zotero-db/storage/TA25UBD8/.zotero-ft-cache

arXiv:2011.00048v1 [physics.space-ph] 30 Oct 2020

Ionization effect in the Earth’s atmosphere during the sequence of October-November 2003 Halloween GLE
events
A.L. Mishev1,2 and P.I.Y. Velinov3
1Space Physics and Astronomy Research Unit, University of Oulu, Finland. 2Sodankyla¨ Geophysical Observatory, University of Oulu, Finland.
3Institute for Space Research and Technology, Bulgarian Academy of Sciences, Soﬁa, Bulgaria
November 3, 2020
Abstract The effect of precipitating high-energy particles on atmospheric physics and chemistry is extensively studied over the last decade. In majority of the existing models, the precipitating particles induced ionization plays an essential role. For such effects, it is necessary to possess enhanced increase in ion production, speciﬁcally during the winter period. In this study, we focus on highly penetrating particles - cosmic rays. The galactic cosmic rays are the main source of ionization in the Earth’s stratosphere and troposphere. On the other hand, the atmospheric ionization may be signiﬁcantly enhanced during strong solar energetic particle events, mainly over the polar caps. A speciﬁc interest is paid to the most energetic solar proton events leading to counting rate enhancement of ground-based detectors, namely the so-called ground level enhancements (GLEs). During solar cycle 23, several strong ground level enhancements were observed. A sequence of three GLEs was observed in OctoberNovember 2003, the Halloween events. Here, on the basis of 3-D Monte Carlo model, we computed the energetic particles induced atmospheric ionization, explicitly considering the contribution of cosmic rays with galactic and solar origin. The ion production rates were computed as a function of the altitude above sea level using reconstructed solar energetic particles spectra. The 24 hours and event averaged ionization effects relative to the average due to galactic cosmic rays were also computed.
Keywords:Solar eruptive events, Ground level enhancement, Atmospheric ionization. For contact: alexander.mishev@oulu.ﬁ
1 Introduction
Various populations of precipitating high-energy particles and/or high-energy radiation contribute to the atmospheric ionization viz. subatomic particles - cosmic rays of galactic or solar origin,
1

precipitating particles from radiation belts, auroral electrons, UV and X-ray solar emissions (for details see the reviews by Vainio et al., 2009; Mironova et al., 2015, as well as the references therein). Energetic particles induced ionization in the upper part of the Earth’s atmosphere is dominated by solar UV and X-rays. At altitudes below about 100 km above sea level (a.s.l.), speciﬁcally in the stratosphere and upper troposphere, the atmospheric ionization is essentially due to the penetrating ﬂux of galactic cosmic rays (GCRs), which is variable to a small degree (for details see Potgieter, 2013), and thus leading to quasi-constant ion production background (for details see Bazilevskaya et al., 2008). In some cases, as a result of solar eruptions, an enhanced high-energy particles ﬂux of solar origin, known as solar energetic particles (SEPs), can impinge the Earth atmosphere, eventually leading to signiﬁcant ion production (e.g. Usoskin et al., 2011b).
The energetic particles precipitation induced ionization in the troposphere and stratosphere results from the nuclear-electromagnetic-lepton cascade, i.e. sequence of successive interactions of the penetrating primary cosmic ray particle with the atmospheric particulates, producing a large amount of secondary particles losing their energy mainly via ionization (e.g. Dorman, 2004; Grieder, 2011; Beatty et al., 2018). The maximum of ion production in the atmosphere due to cosmic rays (CRs) is observed at the altitude of about 12-15 km a.s.l., known as Regener-Pfotzer maximum (Regener and Pfotzer, 1935). The GCR ﬂux is slightly modulated in the Heliosphere and inversely follows the 11-year solar cycle, responding also to transient phenomena leading to short term episodes as the Forbush decreases (Forbush, 1937, 1958). In some cases, the sporadically occurring SEPs possess energy of about a 1 GeV/nucleon or even greater, as a result induce similarly to GCRs atmospheric shower. Hence, in that case, secondaries produced by SEPs penetrate deep into the atmosphere or even reach the ground leading to ground level enhancements (GLEs) (e.g. Poluianov et al., 2017). Therefore, GLEs may cause a signiﬁcant excess of ionization, speciﬁcally over the polar caps (e.g. Jackman et al., 2000, 2011; Mishev et al., 2011; Usoskin et al., 2011b; Mishev and Velinov, 2015c; Mitthumsiri et al., 2017; Mishev and Velinov, 2018a).
A systematic study of the induced by high-energy particles impact ionization allows one to clarify the inﬂuence of precipitating particles on different atmospheric chemistry processes, global electric circuit and atmospheric physics, speciﬁcally on minor components (e.g. Krivolutsky et al., 2006; Randall et al., 2007; Jackman et al., 2008; Rozanov et al., 2012; Nicoll and Harrison, 2014; Verronen et al., 2015; Sinnhuber et al., 2018). Naturally, over the last decade, the energetic particles impact ionization was extensively studied. Thus, the increased high-energy particles ﬂux during GLEs provide a unique opportunity to study such effects in enhanced mode. During the solar cycle 23, sixteen GLEs were observed, the ﬁrst event occurred on 6 November 1997 (GLE # 55), the last occurred on 13 December 2006 (GLE # 70), the full list is available at the Oulu Cosmic Ray Station http://gle.oulu.fi) (e.g. Gopalswamy et al., 2012). GLEs occur sporadically, differ from each other in spectra, particle ﬂuence, anisotropy, duration, apparent source position, geomagnetic conditions (e.g. Moraal and McCracken, 2012). Therefore, they are usually studied case by case. Here, we focus on the sequence of three consecutive GLEs, viz. the three so-called Halloween events of October-November 2003, occurred on 28 October (GLE # 65), 29 October (GLE # 66), and on 2 November (GLE # 67), respectively. On the basis of precisely derived SEP spectra and convenient state of the art model, we assessed the ion production and the corresponding ionization effect during the three Halloween GLE events.
2

2 Employed model for computation of induced ionization

The ion production in the atmosphere due to precipitating high-energy particles can be assessed by analytical (parametrization) and/or semi-empirical models (e.g. O’Brien, 1970; Vitt and Jackman, 1996). However, parameterization models usually exhibit constraints to a given atmospheric region, atmospheric cascade component or primary particle (e.g. Velinov et al., 2013, and references therein). On the other hand, models based on Monte Carlo simulations of the atmospheric cascade allow one to reliably assess the ion production rate considering all the physical processes (Desorgher et al., 2005; Usoskin and Kovaltsov, 2006; Velinov et al., 2009; Paschalis et al., 2014; Banjac et al., 2019). Here, we employed a model similar to Usoskin and Kovaltsov (2006), with the full description and application are given elsewhere (i.e. Mishev and Velinov, 2007; Velinov et al., 2009; Mishev and Velinov, 2015a). The ion production rate as a function of the altitude a.s.l. is given by:

∑ q(h, E) = 1
E ion i

∞ Ecut (Rc)

Ω

Di(E

)

∂

E(h, ∂h

E

)

ρ

(h)d

E

d

Ω

(1)

where ∂ E is the deposited energy in an atmospheric layer ∂ h , h is the air overburden (air mass) above a given altitude in the atmosphere expressed in g/cm2 or altitude a.s.l., Di(E) is the differential cosmic ray spectrum for a given component i: protons p, Helium (α-particles), the lat-
ter representative for heavier nuclei with atomic number Z > 2 (for details see Usoskin and Kovaltsov, 2006; Mishev and Velinov, 2011), ρ is the atmospheric density in g.cm−3, E is the initial energy of the incoming primary nuclei on the top of the atmosphere, Ω is a solid angle and Eion = 35
eV is the average energy necessary for creation of an ion pair in air (Porter et al., 1976). The
integration is over the kinetic energy Ecut (Rc) above the rigidity cut-off Rc for a nuclei of type i
at a given geographic location by the expression:

Ecut,i =

Zi Ai

2
R2c + E02 − E0

(2)

where E0 = 0.938 GeV/n is the proton’s rest mass. Here, the computation of the cut-off rigidity was performed with the MAGNETOCOSMICS
code, explicitly considering the measured Kp index during the events (Desorgher et al., 2005), assuming a combination of the IGRF geomagnetic model as the internal ﬁeld model and the Tsyganenko 89 model as the external ﬁeld (Tsyganenko, 1989). This combination allows one to compute straightforwardly with reasonable precision the local rigidity cut-offs over the globe (Kudela and Usoskin, 2004; Kudela et al., 2008; Nevalainen et al., 2013). We emphasize that employment of newer version of Tsyganenko models e.g. Tsyganenko 96 or Tsyganenko 01 (Tsyganenko, 1995, 2002), would lead to comparable results since the other model uncertainties such as ionization yield function and the used as input SEP spectra are considerably greater as discussed below.
During GLEs, ion production in the atmosphere is presented as a superposition of GCRs and SEPs contributions. For the contribution of GCRs in Eq. (1) the force ﬁeld model is employed (Gleeson and Axford, 1968; Burger et al., 2000), where the parametrization of the local interstellar spectrum is according to Usoskin et al. (2017) and the modulation potential is taken from

3

Usoskin et al. (2011a). Accordingly, the SEPs spectra in equation (1) are considered according to Miroshnichenko et al. (2005); Kocharov et al. (2017).
Note, that for the computations a realistic atmospheric model NRLMSISE 00 is employed, that explicitly considers the speciﬁcs of the atmospheric conditions and type of the incident primary particle (Picone et al., 2002; Mishev and Velinov, 2010, 2014).
3 Sequence of three Halloween GLEs on October-November 2003
A violent solar activity was observed in October–November 2003, which produced a sequence of three consecutive GLEs, with onsets occurring on 28 October, 29 October and on 2 November, respectively (Gopalswamy et al., 2005; Liu and Hayashi, 2006; Gopalswamy et al., 2012). The events were observed by the global neutron monitor network, the details and count rate records are given in great detail in http://gle.oulu.fi).
The GLE # 65 on 28 October 2003 was associated with a large ﬂare (4B, X17.2) occurred in the active region AR10486. The GLE # 65 followed signiﬁcant interplanetary disturbance related to previously ejected coronal mass ejection (CME) on 26 October with correspondence with a 3B/X1.2 ﬂare in the same active region. The SEP spectra were relatively hard with observed softening throughout the event (Fig.1a).
The GLE # 66, occurred on 29 October, was characterized by a notably smaller recorded neutron monitor count rate increases, thus this event was considerably weaker. Softer SEP spectra were observed, with non-signiﬁcant variation throughout the event (Fig.1b). A strong Forbush decrease was also observed prior to and during this event, which was explicitly considered during our computations of ion production rate, i.e. a GCR ﬂux reduction was taken into account during the computations.
The GLE # 67, occurred on 2 November 2003, was related to an X8.3/2B solar ﬂare, with onset at about 17:30–17:35 UT. In general, the event was characterized by a large anisotropy in its initial phase and relatively hard but constantly softened SEP spectra (Fig.1c), the details are given in (Kocharov et al., 2017).
It should be noted that in this period occurred the strongest in 30 years (since march 1989) geomagnetic storm. The planetary Ap index reached values Ap=204 on 29 October 2003, Ap=191 on 30 October 2003 and Ap=116 on 31 October 2003.
The presented in Fig.1 SEP spectra were used as input in Eq. (1) for the computation of ion production rate throughout the events. The spectra were mostly derived on the basis of a veriﬁed method for data analysis of ground-based neutron monitor data (e.g. Mishev et al., 2018; Mishev and Usoskin, 2016), which reliably accounts for the high-energy part of the spectra, usually underestimated by space-borne instruments (for details see Koldobskiy et al., 2019). The derived GLE particles spectra are with good agreement with Koldobskiy et al. (2019). More information about the used spectra is presented in Miroshnichenko et al. (2005); Kocharov et al. (2017). Here, we would like to point out that the input SEP spectra in the model for computation of the ion production is crucial and can lead to an important uncertainty, up to an order of magnitude, in the computations similarly to Bu¨tikofer and Flu¨ckiger (2015). The other model uncertainties, namely the Monte Carlo simulations of the atmospheric cascade used for the com-
4

Flux [Proton m sr s GV ]

-1

6
10
A
5
10
4
10

2200 2230 2300 2330 2400

6
10
B
5
10

4
10

1130 1200 1300 1400

6
10
C
5
10

4
10

1730 1800 1830 1900 1925

-2 -1 -1

3
10

3
10

3
10

2
10

2
10

2
10

1
10

1
10

1
10

0
10 1

2

3 45

0
10 1

2

3 45

R [GV]

0
10 1

2

3 45

Figure 1: Rigidity spectra of SEPs during selected stages of Halloween GLEs as denoted in the legend. Panels a,b,c, correspond to GLE # 65 occurred on 28 October 2003, GLE # 66 occurred on 29 October 2003 and GLE # 67 occurred on 2 November 2003, respectively. The solid line denotes the GCR ﬂux.
.

5

putation of the ionization yield function (e.g. Mishev and Velinov, 2010), integration methods in Eq. (1) and computation of the cut-off rigidities using the corresponding magnetospheric model are signiﬁcantly smaller. Therefore, the employment of SEP spectra based on a veriﬁed method is speciﬁcally important.
4 Atmospheric ionization during Halloween GLEs
The Halloween GLEs differ in duration, features, accordingly anisotropy and spectra, which play an essential role for the computations of ion production throughout the events (Moraal and McCracken, 2012). In addition, GLE # 66 occurred during deep Forbush decrease, which was explicitly considered during our computations, i.e. the GCR ﬂux was adjusted from NMs measurements, the data retrieved from neutron monitor database www.NMDB.eu (Mavromichalaki et al., 2011). Accordingly, the GLE # 67 occurred during the recovery phase of a Forbush decrease, which was taken into account in a similar way.
4.1 Ion production rates during Halloween GLEs
Using the model described in Section 2 and the derived GLE particles spectra (Section 3) we computed the ion production rate in the stratosphere and troposphere from ground level to about 35 km a.s.l. considering the GCRs and SEPs contribution (Mishev and Velinov, 2018b, 2020). In Fig.2 we present the ion production during the Halloween GLEs, speciﬁcally in the polar and sub-polar region with rigidity cut-off Rc ≤ 1 GV (Fig.2a,b,c) and high mid-latitudes region with rigidity cut-off Rc ≈ 2 GV (Fig.2d,e,f).
The computed during GLE # 65 ion production rate was signiﬁcant throughout the initial and main phase of the event, speciﬁcally in the polar low stratosphere (Fig. 2a). The ion production rate diminished but remained signiﬁcant during the late phase of the event. However, in a region with rigidity cut-off of about Rc ≈ 2 GV the ion production rate was comparable to the average due to GCRs (Fig.2d). Moreover, at altitudes of about 10 km a.s.l. and below the ion production rate due to GCR was greater than that due to SEPs, because of the soft spectra of the latter. Accordingly, in the region of Rc ≈ 3 GV, the ion production due to GCR dominated in the whole atmosphere. The time evolution of the ion production rate at an altitude of 15 km a.s.l. during GLE # 65 is presented in the Appendix (Fig.A.1).
The computed ion production rate during GLE # 66 was considerably lower (Fig.2b), because of softer SEP spectra compared to GLE # 65, the notably reduced SEP ﬂux and the accompanying deep Forbush decrease. The ion production rate during GLE # 66 was slightly variable throughout the event with a tendency for diminishing. At polar and sub-polar region with rigidity cut-off Rc ≤ 1 GV, the ion production rate was still signiﬁcant, however, in region with rigidity cut-off Rc ≈ 2 GV the contribution of SEPs was smaller than that due to GCRs (Fig.2e). Similarly to GLE # 65, the time evolution of the ion production rate at an altitude of 15 km a.s.l. during GLE # 66 is presented in the supplementary material Appendix (Fig.A.2).
The ion production rate during the last event - GLE # 67 was greater than GLE # 66, speciﬁcally during the initial and main phase of the event, but rapidly diminished during the late phase (Fig.2c). In addition, because the softer SEP spectra compared to GLE # 65 the computed ion
6

Altitude [m a.s.l. ]

40000 A
35000
30000
25000

GCR

B

11:30

12:00

12:30

13:00

14:00

GCR

C

22:00

22:30

23:00

23:30

00.00

20000

15000

10000

5000 0
40000 D
35000
30000
25000

100

200

300

400

GCR 11:30 12:00 12:30 13:00 14:00

0

50

100

150

200

0

50

-3 -1 Ion production rate [ion pairs cm s ]

E

GCR

F

22:00

22:30

23:00

23:30

00.00

20000

15000

10000

5000 0

5

10

15

20

25

0

5

10

15

20

0

5

-3 -1 Ion production rate [ion pairs cm s ]

GCR 17:35 18:00 18:30 19:00

100

150

200

GCR 17:35 18:00 18:30 19:00

10

15

20

Altitude [m a.s.l. ]

Figure 2: Ion production rates due to CRs during Halloween GLEs on October-November 2003. Panels a,b,c, and d,e,f, correspond to GLE # 65, 66, 67 respectively. The top panels correspond to region with Rc ≤ 1 GV, the bottom panels correspond to region with Rc ≈ 2 GV.
.
production rates were slightly below that the computed during the GLE # 65. In the region of midlatitudes with Rc ≈ 2 GV, the contribution of SEPs was smaller than that due to GCRs (Fig.2f). The time evolution of the ion production rate at an altitude of 15 km a.s.l. during GLE # 67 is presented in the Appendix (Fig.A.3).
One can see that the computed ion production rates were greatly variable throughout the events. The ion production was signiﬁcant in the polar region and considerably diminished in region with Rc ≈ 2 GV. The ion production rates were maximal during the strongest event - GLE # 65. In all cases, the contribution to the ion production due to GCRs in the polar region was smaller that that due to SEPs, but dominated at region with Rc ≈ 2–3 GV.
4.2 Integrated ionization effect in the atmosphere
In order to compute the ionization effect during GLEs, speciﬁcally for atmospheric physics and chemistry purposes, it is more convenient to perform integration over selected time scale(s), corresponding to event duration and/or 24 hours. Here, using the computed ion production rates during the Halloween GLEs, we computed the corresponding ionization effect. The ionization effect represents the averaged over the event or 24 hours ion production rate during a GLE considering the SEP and actual GCR contributions versus averaged ion production rate due to GCR prior to the event, assuming recombination model similarly to Krivolutsky et al. (2006).
The results of those computations for 24 hours averaged ionization effect are shown in Figs.3–

7

Latitude [deg]

90 60 30
0 -30 -60

[%]
200 180 160 140 120 100 80.0 60.0 40.0 20.0 0.00

-90 0

60

120

180

240

300

360

Longitude [deg]

Figure 3: Map of the 24h averaged ionization effect in the region of Regener-Pfotzer maximum during GLE # 65 on 28 October 2003.
.

5 for GLE # 65, GLE # 66 and GLE # 67, respectively. Note, that here we computed the cut-off rigidity during the events, explicitly considering the complex goemagnetospheric conditions employing a combination of IGRF (The´bault et al., 2015) and Tsyganenko 89 (Tsyganenko, 1989) models, as discussed above. This allowed us to perform realistic high-precision computations of the global distribution of ion production over the globe, accordingly the corresponding ionization effect.
The 24 hours integrated ionization effect during GLE # 65 was signiﬁcant in the high-latitude region, where it ranged about 100-200 % in the region of Regener-Pfotzer maximum. The ionization effect diminished at lower latitudes, it was negligible in lower-mid and equatorial latitudes (Fig.3). This is due to softer SEP spectra comparing to GCRs. Therefore SEPs contributed signiﬁcantly in the polar region, but not at low latitudes. The ionization effect is also a function of the altitude. It diminished signiﬁcantly as a function of altitude. At lower altitudes, it was considerably smaller than that at the region of the Regener-Pfotzer maximum. An illustration of the altitude dependence of the event averaged ionization effect is given in Appendix (Fig.A.4). Note that the event integrated ionization effect was considerably greater than 24 hours integrated, since it accounted the SEPs contribution on a shorter time scale.
As was mentioned above, GLE # 66 occurred during a deep Forbush decrease of GCRs and complex magnetospheric conditions (e.g. Belov et al., 2005). This speciﬁc Forbush decrease was one of the largest ever recorded. In particular, the amplitude of the decrease was ∼ 30% in 10 GV particles as reported by Belov (2009) in their Figure 2. This resulted in complicated interplay of SEP contribution and signiﬁcantly reduced GCR ﬂux contribution on the ion production. The

8

Latitude [deg]

90 60 30
0 -30 -60

[%]
10 5.0 0.0 -5.0 -10 -15 -20

-90 0

60

120

180

240

300

360

Longitude [deg]

Figure 4: Map of the 24h averaged ionization effect in the region of Regener-Pfotzer maximum during GLE # 66 on 29 October 2003.
.

Latitude [deg]

90 60 30
0 -30 -60 -90
0

[%]
50 45 40 35 30 25 20 15 10 5.0 0.0

60

120

180

240

300

360

Longitude [deg]

Figure 5: Map of the 24h averaged ionization effect in the region of Regener-Pfotzer maximum during GLE # 67 on 2 November 2003.
.

9

SEP spectra in this case were slightly softer and with reduced ﬂux than that during GLE # 65. While, the event integrated ionization effect was comparable to the previous event, the 24 hours averaged ionization effect during GLE # 66 was marginal, even in the polar region it was of about 5 %. Moreover, it was negative in the equatorial region, due to the reduced GCR ﬂux (Fig.4). The altitude dependence of the event averaged ionization effect during GLE # 66 is given in the Appendix (Fig.A.5).
Accordingly, the ionization effect during GLE # 67 was not signiﬁcant in mid-latitudes and it was marginal in the equatorial region (Fig.5). The last of the sequence of Halloween events, GLE # 67, occurred during the recovery phase of a deep Forbush decrease. Therefore, the reduced GCR ﬂux within temporal evolution was explicitly considered for the computation of background ion rate production. The 24 hours averaged ionization effect during GLE # 67 was of about 40 % in the polar region. It diminished to about 10 % at lower latitudes. Accordingly, the altitude dependence of the event averaged ionization effect during GLE # 67 is given in the Appendix (Fig.A.6).
5 Summary and Discussion
The effect of high-energy particles precipitation, speciﬁcally cosmic rays, via the induced ionization on atmospheric chemistry and physics is subject to extensive scientiﬁc discussion (Mironova et al., 2015). The sporadic rapid change of CR ﬂux, e.g. Forbush decreases and/or GLEs provides an unique possibility to study such possible effects on enhanced magnitude. The studied here sequence of three consecutive GLEs occurred in October-November 2003, the so-called Halloween events, give a good basis to study the possible inﬂuence of precipitating energetic particles, concerning also previous reports (e.g. Funke et al., 2011).
It was recently pointed out that for observation of such effects, it is necessary an essential increase of ion production in the atmosphere e.g. during major GLEs and winter season in order to avoid the eventual inﬂuence of UV (Mironova and Usoskin, 2014). Therefore, the presented here computed ionization effect during Halloween events gives the basis for similar studies (e.g. Krivolutsky et al., 2005; Sinnhuber et al., 2018).
The ion production during the GLEs is governed by SEP spectra. SEPs with harder spectra impact also mid-latitude regions, while soft SEPs contribute mostly to the polar region. In addition, transients such as Forbushes play also an important role. This is clearly seen during the Halloween events. The ion production during GLE # 65 was greater than the subsequent GLE # 66 and GLE # 67. Accordingly, the ionization effect was highly dependent on the time-scale. While, the event averaged ionization effect was in the same order for all the three events, the 24 hours integrated ionization effect was apparently different: during GLE # 65 it was signiﬁcant, marginal even negative in some regions during GLE # 66 and moderate during GLE # 67. Besides, an apparent altitude dependence was observed.
In the work presented here, we computed the ion production rate and the corresponding ionization effect during the Halloween GLEs occurred on October-November 2003, assuming explicitly precisely the derived SEP spectra, their evolution throughout the events, and the corresponding magnetospheric conditions and variable GCRs ﬂux. The computed ion production rates were signiﬁcant during the main phase of the events, speciﬁcally at the polar region with rigidity cut-off Rc ≤ 1 GV. At regions with Rc ≈ 2, the ion production was comparable to the average due
10

to GCR, because of the rapidly falling SEP spectra. At mid-latitudes with rigidity cut-off Rc of about 3 GV or greater, the ion production due to GCR dominated in the whole atmosphere during all the events. The event averaged ionization effects were maximal at altitudes of about 15–18 km a.s.l..
The presented here computation of ionization effect during the sequence of three Halloween events give good basis to study the possible effect of precipitating high-energy particles in the Earth’s atmosphere on a minor constituents, atmospheric physics and chemistry as well as studies related to space weather and solar-terrestrial physics (Miroshnichenko, 2003; Mishev and Velinov, 2015b; Miroshnichenko, 2018).
Acknowledgements
This work was supported by the Academy of Finland (project 330063 QUASARE, 321882 ESPERA and 304435 CRIPA-X). The work beneﬁted from discussions in the framework of the International Space Science Institute International Team 441: High EneRgy sOlar partICle Events Analysis (HEROIC). The NM records used in this study were retrieved from International GLE database http://gle.oulu.fi and neutron monitor database www.NMDB.eu. The authors acknowledge the anonymous reviewers for their useful comments and suggestions that helped us to improve this paper.
11

A Time and altitude evolution of ion production rate during the Halloween GLEs

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

11:30 UT

[ion pairs cm -3 s-1]
300 280 260 240 220 200 180 160 140 120 100 80.0 60.0 40.0 20.0

60

120

180

240

300

360

Longitude [deg]

13:00 UT

[ion

pairs

-3 cm

s-1]

300

280

260

240

220

200

180

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

12:30 UT

[ion

pairs

-3 cm

s-1]

300

280

260

240

220

200

180

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

14:00 UT

[ion

pairs

-3 cm

s-1]

300

280

260

240

220

200

180

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Figure A.1: Ion production rate at altitude of 15 km a.s.l. at selected stages of the event during GLE # 65 on 28 October 2003.

12

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

22:00 UT

[ion

pairs

-3 cm

s-1]

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

23:30 UT

[ion

pairs

-3 cm

s-1]

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

23:00 UT

[ion

pairs

-3 cm

s-1]

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

24:00 UT

[ion

pairs

-3 cm

s-1]

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Figure A.2: Ion production rate at altitude of 15 km a.s.l. at selected stages of the event during GLE # 66 on 29 October 2003.

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

17:30 UT

[ion

pairs

-3 cm

s-1]

200

180

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

18:30 UT

[ion pairs cm -3 s-1]
200 180 160 140 120 100 80.0 60.0 40.0 20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Latitude [deg]

90 60 30
0 -30 -60 -90
0
90 60 30
0 -30 -60 -90
0

18:00 UT

[ion

pairs

-3 cm

s-1]

200

180

160

140

120

100

80.0

60.0

40.0

20.0

60

120

180

240

300

360

Longitude [deg]

19:00 UT

[ion pairs cm -3 s-1]
200 180 160 140 120 100 80.0 60.0 40.0 20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Figure A.3: Ion production rate at altitude of 15 km a.s.l. at selected stages of the event during GLE # 67 on 2 November 2003.

13

Latitude [deg]

90 60 30
0 -30 -60 -90
0

60

5 km a.s.l.

120

180

240

Longitude [deg]

300

[%]
390 370 350 330 310 290 270 250 230 210 190 170 150 130 110 90.0 70.0 50.0 30.0 10.0
360

90 60 30
0 -30 -60 -90
0

60

15 km a.s.l.

120

180

240

Longitude [deg]

300

[%] 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80.0 60.0 40.0 20.0
360

Latitude [deg]

Latitude [deg]

90 60 30
0 -30 -60 -90
0

60

10 km a.s.l.

120

180

240

Longitude [deg]

300

[%]
390 370 350 330 310 290 270 250 230 210 190 170 150 130 110 90.0 70.0 50.0 30.0 10.0
360

90 60 30
0 -30 -60 -90
0

20 km a.s.l.

[%]
400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80.0 60.0 40.0 20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Figure A.4: Event integrated ionization effect as a function of altitude during GLE # 65 on 28 October 2003.

Figure A.5: Event integrated ionization effect as a function of altitude during GLE # 66 on 29 October 2003.
14

Latitude [deg]

90 60 30
0 -30 -60 -90
0

60

5 km a.s.l.

120

180

240

Longitude [deg]

300

[%]
390 370 350 330 310 290 270 250 230 210 190 170 150 130 110 90.0 70.0 50.0 30.0 10.0
360

90 60 30
0 -30 -60 -90
0

60

15 km a.s.l.

120

180

240

Longitude [deg]

300

[%] 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80.0 60.0 40.0 20.0
360

Latitude [deg]

Latitude [deg]

90 60 30
0 -30 -60 -90
0

60

10 km a.s.l.

120

180

240

Longitude [deg]

300

[%]
390 370 350 330 310 290 270 250 230 210 190 170 150 130 110 90.0 70.0 50.0 30.0 10.0
360

90 60 30
0 -30 -60 -90
0

20 km a.s.l.

[%]
400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80.0 60.0 40.0 20.0

60

120

180

240

300

360

Longitude [deg]

Latitude [deg]

Figure A.6: Event integrated ionization effect as a function of altitude during GLE # 67 on 2 November 2003.

References

Banjac, S., Herbst, K., Heber, B., 2019. The atmospheric radiation interaction simulator (ATRIS): Description and validation. Journal of Geophysical Research: Space Physics 124, 50–67. doi:10.1029/2018JA026042.
Bazilevskaya, G.A., Usoskin, I.G., Flu¨ckiger, E., Harrison, R., Desorgher, L., Bu¨tikofer, B., Krainev, M., Makhmutov, V., Stozhkov, Y., Svirzhevskaya, A., Svirzhevsky, N., Kovaltsov, G., 2008. Cosmic ray induced ion production in the atmosphere. Space Science Reviews 137, 149–173.
Beatty, J., Matthews, J., Wakely, S., 2018. Cosmic rays, in: M. Tanabashi et al., Review of Particle Physics. Physical Review D 98, 030001, pp. 424–432.
Belov, A., 2009. Forbush effects and their connection with solar, interplanetary and geomagnetic phenomena. Proceedings of the International Astronomical Union 4, 439–450. doi:10.1017/S1743921309029676.
Belov, A., Baisultanova, L., Eroshenko, E., Mavromichalaki, H., Yanke, V., Pchelkin, V., Plainaki, C., Mariatos, G., 2005. Magnetospheric effects in cosmic rays during the unique magnetic storm on november 2003. Journal of Geophysical Research: Space Physics 110, A09S20. doi:10.1029/2005JA011067.
Burger, R., Potgieter, M., Heber, B., 2000. Rigidity dependence of cosmic ray proton latitudinal gradients measured by the Ulysses spacecraft: Implication for the diffusion tensor. Journal of Geophysical Research 105, 27447–27445.
Bu¨tikofer, R., Flu¨ckiger, E., 2015. What are the causes for the spread of GLE pa-

15

rameters deduced from nm data?

Journal of Physics: Conference Series 632.

doi:10.1088/1742-6596/632/1/012053.

Desorgher, L., Flu¨ckiger, E., Gurtner, M., Moser, M., Bu¨tikofer, R., 2005. A GEANT 4 code for computing the interaction of cosmic rays with the earth’s atmosphere. International Journal of Modern Physics A 20, 6802–6804.

Dorman, L., 2004. Cosmic Rays in the Earth’s Atmosphere and Underground. Kluwer Academic Publishers, Dordrecht.

Forbush, S., 1937. On the effects in cosmic-ray intensity observed during the recent magnetic storm. Physical Review 51, 1108–1109.

Forbush, S., 1958. Cosmic-ray intensity variations during two solar cycles. Journal of Geophysical Research 63, 651–669.

Funke, B., Baumgaertner, A., Calisto, M., Egorova, T., Jackman, C., Kieser, J., Krivolutsky, A., Lo´pez-Puertas, M., Marsh, D., Reddmann, T., Rozanov, E., Salmi S.-M., Sinnhuber, M., Stiller, G., Verronen, P., Versick, S., Von Clarmann, T., Vyushkova, T., Wieters, N., Wissing, J., 2011. Composition changes after the ”Halloween” solar proton event: The high energy particle precipitation in the atmosphere (HEPPA) model versus MIPAS data intercomparison study. Atmospheric Chemistry and Physics 11, 9089–9139. doi:10.5194/acp-11-9089-2011.

Gleeson, L., Axford, W., 1968. Solar modulation of galactic cosmic rays. Astrophysical Journal 154, 1011–1026.

Gopalswamy, N., Barbieri, L., Cliver, E., Lu, G., Plunkett, S., Skoug, R., 2005. Introduction to violent sun-earth connection events of October-November 2003. Journal of Geophysical Research: Space Physics 110, A09S00. doi:10.1029/2005JA011268.

Gopalswamy, N., Xie, H., Yashiro, S., Akiyama, S., Ma¨kela¨, P., Usoskin, I., 2012. Properties of ground level enhancement events and the associated solar eruptions during solar cycle 23. Space Science Reviews 171, 23–60.

Grieder, P., 2011. Extensive Air Showers: High Energy Phenomena and Astrophysical Aspects A Tutorial, Reference Manual and Data Book. Springer, Space Science Library (Book 1009).

Jackman, C., Fleming, E., Vitt, F., 2000. Inﬂuence of extremely large solar proton events in a changing stratosphere. Journal of Geophysical Research Atmospheres 105, 11659–11670.

Jackman, C., Marsh, D., Vitt, F., Garcia, R., Fleming, E., Labow, G., Randall, C., Lo´pez-Puertas M., Funke, B., Von Clarmann, T., Stiller, G., 2008. Short- and medium-term atmospheric constituent effects of very large solar proton events. Atmospheric Chemistry and Physics 8, 765–785.

Jackman, C., Marsh, D., Vitt, F., Roble, R., Randall, C., Bernath, P., Funke, B., Lo´pez-Puertas, M., Versick, S., Stiller, G., Tylka, A., Fleming, E., 2011. Northern hemisphere atmospheric inﬂuence of the solar proton events and ground level enhancement in January 2005. Atmospheric Chemistry and Physics 11, 6153–6166.

16

Kocharov, L., Pohjolainen, S., Mishev, A., Reiner, M., Lee, J., Laitinen, T., Didkovsky, L., Pizzo, V., Kim, R., Klassen, A., Karlicky, M., Cho, K.S., Gary, D., Usoskin, I., Valtonen, E., Vainio, R., 2017. Investigating the origins of two extreme solar particle events: Proton source proﬁle and associated electromagnetic emissions. Astrophysical Journal 839, 79.
Koldobskiy, S., Kovaltsov, G.A., Mishev, A., Usoskin, I.G., 2019. New Method of Assessment of the Integral Fluence of Solar Energetic (>1 GV Rigidity) Particles from Neutron Monitor Data. Solar Physics 294, 94. doi:10.1007/s11207-019-1485-8.
Krivolutsky, A., Klyuchnikova, A., Zakharov, G., Vyushkova, T., Kuminov, A., 2006. Dynamical response of the middle atmosphere to solar proton event of July 2000: Three-dimensional model simulations. Advances in Space Research 37, 1602–1613. doi:10.1016/j.asr.2005.05.115.
Krivolutsky, A., Kuminov, A., Vyushkova, T., 2005. Ionization of the atmosphere caused by solar protons and its inﬂuence on ozonosphere of the earth during 1994-2003. Journal of Atmospheric and Solar-Terrestrial Physics 67, 105–117.
Kudela, K., Bucˇik, R., Bobik, P., 2008. On transmissivity of low energy cosmic rays in disturbed magnetosphere. Advances in Space Research 42, 1300–1306.
Kudela, K., Usoskin, I., 2004. On magnetospheric transmissivity of cosmic rays. Czechoslovak Journal of Physics 54, 239–254.
Liu, Y., Hayashi, K., 2006. The 2003 October-November fast halo coronal mass ejections and the large-scale magnetic ﬁeld structures. Astrophysical Journal 640, 1135–1141. doi:10.1086/500290.
Mavromichalaki, H., Papaioannou, A., Plainaki, C., Sarlanis, C., Souvatzoglou, G., Gerontidou, M., Papailiou, M., Eroshenko, E., Belov, A., Yanke, V., Flu¨ckiger, E., Bu¨tikofer, R., Parisi, M., Storini, M., Klein, K.L., Fuller, N., Steigies, C., Rother, O., Heber, B., WimmerSchweingruber, R., Kudela, K., Strharsky, I., Langer, R., Usoskin, I., Ibragimov, A., Chilingaryan, A., Hovsepyan, G., Reymers, A., Yeghikyan, A., Kryakunova, O., Dryn, E., Nikolayevskiy, N., Dorman, L., Pustil’Nik, L., 2011. Applications and usage of the real-time neutron monitor database. Advances in Space Research 47, 2210–2222.
Mironova, I., Aplin, K., Arnold, F., Bazilevskaya, G., Harrison, R., Krivolutsky, A., Nicoll, K., Rozanov, E., Turunen, E., Usoskin, I., 2015. Energetic particle inﬂuence on the earth’s atmosphere. Space Science Reviews , 96.
Mironova, I., Usoskin, I., 2014. Possible effect of strong solar energetic particle events on polar stratospheric aerosol: A summary of observational results. Environmental Research Letters 9, 015002.
Miroshnichenko, L., 2003. Radiation Hazards in Space, Astrophysics and Space Science Library 297. Springer, Dordrecht.
Miroshnichenko, L., 2018. Retrospective analysis of GLEs and estimates of radiation risks. Journal of Space Weather and Space Climate 8, A52. doi:10.1051/swsc/2018042.
17

Miroshnichenko, L., Klein, K.L., Trottet, G., Lantos, P., Vashenyuk, E., Balabin, Y., Gvozdevsky, B., 2005. Relativistic nucleon and electron production in the 2003 October 28 solar event. Journal of Geophysical Research: Space Physics 110, A09S08. doi:10.1029/2004JA010936.
Mishev, A., Usoskin, I., 2016. Analysis of the ground level enhancements on 14 July 2000 and on 13 December 2006 using neutron monitor data. Solar Physics 291, 1225–1239.
Mishev, A., Usoskin, I., Raukunen, O., Paassilta, M., Valtonen, E., Kocharov, L., Vainio, R., 2018. First analysis of GLE 72 event on 10 september 2017: Spectral and anisotropy characteristics. Solar Physics 293, 136.
Mishev, A., Velinov, P., 2007. Atmosphere ionization due to cosmic ray protons estimated with CORSIKA code simulations. Comptes Rendus de L’Academie Bulgare des Sciences 60, 225– 230.
Mishev, A., Velinov, P., 2010. The effect of model assumptions on computations of cosmic ray induced ionization in the atmosphere. Journal of Atmospheric and Solar-Terrestrial Physics 72, 476–481.
Mishev, A., Velinov, P., 2011. Normalized ionization yield function for various nuclei obtained with full Monte Carlo simulations. Advances in Space Research 48, 19–24.
Mishev, A., Velinov, P., 2014. Inﬂuence of hadron and atmospheric models on computation of cosmic ray ionization in the atmosphere-extension to heavy nuclei. Journal of Atmospheric and Solar-Terrestrial Physics 120, 111–120.
Mishev, A., Velinov, P., 2015a. Determination of medium time scale ionization effects at various altitudes in the stratosphere and troposphere during ground level enhancement due to solar cosmic rays on 13.12.2006 (GLE 70). Comptes Rendus de L’Academie Bulgare des Sciences 68, 1425–1430.
Mishev, A., Velinov, P., 2015b. Ionzation rate proﬁles due to solar and galactic cosmic rays during GLE 59 on Bastille day 14 July 2000. Comptes Rendus de L’Academie Bulgare des Sciences 68, 359–366.
Mishev, A., Velinov, P., 2015c. Time evolution of ionization effect due to cosmic rays in terrestrial atmosphere during GLE 70. Journal of Atmospheric and Solar-Terrestrial Physics 129, 78–86.
Mishev, A., Velinov, P., 2018a. Ion production and ionization effect in the atmosphere during the Bastille day GLE 59 due to high energy SEPs. Advances in Space Research 61, 316–325. doi:10.1016/j.asr.2017.10.023.
Mishev, A., Velinov, P., 2018b. Ionization effects in the middle stratosphere due to cosmic rays during strong GLE events. Comptes Rendus de L’Academie Bulgare des Sciences 71, 523–528.
Mishev, A., Velinov, P., 2020. Ionization effect in the region of regener–pfotzer maximum due to cosmic rays during halloween gle events in october–november 2003. Comptes Rendus de L’Academie Bulgare des Sciences 73, 244–251.
18

Mishev, A., Velinov, P., Mateev, L., Tassev, Y., 2011. Ionization effect of solar protons in the earth atmosphere - case study of the 20 January 2005 SEP event. Advances in Space Research 48, 1232–1237.
Mitthumsiri, W., Seripienlert, A., Tortermpun, U., Mangeard, P.S., Sa´iz, A., Ruffolo, D., Macatangay, R., 2017. Modeling polar region atmospheric ionization induced by the giant solar storm on 20 January 2005. Journal of Geophysical Research: Space Physics 122, 7946– 7955. doi:10.1002/2017JA024125.
Moraal, H., McCracken, K., 2012. The time structure of ground level enhancements in solar cycle 23. Space Science Reviews 171, 85–95.
Nevalainen, J., Usoskin, I., Mishev, A., 2013. Eccentric dipole approximation of the geomagnetic ﬁeld: Application to cosmic ray computations. Advances in Space Research 52, 22–29.
Nicoll, K., Harrison, R., 2014. Detection of lower tropospheric responses to solar energetic particles at mid-latitudes. Physical Review Letters 112, 225001.
O’Brien, K., 1970. Calculated cosmic ray ionization in the lower atmosphere. Journal of Geophysical Research 75, 4357–4359.
Paschalis, P., Mavromichalaki, H., Dorman, L., Plainaki, C., Tsirigkas, D., 2014. GEANT 4 software application for the simulation of cosmic ray showers in the earth’s atmosphere. New Astronomy 33, 26–37. doi:10.1016/j.newast.2014.04.009.
Picone, J., Hedin, A., Drob, D., Aikin, A., 2002. NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientiﬁc issues. Journal of Geophysical Research: Space Physics 107, 1468.
Poluianov, S., Usoskin, I., Mishev, A., Shea, M., Smart, D., 2017. GLE and sub-GLE redeﬁnition in the light of high-altitude polar neutron monitors. Solar Physics 292, 176. doi:10.1007/s11207-017-1202-4.
Porter, H., Jackman, C., Green, A., 1976. Efﬁciencies for production of atomic nitrogen and oxygen by relativistic proton impact in air. The Journal of Chemical Physics 65, 154–167.
Potgieter, M., 2013. Solar modulation of cosmic rays. Living Reviews in Solar Physics 10.
Randall, C., Harvey, V., Singleton, C., Bailey, S., Bernath, P., Codrescu, M., Nakajima, H., Russell, J., 2007. Energetic particle precipitation effects on the southern hemisphere stratosphere in 1992-2005. Journal of Geophysical Research Atmospheres 112, D08308.
Regener, E., Pfotzer, G., 1935. Vertical intensity of cosmic rays by threefold coincidences in the stratosphere. Nature 136, 718–719.
Rozanov, E., Calisto, M., Egorova, T., Peter, T., Schmutz, W., 2012. Inﬂuence of the precipitating energetic particles on atmospheric chemistry and climate. Surveys in Geophysics 33, 483–501.
19

Sinnhuber, M., Berger, U., Funke, B., Nieder, H., Reddmann, T., Stiller, G., Versick, S., Von Clarmann, T., Wissing, J., 2018. Noy production, ozone loss and changes in net radiative heating due to energetic particle precipitation in 2002-2010. Atmospheric Chemistry and Physics 18, 1115–1147. doi:10.5194/acp-18-1115-2018.
The´bault, E., Finlay, C.C., Beggan, C.D., Alken, P., Aubert, J., Barrois, O., Bertrand, F., Bondar, T., Boness, A., Brocco, L., Canet, E., Chambodut, A., Chulliat, A., Co¨ısson, P., Civet, F., Du, A., Fournier, A., Fratter, I., Gillet, N., Hamilton, B., Hamoudi, M., Hulot, G., Jager, T., Korte, M., Kuang, W., Lalanne, X., Langlais, B., Le´ger, J.M., Lesur, V., Lowes, F.J., Macmillan, S., Mandea, M., Manoj, C., Maus, S., Olsen, N., Petrov, V., Ridley, V., Rother, M., Sabaka, T.J., Saturnino, D., Schachtschneider, R., Sirol, O., Tangborn, A., Thomson, A., Tøffner-Clausen, L., Vigneron, P., Wardinski, I., Zvereva, T., 2015. International geomagnetic reference ﬁeld: the 12th generation. Earth, Planets and Space 67, 79. doi:10.1186/s40623-015-0228-9.
Tsyganenko, N., 1989. A magnetospheric magnetic ﬁeld model with a warped tail current sheet. Planetary and Space Science 37, 5–20.
Tsyganenko, N., 1995. Modeling the earth’s magnetospheric magnetic ﬁeld conﬁned within a realistic magnetopause. Journal of Geophysical Research:Space Physics 100, 5599–5612. doi:110.1029/94JA03193.
Tsyganenko, N., 2002. A model of the near magnetosphere with a dawn-dusk asymmetry. Journal of Geophysical Research: Space Physics 107. doi:10.1029/2001JA000219.
Usoskin, I., Bazilevskaya, G., Kovaltsov, G., 2011a. Solar modulation parameter for cosmic rays since 1936 reconstructed from ground-based neutron monitors and ionization chambers. Journal of Geophysical Research 116, A02104.
Usoskin, I., Gil, A., Kovaltsov, G., Mishev, A., Mikhailov, V., 2017. Heliospheric modulation of cosmic rays during the neutron monitor era: Calibration usingpamela data for 2006-2010. Journal of Geophysical Research 122, 3875–3887.
Usoskin, I., Kovaltsov, G., 2006. Cosmic ray induced ionization in the atmosphere: Full modeling and practical applications. Journal of Geophysical Research 111.
Usoskin, I., Kovaltsov, G., Mironova, I., Tylka, A., Dietrich, W., 2011b. Ionization effect of solar particle gle events in low and middle atmosphere. Atmospheric Chemistry and Physics 11, 1979–1988.
Vainio, R., Desorgher, L., Heynderickx, D., Storini, M., Flu¨ckiger, E., Horne, R., Kovaltsov, G., Kudela, K., Laurenza, M., McKenna-Lawlor, S., Rothkaehl, H., Usoskin, I., 2009. Dynamics of the earth’s particle radiation environment. Space Science Reviews 147, 187–231.
Velinov, P., Asenovski, S., Kudela, K., Lastovicˇka, J., Mateev, L., Mishev, A., Tonev, P., 2013. Impact of cosmic rays and solar energetic particles on the earth’s ionosphere and atmosphere. Journal of Space Weather and Space Climate 3, A14.
Velinov, P., Mishev, A., Mateev, L., 2009. Model for induced ionization by galactic cosmic rays in the earth atmosphere and ionosphere. Advances in Space Research 44, 1002–1007.
20

Verronen, P., Andersson, M., Kero, A., Enell, C.F., Wissing, J., Talaat, E., Kauristie, K., Palmroth, M., Sarris, T., Armandillo, E., 2015. Contribution of proton and electron precipitation to the observed electron concentration in October-November 2003 and September 2005. Annales Geophysicae 33, 381–394.
Vitt, F., Jackman, C., 1996. A comparison of sources of odd nitrogen production from 1974 through 1993 in the earth’s middle atmosphere as calculated using a two-dimensional model. Journal of Geophysical Research Atmospheres 101, 6729–6739.
21