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Towards advanced forecasting of solar energetic particle events with the PARASOL model

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper introduces PARASOL, a physics-based forecasting chain for energetic storm particle events, and reports that a test simulation of the 12 July 2012 event reproduced observed intensities within one order of magnitude.

desk verdict A solid, transparent first-model paper: worth refereeing, but the single-event agreement is a capability demonstration, not forecast skill, given three unconstrained free parameters. read the letter →

arxiv 2412.11852 v1 pith:WM4CJW2G submitted 2024-12-16 astro-ph.SR physics.space-ph

Alexandr Afanasiev , Nicolas Wijsen , Rami Vainio This is my paper · ORCID
classification astro-ph.SRphysics.space-ph
keywords solarenergeticparticlesstormCME-drivenshocksdiffusiveshockaccelerationspaceweatherforecastingparticletransportpitch-anglescatteringself-generatedAlfvénwaves
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

PARASOL is a new modeling chain aimed at forecasting energetic storm particle (ESP) events: the sharp spike in low-energy proton intensity when a CME-driven shock sweeps past a spacecraft. Its central idea is to split the problem. A semi-analytical description of the inner foreshock — the region just upstream of the shock where self-generated Alfvén waves dominate scattering — is fitted once to detailed kinetic simulations and then supplies the accelerated-particle spectrum to a fast test-particle transport code for the outer heliosphere. The chain requires only magnetohydrodynamic (MHD) solar wind and shock parameters as input, not in-situ SEP observations of the event being forecast. For the 12 July 2012 event, the paper reports that a test simulation reproduced the observed ESP intensity at energies $\lesssim 5$ MeV in the close vicinity of the shock within one order of magnitude, and that the full chain runs in about two hours on a supercomputer. If that accuracy holds with fixed calibration parameters, physics-based near-real-time ESP forecasting is within reach.

What carries the argument

The load-bearing object is the semi-analytical inner-foreshock model. From fourteen SOLPACS simulation runs spanning shock Alfvénic Mach number, Alfvén speed, shock-normal angle, and injection efficiency, the paper fits the upstream proton mean free path as $\lambda^{(S)}(x,E) = \Lambda(E)\,[1 + (x/\Delta x(E))^{q(E)}]^{1/q(E)}$, where $\Lambda(E)$ is a modified Bell-theory power law with an exponential rollover and $\Delta x(E)$, $q(E)$ are themselves analytical functions of shock parameters and of the rollover energy $E_b$. This mean free path is inserted into the steady-state Parker equation to connect the SOLPACS shock spectrum to a matching distance $x_M$; the spectrum is then demodulated and remodulated with the 1 au-calibrated mean free path used in PARADISE, yielding the shock emission spectrum injected into the focused transport equation. The cutoff energy of the injected spectrum depends on the free acceleration timescale $\Delta t$ through Eq. (27), and the full scheme has three free parameters: injection efficiency $\epsilon_{\rm inj}$, the timescale $\Delta t$, and the matching distance $x_M$.

What would settle it

Run PARASOL with the fixed parameter set $\epsilon_{\rm inj}=5\times10^{-4}$, $\Delta t=10$ h, $x_M=10\,R_\odot$ on several well-observed ESP events at different heliocentric distances; if any event's peak proton intensity at $\lesssim 5$ MeV near the shock deviates from observations by more than one order of magnitude, or if matching required changing the fixed parameters, the central forecasting claim is refuted.

Watch

Extended reading notes

Core claim

The central claim is that a semi-analytical foreshock model, calibrated once on self-consistent simulations of coupled proton acceleration and Alfvén wave generation, can serve as the shock source for a transport code and reproduce a real ESP event without event-specific tuning to observed particle intensities. Concretely, the test simulation of the 12 July 2012 event, driven by EUHFORIA MHD output, matched the observed proton intensity at energies up to about 5 MeV near the shock within one order of magnitude, and produced an ESP peak at the modeled shock arrival as observed. The model also reproduces the observed low-energy spectral slope at the shock while overestimating higher-energy intensities, which the paper attributes to the assumed acceleration timescale $\Delta t = 10$ h. Along the shock surface the model predicts a spatial pattern in which low-energy protons concentrate at the quasi-parallel eastern flank and high-energy protons at the quasi-perpendicular nose and western flank, controlled by the local shock obliquity and Alfvénic Mach number.

Load-bearing premise

The model's forecasting claim rests on the three free parameters — $\epsilon_{\rm inj}=5\times10^{-4}$, $\Delta t=10$ h, and $x_M=10\,R_\odot$ — being set in advance rather than tuned to the event being forecast, and on the SOLPACS-calibrated 1 au mean free path describing scattering near shocks at other distances.

Editorial extensions

If this is right

  • If the fixed parameter choices hold across events, ESP peak intensities near the shock can be forecast from MHD solar wind and shock inputs before the shock arrives, without using in-situ SEP observations of the event.
  • The complete chain consumes about 1500 CPU-hours, about two hours of wall-clock time on a supercomputer, which the paper regards as adequate for timely ESP prediction.
  • Because the injected particle population is derived from MHD shock properties rather than by accelerating particles inside a finite-resolution MHD shock, the model avoids the overly thick shock that softened high-energy spectra in the earlier PARADISE-only simulation of this event.
  • The model makes spatial predictions along the shock: the quasi-parallel eastern flank emits the highest low-energy intensities, while the quasi-perpendicular nose and west flank emit the highest high-energy intensities, reflecting the local shock geometry and Alfvénic Mach number.
  • Adding a coronal MHD model should extend the same chain from ESP events toward full SEP event forecasting, including the early onset phase that the present inner boundary at 21.5 solar radii cannot capture.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct consequence the authors leave for future work is a multi-event test: run PARASOL with $\epsilon_{\rm inj}=5\times10^{-4}$, $\Delta t=10$ h, and $x_M=10\,R_\odot$ on several well-observed ESP events and measure the scatter in peak intensity; the paper's forecasting claim stands or falls on that scatter.
  • The model's predicted inverted (intensity increasing with energy) upstream spectrum at low energies is a distinctive signature of self-generated turbulence; observed flat or overlapping upstream spectra would imply that the mean free path's energy dependence near the shock is not simply increasing with energy, suggesting missing physics such as Alfvén wave damping or distance-dependent resonance b
  • Basing the outer-foreshock mean free path on a SOLPACS calibration at 1 au, together with the $\alpha^{1/2}\epsilon_{\rm inj}=\mathrm{const.}$ scaling property, implies a definite prediction for how foreshock intensities and spectra change with heliocentric distance; radially separated spacecraft observations could test that scaling directly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces PARASOL, a physics-based model for solar energetic particle (SEP) forecasting that couples a semi-analytical description of the inner foreshock, calibrated against SOLPACS self-consistent simulations of shock acceleration, with the PARADISE test-particle transport model. The model is driven by MHD parameters from EUHFORIA and is tested on the 12 July 2012 SEP event, with the central claim that the simulated energetic storm particle (ESP) component (E ≲ 5 MeV) near the shock is reproduced within one order of magnitude in intensity. The paper also discusses discrepancies in the event onset and in the upstream low-energy spectrum, and outlines future work to constrain the model's three free parameters (injection efficiency ε_inj, acceleration timescale Δt, and matching distance x_M).

Significance. If the claimed reproduction is robust, PARASOL represents a valuable step toward operational, physics-based ESP forecasting because it does not use in-situ SEP observations of the event to set parameters, and the full chain can run in roughly two hours on a supercomputer. The model's construction from SOLPACS simulations of self-consistent wave-particle interactions is physically well motivated, and the use of an independent EUHFORIA MHD run for the 2012 event gives the validation a forward-modeling character. However, the current single-event demonstration with hand-set free parameters does not yet establish forecast skill, and the paper's honest acknowledgment of this limitation does not fully remove the need to qualify the headline claim.

major comments (4)
  1. [Section 3.3 and Eq. (27)] The three free parameters ε_inj = 5×10⁻⁴, Δt = 10 h, and x_M = 10 R_sun are not fixed by any a priori rule; Section 3.3 explicitly labels the simulation an illustrative example, and Section 4 states that Δt is 'not necessarily constant' and that the overestimated high-energy intensities are 'largely' due to the assumed Δt = 10 h. Figure 11 shows that reducing ε_inj to 10⁻⁴ lowers intensities across all channels and weakens the ESP peak. Because the agreement therefore depends on parameter choices that are not independently constrained, the statement that the model 'reproduced' the observed ESP event should be presented as a capability demonstration, not as validation of forecast skill, and the paper should either provide a sensitivity analysis or explicitly restrict the claim to the illustrative parameter set.
  2. [Section 4 and Fig. 10b] The simulated upstream low-energy spectrum is inverted (intensity increasing with energy), while the observed spectrum eight hours before shock arrival is nearly flat and the observed time-intensity profiles at low energies overlap. The paper itself calls this a 'striking discrepancy' and attributes it to too-efficient trapping of low-energy particles near the shock. This is a substantive failure to reproduce the pre-shock low-energy enhancement, which is part of the ESP event, and it should be reflected in the scope of the headline claim: the 'within one order of magnitude' agreement applies to the shock-peak intensities, not to the full ESP foreshock behavior.
  3. [Eqs. (8) and (21)] The PARADISE parallel mean free path λ^(P) is taken from the SOLPACS-calibrated 1 au fit and used for shocks at other heliocentric distances along the shock surface. This is an extrapolation: the SOLPACS scaling properties in Appendix A show that the physical mean free path depends on the local ambient parameters (density, magnetic field, Mach number), so the 1 au calibration is not obviously valid for inner heliosphere shock portions, especially when particles are injected along the entire shock front. The manuscript should justify this approximation with a scaling argument or with a test at a different heliocentric distance, as it directly affects the demodulation in Eq. (7) and the source spectrum in Eq. (20).
  4. [Section 2.2.4 and Eqs. (31)-(36)] The semi-analytical model relies on a large set of fitted coefficients (K, β_λ, E_b, δ_λ, C_1, C_2, ΔE_1, ΔE_2, α_1, α_2, and the cutoff-energy fit) derived from only fourteen SOLPACS runs, with no uncertainty quantification or goodness-of-fit statistics reported. For example, C_2 is taken as an average over runs with ~20% scatter, and α_2 is set to a constant. While such fits are acceptable for a first model version, the absence of uncertainty information makes it difficult to assess how much of the 2012 agreement is attributable to the fitted parameter values rather than to the model physics; at minimum, the fit residuals should be shown for the key dependencies.
minor comments (5)
  1. [Abstract and Section 4] The phrase 'within one order magnitude' should read 'within one order of magnitude', and the sentence in Section 4 beginning 'A test PARASOL simulation... have reproduced' has a subject-verb agreement error ('simulation... have' should be 'simulation... has').
  2. [Section 1 and Fig. 1] The title contains a stray space in 'P ARASOL' in the manuscript header; the paper body otherwise uses 'PARASOL' consistently.
  3. [Section 2.1] The notation x_M is introduced as the matching distance and later fixed to 10 R_sun in Section 3.3, but Section 2.1 discusses x_M as energy-dependent and states that x_M > 10 R_sun for the quasi-steady-state energies; this tension should be clarified, for instance by explaining how the illustrative fixed value is chosen relative to the energy-dependent criterion in Eq. (11).
  4. [Section 3.1 and Fig. 10] Figure 10b is discussed only briefly; the reader would benefit from an explicit statement of the time offset relative to shock arrival and from labeling the energy channels used to define 'flat' versus 'inverted' spectra, since these definitions are central to the discussion in Section 4.
  5. [Section 2.3] The downstream mean free path in Eq. (44) contains an exponential damping scale d_0 = 1 R_sun, but no physical justification or sensitivity test is given for this choice; a one-sentence rationale or a reference would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the July 12, 2012 ESP comparison is a forward run of SOLPACS-calibrated physics; free parameters are explicitly labeled illustrative and not adjusted to the event.

full rationale

The derivation chain is self-contained in the relevant sense. PARASOL's semi-analytical foreshock is built from fits to SOLPACS simulations (Eqs. 17-36), and the matching condition j^(P)_M = j^(S)_M (Eq. 7) is a model-construction interface, not a prediction target. The observed comparison is made after PARADISE transport to 1 au (Figs. 9-10), so no equation forces the simulated intensities to equal the observed ones. The paper explicitly labels the three parameters as free and the simulation as illustrative: Section 3.3 states 'The PARASOL model comprises three free parameters... As an illustrative example, we present a PARASOL simulation with ϵ_inj = 5×10−4, Δt = 10 h, and x_m = 10 R_s,' and Section 2.2.3 says Δt 'becomes a free parameter that has to be constrained based on test simulations.' Section 4 admits the overestimated high-energy intensities 'largely result from the assumed Δt = 10 h' and that this parameter is 'not necessarily constant.' These are honest limitations on forecast-skill claims, not circularity: no parameter is fitted to the 2012 event in this paper, and the paper defers parameter constraints to future multi-event studies (§3.3, §5). Self-citations to SOLPACS, PARADISE, and the Wijsen et al. (2022) EUHFORIA simulation provide simulation tools and MHD inputs whose content is either described in this paper (Eqs. 12-16, Table 1, Appendix A) or independently published, so they are not invoked as an unverified authority. The λ^(S)_1au approximation for shocks at other distances is an acknowledged approximation, not a definitional identity with the predicted outcome.

Assumptions & free parameters 16 free parameters · 7 assumptions · 0 invented entities

PARASOL's central claim rests on a chain of fitted quantities. The injected particle spectrum at the shock and the inner-foreshock mean free path are not derived from first principles but are analytical fits to SOLPACS runs, whose fitting coefficients are themselves fits to 14 simulations. Three user-set free parameters (epsilon_inj, Delta_t, x_M) determine the overall intensity, cutoff energy, and the interface position, and the test simulation uses single hand-picked values. The model also inherits SOLPACS's assumptions and omits processes such as Alfven wave damping and resonance broadening that the authors invoke to explain the observed flat upstream spectra.

free parameters (16)
  • Injection efficiency epsilon_inj = 5e-4 (test simulation)
    Sets overall SEP intensity; paper shows strong sensitivity to this parameter and plans a future multi-event study to constrain it.
  • Acceleration timescale Delta_t = 10 h (test simulation)
    Controls the cutoff energy via Eq. (27); overestimated 1 au cutoff is attributed to this choice, and Section 4 says it is not necessarily constant.
  • Matching distance x_M = 10 R_sun
    Interface between the inner semi-analytical foreshock and the PARADISE outer region; the paper notes x_M is energy-dependent but treats it as a free parameter.
  • Mean free path amplitude coefficient C = 0.22
    Linear fit to SOLPACS runs in Fig. 6, used in Eq. (28) for K = 0.22 VA/(epsilon_inj Omega_0).
  • Mean free path low-energy index beta_lambda = 0.2
    Chosen based on an assumed asymptotic k^-2 wave spectrum, not fitted per run.
  • Mean free path bend index delta_lambda = 1.4
    Fixed by hand; the paper notes delta_lambda varies at least with epsilon_inj.
  • Foreshock spatial scale amplitude C1 = 0.35 (MA/(epsilon_inj x_ref) VA/Omega_0)^0.71
    Fit to SOLPACS-derived Delta_x(E) values in Eq. (31).
  • Foreshock spatial scale exponent alpha_1 = 0.83 - 0.02 Eb/Eref
    Linear fit to SOLPACS-derived values in Eq. (32).
  • Foreshock spatial scale energy Delta_E1 = 1.64 (Eb/Eref)^1.07 MeV
    Power-law fit in Eq. (33).
  • Foreshock q amplitude C2 = 0.66
    Average over all simulation runs in Eq. (34); values vary within about 20 percent.
  • Foreshock q exponent alpha_2 = 0.47
    Approximately constant across runs in Eq. (35).
  • Foreshock q energy scale Delta_E2 = 9.45 (Eb/Eref)^0.82 MeV
    Power-law fit in Eq. (36).
  • Cutoff energy fit coefficient and exponent = 8.25e-2 and 0.86
    Power-law fit of theoretical versus fitted cutoff energies in Eq. (26) and Fig. 4.
  • Downstream mean free path damping scale d0 = 1 R_sun
    Ad hoc choice in Eq. (44) to smoothly increase the downstream mean free path to lambda_0.
  • Background parallel mean free path lambda_0 = 0.1 au scaled with rigidity
    Standard PARADISE background value used in Eq. (43) beyond the foreshock.
  • Injection momentum correction factor alpha_inj = 4
    Ad-hoc modification in Eq. (24) of the Vainio et al. (2014) injection momentum expression.
assumptions (7)
  • domain assumption The shock is an MHD discontinuity and diffusive shock acceleration is described by the steady-state Parker equation (Eq. 2) with an isotropic distribution.
    Standard DSA framework; enters Section 2.1 and underlies the source term and demodulation formulas.
  • domain assumption SOLPACS simulations correctly capture proton acceleration coupled to self-generated Alfven waves, including the scaling property in Appendix A.
    The entire semi-analytical foreshock model is calibrated against SOLPACS output; if SOLPACS misses processes such as wave damping or resonance broadening, PARASOL inherits the error.
  • ad hoc to paper The fitting ansatze in Eqs (17)-(19) and (23) represent the SOLPACS mean free path and shock spectrum over the whole parameter space.
    These functional forms are chosen to match 14 SOLPACS runs; no first-principles derivation is given, and some parameters (beta_lambda, delta_lambda, C2, alpha_2) are fixed rather than fitted.
  • domain assumption Upstream particles scatter only on parallel-propagating Alfven waves, giving u1 = U1 - VA cos(theta_Bn) and rsc = r(1 - MA^-1).
    Used to derive the emission rate in Eq. (6); follows Vainio et al. (2014).
  • domain assumption PARADISE's quasi-linear pitch-angle diffusion coefficient (Eq. 41) with lambda_parallel = min[lambda_0, lambda^(P)] adequately describes transport from the inner foreshock to 1 au.
    Standard transport modeling; perpendicular diffusion and drifts are omitted, which the paper says will be tested later.
  • domain assumption The EUHFORIA spheromak CME simulation from Scolini et al. (2019) and Wijsen et al. (2022) accurately provides shock and IMF input for the 2012 event.
    PARASOL's ESP prediction is conditioned on this MHD input; the paper attributes the onset mismatch to the CME width and modeled IMF in this simulation.
  • domain assumption The SOLPACS-calibrated mean free path for a 1 au shock, lambda^(S)_1au, remains valid when used in the demodulation (Eqs 7-8, 20-21) for shocks at other heliocentric distances.
    This extrapolation is required by the model but not validated; x_M is also treated as constant though noted to be energy-dependent.

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Pith. "Pith review of Towards advanced forecasting of solar energetic particle events with the PARASOL model." pith.science (2026). https://pith.science/paper/WM4CJW2G

@misc{pith2026241211852,
  author       = {Pith},
  title        = {Pith review of: Towards advanced forecasting of solar energetic particle events with the PARASOL model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WM4CJW2G}},
  note         = {Machine review of arXiv:2412.11852}
}
abstract

Gradual solar energetic particle (SEP) events are generally attributed to the particle acceleration in shock waves driven by coronal mass ejections (CMEs). Space-weather effects of such events are important, so there has been continuous effort to develop models able to forecast their various characteristics. Here we present the first version of a new such model with the primary goal to address energetic storm particle (ESP) events. The model, PARASOL, is built upon the PArticle Radiation Asset Directed at Interplanetary Space Exploration (PARADISE) test-particle simulation model of SEP transport, but includes a semi-analytical description of an inner (i.e., near the shock) part of the foreshock region. The semi-analytical foreshock description is constructed using simulations with the SOLar Particle Acceleration in Coronal Shocks (SOLPACS) model, which simulates proton acceleration self-consistently coupled with Alfven wave generation upstream of the shock, and subsequent fitting of the simulation results with suitable analytical functions. PARASOL requires input of solar wind and shock magnetohydrodynamic (MHD) parameters. We evaluate the performance of PARASOL by simulating the 12 July 2012 SEP event, using the EUropean Heliospheric FORecasting Information Asset (EUHFORIA) MHD simulation of the solar wind and CME in this event. The PARASOL simulation has reproduced the observed ESP event ($E \lesssim 5$ MeV) in the close vicinity of the shock within one order of magnitude in intensity.

Figures

Figures reproduced from arXiv: 2412.11852 by the authors.

Figure 1
Figure 1. Diagram of the PARASOL model. The thin black line upstream of the shock schematically depicts the interface between the inner foreshock modeled analytically based on self-consistent SOLPACS simulations and the outer foreshock simulated in PARADISE. It should be noted that the actual shock-normal distance from the shock front to the model matching interface depends on the shock magnetic geometry (see Section 2 for de… view at source ↗
Figure 2
Figure 2. Flow chart of PARASOL indicating the input required by the constituting models. The paper is structured as follows. In Section 2, we outline the derivation of the semi-analytical model and its integration with PARADISE. In Section 3, we present the results of EUHFORIA + PARASOL simulations of an SEP event that was observed in-situ in July 2012. In Section 4, we discuss in detail some deviations of the simulation res… view at source ↗
Figure 3
Figure 3. Examples of the fits of the spatial (left panel) and energy (right panel) dependencies of the mean free path in the simulation run 6. The former is obtained at E = 5.27 MeV. The crosses indicate points that were not considered during the fitting process. 2.2.2. Fitting particle mean free paths and deriving particle intensity distributions As outlined above, our approach consists of fitting the simulated mean free pa… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Left panel: Cut-off energy obtained in Runs 1-7 vs. the cut-off energy calculated based on Eq. (27). The red line is a power-law fit given by Eq. (26). Right panel: Example of the simulated particle spectrum at the shock (blue line) and the reproduced spectrum based on…
Figure 5
Figure 5. Figure 5: Example of temporal evolution of the parameters of the fitting function Λ(E) in a SOLPACS simulation. The plots show each parameter versus a simulation snapshot number. The case presented is run 13. Clearly, the evolution of the amplitude factor K and the power-law ind…
Figure 6
Figure 6. Figure 6: Fit to the amplitude factor K of the mean free path Λ at the shock versus VA/(ϵinjΩ0). K = 0.22 VA ϵinjΩ0 . (28) Regarding the parameter δλ, we fix it at 1.4. It should be noted that δλ in fact varies at least with ϵinj (see, e.g., [PITH_FULL_IMAGE:figures/full_fig_p0…
Figure 7
Figure 7. Figure 7: Fits to the parameters of the energy dependence of the foreshock spatial scale ∆x. 10 2 cos Bn/( inj MA) 6 × 10 1 7 × 10 1 8 × 10 1 C2 2 4 6 8 10 Simulation run # 0.0 0.2 0.4 0.6 0.8 1.0 2 10 1 10 0 10 1 Eb [MeV] 10 0 10 1 10 2 E2 [MeV] [PITH_FULL_IMAGE:figures/full_f…
Figure 8
Figure 8. Figure 8: Fits to the parameters of the energy dependence of the foreshock spatial parameter q. C2 = 0.66, (34) α2 = 0.47, (35) ∆E2 = 9.45 Eb Eref!0.82 [MeV], (36) where xref = 1 R⊙ and Eref = 1 MeV are the reference values. The idea underlying the derivation of Eqs. (31) – (36)…
Figure 9
Figure 9. Figure 9: Comparison of observed and simulated proton intensities and solar wind plasma parameters for the 12 July 2012 SEP event. The panels correspond to (a) omnidirectional particle intensities, (b) IMF magnitude, (c) solar wind speed and (d) number density. The left figure d…
Figure 10
Figure 10. Figure 10: Energy spectra of observed and simulated proton intensities for the 12 July 2012 ESP event. Panel (a) presents the energy spectrum at the shock arrival, while panel (b) displays it eight hours before the shock arrival. Solid lines represent simulated intensities, with…
Figure 11
Figure 11. Figure 11: Modeled omnidirectional particle intensities for the W25 observer in a PARASOL simula￾tion with ϵinj = 10−4 . et al. (2022). Consequently, in the simulation Earth establishes a magnetic connection with the shock only on July 13, around 22:00 UT. In contrast, the obser…
Figure 12
Figure 12. Figure 12: The modeled omnidirectional proton intensities within the plane of constant latitude en￾compassing Earth, 27h after the insertion of the CME in the simulation domain. The left panel displays proton intensities within the 310–580 keV range, while the right panel presen…
Figure 13
Figure 13. Figure 13: The CME-driven shock, observed 27 h after its introduction into the simulation domain, is depicted. The shock surface is color-coded to represent various parameters: the shock obliquity θBn (in panel (a)); the Mach Alfven number ´ MA (in panel (b)); the intensity J an…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.