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Advances in Space Research 69 (2022) 2893–2901

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Ionization eﬀect in the Earth’s atmosphere due to cosmic rays during the GLE # 71 on 17 May 2012
Susanna Pa¨tsi a, Alexander Mishev b,c,⇑
a Faculty of Science, University of Oulu, Oulu, Finland b Sodankyla¨ Geophysical Observatory, University of Oulu, Oulu, Finland c Space Physics and Astronomy Research Unit, University of Oulu, Oulu, Finland
Received 29 December 2021; received in revised form 2 February 2022; accepted 7 February 2022 Available online 11 February 2022
Abstract
Nowadays the systematic study of the possible eﬀect of precipitating high-energy particles on atmospheric physics and chemistry is in great expansion. Most of the recent models studying the precipitating energetic particles eﬀects in the Earth’s atmosphere are based on reliable quantiﬁcation of the induced ionization, that is, the cosmic ray impact ionization, which is extensively studied over the last decade. While the galactic cosmic rays are the main source of ionization in the Earth’s stratosphere and troposphere, the energetic particles of solar origin can signiﬁcantly enhance the ion production following strong solar eruptions, speciﬁcally over the polar caps. A particular interest represents solar protons observed by ground-based detectors, viz. the so-called ground level enhancements (GLE), observed as an increase of the count rate of e.g. neutron monitors. Here, employing 3-D Monte Carlo model, we computed the solar protons induced atmospheric ionization during the moderate GLE # 71 on 17 May 2012. The ion production rates were computed during various stages of the event as a function of the altitude above sea level using derived by veriﬁed model particles spectra. The 24 h averaged ionization eﬀect relative to the average due to the galactic cosmic rays was computed at several depths in the atmosphere. Ó 2022 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Keywords: Galactic cosmic rays; Solar energetic particles; Ground level enhancement; Atmospheric ionization; Stratosphere and troposphere

1. Introduction
The precipitation of high-energy charged particles of extra-terrestrial origin impacts various processes in the Earth’s atmosphere, speciﬁcally by the induced ionization and the corresponding inﬂuence on atmospheric physics and chemistry (e.g. Turunen et al., 2009; Calisto et al., 2011; Rozanov et al., 2012; Mironova et al., 2015; Nilsen et al., 2021, and references therein). Diﬀerent populations of energetic precipitating particles (EPPs) and/or radiation contribute to the atmospheric ionization, that is,
⇑ Corresponding author at: Space Physics and Astronomy Research Unit, University of Oulu, Finland
E-mail address: alexander.mishev@oulu.ﬁ (A. Mishev).

high-energy solar electromagnetic radiation such as UV, EUV, and X-ray determine the ion production in the upper atmosphere. At the same time, high-energy particles contribute mainly to the stratospheric and tropospheric ionization, that is below circa 100 km above sea level (asl), the atmospheric ionization is predominantly due to the omnipresent slightly variable ﬂux of galactic cosmic rays (GCRs), which secodaries produced in the particle shower induce ionization (for details see the review by Mironova et al., 2015, and references therein). The atmospheric ionization is sporadically enhanced following solar eruptions by the so-called solar energetic particles (SEPs) (e.g. Funke et al., 2011; Jackman et al., 2011; Usoskin et al., 2011b; Mishev and Velinov, 2018). Detailed study of the GCRs/SEPs induced ionization allows one to provide

https://doi.org/10.1016/j.asr.2022.02.008 0273-1177/Ó 2022 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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reliable basis to study and/or quantify the impacted by EEPs atmospheric eﬀects (e.g. Usoskin et al., 2009; Mishev et al., 2011; Krivolutsky and Repnev, 2012; Mishev and Velinov, 2018; Riley et al., 2018; Mishev and Velinov, 2020) and the related phenomena (e.g. Bazilevskaya et al., 2008; Vainio et al., 2009; Mironova et al., 2015; Miroshnichenko, 2018, and references therein).
The high-energy GCRs and SEPs, the latter when occur, entering the Earth’s atmosphere, initiate particle shower, that is nuclear-electromagnetic-meson cascade yielding large amounts of secondaries, eventually deposing their energy in the atmosphere mostly by ionization of the ambient air (for details see Gaisser et al., 2016). The omnipresent ﬂux of GCRs consists of protons ($90%) and a-particles ($8%), yet small amount of heavier nuclei are also observed (Aguilar et al., 2021). The GGRs are modulated in the heliosphere (e.g. Potgieter, 2013, and references therein) and their ﬂux is also inﬂuenced by transients and/or other short duration anisotropy of GCR ﬂux not related to the modulation (see e.g. Forbush, 1937; Gil et al., 2018). High-energy SEPs are accelerated during solar eruptive events, such as solar ﬂares and coronal mass ejections (CMEs) (e.g. Desai and Giacalone, 2016; Klein and Dalla, 2017, and references therein) and similarly to GCRs can induce particle shower in the atmosphere, whose secondary particles eventually ionize the ambient air. A speciﬁc interest is paid to SEPs whose secondary particles can reach the ground, that is ground level enhancements (GLEs) (e.g. Poluianov et al., 2017). GLEs may considerably enhance the atmospheric ionization speciﬁcally over the polar caps (e.g. Jackman et al., 2000; Jackman et al., 2011), thus giving basis to decipher the inﬂuence of EEPs on diﬀerent atmospheric chemistry processes (e.g. Krivolutsky et al., 2006; Randall et al., 2007; Nicoll and Harrison, 2014; Verronen et al., 2015; Sinnhuber et al., 2018).
Since GLEs occur sporadically and naturally diﬀer from each other in spectra and duration (e.g. Moraal and McCracken, 2012; Gopalswamy et al., 2012; Gopalswamy et al., 2014) as well as geomagnetic conditions, they are usually studied on a case-by-case basis (e.g. Miroshnichenko, 2018, and references therein). Besides, diﬀerent teams derive considerably diﬀerent SEP spectra, even for the same GLE, resulting on signiﬁcantly diﬀerent assessment of CR impact on the atmospheric and/or space weather eﬀects (e.g. Bu¨ tikofer and Flu¨ ckiger, 2013). Here we consider the GLE # 71, occurred on 17 May 2012, using recently derived and veriﬁed by direct space-borne measurement SEP spectra (e.g. Mishev et al., 2014; Koldobskiy et al., 2019b; Koldobskiy et al., 2019a; Mishev et al., 2021) and appropriate model described in Section 2.
2. Employed model for computation of cosmic ray induced ionization
The ion production rate in the atmosphere due to GCRs and SEPs can be assessed by analytical or empirical models

(e.g. Vitt and Jackman, 1996), yet naturally they reveal lim-

ited application to given atmospheric region, cascade com-

ponent, or primary particle (e.g. Velinov et al., 2013, and

references therein). This fact implied the development of

more sophisticated models, that is, based on simulations.

Over the last two decades several full target models based

on Monte Carlo simulations of the cosmic ray induced cas-

cades have been developed, which allowed one to compute

the ion production rate in the Earth’s atmosphere realisti-

cally considering all the physical processes (e.g.

Desorgher et al., 2005; Usoskin and Kovaltsov, 2006;

Paschalis et al., 2014; Banjac et al., 2019). Here, we

employed a model similar to Usoskin and Kovaltsov

(2006), the full description given by Velinov et al. (2009).

The ion production rate in ionpars=s:cm3 as a function of

the altitude asl is given by:

1 XZ 1 Z

qðh; EÞ ¼ Eion i

DiðEÞY ðh; EÞqðhÞdEdX
Ecut ðRcÞ X

ð1Þ

h is the air overburden (air mass) above a given altitude

in the atmosphere expressed in g=cm2 or altitude asl, DiðEÞ

is the diﬀerential cosmic ray spectrum for a given compo-

nent i: protons p, Helium (a-particles), q is the atmospheric

density in g=cm3, which can be expressed using arbitrary

models, E is the initial energy of the incoming primary

nuclei on the top of the atmosphere, X is a solid angle

and Eion = 35 eV is the average energy necessary to yield

an ion pair in air (Porter et al., 1976). Note that the heavier

nuclei with atomic number Z > 2 of the GCRs are scaled to

a-particles according to Usoskin and Kovaltsov (2006),

Mishev and Velinov (2011). The integration is over the

kinetic energy EcutðRcÞ above the rigidity cut-oﬀ Rc (Cooke et al., 1991) for a nuclei of type i at a given geo-

graphic location by the expression:

Ecut;i ¼ sﬃ ﬃﬃﬃZAﬃﬃﬃiiﬃ ﬃﬃﬃﬃ2ﬃRﬃﬃﬃ2cﬃﬃﬃþﬃﬃﬃﬃﬃEﬃﬃﬃ20ﬃ À E0

ð2Þ

where E0 = 0.938 GeV/n is the proton’s rest mass and the ionization yield function and given altitude h or mass overburden is deﬁned as:

Y

ðh;

EÞ

¼

@Eðh; @h

EÞ

ð3Þ

where @E is the deposited energy in an atmospheric layer @h. The yield function is the response of the ambient air at a given atmospheric depth as deposited energy (ionization) to a mono-energetic unit ﬂux of primary particle entering into the Earth’s atmosphere. The formalism of precomputed yield functions is well known, widely used and easy for application. Once the yield functions been obtained by Monte Carlo simulations, allow one, without subsequent extensive computations, to assess the ion production rate as an integral of the product of the primary particle spectrum and the yield functions. In the model we use yield functions computed with the PLANETOCOSMICS code (for details see Desorgher et al., 2005), which

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diﬀers from Usoskin and Kovaltsov (2006),Velinov et al. (2009) in the employed hadron generators (for details see Mishev and Velinov, 2010; Mishev and Velinov, 2014), yet the diﬀerence in ion production is about 15–20% (for details see Usoskin et al., 2009), mostly due to the particle shower development (for details see Engel et al., 2011).
Here the rigidity cut-oﬀs over the globe can be computed with the MAGNETOCOSMICS code, explicitly considering the measured Kp index corresponding to the exact period of the GLE occurrence (Desorgher et al., 2005). Routinely, during the computations, a combination of the IGRF geomagnetic model as the internal ﬁeld (The´bault et al., 2015) and the Tsyganenko 89 model as the external ﬁeld (Tsyganenko, 1989) were employed allowing straightforward computations (Kudela and Usoskin, 2004; Kudela et al., 2008; Nevalainen et al., 2013). Note, that during GLEs, the atmospheric ionization is a superposition of GCRs and SEPs contributions (e.g. Usoskin et al., 2009; Mishev et al., 2013; Mishev and Velinov, 2015).
A simple one-parameter model allows one to consider with reasonable precision the contribution of GCRs in Eq. (1), that is the force ﬁeld model (Gleeson and Axford, 1968; Caballero-Lopez and Moraal, 2004), where the parametrization of the local interstellar spectrum is according to Usoskin et al. (2017) and the modulation potential is computed as in Usoskin et al. (2011a). Accordingly, the SEPs spectra in Eq. (1) are taken from Mishev et al. (2021). Note, that for the computations is employed a realistic atmospheric model NRLMSISE-00 (Picone et al., 2002).
3. GLE # 71 and the corresponding ionization eﬀect
GLE # 71 occurred on 17 May 2012, following eruptive processes in the active region NOAA 11476, namely CME and a moderately strong ﬂare (class M5.1) at 01:25 UT. It was registered by the global neutron monitor (NM) network at around 01:50 UT with a moderate increase revealed by APTY, OULU, and SOPO/SOPB (Apatity, Oulu, and South Pole) NMs, while the other NMs registered only marginal count rate increases. The NM count rate increase was observed for about two hours (e.g. Kocharov et al., 2018; Anastasiadis et al., 2019).

Advances in Space Research 69 (2022) 2893–2901
peak intensity phase (02:00 UT) of GLE # 71 at depths 100 g cmÀ2 and 200 g cmÀ2 roughly corresponding to the due to GCRs Regener-Pfotzer maximum (Regener and Pfotzer, 1935) is presented in Fig. 2 and Fig. 3, respectively (detailed information is provided in the suppl. material as. csv ﬁle). The ion production rate is comparable to that during the peak phase of the third Halloween event, that is GLE # 67 on 2 November 2003 (for details see the supplementary material and Fig. 2 in Mishev and Velinov, 2020), yet the SEP spectra are softer, therefore the altitude of maximum ion production rate during GLE # 71 is greater than the recently studied GLE # 65 and GLE # 67 (for details see Mishev and Velinov, 2020). This is clearly seen by the altitude dependence of the ion production rate due to the GCRs and SEPs during GLE # 71, presented as supplementary material (animation). While the RegenerPfotzer maximum is clearly seen for the GCRs (suppl. material 1), the SEPs depose their energy at greater altitudes, that is, at depths of about 10–25 g cmÀ2 as presented in the supplementary materials 2 and 3 (the ion production rate due to the superimposed GCRs and SEPs contributions as a function of the altitude during the event onset and peak phase of the event). Note, that the contribution of the GCRs to the ion production rate is in agreement with widely used and/or recent models for computation of the atmospheric ionization (e.g. Usoskin and Kovaltsov, 2006; Banjac et al., 2019; Makrantoni et al., 2021).
The ion production rate during the GLE # 71 was signiﬁcant throughout the event onset and peak phase of the event, speciﬁcally in the polar stratosphere and troposhere (see Fig. 2, Fig. 3 and the suppl. material). Because of the softer SEP spectra compared to that of GCRs, the ion production rate rapidly diminished, speciﬁcally at depths below 200–250 g cmÀ2. At depths of about 200 g cmÀ2, the contribution of the GCRs and SEPs are almost equal, whilst below this level the contribution of the former dominated. Besides, the ion production rate due to SEPs govern the atmospheric ionization in a region with rigidity cut-oﬀ till of about Rc % 3 GV, whilst at greater rigidity cut-oﬀ the ion production rate was due mainly to GCRs, that is, in the region of Rc P3 GV, the ion production due to GCRs dominated in the whole atmosphere.

3.1. Ion production rate in the atmosphere

3.2. Averaged ionization eﬀect

Using the model described in Section 2 and the derived SEP spectra by Mishev et al. (2021), depicted in Fig. 1, we computed the ion production rate at several depths (mass overburden) in the atmosphere. Here we considered 5min SEP spectra (for details see their Table 2 Mishev et al., 2021). Therefore, we computed the ion production rate in the atmosphere with 5-min time resolution considering explicitly the dynamical evolution of the SEP spectra.
An illustration of the computed ion production rate as a superposition of GCRs and SEPs contributions during the

For providing reliable basis for quantiﬁcation of the terrestrial eﬀects of the precipitating high-energy particles in the atmosphere, namely SEPs and GCRs, speciﬁcally for the atmospheric physics and chemistry purposes, it is necessary to normalize the ion production. Therefore, we computed the ionization eﬀect over selected time scale e.g. 24 h (Turunen et al., 2009; Mironova et al., 2015).
Here, employing the recombination model by Krivolutsky et al. (2006) and integrating the ion production rates during the GLE # 71 (see subSection 3.1), we

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Fig. 1. Top panels: spectra and PAD of SEPs during several stages of GLE # 71 on 17 May 2012 as depicted in the legend. Bottom panels: averaged over the event spectra and PAD of SEPs during GLE # 71.

assessed the 24h averaged ionization eﬀect in the atmosphere during GLE # 71 at selected atmospheric depths (altitudes). The averaged ionization eﬀect represents the integrated on a step of 5-min ion production during the event considering the actual SEP ﬂux including its time evolution with the GCR contributions versus the averaged

ion production rate due to GCRs before the event on a 24 h
time scale.
An example of the ionization eﬀect at an atmospheric depth of 50 g cmÀ2 is shown in Fig. 4. While the 24h aver-
aged ionization eﬀect is signiﬁcant at altitudes of about 10– 50 g cmÀ2, it drops at depths of 100 g cmÀ2 and 200 g cmÀ2,

Fig. 2. Ion production rate at 100 g cmÀ2 during the peak phase of GLE # 71 on 17 May 2012.
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Advances in Space Research 69 (2022) 2893–2901

Fig. 3. Ion production rate at 200 g cmÀ2 during the peak phase of GLE # 71 on 17 May 2012.

as depicted in Fig. 5 and Fig. 6, respectively (the details are given in the suppl. material as.csv ﬁles). Note, during all the computations of ion production rates, accordingly the ionization eﬀect, the cut-oﬀ rigidities were considered taking into account the goemagnetospheric conditions during the event, that is, the computations were performed employing a combination of IGRF and Tsyganenko 89

models, as discussed above. This allowed us to quantify
with good precision the ionization eﬀect on a global scale during the GLE # 71.
One can see that the 24 h overaged ionization eﬀect during GLE # 71 ranges from about 90% at depths of 50 g cmÀ2 and drops to %20% at depths of 200 g cmÀ2. At lower depths the 24 h ionization eﬀect was marginal.

Fig. 4. 24h averaged ionization eﬀect at 50 g cmÀ2 during GLE # 71 on 17 May 2012.
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Fig. 5. 24h averaged ionization eﬀect at 100 g cmÀ2 during GLE # 71 on 17 May 2012.

4. Summary
In this work, we computed the ion production rate and the corresponding ionization eﬀect during the GLE # 71 on 17 May 2012. Here we used high-precision veriﬁed SEP spectra including their time evolution throughout

the event, and state-of-the-art based on Monte Carlo simulations model, considering explicitly the geomagnetospheric conditions.
The computed ion production rates were signiﬁcant during the event onset and peak phase of the event, and diminished during the late phase of the event. The ion production

Fig. 6. 24h averaged ionization eﬀect at 200 g cmÀ2 during GLE # 71 on 17 May 2012.
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rates were signiﬁcant, speciﬁcally in the polar stratosphere and polar upper troposphere. At regions with Rc % 2–3 GV, the ion production was comparable to the average due to GCRs, because of the relatively soft SEP spectra. At mid-latitudes, the ion production due to GCRs dominated in the whole atmosphere. An illustration of the ion production rates and its altitude dependence during the event onset and peak phase was depicted in the supplementary materials (animations and.csv ﬁles). The 24h averaged ionization eﬀect at several depths is also computed and it was shown that it ranged from about 90% at depths of 50 g cmÀ2 to about 20% at depths of 200 g cmÀ2, respectively.
The presented here study of the ionization eﬀect during a moderately strong GLE, allows one to quantify the possible CR-induced eﬀects in the Earth’s atmosphere (e.g. Miroshnichenko, 2018, and references therein).
Declaration of Competing Interest
The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper.
Acknowledgements
This work was supported by the Academy of Finland (projects 330064 QUASARE, 321882 ESPERA). We warmly acknowledge prof. Ilya Usoskin for the commnents and suggestions related to this work and all the colleagues from the Space Physics and Astronomy Research Unit of the University of Oulu for their hospitality.
Appendix A. Supplementary material
Animation 1: The contribution of GCRs to the ion production rate as function of the altitude during GLE # 71 on 17 May 2012. Animation 2: The superimposed (GCRs and SEPs) ion production rate as function of the altitude during the event onset of GLE # 71 on 17 May 2012. Animation 3: The ion production rate as function of the altitude during the peak phase of GLE # 71 on 17 May 2012. 100gIonRate.csv Global map (column 1 latitude, column 2 longitude) of ion production rate due to GCR protons (column 3) and a-particles (column 4), SEPs (column 5) and superimposed (column 6) at depth of 100 g cmÀ2 during the peak phase of GLE # 71 on 17 May 2012. 200gIonRate.csv Global map (column 1 latitude, column 2 longitude) of ion production rate due to GCR protons (column 3) and a-particles (column 4), SEPs (column 5) and superimposed (column 6) at depth of 200 g cmÀ2 during the peak phase of GLE # 71 on 17 May 2012. IonizationEﬀect.csv Global map (column 1 latitude, column 2 longitude) of the 24 h averaged ionization eﬀect at depth of 100 g cmÀ2 (column 3) and 200 g cmÀ2 (column 4) during GLE # 71 on 17 May 2012. Supplementary data asso-

ciated with this article can be found, in the online version, at https://doi.org/10.1016/j.asr.2022.02.008.
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