11institutetext: University of Surrey 22institutetext: CSDRadConsultancy

# The Variation of Radiation Effective Dose Rates and Single Event Effect
Rates at Aviation Altitudes with Magnetospheric Conditions and Geographic
Location

C. S. W. Davis 11 K. Ryden 11 F. Lei 11 B. Clewer 11 A. Hands 11 C. Dyer 1122

###### Abstract

The geographic structure of radiation dose rates at aircraft altitudes in
Earth’s atmosphere during the irradiation of Earth by proton spectra from
incoming solar particle events is examined using the recently developed MAIRE+
software. Conditions are examined under two incoming proton spectra, a
low/hard spectral index and a high/soft spectral index spectra, which are
representative of some of the solar particle events that have caused
reasonably sized Ground-Level Enhancements/Events (GLEs) over the past 70
years. It is found through the use of ‘cut-throughs’ of the atmosphere, that
the atmosphere can be divided into three volumes; a high dose rate polar
region, a low dose rate equatorial region, and a transition region between the
two. The location of these regions as a function of latitude, longitude and
altitude is characterised. It is also found that the location of the
transition region changes for different magnetospheric disturbance levels,
implying that the total radiation dose rate an aircraft will experience if it
passes through the transition region will be subject to large systematic
uncertainties, particularly during the currently unknown levels of
magnetospheric disturbance that a major solar event could cause. The impact
that various magnetospheric conditions might have on dose rates that specific
flight routes might experience is also discussed.

###### keywords:

radiation – aviation – magnetosphere

##  1 Introduction

Radiation dose rates in Earth’s atmosphere are reasonably predictable most of
the time. During quiet periods of relative solar inactivity, cosmic rays and
the secondary particles they produce when passing through matter are the main
source of atmospheric radiation levels. Cosmic rays originate from outside the
solar system, and bombard Earth at a roughly constant rate day-to-day,
typically only varying in intensity on the scale of years as the solar cycle
varies. However, every so often events such as Coronal Mass Ejections (CMEs)
or solar flares can cause the Sun to eject a large cloud of charged particles.
If such an event is sufficiently high energy, such that it would cause
significant radiation increases, it is known as a Solar Particle Event (SPE)
(Reames, 2013), or in more common English, a solar storm. If an SPE happens to
hit Earth and is comprised of particles that are sufficiently high energy such
that detectable levels of dose-inducing radiation are generated in Earth’s
atmosphere from the event, the SPE can cause what is known as a Ground-Level
Enhancement (GLE) (Poluianov et al., 2017), which is also sometimes called a
Ground-Level Event.

During a Ground-Level Enhancement (GLE), high energy solar particles hitting
the Earth’s atmosphere generate showers of particles, which can hit both
electronics and humans and lead to radiation effects (Dyer et al., 2020;
Hubert et al., 2020; Matthiä et al., 2015). Major GLEs, such as the GLE of
February 1956 (sometimes labeled as GLE05) (Belov et al., 2005), have been
known to induce so much radiation in the atmosphere that it dwarfs the
radiation induced by cosmic rays by orders of magnitude. It is unknown exactly
how strong these events can get, as the radiation dose rate due to GLEs has
only been detectable since the 1940s, and only 73 GLEs have been directly
measured to date, as of the time of writing (database, 2022). However recent
research into cosmogenic radionuclides has revealed several events in the past
that have exceeded events such as GLE05 by orders of magnitude (Dyer et al.,
2017). If such an event happened today, it could pose a serious risk to the
electronics in planes flying at any particularly susceptible regions of the
atmosphere.

Because GLEs occur on a highly intermittent irregular timescale and only last
for several days at maximum, there are only a few experimental datasets
available that directly measured the full radiation dose experienced by
aircraft during such events (Beck et al., 2009) as there are only a few
regular flights that have contained permanently stationed dose rate monitors.
MAIRE+, which is used for the simulations in this paper, was validated against
data during the GLEs of 1989 from CREAM on Concorde (Hands et al., 2022; Dyer
et al., 1989). While there are some projects underway to develop sensors that
are capable of detecting such dose rates (Clewer et al., 2019; Clewer, 2020)
while being permanently stationed on aircraft such that they catch an event in
action, for the time being it is necessary to rely on simulation data to
understand what might happen during such events.

There has been a reasonable level of past research that has been done into the
variation of dose rates during a GLE with location and magnetospheric
conditions. Such research in the past has been generally limited by the
computational power available at the time, as both trajectory calculations
within Earth’s magnetosphere and dose rate calculations are quite
computationally complex. It has therefore only been possible to perform full-
scale calculations of dose rates on reasonable timescales and without the aid
of high-performance computers in recent years.

It has been known for a long time from theoretical calculations, simulations
and experimental observations from sources such as the global neutron monitor
network (Mishev and Usoskin, 2020) that dose rates generally increase with
latitude, and also increase with altitude until about 20 km/65 kft in altitude
(this altitude is known as the Pfotzer maximum, and is higher in altitude than
most currently operating commercial aviation) (Grieder, 2001). The increase in
dose rates with altitude below the Pfotzer maximum is caused by the complex
physics underlying the penetration of the atmosphere by incoming particles,
and the generation of secondary particles at different atmospheric levels. The
increase in dose rates with increasing latitude on the other hand, is caused
by Earth’s magnetic field becoming less effective at shielding Earth from
incoming particles at regions closer to Earth’s magnetic poles. This effect is
typically quantified by a value at each latitude-longitude coordinate known as
‘vertical cut-off rigidity’ (also sometimes referred to as effective vertical
cut-off rigidity) (Cooke et al., 1991), a parameter that quantifies how
difficult it is for a particle traveling towards Earth to penetrate the
magnetic shielding of Earth.

It is also generally well known that increases in magnetospheric disturbance
levels caused by solar wind and solar storms also generally cause increases in
dose-rate across Earth. This is because disturbances to Earth’s magnetosphere
generally cause reductions in vertical cut-off rigidity across Earth (Smart
and Shea, 2005), allowing more dose-inducing particles to penetrate Earth’s
magnetosphere and hit the atmosphere.

While the general characteristics of how dose rate varies with changes in
single parameters and at single locations are known, there has been little
published modern research examining how dose rates vary as a complex
multidimensional function of all geographic location and relevant parameters
associated with a solar storm. The atmosphere is a 3-dimensional environment,
and so understanding the full volumetric picture of dose rates in the
atmosphere is crucial for gaining a qualitative understanding of the
atmosphere during GLEs. A knowledge of the big picture for how dose rates can
vary across the atmosphere is especially important for airlines and policy
makers, who will have to provide guidance to pilots on the safe locations to
fly, and volumes of the atmosphere to avoid, during major solar storms.

Additionally, it is well known that during a solar event of the sort of scale
that has not been seen so far since the invention of proper measurement
equipment at the dawn of the space age, levels of disturbance in Earth’s
magnetosphere could reach levels that have never been seen before and that it
is not currently possible to simulate with verifiable accuracy. Therefore
building a qualitative picture of what happens to the volumes of the
atmosphere that are associated with certain dose rates as magnetospheric
disturbance increases would be useful for qualitatively understanding what
might happen during a major GLE.

The work presented in this paper has been therefore performed to examine the
full structure of the radiation dose rate field in the atmosphere during the
bombardment of Earth by two representative simulated spectra of protons that
may occur during a GLE, a low spectral index spectrum, and a high spectral
index spectrum. The atmospheric structure of dose rates were examined through
the use of atmospheric ‘cut-throughs’, and the variation of the volumes
associated with these dose rates with changes in magnetospheric disturbance
levels were investigated. Only the ambient dose equivalent rate field is
investigated within this paper, however it should be expected that other
classifications of radiation dose rate will exhibit the same or similar
atmospheric structure. Specific dose rates that transatlantic flights will
experience during different magnetospheric conditions are also discussed.

##  2 Methodology

Simulation results were gathered using a variant of MAIRE+(Hands et al., 2022)
known as MAIRE-S. MAIRE+ is a new software that has been developed recently to
calculate radiation dose rates at aircraft altitudes at any time using the
current solar and magnetospheric conditions. During quiet solar conditions,
MAIRE+ uses a variant of the ISO model developed by Matthiä et al. (Matthiä et
al., 2013) to determine the cosmic ray spectrum. During high energy solar
event conditions, MAIRE+ adds a ‘GLE’ dose rate component onto dose rates by
assuming a rigidity power law spectrum and applies an algorithm to determine
the extra GLE proton spectrum occurring at a given time(Hands et al., 2022).
MAIRE-S is simply a version of MAIRE+ that has been modified to be able to be
programmatically run across historic and user defined solar and magnetospheric
conditions. The assumptions that are present in MAIRE+ are therefore the
assumptions that should also be considered with regards to the data presented
in this paper. Some of the main assumptions of MAIRE+ include:

  * •

The incoming particle distribution hitting Earth’s magnetosphere is isotropic.
This is true for many GLEs, particularly during the tail end of a GLE.

  * •

Vertically incident particles dominate radiation doses, such that vertical
cut-off rigidities can be used to describe the full effect of Earth’s
magnetosphere on dose rates.

  * •

The assumptions present in the Tsyganenko 1989 (Tsyganenko, 1989) magnetic
field model and the extension to the Tsyganenko 1989 model made by Boberg et
al. (Boberg et al., 1995).

All results in this paper were generated from two single ‘snapshot’ input
spectra. The two spectra and corresponding atmospheric dose rates, and
vertical cut-off rigidities, were taken from MAIRE+ simulations of GLE42,
which occurred in September 1989. The spectra were chosen somewhat arbitrarily
in order to showcase a relatively hard differential power law spectral index,
and a relatively soft differential power law spectral index; due to the
variability in GLE intensity the normalisation factor of the spectra were not
considered to be too significant within the scope of this particular study
into the geographic structure and variability of the dose rates. According to
Tylka et al. (Tylka and Dietrich, 2009), spectral indices for most recorded
GLEs range between about 3 and 10 (the spectral indices reported by Tylka et
al. are reported in terms of an integral power law and therefore the number 1
needs to be added to it to get the differential spectral indices used here).

Only dose rates due to the GLE component of incoming particles were considered
here. The total dose rate would actually be the summation of GLE component +
cosmic ray component, however for the purposes of this study only the GLE
component was considered. In any case, during a major GLE of importance, the
GCR component would be dwarfed by the GLE component. This GLE component was
described by a simple power law in rigidity, with the relevant parameters for
the two spectra shown in table 1.

Table 1: Characteristics defining the spectra used in the simulations described in this paper. GLE proton spectra were modelled as a power law distribution in rigidity (with units of GV). Spectrum label | GLE normalisation factor used | GLE spectral index |
---|---|---|---
| (protons/m²/s/sr/GV) |  |
‘hard’ | $1.69\times 10^{4}$ | 2.65 |
‘soft’ | $2.67\times 10^{5}$ | 6.54 |

These two spectra were chosen as representative of periods of time during GLEs
where the GLE spectra might be soft and hard respectively. The spectra given
in table 1 where directly taken from runs of MAIRE-S across GLE42 in 1989, so
both spectra are possible in real world scenarios, and the spectral indicies
represent different regions of the potential range of GLE spectral indicies as
aggregated by Tylka et al.(Tylka and Dietrich, 2009). The main parameter of
interest for spectra that may significantly alter the structure of radiation
dose rates throughout the atmosphere is spectral index, which will affect how
many particles are able to penetrate the atmosphere at different locations due
to cut-off rigidity, and alter the geographic structure of radiation dose
rates. The normalisation factors used here are somewhat arbitrary. While the
normalisations do represent real MAIRE-S-predicted normalisation factors
during GLE42, they do not affect the structure of dose rates throughout
Earth’s atmosphere, and only act to scale overall dose rates. Normalisation
factors also vary by orders of magnitude between different GLEs.

Throughout this paper, dose rate ‘cut-throughs’ have been generated using
output dose rate maps generated by MAIRE-S. These cut-throughs are effectively
geometric cross-sections of the atmosphere, showing dose-rates as a function
of latitude and altitude at a given longitude, as displayed in figure 1. The
term ‘cut-through’ will be used in this paper as opposed to cross-section in
an attempt to prevent possible confusion with the entirely different concept
of interaction cross-sections which are also used in radiation physics.

Figure 1: An example of an atmospheric ‘cut-through’ as used in this paper.
The cut-throughs are effectively atmospheric cross-sections at a particular
latitude. The displayed cut-through shows ambient dose equivalent rates as a
function of latitude and altitude at a longitude of 0.0°.

##  3 The Variation of Dose Rates as Function of Kp Index

The rigidity cut-off at (50.0°N, 0.0°E) in each of the Kp index simulations is
plotted in figure 2 as a function of date and time. The date and time here
correspond to the internal geomagnetic field between 28/09/1989 00:00 UTC and
30/09/1989 12:00 UTC. As Kp was held constant for each of these simulations,
all variations in the rigidity cut-off are therefore caused by the rotation of
the Earth rather than direct magnetospheric phenomena. Similar results for the
magnitude of daily variation of cut-off rigidity can be found in (Smart et
al., 2000) albeit for a different time period, and at Durham, USA rather than
the (50.0°N, 0.0°E) used here.

Figure 2: Vertical cut-off rigidities as a function of Kp-index and datetime
at (50.0°N, 0.0°E). Increases in Kp index decrease the effective cut-off
rigidity by up to approximately 0.7 GV at maximum, and the vertical cut-off
rigidity varies by up to about 0.25 GV across a full day. The curves are
somewhat jagged in this plot due to the relatively granular interpolation with
respect to time that MAIRE+ uses to calculate cut-off rigidities within a day.

figure 2 indicates that the rigidity cut-off at (50.0°, 0.0°) decreases from
lows of about 3.0 GV to lows of below 2.4 GV when Kp index is changed from 0
to 8. This lines up with research on rigidity cut-offs that has been performed
before by Smart et al. (Smart et al., 2006; Smart and Shea, 2009), as does the
general structure of the variation in cut-off rigidity over time shown in
figure 2. One interesting point to note is that the variability of cut-off
rigidity over time increases as Kp index increases here (from a range of
approximately 0.1 GV at Kp = 0 to a range of approximately 0.25 GV at Kp = 8),
indicating that the time of day may become an important variable in dose rate
calculations at high Kp indices.

The effect of Kp index on the MAIRE-S GLE dose rates can be seen in the
atmospheric cut-throughs plotted in figure 3. There is minimal variation in
dose rate at most regions of the atmosphere, except for regions that are
already slightly south of the transition region between the equatorial region
of the sky and the polar region.

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Figure 3: Ambient dose equivalent rate atmospheric cut-throughs for multiple
Kp indices. The 30 $\mu Sv/hr$ curve plotted shows the overall shape of the
high dose rate polar region, and shows where the region where an aircraft may
cross between ICAO thresholds. The main variations in dose rate with Kp index
occur at the lower latitude side of the high dose rate polar region, where the
region expands to slightly lower latitudes as Kp index increases. Note that
the color scales for each spectral case are slightly different.

Essentially this could be thought of as the transition region moving to lower
altitudes as Kp index increases. While the transition region is relatively
narrow with respect to the whole atmosphere, the latitude of the transition
region is positioned at a location that a significant proportion of flights
cross daily, such as transatlantic flights for instance. Additionally, and
perhaps more importantly, during a GLE on the scale of a 1 in a 100 or 1 in a
1000 year event, magnetospheric conditions could reach extreme levels that
have never been measured before, such that they could vastly exceed the
magnetospheric upset levels described by Kp = 8, as the physics of such an
event is not well understood yet. The results given in figure 3 indicate that
in such an event, the transition region between high and low dose rates would
move southwards, perhaps even approaching latitudes of 50°N, which roughly
corresponds to cities such as London, Paris, Brussels and Frankfurt near the
simulated longitude of 0°E in figure 3. The results given here are consistent
with similar findings from Shea and Smart (2005)(Smart and Shea, 2005), where
it was found that the latitude corresponding to a given vertical cut-off
rigidity decreases with increasing Kp-index, across the entire vertical cut-
off rigidity range.

figure 4 below displays the percentage increase of ambient dose equivalent
rate as Kp index increases, and further highlights the influence that changing
Kp has on radiation dose rates in the transition area between equatorial and
polar regions. It also shows how much more significant the effect is between
Kp=0 and Kp=8, where dose rates within the transition region increase by up to
about 1250% in the soft spectrum case relative to dose rates in the more
equatorial region. Dose rates for the hard spectrum case increase by up to 40%
near the transition region at 60 kft altitudes.

in 4,8 in 1,2

Figure 4: Percentage increases in total ambient dose equivalent rate (GCR-
induced + GLE-induced) between different Kp indices. Changes in Kp index
between Kp=0 and Kp=8 show increases of up to 1250% around the transition
region between the equatorial and polar areas in the soft spectral index case.
In the hard spectral index case, the percentage increase is only up to
approximately 40% at maximum.

##  4 The Variation of Dose Rate Atmospheric Cut-through Structures as a
Function of Longitude

In addition to examining how changes in Kp indices affect radiation dose
rates, it is also useful to examine the impact that longitude has on
atmospheric cut-throughs. Cut-throughs of the atmosphere are displayed in
figure 5 and illustrate that the main impact of longitude appears to be to
move the cut-off threshold position towards lower latitudes at certain
locations, while not significantly altering the dose rate profile as a
function of changing altitude. This effect is caused by the location of the
magnetic north pole differing somewhat from the location of the geographic
north pole, which was positioned over northern Canada in 1989 (and still is
today).

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Figure 5: Ambient dose equivalent cut-throughs for different longitudes.
Several cities near to the plotted longitudes are also displayed for
geographic context. There is minimal change in dose rate with altitude as
longitude changes, however the high dose rate polar region stretches and
contracts as longitude changes. At longitude=270.0°E, corresponding to North
American airspace, the high dose rate region stretches as far south as
approximately 45°N-50°N, due to its closer proximity to the North magnetic
pole in 1989.

Plots showing the full range of Earth’s latitudes are also displayed in figure
6, so that the qualitative full dose rate structure in Earth’s atmosphere can
be seen, as well as dose rates above several southern hemispheric locations.

Figure 6: Cut-throughs of the full range of latitudes above Earth’s atmosphere
during hard spectral index conditions at longitudes corresponding to Cape
Town, South Africa and Sydney, Australia.

figure 5, together with figure 3 highlights the fact that almost the entirety
of the geometry for the event can be described by a narrow transition region
which varies with longitude and magnetospheric conditions under the
approximations and spectra given earlier in table 1. The low
latitude/‘equatorial’ side of this transition region has relatively low dose
rates at all altitudes. In contrast, high latitude/‘polar’ sides of the
transition region exhibit high dose rates but with a reasonably consistent
profile at constant altitude. It should be noted that this high latitude dose
rate region stretches to much lower latitudes than the auroral region.

While the transition region between these two areas is reasonably narrow with
respect to the total range of possible latitudes, it still wide enough, on the
order of several degrees latitude, such that some aircraft may spend a
reasonable time in the transition region during a flight. While an aircraft
will experience a lower overall dose rate in this region than if it flew
exclusively over polar regions, flying over the transition region would lead
to a significant uncertainty in dose rates, given how much dose rates in this
region appear to vary with magnetospheric conditions and with flight latitude.
It should also be noted that some of the busiest flight routes in the world
pass through the latitudes associated with this transition region, including
most transatlantic Europe to USA flights for instance. Therefore it is useful
to examine the structure and properties of this transition region in more
detail.

##  5 The Sensitivity of Dose Rate to Latitude

The transition region described above can be thought of as the region of
atmospheric cut-throughs that are most sensitive to changes in latitude. The
appropriate quantity that can be used to describe the transition region is
therefore the rate of change of dose rate with respect to latitude,
$\frac{\partial H^{*}(10)}{\partial\theta}$, where $H^{*}(10)$ is ambient dose
equivalent, and $\theta$ is latitude.

$\frac{\partial H^{*}(10)}{\partial\theta}$ could be determined using the data
for the atmospheric cut-throughs in this paper through taking the difference
between dose rates as latitude changes, i.e. $\frac{\partial
H^{*}(10)}{\partial\theta}\approx\frac{\Delta H^{*}(10)}{\Delta\theta}$. The
difference in latitudes corresponding to these changes was therefore always
5°, the resolution of the outputted data here. $\frac{\Delta
H^{*}(10)}{\Delta\theta}$ is plotted as a function of latitude and altitude in
figure 7 and figure 8.

in Hard,Soft in 0,270

Figure 7: The sensitivity of dose rates to changing latitude, expressed in
terms of the derivative of ambient dose equivalent to latitude,
$\frac{\partial H^{*}(10)}{\partial\theta}$. The area of maximum sensitivity
corresponds to the transition area between the equatorial and polar dose rate
regions. As was previously indicated in figure 5, the transition region for
longitude=270.0°is at a lower latitude than for longitude=0.0°.

Figure 8: The sensitivity of ambient dose equivalent rate to latitude,
$\frac{\partial H}{\partial\theta}$, plotted as a function of latitude and
altitude for longitude=0.0°E. Spectrum 1, which was had a lower spectral
index, shows a much wider transition region than spectrum 2, which had a
higher spectral index.

figure 7 shows the feature that has been discussed previously; that there is a
reasonably thin transition region which is positioned at a specific latitude
that varies with longitude. figure 8 shows the same data but displayed as a
line plot rather than as a cut-through. It is straightforward to see the
location of the transition region as a peak in $\frac{\Delta
H^{*}(10)}{\Delta\theta}$ on figure 8. It is interesting to note that the
transition region is significantly wider and less sharp in ‘hard spectrum’
case than in the ‘soft spectrum’ case. This could reflect how the spectrum is
broader in the case of the harder spectrum, and is therefore susceptible to a
broader range of cut-off rigidities than in the softer spectrum case.

In both spectral cases, the latitude sensitivity of dose rates increases
significantly with altitude, as might be expected given that overall dose
rates also increase significantly with increasing altitude.

Its possible to use the data in figure 8 to characterise the location of the
transition region by taking the location of the transition region as the
latitude at which the latitude sensitivity $\frac{\Delta
H^{*}(10)}{\Delta\theta}$ is at a maximum. Determining the location of the
maximum latitude sensitivity for each atmospheric cut-through gives a curve
when plotted on a map as in figure 9. Ambient dose equivalent rates at 37 kft
are also plotted on figure 9 for comparison.

Figure 9: Positions of maximum sensitivity of ambient dose equivalent to
latitude, $\frac{\Delta H^{*}(10)}{\Delta\theta}|_{max}$, plotted on a dose
rate map of Earth’s atmosphere at 61,000 ft. The positions of maximum
sensitivity correspond well with the clear transition regions in dose rate
between polar and equatorial dose rate areas that can be observed on the dose
rate map. The transition region moves slightly towards the poles as altitude
is increased.

figure 9 shows how the location of maximum latitude sensitivity divides the
dose rate map into two regions quite well. Its also interesting to note that
the curves of maximal latitude sensitivity move further from the equator as
altitude is increased. This is likely to be due to dose rates at lower
altitudes being less affected by lower energy particles than at higher
altitudes, and therefore being slightly less susceptible to lower vertical
cut-off rigidities.

##  6 Implications for Aircraft, Air Crew, and Airlines

Radiation in general has two consequences for the aviation industry. The first
and most well-known about impact is the effect of radiation on crew and
passengers. Pilots and cabin crew consistently flying through routes that
experience high dose rates, such as any flights traveling across the North
Atlantic (most transatlantic flights from Europe to North America) are at
higher risk of developing cancer than the general public. This is true during
quiet solar conditions, however during a major solar particle event this
effect is even more dangerous to crew, as radiation doses can increase by
factors of 1000 or more. In instances like that, air crew might breach the
recommended general public exposure limit within a single flight (Dyer et al.,
2007; Cannon et al., 2013; Tobiska et al., 2015; Dyer et al., 2017), and could
even go well above this during a solar particle event on the largest scales
that research using tree rings and ice cores has indicated have occurred
during the last few millennia (Miyake et al., 2012, 2013; Dyer et al., 2017;
Mekhaldi et al., 2015; Kovaltsov et al., 2014).

The second impact is often less discussed but has a potentially higher impact
than crew exposure, and deadlier. Electronics exposed to radiation can
experience device errors (Olsen et al., 1993; Hands et al., 2009; Cannon et
al., 2013; Dyer et al., 2017), including issues known as Single Event Upsets
(SEUs) and Single Event Latch-ups (SELs). SEUs are single errors introduced in
electronics, often memory devices, as a particle passes through it, flipping
individual bits.

If a Single Event Upset (SEU) happens in a particularly important part of a
device, or if so many upsets are happening at once that the aircraft
electronics are overwhelmed, aircraft electronics could respond in unknown and
dangerous ways. Alternatively, electronic devices may shut down, potentially
leaving pilots to deal with multiple electronics failures simultaneously
during extreme radiation conditions.

Single Event Latch-ups (SELs) on the other hand, represent more permanent
damage to devices, and cannot be fixed by on-board systems. SELs could
therefore not only cause electronics to crash or give false readings, but
could actually cause devices to completely fail.

Each of these issues represent a potential immediate threat to aircraft and
passengers aboard as soon as the aircraft enters a region with high enough
radiation levels that electronics failures could occur. Dyer et al. (Dyer et
al., 2020) found that modern electronics devices at ground-level may have a
significant probability of failure during an event ten times greater than the
GLE that occurred in February 1956 (21% of silicon power
metal–oxide–semiconductor field-effect transistors and 14% of insulated gate
bipolar transistors if the devices are unrated). As has been discussed in this
paper, the single-event effect rate is orders of magnitude greater at aviation
altitudes.

MAIRE+ is capable of estimating static RAM (SRAM) SEU and SEL rates at a
particular location by multiplying its internally calculated $>$10 MeV neutron
flux by cross-sections of $10^{-13}$ upsets/cm²/bit and $10^{-8}$ latch-
ups/cm²/device respectively. These cross-sections are representative values
that are within the range of cross-sections that devices have been shown to
exhibit (Dyer et al., 2020). It should be noted that individual devices have
highly variable cross-sections, although devices with these cross-sections
have been used in avionics. Figure 10 and figure 11 below shows SEU and SEL
rates plotted in the same format as the ‘cut-through’ plots above and for the
incoming particle spectra that have been investigated in this paper.

Figure 10: The MAIRE+ predicted Single Event Upset (SEU) rates as a function
of latitude and altitude at longitude = 0.0°N during the spectral conditions.
The threshold of 0.5 upsets/hr/Gb is primarily a guide to the eye in this plot
rather than a hard boundary between some safe level and some dangerous level.

Figure 11: The MAIRE+ predicted Single Event Latch-up (SEL) rates as a
function of latitude and altitude at longitude = 0.0°N during the spectral
conditions. The threshold of 1$\times 10^{-4}$ latch-ups/hr/device is
primarily a guide to the eye in this plot rather than a hard boundary between
some safe level and some dangerous level.

Figure 10 and figure 11 show a very similar relationship between SEU/SEL rates
and latitude as were shown in figure 3 and figure 5 previously. The actual
rate of SEUs that aircraft electronics can cope with at 40,000 feet during an
event similar to something like the GLE that occurred in February 1956 is
unknown, as most devices are not tested for these conditions. It is possible
that aircraft electronics are indeed safe under the conditions of a 1 in 100
year intensity radiation storm, but it is not yet possible to rule out a
worst-case scenario where aircraft to the north of approximately 65°North in
latitude (and approximately 50°North above the USA) all suffer multiple
electronics failures simultaneously.

The message that airlines should take from this and the earlier plots
displaying radiation dose rates is that during a major solar storm they should
endeavour to reduce aircraft altitude, and also possibly reduce their
latitude, depending on what route the flight is taking. This is already
somewhat known to airlines, and has been suggested by other previous papers
(Matthiä et al., 2015). ICAO advice does suggest that planes in high latitude
regions could attempt to reduce both altitude and geomagnetic latitude during
radiation storms (Organization., 2018). However, this advice is usually
discussed from the perspective of generally reducing the longer term
accumulated doses received by the aircraft crew, rather than addressing the
potential immediate threat that SEU/SEL errors pose to the aircraft. The
existence of threats due to high SEU/SEL rates means that speed and urgency
may be paramount once an alert has been issued for a large GLE. This necessary
rapidity would also be currently nearly impossible if this large solar event
occurs at the same time as a HF radio blackout, which would render
communication with many aircraft nearly impossible. This is not to mention the
difficulties that would occur with such an event happening at the same time as
other solar storm related effects on society.

What the research presented in this paper adds to this discussion is some
clarity over which strategies could be chosen by an aircraft during a large
GLE. For the incoming radiation distribution discussed in this paper,
radiation dose rates were found not to vary significantly with latitude except
at the boundary between the low dose rate, equatorial, region and the high
dose rate, polar, region. Under these conditions most aircraft situated well
within the polar region would not benefit much from changing latitude, and
reducing their altitude might be preferable. It should be noted that flying at
lower altitudes can take a significant amount of fuel, so it may not always be
possible for an aircraft to fly at low altitudes underneath a region of high
dose rates for long, but an aircraft may be able to at least do so for long
enough to miss the peak of an event.

In contrast, an aircraft traveling approximately along the boundary/transition
between the two dose rate regions (which happens to align approximately with
many commonly used transatlantic routes) might be able to significantly to
reduce their radiation dose and SEU/SEL rate by traveling just a few degrees
further south - providing the location of the transition region could be
accurately determined in real time, which would require an accurate real-time
determination of magnetospheric disturbance levels and incoming particle
spectral index. Flight routes are constantly updated according to atmospheric
factors such as zones of high turbulence, and zones of high radiation dose
could simply be considered another factor for such flights in what route they
should take.

This is illustrated by figure 12, which shows a map of four flight routes
heading between Heathrow airport (London, UK) and John F. Kennedy airport (New
York City, USA), as well as the corresponding dose rates at 37,000 ft from the
simulations described in this paper. The latitude and altitude profiles can
also be seen in figure 13. These are real flight routes collected from
FlightRadar24 (FlightRadar24, 2022), which flew between 2020 and 2022. It
should however be noted that the ‘time’ on the x-axis does not necessarily
correspond with the actual take-off time of the aircraft, rather the time that
Flightradar24 began recording the aircraft’s location. In addition, the
Eastern high latitude flight and the second lowest latitude flight’s time
coordinates have been translated backwards to be 2 hours less than the value
given by Flightradar24 for easier comparison with the other flights on time
plots, as the flights took several hours to take-off from the beginning of
Flightradar24’s recording. The lowest latitude flight was actually a flight
from New York JFK to London Heathrow, in contrast to the other flights, which
travelled in the opposite direction. The flight route was therefore reversed
in this analysis so that coordinates roughly correspond with those of the
other flight routes (i.e. in the lowest latitude flight case, time represents
approximately the time until landing, whereas in all the other flights, time
represents approximately the time from the flight beginning).

The routes encompass a range of different latitudes, and it can be seen in
figure 12 that in the low spectral index/soft spectrum case at Kp = 4, some of
the flights cross through the transition region into and out of the high dose
regions, while others stay in the low dose rate region for the entirety of the
flight. During the hard spectrum conditions, all of the flights investigated
happen to be within the high dose rate region for Kp = 4.

Figure 12: Dose rate maps of Earth at 34,000 ft and the paths of the flight
routes that were investigated in this paper. The maximum rate of change of
dose rate with respect to latitude is also plotted to indicate the location of
the transition region between the low and high dose rate regions. In the high
spectral index case, the transition region between the low dose rate
‘equatorial’ region and the high dose rate region lies between the flight
routes.

Figure 13: The latitude and altitude time profiles for the flights shown in
figure 12. The lowest latitude flight was a flight from New York JFK to London
Heathrow LHR, in contrast to the other flights which went from LHR to JFK, and
the flight route profile has therefore been reversed for the lowest latitude
flight for better comparison.

The dose rates and accumulated doses for these flight routes are displayed in
figure 14, table 2, figure 15 and figure 16, where it can be seen that in the
soft input spectral index case, the high latitude flights are subject to
significantly higher dose rates than the lower latitude flights. This is not
the case in the low spectral index/hard spectrum case, which is likely caused
by the fact that the transition region boundary is consistently lower than all
the flight routes in the hard spectrum case, while the high latitude flights
cross the transition region in the soft spectrum case.

Accumulated doses were calculated through integrating the dose rate over time
for each flight route. Accumulated SEU and SEL count rates were also found
using this method, giving accumulated latch-up probabilities for each SRAM
device on the western high latitude flight route of about 0.06% in the hard
spectrum case and 0.11% in the soft spectrum case. These accumulated
probabilities assume a static event with constant spectral conditions taken
from two arbitrary snapshots within GLE42 in 1989. Taking into the account the
fact that aircraft may have many SRAM devices, that many devices aboard an
aircraft may have significantly higher single event damage cross-sections than
SRAMs (Dyer et al., 2020), and most importantly that GLEs can be significantly
larger than the event used here (The peak GLNM percentage increase in GLE05,
February 1956 was approximately 12 times higher than the peak GLNM percentage
increase in GLE42, 1989 (Dyer et al., 2017)) means that the probability of
many high latitude aircraft experiencing numerous devices becoming damaged
simultaneously may become high during a large ground-level enhancement.

in adose,SEU,SEL in Hard,Soft

Figure 14: Dose rate characteristics of the flight routes investigated. In
both spectral index cases, the higher latitude flights experience generally
higher dose rates, however in the high spectral index case the high latitude
flights experience significantly higher doses than the low latitude flight.
Table 2: Peak dose rates and accumulated doses for each of the investigated
flight routes and incoming spectra. The integrated values were determined
through taking the integral over the curves displayed in figure 14

| Western high latitude route | Eastern high latitude route | Second lowest latitude route | Lowest latitude route
---|---|---|---|---
| Hard spectrum | Soft spectrum | Hard spectrum | Soft spectrum | Hard spectrum | Soft spectrum | Hard spectrum | Soft spectrum
Ambient dose equivalent | Peak dose rate ($\mu Sv/hr$) | 13.35 | 33.58 | 10.43 | 13.14 | 10.54 | 7.22 | 8.52 | 4.44
Accumulated dose ($\mu Sv$) | 82.37 | 105.8 | 60.76 | 41.57 | 57.19 | 17.68 | 40.67 | 8.62
Single event upset rate | Peak upset rate (Upsets/hr/Gb) | 0.98 | 3.35 | 0.74 | 1.42 | 0.75 | 0.76 | 0.61 | 0.47
Accumulated upset count (Upsets/Gb) | 5.89 | 10.98 | 4.34 | 4.47 | 3.91 | 1.77 | 2.74 | 0.87
Single event latch-up rate | Peak latch-up rate ($\times 10^{-5}$ Latch-ups/hr/device) | $9.76$ | $33.47$ | $7.41$ | $14.21$ | $7.55$ | $7.59$ | $6.09$ | $4.72$
Accumulated latch-up count ($\times 10^{-5}$ Latch-ups/device) | $58.94$ | $109.8$ | $43.42$ | $44.73$ | $39.05$ | $17.67$ | $27.44$ | $8.71$

Figure 15: The total accumulated/integrated dose for each of the flights as a
function of Kp index. There are only slight variations for each of the
selected flights in dose with Kp index in the hard spectrum case, however
there are large variations in dose in the soft spectrum case for all of the
flights.

in Westernhighlatitude,Easternhighlatitude,Secondlowestlatitude,Lowestlatitude
in Hard,Soft

Figure 16: The full dose rates over time for each flight route and each
simulated Kp index. As shown previously in figure 15, dose rates are
significantly higher for higher Kp indices in the soft spectrum case.

It can also be seen that all flight routes experience significantly higher
dose rates at higher Kp indices in the soft spectrum/high spectral index case.
This does not seem to be true in the hard spectrum/low spectral index case,
where high Kp indices only slightly increase dose rates. This is likely due to
the transition region between moving southwards with increasing Kp index in
the soft spectrum case, such that it encompasses a higher percentage of each
flight route, an effect that was previously shown in figure 3 and figure 4.
This effect is also shown in figure 17, which shows how dose rate maps at 37
kft change with varying Kp index for both spectral cases.

in 0,4,8 in Hard,Soft

Figure 17: Dose rate maps around the investigated flight routes for several Kp
indices. In the high spectral index case, the transition dose rate region
moves towards lower latitudes with increasing Kp index, as was previously
shown in figure 3, and crosses over the flight routes.

These results for the high spectral index case in figure 16 and in figure 4
previously complicate the possible strategy of flying to lower latitudes
during a large ground-level enhancement. During high spectral index
conditions, the actual location of the boundary between the low and high dose
rate regions will be subject to a large amount of uncertainty, as it will be
highly susceptible to the current conditions of Earth’s magnetic field and of
the spectral index of the solar particle spectrum bombarding Earth -
parameters which currently have a large degree of uncertainty. Previous work
using the QARM model has also made this point by showing the deviation flight
route dose rates can have from those of a great circle route (Dyer et al.,
2007). The effect of Earth’s magnetic field on dose rates that an aircraft
might experience is displayed in figure 17.

It should be noted that not every model uses Kp index as an input parameter.
However, all models use complex methods of representing Earth’s magnetosphere
and its effect on radiation dose rates in Earth’s atmosphere. Given how
quickly dose rate varies with latitude at the transition region under the
softer spectral conditions in this work, small deviations in simulations of
Earth’s magnetosphere from reality may lead to large errors in dose rate
predictions near the transition region and for transatlantic flights.

This means that at least for the current level of technology and scientific
knowledge of Earth’s magnetosphere, a large buffer zone might have to be
assumed a number of degrees south of the boundary zone location as predicted
by current dose rate calculation software. Aircraft attempting to fly out of
the high dose rate polar region would have to ensure they crossed the whole
buffer zone to be reasonably confident of no longer experiencing high
radiation dose rates.

Alternatively, the only way for an aircraft to know if and when it has truly
crossed into the lower dose region would be if they are equipped with a multi-
particle onboard radiation detector, and the possibility of equipping all
aircraft with radiation dose monitors has been discussed in previous work
(Clewer et al., 2019). Monitors for this purpose were previously used on
Concorde aircraft (Dyer et al., 2003; Bagshaw, 2000), and emergency descent
procedures were put in place in case of high radiation dose rate levels.

##  7 Conclusions

The results create an overall picture that during a ground-level enhancement,
the Earth’s atmosphere can be divided into three approximate zones; a low dose
rate equatorial and low altitude region, a high dose rate polar and high
altitude region, and a transition region between the two.

The properties of the transition region define many of the geometric features
of the GLE. The transition region varies in shape and structure with both the
incoming particle spectra and Earth’s magnetospheric conditions. This
transition region is therefore the region where dose rates exhibit the highest
levels of systematic uncertainty and any aircraft flying through this region
(such as transatlantic flights) will experience a highly uncertain radiation
dose. This is shown in this paper, where several flight routes between London
Heathrow and New York JFK airports were simulated to experience significantly
different dose rates during the same spectral and magnetospheric conditions.
Dose rates for these flights were also shown to vary significantly with Kp
index during relatively soft spectral conditions.

The results presented in this paper indicate that the high dose rate polar
region stretches further south during highly disturbed solar conditions.
During extreme ground-level enhancements that have an intensity on a scale
that hasn’t been so far recorded in modern history, Earth’s magnetosphere
could be significantly more disturbed than has been measured since the dawn of
the space age and the high dose rate polar region in such events may therefore
move significantly further south. It would likely pass closer to the equator
than 45°in latitude, particularly over North America and Australia. This would
breach well into the ICAO latitude bands of MNH and MSH (Middle latitudes
Northern Hemisphere and Middle latitudes Southern Hemisphere), but
specifically at these longitude regions.

##  8 Open Research Statement

All of the data used to generate the results and plots in this paper can be
found at https://doi.org/10.5281/zenodo.7410799 along with relevant usage
instructions.

##  9 Funding Information

This research was funded as part of the UKRI SWIMMR SWARM project.

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