) = \begin{cases} A (E/E_0)^{-\gamma_1} \exp[-E/E_c], & E < E_\mathrm{break} \ A' (E/E_0)^{-\gamma_2} \exp[-(E_\mathrm{break}/E_c)], & E \geq E_\mathrm{break} \end{cases}$$9 km ($\gamma_1$0 g cm$\gamma_1$1) or $\gamma_1$2 km ($\gamma_1$3 g cm$\gamma_1$4) reduces doses by 60–90% at a 56–107% fuel cost penalty, which remains economically preferable to full flight cancellation (Yamashiki et al., 2020).

For lunar and surface planetary missions, even 1 g cm$\gamma_1$5 aluminum shielding is insufficient against low-energy-rich SPEs (August 1972), with organ dose equivalents in skin and internal tissues reaching hundreds of cSv per event. With increasing shielding (20 g cm$\gamma_1$6), secondary ("albedo") neutron and proton dose fractions can exceed 20% in some organs, requiring optimized shield material choices (e.g., hydrogen-rich, regolith-augmented storm shelters) in addition to operational precaution (Pak et al., 2024). For Mars, minimal atmospheric columns translate to SPE doses approaching or exceeding the 1 Sv career limit in rare, worst-case scenarios (Atri et al., 2020).

8. Outstanding Issues and Future Directions

Major current research aims include filling the 1–2 order-of-magnitude gap in SPE historical fluence statistics between the largest directly observed events (e.g., 1956) and cosmogenic-proxy-inferred super-extremes (e.g., AD 775) by multirecord isotopic stacking (Usoskin et al., 2020), refining atmospheric chemistry–transport and deposition models (including polar stratospheric cloud and nitrate microphysics) (Duderstadt et al., 2016, Laird et al., 2016), quantifying planetary surface dose from highly variable M-dwarf SPEs (Atri, 2019), and extending ML pipeline validation across solar cycles and operational data transitions (Ali et al., 2023, Yi et al., 6 Oct 2025).

The field also recognizes the necessity of cross-disciplinary fusion between event-driven particle physics, climatological and atmospheric modeling, data-driven statistics, and operational system engineering as SPE-driven hazards permeate an expanding domain of technological and human exploration.