Assessment of the radiation risk at ﬂight altitudes for an extreme solar particle storm of 774 AD

– Intense solar activity can lead to an acceleration of solar energetic particles and accordingly increase in the complex radiation ﬁ eld at commercial aviation ﬂ ight altitudes. We considered here the strongest ever reported event, namely that of 774 AD registered on the basis of cosmogenic-isotope measurements, and computed the ambient dose at aviation altitude(s). Since the spectrum of solar protons during the 774 AD event cannot be directly obtained, as a ﬁ rst step, we derived the spectra of the solar protons during the ground level enhancement (GLE) #5 on 23 February 1956, the strongest event observed by direct measurements, which was subsequently scaled to the size of the 774 AD event and eventually used as input to the corresponding radiation model. The GLE #5 was considered a conservative approach because it revealed the hardest-ever derived energy spectrum. The global map of the ambient dose was computed under realistic data-based reconstruction of the geomagnetic ﬁ eld during the 774 AD epoch, based on paleomagnetic measurements. A realistic approach on the basis of a GLE #45 on 24 October 1989 was also considered, that is by scaling an event with softer spectra and lower particle ﬂ uxes compared to the GLE #5. The altitude dependence of the event-integrated dose at altitudes from 30 kft to 50 kft (9.1 – 15.2 km) was also computed for both scenarios. Our study of the radiation effects during the extreme event of 774 AD gives the necessary basis to be used as a reference to assess the worst-case scenario for a speci ﬁ c threat, that is radiation dose at ﬂ ight altitudes


Introduction
An omnipresent flux of subatomic particles in the vicinity of the Earth, that is cosmic rays (CRs) constantly enter the Earth's atmosphere.It is composed mostly of protons, a-particles, and a small amount of heavier nuclei, with their energy ranging from about 10 6 to 10 21 eV/n and following a nearly power-law distribution in the energy spectrum (e.g.Gaisser et al., 2016;Beatty et al., 2018, and references therein).The deka-MeV kinetic energy particles are absorbed in the upper atmosphere.On the other hand particles with kinetic energy of about hundred MeV and GeV range produce secondaries following consecutive interactions with the medium constituents when entering the atmosphere.In such a way, each collision adds the next generation of particles, producing a complicated nuclearelectromagnetic-muon cascade known as an extensive air shower (for details see Dorman, 2004;Grieder, 2011, and references therein).Hence, the CRs, specifically those originating from the Galaxy, called galactic cosmic rays (GCRs), determine the complex radiation field in the atmosphere, particularly at aviation flight altitudes.The GCR flux is slightly modulated in the heliosphere, responding in anti-correlation to the 11-year solar cycle (e.g.Potgieter, 2013, and references therein).The GCR flux, respectively the radiation field at aviation altitudes, are impacted by transients and disturbances in the heliosphere, due to coronal mass ejections (CMEs) and corotating interaction regions of the solar wind, leading to the so-called Forbush decreases (Forbush, 1937;Belov, 2009).In addition, taking into account that CRs are charged particles, therefore experience the Lorentz force when propagating in a magnetic field, the geomagnetosphere deflects part of the incoming CRs preventing them from penetrating the atmosphere, yet during geomagnetic storms, the cutoff rigidity is usually reduced, leading to a small increase of incident CRs, and thus the atmospheric radiation environment.This particularly affects low and mid-latitudes, being more sensitive to changes in cutoff rigidity than the high latitudes, where the geomagnetospheric deflection is anyway marginal.
Topical Issue -Space Climate: Long-term effects of solar variability on the Earth's environment While the GCR flux is slightly variable, resulting in a quasiconstant radiation field in the atmosphere, the situation could change dramatically during solar energetic particle (SEP) events.Solar eruptions, viz.solar flares and/or CMEs can accelerate solar ions to high energies, known as SEPs (e.g.Cliver et al., 2004;Desai & Giacalone, 2016, and references therein).The energy of SEPs is in the deka-MeV range in most cases, and sometimes in the 100-MeV kinetic energy range, but rarely, SEPs can be accelerated to the GeV/n range.When the kinetic energy of SEPs is %300 MeV or about 433 MeV for the highmountain polar region and sea level respectively (for details see Mishev & Poluianov, 2021), the secondaries produced in the particle shower can reach the ground, eventually registered by ground-based detectors such as neutron monitors (NMssee, e.g.Hatton, 1971;Simpson, 2000).Such type of events is called ground-level enhancements (GLEse.g., Shea & Smart, 1982;Aschwanden, 2012;Poluianov et al., 2017).
Despite GLEs being relatively rare compared to the bulk of solar particle events, occurring only several times per solar cycle (Shea & Smart, 2000, 2012), they represent a significant space weather thread (e.g.Schwenn, 2006;Pulkkinen, 2007;Miroshnichenko, 2018, and references therein).High-energy SEPs can degrade electronic components in space missions and none the least pose an increased radiation threat to astronauts as well as aircrews, specifically during transpolar flights for the latter (e.g.Vainio et al., 2009, and references therein).
Here we focus on a very specific type of event, called extreme solar particle events (ESPEs) that produce such an enormous amount of cosmogenic isotopes that they can be measured via their signatures in natural archives over the past millennia (for details see Usoskin, 2017;Miyake et al., 2019;Cliver et al., 2022, and references therein).In this study, we consider the strongest ever recorded such type of event: the 774 AD SEP (Miyake et al., 2012;Cliver et al., 2022).On the basis of recent reconstructions and corresponding scaling based on extensive Monte Carlo simulations (Usoskin et al., 2020b), and a realistic reconstruction of the geomagnetic field during that epoch, based on paleomagnetic measurements, we assessed the radiation dose at flight altitudes during this historical extreme event using two different approaches: a conservative i.e. worst case scenario, and a realistic one.As a first step, we derived the SEP spectra of GLE #5 and GLE #45 (Section 2) using after scaling as inputs for the corresponding radiation dose model (Section 3).Then we computed accordingly the ambient dose at several altitudes during the 774 AD event employing a reconstructed geomagnetic field at the epoch.

GLEs and the 774 AD event
At present the only known way to find a notable signature of extreme SEP event that occurred in the past is based on cosmogenic isotopes measurements, that is by radiocarbon ( 14 C; halflife = 5.73 Â 10 3 years), Beryllium-10 ( 10 Be; halflife = 1.36 Â 10 6 years), and Chlorine-36 ( 36 Cl; halflife = 3.01 Â 10 5 years) imprints.These radionuclides are produced following secondary CR interactions with the atmospheric constituents, namely neutron capture 14 N(n,p) 14 C for the radiocarbon, spallation of Oxygen and Nitrogen nuclei by secondary energetic particles for 10 Be, and spallation of 40 Ar for the Chlorine.While the background of cosmogenic radionuclides is determined by the omnipresent flux of GCRs (e.g.Lingenfelter & Ramaty, 1970;Castagnoli & Lal, 1980), extreme SEP events may also provide their signatures in the isotope records, namely by the secondary particle interactions (e.g.Usoskin, 2017;Usoskin & Kovaltsov, 2021;Cliver et al., 2022).
Up to now, the largest SEP event identified on the basis of cosmogenic-isotope records is the 774 AD event discovered by Miyake et al. (2012), also confirmed by other teams by various cosmogenic isotopes measurements including both hemispheres (e.g.Usoskin et al., 2013;Jull et al., 2014;Sukhodolov et al., 2017;Uusitalo et al., 2018).At present, considering the latitudinal gradient and inferred global symmetry of the cosmogenic signal, the response in 10 Be and none the least the identification of similar cosmogenic nuclide events, suggest the SEP origin as a plausible scenario (for details see the discussion in Usoskin et al., 2013;Usoskin & Kovaltsov, 2021;Cliver et al., 2022, and the corresponding references therein).
Naturally, in order to assess space weather effects during the 774 AD SEP event, it is necessary to possess reliable information about the spectra of the incoming CR particles, as well as the magnetospheric field at the epoch.We emphasize that the strongest directly recorded event, the GLE #5 on 23 February 1956, is not large enough to produce a notable cosmogenic isotope signal, yet it is used as a reference (Usoskin et al., 2020b).Taking into account that SEP event magnitude correlates with the spectrum hardness, that is, stronger events reveal hard spectra (Asvestari et al., 2017), and that the 23 February 1956 event exhibited one of the hardest spectra for the directly recorded events (Vashenyuk et al., 2006;Tuohino et al., 2018), we derived the spectra of the latter (discussed below) and scaled to the 774 AD event.However, the realistic spectrum of the ESPE of 774 AD might have been softer than that of GLE#5 (Koldobskiy et al., 2023), and accordingly, we also considered an event with a softer SEP spectrum, that is GLE #45 on 24 October 1989 (for details see their Fig.49 in Cliver et al., 2022;Koldobskiy et al., 2023).
For the analysis of GLE #5, we employed a method based on the modeling of the global NM network response and optimization of the model parameters describing the SEP spectra and anisotropy, over the experimental NM count rate increases.The method is adopted from the study by Cramp et al. (1997), details and applications are given elsewhere (Mishev et al., 2018b(Mishev et al., , 2021a(Mishev et al., , 2022b)).
The response of each NM used in the analysis is computed by an integral of the product of the primary CR spectrum J(P, t) with the NM yield function S(P, h), that is the count rate of an NM at a given altitude (atmospheric depth) h and time t is expressed as: where P c is the local geomagnetic cutoff rigidity (e.g.Cooke et al., 1991), h is the atmospheric depth (or altitude), S i (P, h) [m 2 sr] is the NM yield function for primaries of particle type i (protons and/or a-particles), J i (P, t) [GV m 2 sr sec] À1 is the rigidity spectrum of the primary particle of type i at time t (Clem & Dorman, 2000).
Using de-trended records retrieved from the GLE database (Usoskin et al., 2020a), and the method described in Mishev (2023), we assessed the spectra and angular distribution of SEPs during the GLE #5, where the best fit of the derived spectra was achieved using a modified power-law: where the flux of particles with rigidity P in [GV] is along the axis of symmetry of arriving SEPs, the power-law exponent is c with the steepening of dc.
Accordingly, the angular distribution, that is the pitch angle distribution (PAD) was approximated with Gaussian: where a is the pitch angle, r accounts for the width of the distribution.While earlier estimates (e.g., Usoskin et al., 2020b) were based on an explicit assumption of the isotropic SEP flux for GLE #5, here we used a more realistic reconstruction considering also the angular distribution of SEPs.
The derived spectra and anisotropy of SEPs during GLE #5 for selected periods of the event are presented in Figure 1, the details are given in Table 1.We emphasize that the SEP spectra during GLE #5 remained hard throughout the whole event and revealed significant flux (for details see Vashenyuk et al., 2006Vashenyuk et al., , 2008, and the comparison with other events therein).
Similarly, we derived the SEP spectra during another event used for the scaling to the 774 AD event, namely GLE #45 on 24 October 1989, depicted in Figure 2, the details are given in Table 2.
We note, that in this case the angular distribution is approximated with a more complicated shape, which accounts for particles arriving from the anti-sun direction: where a is the pitch angle, r 1 and r 2 are parameters corresponding to the width of the pitch angle distribution, B is a parameter corresponding to the contribution of the particle flux arriving from the anti-sun direction.
We note that during the unfolding, we derived simultaneously the SEP spectra and PAD, the latter important to obtain as realistically as possible the former (for details see Cramp et al., 1997, and the discussion therein), however, the derived PADs are not used for the subsequent computations of the space weather effects as discussed below.Both events had relatively hard SEP spectra.In most cases the SEP spectra during GLEs gradually softened throughout the events (e.g.Vashenyuk et al., 2008;Tuohino et al., 2018, and references therein), which is the case for GLE #45, yet during GLE #5, they remained hard during the whole event.In both events the particle flux rapidly increased, reaching a maximum and thereafter gradually decreased.Table 1.Derived spectral and angular characteristics of the GLE #5.The columns correspond to the integration interval, particle flux J 0 , spectrum slope c, steepening of the spectrum dc, width of the PAD r 2 (see Eqs. ( 2) and ( 3)).Hereby, we derived the spectra of two GLEs, namely GLE #5, revealing the hardest ever observed spectra, used as a conservative approach after scaling to 774 AD event, and GLE #45, with softer spectra, used as realistic approach, accordingly.We emphasize that only SEPs with energy greater than about 200 MeV/n can contribute to the enhancement of the radiation field at flight altitudes (e.g.Ferrari et al., 2001;Spurny et al., 2002;Matthiä et al., 2008;Mertens et al., 2013;Paschalis et al., 2014).

CRAC:DOMO radiation model
For the computation of the ambient dose during the 774 AD event we employed the updated radiation model Oulu CRAC: DOMO (Cosmic Ray Atmospheric Cascade: Dosimetric Model) (Mishev & Usoskin, 2015) and scaling of the effective dose to ambient dose H*, the latter recommended as new operational dose quantity, according to Matthiä et al. (2022).The model is based on precomputed yield functions of the radiation dose (e.g.Hands et al., 2022), obtained by Monte Carlo simulations with a GEANT 4 based tool PLANETOCOSMICS (Agostinelli et al., 2003;Desorgher et al., 2005), that is a response matrix over a layered NRLMSISE-00 atmospheric model (Picone et al., 2002) giving the secondary particle flux and spectra as a function of altitude for a monoenergetic incident particles ranging in a logarithmic step from MeV up to TeV kinetic energy range, computed separately for protons and alphas.The full description and applications of the model including verification and comparison with other models and experimental data are given in (Meier et al., 2016(Meier et al., , 2018;;Mishev & Usoskin, 2018;Mishev et al., 2018aMishev et al., , 2021bMishev et al., , 2022a)).
The dose rate (effective, ambient, ambient equivalent) at a given atmospheric altitude (depth) h induced by the ith component of CRs (proton or a-particle, the latter accounting effectively all heavy particles) is the integral of a product of the primary particle spectrum with the corresponding yield function: where J i (T) is the differential energy spectrum of the primary CR for the ith component and Y i is the corresponding effective dose/ambient dose yield function.The integration is over the kinetic energy T above T(P c ), the latter determined by the local cutoff rigidity P c and over the solid angle X.
Accordingly, the effective/ambient dose yield function Y i is a summation of the contributions from different secondary particles defined as: where C j (T*) is the fluence to effective/ambient dose conversion coefficient for a secondary particle of type j (neutron, proton, c, e À , e + , l À , l + , p À , p + ) with energy T*, F i,j (h, T, T*, h, u) is the fluence of secondary particles of type j, produced by a primary CR particle of type i (proton or a-particle) with given energy T arriving at the top of the atmosphere from zenith angle h and azimuth angle u.The employed fluence-todose conversion coefficients C j (T*) are taken according to Pelliccioni (2000) and Petoussi-Henss et al. ( 2010) for the ambient dose equivalent and effective dose respectively.We note that equivalent dose accounts for the stochastic health effects on the human body due low radiation levels, which explicitly considers the biological effectiveness of the radiation, namely the type and energy, whilst the effective dose represents the tissue-weighted sum of the equivalent doses.The effective dose E accounts for not only the type of radiation, but also the type of the organ or tissue being irradiated, and it is used for radiation protection purposes.Despite E is not a measurable quantity, it is usually estimated using models, whilst ambient dose equivalent H(10)* is measured with suitable detectors.Recently, a new quantity for assessment of the effective dose was proposed to replace H(10)*, which takes into account the energy and particle type, that is ambient dose H*, (for details see Matthiä et al., 2022, and the discussion therein), which we employ in this study.
For SEP events, the radiation dose is computed using equation (5) as a superposition of the GCRs contribution and solar protons contribution, the former obtained using the force field model (Caballero-Lopez & Moraal, 2004;Usoskin et al., 2005) with the local interstellar spectrum provided by Vos & Potgieter (2015) and modulation potential from Usoskin et al. (2017), while the latter is computed using the derived spectra for a given event, assuming pure proton mass composition (e.g.Reames, 2013, and references therein).
We would like to emphasize that despite the naturally derived anisotropy during strong SEP events, we conservatively assumed an isotropic angular distribution of the solar protons similar to Copeland et al. (2008) and Mishev & Usoskin (2018).We note that the use of the former generation conversion coefficients C j (T*) by ICRP (1996) increased the assessed Table 2. Derived spectral and angular characteristics of GLE #45 (24 October 1989).The columns correspond to the integration interval, particle flux J 0 , spectrum slope c, steepening of the spectrum dc, width of the PAD for particles arriving from sunward direction r 2 1 , the contribution of the particles from anti-sunward direction B and their PAD width r 2 2 .
Integration interval UT radiation dose of about 15-20%, yet considerably below the other model uncertainties (for details see Copeland & Atwell, 2019;Yang & Sheu, 2020, and the discussion therein).Besides, since the effective dose is not a conservative approach at flight altitudes, an aforementioned scaling to the new recommended operational dose quantity, that is ambient dose H* is performed similarly to Matthiä et al. (2022).Most radiation models developed in recent years (e.g.Matthiä et al., 2008;Latocha et al., 2009;Banjac et al., 2019;Hands et al., 2022), nicely agree with each other (e.g. for earlier versions see Bottollier-Depois et al., 2009, and references therein), however a significant discrepancy in the computation of the radiation dose during SEP events was shown to be predominantly due to the SEP spectra employed as input for the corresponding model (for details see Bütikofer & Flückiger, 2013).Therefore, it is important to possess precise SEP spectra, if possible derived with verified method(s) (e.g.Jiggens et al., 2019;Mishev & Jiggens, 2019), as in the study presented here.
4 Global mapsof ambient dose H* for the 774 AD event For the computation of the ambient dose H* corresponding to the 774 AD event, we considered the derived spectra during GLE #5 (Table 1) with a scaling factor %100, as a conservative approach, and GLE #45 (Table 2), with a scaling factor %500 as a realistic approach.The scaling is selected so that the scaled event-integrated fluence is consistent with the measured cosmogenic production (Usoskin et al., 2020b;Cliver et al., 2022;Koldobskiy et al., 2023).Besides, we assumed that the cosmogenic production during 774 AD ESEP is due to a single event, (the other possibility is a sequence of events such as Halloween events or September-October 1989 (Humble et al., 1991;Cramp et al., 1997;Vashenyuk et al., 2006), not considered here), lasting 24 h and with a time profile similar to other strong events (Vashenyuk et al., 2008;Moraal & McCracken, 2012;Copeland and Atwell, 2019), namely following Tables 1 and  2 as a conservative approach, that is we considered the last derived spectra to remain unchanged till the end of the event.
Then we employed the model described in Section 3, equation (5) following the scheme by Mishev (2023).
In addition, in order to model the effects of the GCRs background and the SEPs itself we assumed a moderately active Sun, that is with the modulation parameter of about 500 MV (Usoskin et al., 2021).Since both GCR and SEP are deflected by the geomagnetic field in the vicinity of Earth, we modelled realistically the geomagnetic field on the basis of recent archaeomagnetic reconstructions, namely we computed the effective geomagnetic cutoff rigidities on a step 1 Â 1°applying an eccentric dipole approximation (Nevalainen et al., 2013).Nowadays, the scientific community possesses paleomagnetic data from different sources e.g.archeological artifacts, volcanic and sediment data (e.g. Brown et al., 2015aBrown et al., , 2015b)).In this study, we used a global geomagnetic field model covering the Holocene, CALS10k.2 (Constable et al., 2016).Details on the modeling approach and cutoff rigidity can be found in (Panovska et al., 2019;Gao et al., 2022).
The first computation was performed as a conservative approach i.e. by scaling 100-fold the spectra of the GLE #5 (see Fig. 3), assuming an isotropic angular distribution similar to Copeland et al. (2008); Mishev & Usoskin (2018).As expected the radiation dose is maximal in the polar region.An illustration of the peak ambient dose, corresponding to GLE particles with maximal intensity is given in Figure 4.One can see that the ambient dose H* at 40 kft (12.2 km) above sea level (a.s.l.) is slightly below 1 Sv/h.We emphasize that the SEP spectra are highly variable (Moraal & McCracken, 2012).Hence, in most cases the radiation dose peaks on a short time scale (for details see the discussion in Spurny & Dachev, 2001;Matthiä et al., 2009;Al Anid et al., 2014;Mishev et al., 2021b).Therefore, for a realistic assessment of the radiation dose it is natural to perform computation over a period corresponding to the whole event or for a period corresponding to the flight duration, specifically in the polar region.Therefore, for the following computation, we explicitly considered the time variation of the SEP spectra similar to GLE #5 in Table 1.
In Figure 5, we present the distribution of the ambient dose H* over the globe at an altitude of 40 kft (12.2 km) a.s.l., integrated over the first 4 h of the modeled 774 AD event, considering the aforementioned assumptions.The altitude of 40 kft (%12,192 m a.s.l.) is representative of a polar flight, while the 4-h period corresponds to the time span over the poles of a typical intercontinental flight.As expected, the radiation dose is maximal in the polar region, where the magnetospheric shielding is marginal.One can see that the ambient dose integrated over a selected period of 774 AD-like event would lead to severe effects including acute radiation syndrome (e.g.see chapter 18 in Kiefer, 1990).
Finally, we computed the event-integrated ambient dose H* over the globe at an altitude of 40 kft (12.2 km) a.s.l., employing the assumptions (GLE #5 spectra from Table 1, isotropic angular distribution) and 24 h duration of the event similar to other long-duration events (for details see Vashenyuk et al., 2008;Tuohino et al., 2018).In Figure A.1 in Appendix, we present the event-integrated distribution of the ambient dose H* over the globe at an altitude of 40 (12.2 km) kft a.s.l.Moreover, we also present the altitude dependence of the event-integrated H* ranging from 50 kft (15.2 km) a.s.l. to 30 kft (9.1 km) a.s.l., A. Mishev et al.: J. Space Weather Space Clim. 2023, 13, 22 given in the Supplementary material.One can see that the eventintegrated H* significantly decreases as a function of altitude, ranging in the polar region from about 9.5 Sv at an altitude of 50 kft (15.2 km) a.s.l., 6 Sv at an altitude of 40 kft (12.2 km) a.s.l. and 2 Sv at an altitude of 30 kft (9.1 km) a.s.l., all representing significant threat.
The second computation was performed assuming a realistic scenario, that is softer spectra and scaling 500-fold the GLE #45 (Fig. 3), assuming similarly an isotropic angular distribution of the SEPs.The peak ambient dose, in this case, is considerably lower compared to the conservative approach, namely of about 35 mSv/h at an altitude of 40 kft (12.2 km) a.s.l.over the polar caps, details presented in Figure 6.
Accordingly, the distribution of the ambient dose H* over the globe at an altitude of 40 (12.2 km) kft a.s.l., integrated over the first four hours of 774 AD event, considering the realistic scenario is presented in Figure 7.One can see that the integrated radiation dose of about 100 mSv, can be harmful.
The event-integrated ambient dose H* over the globe at an altitude of 40 kft (12.2 km) a.s.l., assuming a realistic scenario (GLE #45 spectra from Table 2, isotropic angular distribution) and assuming 24 h duration of the event is given in Figure A.2.In this case, the event-integrated ambient dose H* ranges in the polar region from about 1.2 Sv at an altitude of 50 kft (15.2 km) a.s.l., 0.9 Sv at an altitude of 40 kft (12.2 km) a.s.l. and 0.3 Sv at an altitude of 35 kft (10.7 km) a.s.l., and drops below 0.1 Sv at an altitude of 30 kft (9.1 km) a.s.l.(for details see the Supplementary material).
Thus, in this section, we presented global maps of the peak, four hours integrated, and event-integrated ambient doses during the 774 AD extreme SEP event assuming the worst case, that is, very hard spectra, scenario and a realistic one with softer SEP spectra, lower flux.We also presented the altitude dependence of the event-integrated dose for both cases.A. Mishev et al.: J. Space Weather Space Clim. 2023, 13, 22 Study of the historical extreme SEP events, viz.events with cosmogenic-isotope imprints, specifically their possible terrestrial effects, including radiation dose at flight altitudes as considered in this study, allows one to assess the worst-case scenario during extreme events.Employing recent model studies and plausible assumptions related to event duration, spectral shape and non-the-least realistic reconstructions of the geomagnetic field during the epoch, we studied the possible impact of the 774 AD event.Here we assume that the 774 AD event was an ESPE (e.g.Usoskin & Kovaltsov, 2021;Cliver et al., 2022, and references therein).We assumed a single-event scenario, that is one event of the duration of 24 hours similar to the bulk of the strongest GLEs (Tuohino et al., 2018;Usoskin et al., 2020a), not considering a possible sequence of events such as September-October 1989 events (Humble et al., 1991) or Halloween events of October-November 2003 (Gopalswamy et al., 2005(Gopalswamy et al., , 2012)).Finally, we assumed moderate solar activity at the epoch of 774 AD and a conservative approach for the angular distribution of SEPs, which is isotropic, in order to assess the maximal radiation dose, considering the impossibility of obtaining any information about the PAD of SEPs during 774 AD.Here, we studied two scenarios: a conservative by employing hard spectra scaled from GLE #5, and a realistic one by employing softer spectra scaled from GLE #45.
We summarized the results as follows: 1. We derived SEP spectra for two strong GLEs, namely the strongest ever directly observed by ground-based NMs GLE #5 on 23 February 1956 and GLE #45 on 24 October 1989.2. The cutoff rigidity during the 774 AD SEP event is computed with the greatest possible angular resolution of one degree, on the basis of paleomagnetic measurements, giving the necessary Gauss expansion coefficients and employing eccentric dipole approximation.3. Using the reconstructed spectra and a 100-fold scaling of GLE #5 as a conservative approach and 500-fold of GLE #45 as a realistic approach, state-of-the-art model, and the computed cutoff rigidity, we calculated the global map of the peak ambient dose H*, the integrated over the first 4 h H* and the event-integrated H* at an altitude of 40 kft (12.2 km) during the 774 AD event.4. The altitude dependence of the event-integrated dose ranging from 30 kft (9.1 km) to 50 kft (15.2 km) is presented in the Supplementary material.
The 774 AD ESPE considered in this study is the strongest ever reported on the basis of cosmogenic-isotope records.The event can be estimated conservatively by scaling with a factor of 100 the GLE #5 spectra, so that it can be used to assess the worst-case scenario for a specific threat, that is radiation dose at flight altitudes.The results presented in the article can serve a as reference for studying the worst-case scenario based on historical events, and the work opens a new window in space weather studies.

Figure 3 .
Figure3.The spectra of GLE #5 and GLE #45 scaled to 774 AD as denoted in the legend, considered as a worst-case scenario and realistic scenario computation of the ambient dose, respectively.

Figure 4 .
Figure 4. Global map of the ambient dose at altitude 40 kft (12.2 km) during the peak phase of 774 AD event, assuming worst case scenario.

Figure 5 .
Figure5.Global map of the integrated ambient dose at altitude 40 kft (12.2 km) over the first 4 h starting from the event onset during 774 AD event, assuming worst case scenario.

Figure 6 .
Figure 6.Global map of the ambient dose at altitude 40 kft (12.2 km) during the peak phase during 774 AD event, assuming realistic case scenario.

Figure 7 .
Figure 7. Global map of the integrated ambient dose at altitude 40 kft (12.2 km) over the first 4 h starting from the event onset during 774 AD event, assuming realistic case scenario.