Cosmogenic Isotopes as Proxies for Solar Energetic Particles

The first documented observation of a solar storm was the sighting in 1859 CE by Richard C. Carrington of "two patches of intensely bright and white light" emanating from a large group of sunspots that he was studying (see Section 6.3.2 and Figure 6.7). It is believed that no event of a similar magnitude has hit Earth since then, although our planet was nearly hit by an extreme coronal mass ejection (CME) in 2012 July believed to rival the magnitude of the Carrington event (Section 2.2, Baker et al. 2013). The 2012 July event took place on the side opposite from Earth and was detected by the STEREO-A spacecraft, which monitors and observes solar flares and CMEs from different vantage points. Such systematic monitoring of the Sun using spacecraft only dates back to a few decades. Before the advent of satellites, we had to rely on the data from ground-based neutron monitors, which can detect ground-level enhancements (GLEs) as a very energetic class of SEP events (see Section 2.2). These measurements has allowed us to gain insights into SEP events since about the 1950s. Prior to the 1950s, magnetometers recorded changes in the external geomagnetic field. There, disturbances in the magnetic field would be indicative of a geomagnetic storm caused by CMEs or fast solar-wind streams. Unlike GLEs and spacecraft measurements though, these observations are not directly related to SEP events. Moreover, these different types of events are not directly related to each other as caused by different processes. Therefore, we have a reliable and continuous record of the occurrence of SEP events for only about 70 years. Such a limited perspective on these events is not enough to constrain the occurrence rate as well as the upper limit of the strength of SEP events.

We can take very strong volcanic eruptions here as an analogy. The largest volcanic eruption in the past 70 years was the Pinatubo eruption in 1991, with a volcanic explosivity index of 6. However, owing to the study of geological archives, we know that more explosive eruptions have occurred in the past, the so-called "supervolcanoes," and could occur again. As a result, we can ask ourselves whether the possibility of extreme and rare solar events exists for which we would miss data. To answer this question, we can fortunately rely on different means.

The best-suited method thus far has been the use of cosmogenic radionuclides (e.g., ¹⁰Be, ¹⁴C, and ³⁶Cl) in ice cores and tree rings that give us the opportunity to investigate and extend our temporal perspective on solar activity as a whole (e.g., Bard et al. 2000; Beer et al. 1990; Muscheler et al. 2016). Studying solar activity in the past, including SEP events, is immensely valuable to our ever-modernizing society because it helps us better identify the risk that they represent to us in order to be better prepared.

The hypothesis that SEPs may produce radionuclides in the atmosphere was first put forward by Simpson (1960), some 60 years ago. This was shortly followed by a prediction by Lal & Peters (1962) that the SEP event of 1956 February 23 could have induced a significant increase in ¹⁰Be atmospheric production. This prediction was later revisited (e.g., Masarik & Beer 1999; Usoskin et al. 2006; Webber et al. 2007) with the improvement of radionuclide cross sections and in computer power, allowing us to simulate the nuclear cascade that is triggered when (solar) cosmic rays penetrate the atmosphere. In fact, Webber et al. (2007) calculated the amount of additional ¹⁰Be and ³⁶Cl nuclides that major SEP events from a period ranging between 1956 and 2005 would have produced both for the polar regions and globally. Based on their estimates, a strong SEP event with a hard spectrum, such as that on 1956 February 23, would cause an increase in the global annual atmospheric ¹⁰Be production rate of about 12% (cf. Usoskin et al. 2006). This is based on the yield-function approach detailed in Section 4.2 and with the assumption that complete atmospheric mixing occurs before deposition of ¹⁰Be. This assumption is acceptable for quick estimates given that production of ¹⁰Be by SEPs occurs mostly in the stratosphere (Poluianov et al. 2016), which ensures a nearly global mixing of the production enhancement signal due to its longer residence time in comparison to the troposphere (Heikkilä et al. 2009). On the other hand, full modeling of the isotope's transport is required for a detailed analysis of SEP events (e.g., Sukhodolov et al. 2017).

Unfortunately, testing of nuclear weapons performed in the 1950–1960s caused an enormous injection of ¹⁴C, ³⁶Cl, and ³H into the atmosphere, resulting in a very large "bomb peak." This rendered isotopes following these decades unsuitable proxies for SEP events. However, the first high-resolution and continuous ¹⁰Be measurements from Greenland were obtained in the 1980–1990s from the Dye-3 ice core (South-East Greenland; Beer et al. 1990) and the NGRIP ice core in the early 2000s (North-central Greenland; Berggren et al. 2009). Both records offer annual resolution and provide insights into short-term variations of the cosmic-ray influx, mainly of galactic origin but potentially also of solar origin. They show a significant influence of solar modulation variations, for instance through the 11 year solar cycle. Yet, no obvious rapid increase due to known SEP events has been reported in either Greenland ice cores, including around the event of 1956 February 23 (which still holds the record for the largest GLE in neutron monitor records) and around the Carrington event of 1859 CE. The lack of SEP-induced peaks in modern times is illustrated in Figure 4.1, which shows the ¹⁰Be concentration from both the Dye-3 and the NGRIP ice cores for the period 1950–1995 CE and where the five largest GLEs from this period are indicated. It can be seen that no significant rapid increase follows any of these five major events for either ice cores.

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Meanwhile, another method for detecting past SPEs from ice cores was proposed, suggesting that spikes in nitrate (${\mathrm{NO}}_{3}^{-}$) content, measured in polar ice cotes, can be linked to the occurrence of SEP events. However, as discussed in Section 6.1, it has been proven that the nitrate method is not applicable for detecting SEP events from the past.

With cosmogenic radionuclides as the only potential markers of past SEP events, further attention has been given to ice-core and tree-ring records. For instance, Usoskin & Kovaltsov (2012) reinvestigated a number of ${{\rm{\Delta }}}^{14}{\rm{C}}$ records from tree rings, in addition to several ¹⁰Be concentration data from ice cores (including the aforementioned Dye-3 and NGRIP records) with the aim of finding coinciding peaks that can be connected to past SEP events. Despite the framework of several records that are highly resolved with periods ranging from centuries to the whole of the Holocene (circa 11,600 yr), no candidates could clearly be put forward, with the exception of the 774/775 CE (called 780 CE in Usoskin & Kovaltsov 2012) event. This highlights how challenging detecting past events within environmental archives is and how crucial obtaining high-quality and high-resolution data is. Nevertheless, authors could establish an observational upper limit on the strength of SPEs on the order of ${F}_{30}\gt 5\times {10}^{10}\,\mathrm{protons}/{\mathrm{cm}}^{2}$ for the Holocene epoch. Another approach to establish an empirical link between increased radionuclide production and SEPs is to target known events from the recent past. This was done by Pedro et al. (2009), who measured ¹⁰Be concentrations at monthly resolution in samples from a snow pit from Law Dome Summit in Antarctica following the SEP events of 2003 October 29 and 2005 January 20 for which Webber et al. (2007) offered model calculations of the expected annual ¹⁰Be atmospheric production. For the larger of the two events (2005 January 20), the authors argued that it may have caused a sharp peak in ¹⁰Be concentration that they observe as being dated a month following the event, although they also showed evidence that short-term variation in ¹⁰Be concentration is highly impacted by meteorological influences, which highlights another challenge in the study of past SPEs from ice cores. In addition, it was later reported by the same group of authors (Simon et al. 2013) that the samples used for this study were contaminated with too much boron-10 (¹⁰B), which is an isobar of ¹⁰Be and can thus lead to biased measurements.

In summary, we know that SEPs can effectively increase the atmospheric production of radionuclides, owing to pioneering work in the 1960s by Simpson (1960) and Lal & Peters (1962). However, obtaining conclusive empirical evidence from environmental archives has proven to be particularly challenging, due in part to the noise inherent to these data and to the small expected signal. In fact, no SEPs from the space era have robustly been identified in ice-core ¹⁰Be. This emphasizes that it would take a particularly remarkable event to leave its imprint in the concentration of ¹⁰Be in ice cores and in ${{\rm{\Delta }}}^{14}{\rm{C}}$ data from tree rings. This was eventually shown recently following the discovery of the 774/775 CE event (Miyake et al. 2012), which serves as the cornerstone of this book.

Upon the publication of the discovery of the 774/775 CE event in ${{\rm{\Delta }}}^{14}{\rm{C}}$ data from Japanese cedar trees (Miyake et al. 2012), a variety of studies have attempted to pinpoint its cause. This led to a vast number of measurements in both tree rings (Büntgen et al. 2018; Güttler et al. 2015; Jull et al. 2014; Usoskin et al. 2013) and ice cores (Mekhaldi et al. 2015; Miyake et al. 2015; Sigl et al. 2015), which gives us the opportunity to study this particular event in detail. The additional information that ice-core ¹⁰Be and ³⁶Cl data provided ruled out all other suggested sources and thereby confirmed a solar cause for the 774/775 CE event (Mekhaldi et al. 2015). More specifically, according to the model by Webber et al. (2007), extreme SEP events are expected to leave their footprints in the production rate of cosmogenic radionuclides (see Section 6.2).

As mentioned above, the strongest SEP event of the space era is considered to be that of 1956 February 23, which was characterized by a particularly hard energy spectrum and led to the largest GLE peak recorded in neutron monitors (Meyer et al. 1956). Its F₃₀ was $(1.5\pm 0.3)\times {10}^{9}\,\mathrm{protons}/{\mathrm{cm}}^{2}$ (Webber et al. 2007; Raukunen et al. 2018), although this figure is somewhat uncertain as it is based on measurements that do not meet today's standards of accuracy. In any case, this F₃₀ value was considered as the upper limit for the strength of SEP events with a hard spectrum (although soft-spectrum events can reach ${F}_{30}\approx 7\times {10}^{9}\,\mathrm{protons}/{\mathrm{cm}}^{2}$, as for the event of 1972 August 4) until the discovery of the 774/775 CE event. As for the Carrington event of 1859 CE (considered as the "worst-case" scenario thus far), it is still unknown whether the solar flare that Carrington witnessed was accompanied by an SEP event at Earth. Anyway, it is considered to be characterized by a soft spectrum, and an estimate of its potential F₃₀ reaches as high as 10¹⁰ protons/cm² (Cliver & Dietrich 2013). We note that some earlier estimates were based on the unreliable ice-core nitrate method (see above), which we do not consider here. Studying environmental archives and in particular the 774/775 CE event thus taught us that the Sun can be significantly more hostile than what we have witnessed since the advent of physical observations. Figure 4.1(B) shows the rapid and large increase in ¹⁰Be concentration from four different ice cores (NEEM, NGRIP, and TUNU from Greenland and WAIS from W. Antarctica; Sigl et al. 2015) that the 774/775 CE event caused.

Based on the amount of ¹⁰Be, but also ¹⁴C and ³⁶Cl nuclides produced by the event in 774/775 CE, it is estimated (see Section 6.2) that the associated SPE had an F₃₀ in the range of (2.4–2.8) $\times {10}^{10}\,\mathrm{protons}/{\mathrm{cm}}^{2}$ (Mekhaldi et al. 2015). This means that the 774/775 CE event was about a factor of 3 stronger than the largest SEP event of the space era and at least twice stronger than the very uncertain Carrington event. Pushing the upper limit of the strength of SPEs has obvious implications for our spacecraft-dependent society as well as for air-travel safety (see Section 8.2), and better constraining the occurrence rate, and therefore risk, of such events has become paramount. As a result, increasing effort to provide high-quality resolution ${{\rm{\Delta }}}^{14}{\rm{C}}$ data from tree rings has allowed us to discover more event candidates, as detailed in Section 6.1. We can mention that two additional extreme SEP events have been confirmed for 993/994 CE (Mekhaldi et al. 2015; Miyake et al. 2013) as well as at ∼660 BCE (O'Hare et al. 2019; Park et al. 2017). Both of these events were also larger than that of the 1956 February 23 event and the Carrington event albeit somewhat weaker than the 774/775 CE event as evidenced by their imprint on the ¹⁰Be concentration from Greenland ice cores shown in Figures 4.1(C) and (D). There exist many ¹⁴C records and ice-core records of radionuclide concentration spanning the past 3000 yr, and it is therefore tempting to note an occurrence rate of one in a thousand (three events in the past 3000 years). However, we emphasize here that the statistics concerning past extreme events are still relatively poor and that further sustained efforts in providing high-quality radionuclide data are therefore needed.

In addition to solar physics, space engineering, and solar–terrestrial science, extreme SEP events from the past also have relevance in the field of paleoclimatology and more particularly in the field of geochronology. The peaks in annual radionuclide production that they cause are so distinct and outstanding that they can be utilized as robust time markers, like volcanic horizons which are found in ice cores from both hemispheres. In contrast to volcanic eruptions, however, SEP-induced peaks in radionuclide concentration can be systematically retrieved throughout the globe and at both poles. For instance, tree-ring chronologies are considered to be very robust for the Holocene epoch, in comparison to ice-core records. As a consequence, it is possible to ascertain ice-core chronologies by synchronizing ¹⁰Be peaks from ice cores to ¹⁴C peaks in tree rings. In doing so for the 774/775 CE event, Sigl et al. (2015) showed that the Greenland Ice Core Chronology (GICC05; Rasmussen et al. 2006) was offset by seven years, with the corresponding ¹⁰Be peaks measured from around 768 CE in the Greenland ice cores NGRIP, NEEM, and Tunu. Correcting for this offset, they were able to synchronize GICC05 to tree-ring chronologies and investigate with higher accuracy how volcanic eruptions (as marked by peaks in sulfate content in ice cores) have impacted the global temperature (as implied from the width of tree rings) in the past 2500 years.

In summary, cosmogenic radionuclides measured in tree rings and ice cores are a valuable tool for us to extend our temporal perspective on SEP events beyond the spacecraft and neutron monitor era as detailed in Table 4.1. Owing to such data, we are now aware that the Sun can be significantly more extreme than what we have assumed before, based on observations made since the onset of systematic monitoring of our star. During the past three millennia, Earth was hit at least three times by extreme SEP events (or a series of events) with fluence ${F}_{30}\gt {10}^{10}\,\mathrm{protons}/{\mathrm{cm}}^{2}$. In the following sections, we will review how cosmogenic radionuclides are produced in the atmosphere by solar and galactic cosmic rays, how they are subsequently transported within the climate system, and finally, how they are archived.

Table 4.1.  Summary of Different Methods to Detect the Occurrence of Solar Proton Events, at Present and in the Past

Method	Main Asset	Limits	New Insight	Time Range
Spacecrafts	Direct SEP measurements	Only for the last decades	—	Since 1970s
Neutron monitors	Indirect SEP measurements	Only for the last 70 years	—	Since 1950s
Low-latitude auroral sightings	– Strong geomagnetic storms– Potential event candidates	–   Qualitative –   Inhomogeneous –   Not directly related to SEP events	—	Last millennia, sporadic
Tree-ring ${{\rm{\Delta }}}^{14}{\rm{C}}$	–   Stable-quality data –   Annual resolution	–   Proxy data –   Damped signal –   Can detect only extreme events	Initial discovery of three extreme events	Holocene ∼10,000 years
Ice-core 10Be/36Cl	–   Stable-quality data –   Annual and higher resolution	–   Proxy data –   Noisy data –   Can detect only extreme events	Confirmation of the events and constraining the cause to SPEs	∼10,000 years

Note. The main advantages and limits as well as the applicable timescale of each method are listed.

The production rate of cosmogenic isotope Q(E, d) (typically expressed in atoms per second per gram of air) at the atmospheric depth d by a primary cosmic-ray particle with kinetic energy E can be calculated as

$$\begin{eqnarray}&&Q(E,d)=\sum _{k}{\int }_{0}^{E}{\eta }_{k}\cdot {N}_{k}(E,E^{\prime} ,d)\cdot {\mathit{\unicode[Book Antiqua]{x76}}}_{k}(E^{\prime} )\cdot {\rm{d}}E^{\prime} ,\end{eqnarray} \tag{ 4.1 }$$

where N_k and ${\mathit{\unicode[Book Antiqua]{x76}}}_{k}$ are the concentration (in [MeV cm³]⁻¹) and velocity (in cm s⁻¹) of secondary (or primary) particles of type k with energy $E^{\prime}$ at the atmospheric depth level d. The summation is over the type of particles k. For this kind of modeling, it is convenient to express the vertical location not in height h above sea level, but in atmospheric depth d, which is the thickness of the atmosphere (in g cm⁻²) above the given location. The atmospheric depth is proportional to the static barometric pressure. The standard sea level corresponds to 1033 g cm⁻².

The term η is a product of the cross sections ${\sigma }_{j,k}$ of the corresponding reactions of the production of the isotope by particles of type k on a target nucleus j and content ${\kappa }_{j}$ of the target nuclei in one gram of air:

$$\begin{eqnarray}&&{\eta }_{k}(E^{\prime} )=\sum _{j}{\kappa }_{j}\cdot {\sigma }_{j,k}(E^{\prime} ).\end{eqnarray} \tag{ 4.2 }$$

An example of the η function for the production of ¹⁰Be and ³⁶Cl by protons and neutrons in air is shown in Figure 4.2. The main target nuclei in air are nitrogen (${\kappa }_{{\rm{N}}}=3.22\times {10}^{22}\,{{\rm{g}}}^{-1}$), oxygen (${\kappa }_{{\rm{O}}}=8.67\times {10}^{21}\,{{\rm{g}}}^{-1}$), and argon (${\kappa }_{\mathrm{Ar}}=1.94\times {10}^{20}\,{{\rm{g}}}^{-1}$), and the corresponding reactions are p + O, p + N, p + Ar, n + O, n + N, and n + Ar. Production of the isotopes by secondary pions can be ignored because of the very short lifetimes of those particles. Muons can be ignored, too, because of the small cross sections.

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In earlier years, ${N}_{k}(E,E^{\prime} ,d)$ was typically calculated using analytical approximations or semiempirical approaches to model the nucleonic cascade in the atmosphere (see, e.g., Lal & Peters 1962; Lingenfelter 1963; O'Brien 1979). With the fast growth of computational power in recent decades, a more precise and physical Monte Carlo approach was developed to compute the cascade details. This method requires massive computations (it may take up to 10⁸ simulated incident particles per one energy point), but offers high precision and full physical understanding including all known effects. For that purpose, many sophisticated codes have been developed, which can be used to simulate the cosmic-ray-induced atmospheric cascade. The most widely used codes are CORSIKA (COsmic Ray SImulations for KAscade), which was designed specifically for the simulation of air showers from high-energy galactic cosmic rays (Heck et al. 1998); MCNP (Monte Carlo N-Particle Transport) with an emphasis on accurate simulation of neutron transport (Werner et al. 2017); general-purpose FLUKA (Ferrari et al. 2005; Böhlen et al. 2014) and GEANT4 (GEometry ANd Tracking, v. 4; Agostinelli et al. 2003; Allison et al. 2006); and some others.

During the last decades, several Monte Carlo models have been developed to compute the production of different cosmogenic isotopes. Masarik & Beer (1999, 2009) based their model on the GEANT+MCNP code; Webber & Higbie (2003) and Webber et al. (2007) used FLUKA; Usoskin & Kovaltsov (2008), Kovaltsov & Usoskin (2010), and Leppänen et al. (2012) used the CORSIKA and FLUKA codes; Kovaltsov et al. (2012) used the PLANETOCOSMICS tool (Desorgher et al. 2005) based on GEANT4; and Matthiä et al. (2013), Pavlov et al. (2017), and Poluianov et al. (2016) used GEANT4. The results of the different simulations may be slightly different because of different physical models of particle interactions (e.g., Kang et al. 2013; Pavlov et al. 2017). Here we show, as illustration, the results for the model (Poluianov et al. 2016), unless stated otherwise.

Beryllium isotopes are produced in the atmosphere as a result of the spallation of nitrogen and oxygen, with the energy threshold of several tens of megaelectronvolts. The lowest value of the threshold (12 MeV) is for the reaction ¹⁴N(n,αp)¹⁰Be, which has the maximum at the neutron energy around 20–30 MeV (see Figure 4.2).

Chlorine-36 is produced mostly as a product of spallation of the most abundant argon isotope ⁴⁰Ar, which is 99.6% of all atmospheric argon. The reaction ⁴⁰Ar(p,αn)³⁶Cl has a lower threshold ($\approx$9 MeV) and a maximum at 20–30 MeV. However, the much less abundant isotope ³⁶Ar can also significantly contribute to the production of ³⁶Cl because of the reaction ³⁶Ar(n,p)³⁶Cl, which has no threshold and a high cross section at low energies. Because of the low abundance of argon versus oxygen and nitrogen in the atmosphere, the production rate of ³⁶Cl is roughly an order of magnitude lower than that of ¹⁰Be.

Radiocarbon ¹⁴C is produced in another type of reaction. By far the most important channel of ¹⁴C production is the exothermic reaction ¹⁴N(n,p)¹⁴C, sometimes called neutron capture. The other channel, spallation reaction ¹⁶O(p,3p)¹⁴C, has a high energy threshold and low cross section; thus, its contribution to the total atmospheric production is negligible. The cross section of the main reaction inversely depends on the energy of neutrons, $\sigma \propto {E}^{-1/2}$ ($E\lt 0.1\,\mathrm{MeV}$), so that the lower the neutron's energy is, the more effectively it is captured by nitrogen. Because of that, energetic neutrons get thermalized in elastic scattering with nuclei of atmospheric gases before being captured. This process leads to the diffusion of neutrons in the atmosphere which should be taken into account in computations of the altitudinal profile of ¹⁴C production in the atmosphere. Because this process is relatively fast, the decay of neutrons and their leakage from the atmosphere can be typically ignored.

In earlier years, it was usual to compute the cosmogenic isotopes production using Equation (4.1) directly for a prescribed spectrum of primary cosmic rays (e.g., Masarik & Beer 1999). However, this ties the result to the fixed spectral shape and does not make it possible to model the isotope production for other spectral shapes, for example, for SEPs. For computations of the isotope production in the atmosphere, it is much more practical to use the so-called production function S(E, d) (in units of atoms g⁻¹ cm²), which gives the production of the cosmogenic isotope (number of atoms) at a given atmospheric level d per primary particle impinging on the top of the atmosphere with initial energy E (e.g., Webber et al. 2007; Poluianov et al. 2016). The production function is typically computed for the isotropic angular distribution of the primary particles on the top of the atmosphere, which is a valid assumption for GCR and less so for SEP sources. The full model of the function S for the production of ¹⁰Be, ¹⁴C, ³⁶Cl, and other cosmogenic isotopes by primary protons and α-particles (the latter effectively includes heavier species) was presented by Poluianov et al. (2016; see also the supporting information therein).

Examples of the altitude profile of the production function S(E, d) are shown in Figure 4.3. One can see that for low-energy incident particles (panel A), the profile of ¹⁰Be and ³⁶Cl is mostly defined by direct reactions of the primaries in the upper layers (small d) in the atmosphere, while the secondaries are less effective, which is observed as a second "step" in the distribution at depths $d\gt 10\,{\rm{g}}\,{\mathrm{cm}}^{-2}$. For higher energy primary particles (panel B), the atmospheric cascade (Figure 2.12) is fully developed, defining the profile of the production, which has a maximum at the depth of a few tens of g cm⁻² with an exponential decay to deeper layers. Although proton cross sections are greater than neutron ones (see the ³⁶Cl curves in Figure 4.2), production is mostly defined by secondary neutrons, as protons are quickly stopped in the atmosphere by Coulomb losses, having a smaller chance to initiate a reaction. Altitude profiles of ¹⁴C production are totally defined by the secondary neutron production and thermalization, and has a typical pattern with a maximum at ∼100 g cm⁻² depth (the so-called Pfotzer–Regener maximum of the greatest intensity of secondary nucleons of the atmospheric cascade).

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By integrating the production function over depth, one can obtain the columnar production (viz. integrated within the entire atmospheric column) of the cosmogenic isotope (e.g., Webber et al. 2007; Kovaltsov et al. 2012):

$$\begin{eqnarray}&&{S}_{{\rm{C}}}(E)={\int }_{0}^{D}S(E,d)\cdot {\rm{d}}d,\end{eqnarray} \tag{ 4.3 }$$

where D = 1033 g cm⁻² is the atmospheric depth at the mean sea level. The columnar production gives the total number of isotope atoms per primary particle in the entire atmosphere. Columnar productions of the isotopes ¹⁰Be, ¹⁴C and ³⁶Cl for primary protons are shown in Figure 4.4 (panel A) in comparison with the yield function (see below) of a standard sea-level neutron monitor.

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The production function is computed for one incident primary particle, but cosmic rays are usually quantified via the intensity in units of particles (cm² s sr)⁻¹. Therefore, instead of the production function S, the yield function Y is used, which is defined as the production (the number of atoms per gram of air) of the isotope, at the given atmospheric depth d by primary particles of type i with units of intensity. The units of Y are (atoms g⁻¹ cm² sr). For the isotropic angular distribution of primary cosmic rays near Earth, the yield function is related to the production function as $Y=\pi \cdot S$.

The production rate Q of cosmogenic isotope can be defined as an integral of the product of the yield function and the differential energy spectrum of cosmic rays ${J}_{i}(E)$ (in particles (cm² s sr)⁻¹) above the energy E_c corresponding to the local geomagnetic cutoff rigidity P_c:

$$\begin{eqnarray}&&Q(d,{P}_{{\rm{c}}})=\sum _{i}{\int }_{{E}_{{\rm{c}},{i}}}^{\infty }{Y}_{i}(E,d)\cdot {J}_{i}(E)\cdot {\rm{d}}E,\end{eqnarray} \tag{ 4.4 }$$

where the summation is over different types of primary cosmic-ray particles (protons, α-particles, etc.). The relation between ${E}_{{\rm{c}},{i}}$ and the local geomagnetic rigidity cutoff P_c (defined independently) is

$$\begin{eqnarray}&&{E}_{{\rm{c}},i}=\sqrt{{\left(\frac{{Z}_{i}}{{A}_{i}}{P}_{{\rm{c}}}\right)}^{2}+{E}_{{\rm{r}}}^{2}}-{E}_{{\rm{r}}},\end{eqnarray} \tag{ 4.5 }$$

where Z_i and A_i are the charge and mass numbers of particles of type i, respectively; E_r = 0.938 GeV is the rest mass of a proton.

While all types of primary cosmic-ray particles (protons and heavier nuclei) should be considered for GCR, because $Z\gt 1$ particles can contribute up to half of the production, only protons are usually taken for SEP events.

The global production rate Q_G of an isotope can be computed as the spatial average over the global columnar production rate, defined as

$$\begin{eqnarray}&&{Q}_{{\rm{G}}}=\frac{1}{4\pi }\,{\int }_{{\rm{\Omega }}}{\int }_{0}^{D}Q(d,{P}_{{\rm{c}}}({\rm{\Omega }}))\cdot {\rm{d}}d\cdot {\rm{d}}{\rm{\Omega }},\end{eqnarray} \tag{ 4.6 }$$

where Q is given by Equation (4.4), and integration is over the entire atmospheric column (as in the columnar production) and over Earth's surface (longitude and latitude) Ω.

Cosmogenic Isotope Production by SEPs

Figure 4.5 (panel A) depicts the distribution of the global production rate of ¹⁰Be over different latitudinal bands for a hard-spectrum SEP event and for moderately modulated GCR. Panel B of the same figure depicts the fraction of tropospheric production in 10° latitudinal bands to the total production in the same bands. One can see that ¹⁰Be is mostly produced by SEP at high latitudes (60°–80°), and the tropospheric production is small. On the other hand, GCR produce the isotope more evenly over the latitude, and a significant fraction is produced in the troposphere. This pattern is also typical for other isotopes.

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Table 4.2 collects the quantities of the global isotope production in the atmosphere for the event of 775 CE assuming hard (similar to that of the GLE on 1956 February 23) and soft (similar to that of the GLE on 1972 August 4) SEP spectra.

Figure 4.4(B) depicts the so-called "differential response function" for the cosmogenic isotope production, which is a product of the production function S_C(E) and the hard SEP energy spectrum J_p(E). Because isotope production by SEPs takes place mostly at high latitudes with no or low geomagnetic rigidity cutoff, this differential response function allows one to evaluate the most effective energy ranges for the production of different isotopes. One can see from the figure that ¹⁰Be and ¹⁴C have very close effective energy ranges for SEP events (a few hundred megaelectronvolts to about 1 GeV) owing to their similarly shaped columnar production functions (panel A). In contrast, ³⁶Cl is most effectively produced by SEPs with a significantly lower energy of tens of megaelectronvolts, owing to the low-energy production channel with the reaction ³⁶Ar(n,p)³⁶Cl. This feature makes it possible to estimate, using simultaneous measurements of different isotopes produced by an extreme SEP event, the SEP spectrum in the energy range between tens and hundreds of megaelectronvolts (see Section 6.2).

Table 4.2.  Cosmogenic Isotope Production (Following the Model of Poluianov et al. 2016) by an Extreme SEP Event (Corresponding to the Event of 775 CE for Hard and Soft Energy Spectra) and GCR (Solar Minimum and Maximum Conditions)

	SEP Event		GCR
	Hard	Soft	ϕ = 400 MV	ϕ = 1000 MV
Globally averaged production
14C†	$1.88\cdot {10}^{8}$	$1.88\cdot {10}^{8}$	$5.43\cdot {10}^{7}$	$3.82\cdot {10}^{7}$
Tropospheric fraction in the total global production
Rtrop(14C)	0.073	0.007	0.32	0.36
Rtrop(10Be)	0.049	0.003	0.30	0.34
Rtrop(36Cl)	0.033	0.0003	0.30	0.35
Total atmospheric production ratios
14C/10Be	46	45	55	56
14C/36Cl	340	62	631	645

Notes. The parameters are the globally averaged production (in cm⁻²) of ¹⁴C for the 775 CE event (Güttler et al. 2015) (left block) and the annual production by GCR (right block), the tropospheric fraction R_trop (with a realistic tropopause profile) in the total global production for the three isotopes, and the ratio of the total atmospheric production of two isotope pairs.

In Figure 4.6, we show the ratio of the modeled production of different cosmogenic isotopes as a function of the softness (quantified via the ratio of the integral fluences F₃₀/F₂₀₀—see Section 2.2 for definitions) of the SEP spectrum for all GLE events recorded after 1956 (Raukunen et al. 2018). One can see that the ratio for ¹⁴C/¹⁰Be is nearly independent of the spectral softness, varying within less than a factor of 2 over two orders of its magnitude. Accordingly, the ratio of these two isotopes does not provide direct information on the particle spectrum. On the other hand, the ratio of ³⁶Cl/¹⁰Be is tightly linked to the softness index, varying by nearly an order of magnitude between soft- and hard-spectrum events. This allows the SEP spectrum to be estimated directly from the measured isotope ratio (see Section 6.2).

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Cosmogenic isotopes in natural archives are often called "a natural neutron monitor" (e.g., Beer 2000). This is correct in the sense that cosmogenic isotopes are also an integral detector, with the columnar production of cosmogenic isotopes similar to the yield function of a polar neutron monitor (Figure 4.4(A)). However, they are not identical, because the effective energy ranges of the isotopes and NMs are different (see Figure 4.4(B)), particularly for SEP events. Cosmogenic isotopes, especially ³⁶Cl, are more sensitive to lower energies than a standard sea-level NM is. While the effective energy for SEP/GLE E_eff is $\approx 200\,\mathrm{MeV}$ for ¹⁴C and ¹⁰Be (Kovaltsov et al. 2012), it is much higher for a sea-level polar NM, being $\approx 800\,\mathrm{MeV}$ (Koldobskiy et al. 2018).

It is not only energetic ions of GCR and SEP but also γ-radiation from nearby supernovae (SN) or gamma-ray bursts (GRBs) that can potentially lead to the production of cosmogenic isotopes (Menjo et al. 2005; Hambaryan & Neuhäuser 2013). Details of the cosmogenic production of long-living isotopes by primary γ-radiation are provided by, e.g., Pavlov et al. (2013a, 2013b).

Figure 4.7 shows the production functions for ¹⁴C, ¹⁰Be, and ³⁶Cl in Earth's atmosphere by primary γ-radiation, according to a recent model (Pavlov et al. 2013a). Photonuclear reactions of photons with energy above 10 MeV lead to generation of secondary neutrons and protons, which further produce cosmogenic isotopes in a way similar to that descried above for incident ions. The maximum of the γ-ray production function for ¹⁴C corresponds to the giant dipole resonance of photonuclear reactions on the target nuclei of nitrogen and oxygen. In this energy range, photons produce secondary neutrons and protons with energy of several megaelectronvolts, which is below the spallation threshold of ¹⁰Be production on nitrogen and oxygen. Production of ¹⁰Be becomes significant when the photon's energy reaches 50 MeV or more and goes in both direct photodisintegration reactions and spallation reactions by secondary nucleons. Because typical spectra of γ-quanta for SN and RGB sources are steep, this leads to a much smaller production ratio ¹⁰Be/¹⁴C than the one for GCR or SEP. Detailed simulations (Pavlov et al. 2013b, 2014) yield the expected ratio of ¹⁴C/¹⁰Be of 400–800 versus ∼50 for energetic particles (see Table 4.2). Production of ³⁶Cl on ⁴⁰Ar by photons is similarly suppressed, leading to an even greater ratio of ¹⁴C/³⁶Cl of 800–1600 (Pavlov et al. 2013b, 2014). As in the case of SEPs, the production of cosmogenic isotopes by γ-quanta takes place dominantly in the stratosphere. On the other hand, because photons are not deflected by the geomagnetic field, the production is limited not to the polar regions but to the spot on Earth irradiated by photons.

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Thus, the ratio of nuclides produced in the atmosphere may clearly distinguish cases related to energetic particles and γ-radiation. In the latter case, no measurable signal by γ-radiation is expected in ¹⁰Be or ³⁶Cl even for such a pronounced ¹⁴C spike as for the 775 CE event. Both beryllium and chlorine spikes were measured for the events discussed here. This fact ultimately rejects the proposed earlier hypothesis (Hambaryan & Neuhäuser 2013; Miyake et al. 2012; Pavlov et al. 2013a) that they were caused by SN/GRBs.

Atmospheric circulation is air motion driven by many forces acting in the rotating atmosphere of Earth. The most important driving forces are the inhomogeneity of the solar radiative heating, Coriolis force, and forcing from atmospheric waves (e.g., Holton 2004). The joint action of these forces is responsible for large-scale circulation features, which are relatively persistent on long-term timescales. The zonal mean structure of the main atmospheric advective transport pathways is shown in Figure 4.8.

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In the stratosphere, advective mass transfer, known as the Brewer–Dobson circulation (BDC hereafter), is carried out by two circulation cells. They both start from the tropical upwelling driven mostly by tropospheric convection. The poleward and descending motions are driven by the forcing from the breaking of vertically propagating planetary, synoptic-scale, and gravity waves (Plumb 2002). The seasonal behavior of the BDC branches is driven by solar radiative heating directly in the stratosphere as well as indirectly from the changing wave forcing, due to solar irradiance absorption lower in the troposphere. Seasonality is expressed as atmospheric polar night (geographical latitude $\gt 67^\circ$) and extratropical jet variability. Polar night jets appear on the edges of the polar night area and therefore the upper BDC branch provides more intensive downward transport in the winter hemisphere. The seasonal behavior of the extratropical jets is not very pronounced, leading to a weak seasonal cycle of shallow BDC branch intensity. Advective transport is constrained by transport barriers, where the absence of wave forcing does not provide the necessary conditions for the poleward/downward advective mass transport. In the troposphere, the zonal mean mass transport follows three circulation cells (Polar, Ferrel, and Hadley) covering the entire troposphere. These cells provide rather fast (up to six months between equator and high latitudes) hemispheric transport of the material that entered the troposphere. The interhemispheric transport timescale in the troposphere is longer, reaching a timescale of around one to two years.

The isotopes are also involved in different diffusion processes driven by turbulent mixing caused by air flow fluctuations and the formation of different vortices or eddies. These vortices can absorb the air parcel and move it for some distance until destruction and final mixing with ambient air. This process is called turbulent or eddy diffusion and usually works in the direction perpendicular to the air flow or in the case when strong horizontal/vertical gradients of the gas or aerosol mixing ratios appears. In the stratosphere, eddy transport is driven by breaking waves, which form eddies (Plumb 2002). The turbulent mixing pathways are shown by the wavy orange lines in Figure 4.8. This mechanism is especially important for the transport of species across their production area boundaries. For example, enhanced vertical ozone diffusion across the tropopause occurs in the summer season, when the ozone mixing ratio in the stratosphere exceeds its tropospheric values (e.g., Škerlak et al. 2014). The intensity of the eddy transport also depends on atmospheric properties and substantially varies in space and time. Irregularities of the air flows in the planetary boundary layer produce very intensive turbulent mixing during the day time, while in more quiet night-time conditions, the mixing intensity is greatly reduced. The representation of mixing processes in the numerical isotope transport models depends on the model complexity. In a simplified box, 1D and 2D models of the description of mixing are based on the application of empirical turbulent diffusion coefficients acquired from observation analysis (e.g., Talpos & Cuculeanu 1997). In the case of general circulation models, some part of the eddy transport related to the resolved waves is treated by the dynamical core and transport module, while the other mixing processes need to be parameterized (Heikkilä et al. 2013). The isotopes can also be transported by small-scale convection in the troposphere. Convective motions are generated in unstable tropospheric layers, when the vertical temperature gradient is larger than either the dry or the wet adiabatic lapse rates. In this case, the air parcel being moved up tends to remain in this direction because it stays warmer than ambient air. In the dry convection case, the air is distributed fast and uniformly in the air column (e.g., Jacob & Prather 1990). This process is active mostly during the day time in the planetary boundary layer from the surface to approximately 1–2 km altitude. The treatment of this process in models is based on the analysis of the temperature gradient to define regions with unstable stratification. Moist convection can generate vertically extended or convective clouds and substantially contributes to the intensity of vertical mixing in the troposphere, accelerating surface-to-tropopause exchange from weeks to hours (e.g., Tost et al. 2010). Overall, convective mixing is less important for cosmogenic isotopes because they are produced mostly in the stratosphere; however, it can accelerate their downward propagation after they cross the tropopause.

The most important component of isotope transport is the transport across the tropopause, i.e., from the stratosphere to the lower troposphere, which is also known as the stratosphere–troposphere transport (STT). The main mechanisms are related to advective downward air motion as part of the BDC, mixing across the tropopause and the presence of stratospheric air intrusions through tropopause discontinuities. Figure 4.9 illustrates the main pathways of stratospheric air propagation to the lower troposphere: quasi-horizontal eddy transport through the middle-latitude tropopause (wavy orange arrows) and advective downward propagation across the polar tropopause as part of the large-scale BDC (blue arrows). According to Liang et al. (2009), the stratospheric air penetrating through the tropopause can reach the surface in approximately three months. This transport time agrees reasonably well with the results from Stohl (2006), who estimated that the mean time of the air transport from the tropopause to the lower troposphere is about 100 days; however, it was also mentioned that the transport to the Arctic and tropical lower troposphere could take longer. During this process, stratospheric air is also involved in intensive mixing between the middle and high latitudes caused by large-scale advection (see Figure 4.8), as well as by mixing via tropospheric eddies and vortices (cyclones and anticyclones), which lead to approximately one month for the mixing of the middle latitudes and the polar air masses. It was also found out (Liang et al. 2009) that 67%–81% of the stratospheric air in the NH troposphere arrived via stratosphere–troposphere transport (STT) over the midlatitudes.

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Radiocarbon ¹⁴C produced by cosmic rays becomes gaseous CO₂ through CO. After the atmospheric transport described above, ¹⁴C concentrations in the troposphere become nearly uniform. Trees, the main archive sample of ¹⁴C, absorb CO₂ by photosynthesis. Therefore, the ¹⁴C concentrations of tree rings reflect tropospheric conditions.

Carbon transport occurs not only in the atmosphere but also in various types of reservoirs such as oceans and biotas, and such transport is known as the global carbon cycle. Reservoirs define spaces on the globe for the movement and storage of matter. Each reservoir can be considered uniform to a certain extent with respect to general properties, such as composition, pressure, and temperature, and is separated by discontinuous surfaces. Reservoirs are mainly divided into the atmosphere, oceans, and biosphere. The carbon exchange between the atmosphere and seawater is caused by changes in CO_2gas and CO_2aq, and that between the atmosphere and biosphere is caused by photosynthesis and the respiration of plants and decomposition of organic matter by microbes. These aforementioned reservoirs of the atmosphere, oceans, and biosphere can also be classified according to their characteristics: e.g., the atmosphere is often divided into two subreservoirs—the stratosphere and troposphere. The state in which the inflow and outflow of matter in each reservoir are balanced is called the steady state. In this state, carbon fluxes of the inflow and outflow in each reservoir, often expressed as GtC (gigaton carbon) per year, are equal, i.e., a reservoir size (total carbon amount of each reservoir) is constant. Such a concept of carbon transfer between reservoirs is known as a box model. The sizes of reservoirs and carbon fluxes between reservoirs are determined using present-day observations or at the bomb peak (see Section 7.1). Figure 4.10 shows a recent box model by Büntgen et al. (2018). This box model details the main reservoirs, reservoir sizes, and fluxes between them.

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Tree-ring ¹⁴C data (in particular, with a resolution worse than one year) show nearly uniform tropospheric values, so that the ¹⁴C difference between tree-ring regions is small. Therefore, previous researches have estimated that cosmic-ray-induced ¹⁴C production rates via ¹⁴C concentrations of tree rings mainly using this type of box model. Calculations made using such a box model often only required the ¹⁴C production rate input into the atmospheric reservoir (used as a variable parameter). However, regional differences in ¹⁴C concentrations exist. The most remarkable regional difference is known as an interhemispheric offset, i.e., ¹⁴C concentrations in the southern hemisphere show lower values than those in the northern hemisphere (Hogg et al. 2013). This is explained by the higher fraction of oceanic area comprising the southern hemisphere (because ¹⁴C is mainly produced in the atmosphere, the atmospheric reservoir has a higher ¹⁴C concentration than the marine reservoir). As described above, because the stratosphere–troposphere exchange occurs at mid to high latitudes, it is considered that the ¹⁴C concentration at these latitudes is higher than at the equator (Hua & Barbetti 2014).

Recent ¹⁴C measurements with improved temporal and spatial resolution have emphasized such regional ¹⁴C differences and seasonal ¹⁴C variations (Büntgen et al. 2018; Uusitalo et al. 2018). Although the differences between the northern and southern hemispheres were explained in the detailed box model (Figure 4.10), it is quite difficult to explain ¹⁴C data which possess higher spatial resolution by using box models. In addition, changes in the carbon cycle caused by climate change cannot be dealt with by the box model, which assumes steady state. Recently, ¹⁴C production rates were reconstructed using Bern3D-LPJ (Figure 4.11), which is a dynamic model of a realistic three-dimensional time-dependent transport and distribution of radiocarbon (Roth & Joos 2013). In the future, an interpretation using such 3D carbon-cycle models will be important, particularly with the available high-precision (both spatial and temporal resolution) ¹⁴C data.

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Some of the isotopes (e.g., ¹⁴C) form gases, and their transport in the atmosphere depends on the above-mentioned processes. Other isotopes form ion clusters or primary particles, which can be captured by different aerosols (Junge 1963; Lal & Peters 1967). In this case, the transport can be enhanced or suppressed by gravitational sedimentation. Figure 4.12 shows the gravitational settling speed for the spherical sulfate aerosol particles in the lower stratosphere (Pierce et al. 2010).

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The sulfate aerosol particle radius is usually less than $0.2\,{\rm{\mu }}{\rm{m}}$ (Figure 2 in Pierce et al. 2010), with a modal value at $0.05\,{\rm{\mu }}{\rm{m}}$. For these particles, the gravitational sedimentation velocity ranges between 200 m yr⁻¹ and 1 km yr⁻¹ and does not play an important role in the lower stratosphere, where it is much smaller than the vertical wind speed (e.g., Weisenstein et al. 2015; Zhou et al. 2006). After a strong volcanic eruption, the size distribution is shifted to larger values. Stratospheric aerosol particles after Pinatubo had mean radii around 0.6 and $0.4\,{\rm{\mu }}{\rm{m}}$ (Figure 3 in Pierce et al. 2010) in the tropical and lower middle-latitude stratosphere, respectively, which sediment at around 10 and 6 km yr⁻¹. These values are comparable to advective upward motions speed in the tropical BDC branch (Weisenstein et al. 2015), preventing aerosol (with embedded isotopes) from being transported to the middle stratosphere. Over the middle latitudes, the annual mean downward wind speed is around 10 km yr⁻¹ (e.g., Zhou et al. 2006), but can reach higher values during the dynamically active winter season. In this case, the downward advective transport of the volcanic aerosol across the tropopause can be substantially enhanced by sedimentation. Some evidences of this enhancement have been identified (Baroni et al. 2011, 2019), in the form of a simultaneous increase in cosmogenic ¹⁰Be and sulfate deposition in polar ice cores after powerful stratospheric volcanic eruptions. This fact contradicts earlier statements (e.g., Lal & Peters 1967) about the marginal importance of gravitational settling and identical transport of isotopes in gas and aerosol forms. Gravitational sedimentation can also be important in the middle/upper stratosphere even for background aerosol because of gravitational sedimentation speed increasing with altitude. It was estimated (Figure 1(a) in Weisenstein et al. 2015) that in the tropical stratosphere, the sedimentation speed of an aerosol particle with $0.2\,{\rm{\mu }}{\rm{m}}$ radius increases from 1 km yr⁻¹ at 20 km to almost 100 km yr⁻¹ at 50 km. The role of gravitational sedimentation was evaluated by Delaygue et al. (2015) using numerical experiments with a 2D model, which includes detailed sulfate aerosol microphysics. An experiment with gravitational sedimentation switched off was compared with a reference model run with all processes switched on. The ratio of ¹⁰Be concentrations simulated without and with sedimentation of particles is presented in Figure 4.13. The main effects are confined to the middle/upper stratosphere, where ¹⁰Be accumulates when gravitational sedimentation is turned off. It is interesting to note that gravitational sedimentation does not contribute to the ¹⁰Be distribution around the tropopause in nonvolcanic conditions.

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The gravitational settling in this model also leads to an almost doubling of the stratospheric ¹⁰Be burden (Delaygue et al. 2015, Table 1), but has no effects on the ⁷Be burden. Unfortunately, the applied model does not have a good treatment of the tropospheric processes and does not allow the estimation of gravitational settling on isotope surface deposition.

Aerosols, with embedded cosmogenic isotopes, are ultimately removed by dry and wet deposition. Dry deposition of aerosols occurs when particles become attached to surfaces under dry conditions. This process depends on several environmental parameters, including the radius and density of particles, atmospheric turbulence, and Earth surface type (Seinfeld & Pandis 2006). The dry deposition flux is usually calculated by models with a dry deposition velocity, assuming first-order loss. Models parameterize dry deposition velocities with a resistance-based approach, which considers the individual steps of dry deposition: transport of the species to the air layer directly above the surface, transport across the quasi-laminar sublayer, and finally uptake at the surface (Khan & Perlinger 2017; Kerkweg et al. 2006). Larger particles ($\gt 2\,{\rm{\mu }}{\rm{m}}$ in diameter) are removed efficiently at the surface by impaction and interception, whereas ultrafine particles ($\lt 0.05\,{\rm{\mu }}{\rm{m}}$) are removed, due to their fast Brownian motion. Dry deposition velocities are slowest for particles between 0.1 and $1\,{\rm{\mu }}{\rm{m}}$ in diameter, which includes the range of sulfate aerosol sizes (Seinfeld & Pandis 2006). Wet deposition encompasses removal through in-cloud or below-cloud processes. In-cloud scavenging occurs when particles act as cloud condensation nuclei and form new cloud droplets, or when particles collide with existing cloud droplets. Nucleation of new cloud droplets is a sink for aerosol particles with diameters ⩾0.1 μm (Tost et al. 2006).

Below-cloud scavenging is the result of falling rain and snow colliding with aerosol particles. The number of scavenged particles can be calculated by multiplying the collection volume of the droplets (dependent on the rain-drop size and falling velocity, i.e., rainfall rate) and the collision efficiency. The collision efficiency between rain drops and aerosols is usually much smaller than 1, as particles are deflected away from the falling droplet by turbulent air flow around the droplet (Lohmann et al. 2016). Collision efficiencies are enhanced for ultrafine particles (<0.2 μm), due to their rapid Brownian motion, and for larger particles (>1 μm), due to inertial impaction. As with dry deposition, wet scavenging of particles with diameters between 0.1 and 1 μm is the least efficient, leading to longer atmospheric lifetimes compared to other particle sizes (Seinfeld & Pandis 2006). Wet deposition is the dominant sink of sulfate aerosol particles, accounting for around 65% of the total sulfate deposition (e.g., Sheng et al. 2015; Kravitz et al. 2009). Estimates from ⁷Be models (Heikkilä et al. 2008; Koch et al. 1996) suggest that wet deposition is even more dominant for cosmogenic isotopes (>90% of total deposition), as they appear in the troposphere from above and, only a small fraction reaches the surface without attaching to water droplets. Figure 4.14 shows the ratio of wet to dry ¹⁰Be deposition calculated in Heikkilä et al. (2013) using the ECHAM5-HAM model. The obtained results confirm the dramatic dominance of wet removal in many regions except for some areas with low cloud water content over the subtropical latitudes.

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However, over the Greenland and Antarctica ice sheets, dry deposition could play an important role. It was demonstrated (Figure 1 in Field et al. 2006) that at least from some areas, ¹⁰Be surface flux due to dry deposition can substantially exceed the contribution from wet deposition. For most regions, it is logical that dry deposition of cosmogenic isotopes is a minor sink, because the isotopes are produced in the middle atmosphere rather than at the surface. Due to the importance of wet deposition, sulfate deposition patterns correlate with precipitation: higher deposition is observed in the midlatitude storm tracks and tropical regions, and very low deposition fluxes are observed over the Sahara Desert and polar regions (Tost et al. 2007; Vet et al. 2014). Sulfate deposition maps are affected mainly by tropospheric transport rather than stratospheric transport, due to the large surface emissions of short-lived species. A better analogy for cosmogenic isotope deposition would be modeling studies that investigated deposition changes after stratospheric injections of SO₂, in cases of geoengineering (Visioni et al. 2018; Kravitz et al. 2009) or volcanic eruptions (Marshall et al. 2018). The deposition response from stratospheric inputs of SO₂ is largest in the midlatitudes of both hemispheres (Figure 4.15).

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Trajectory studies have determined that the highest mass fluxes of stratospheric air to the troposphere are located in the midlatitude storm tracks, especially in the northern hemisphere (Škerlak et al. 2014). Stratospheric aerosols likely enter the troposphere in the midlatitudes (Section 4.3.3), and therefore are likely deposited in the midlatitudes while only a small part can be transported and deposited over the polar areas. The same conclusions are valid for isotopes in soluble particulate forms. The isotopes in gas form (e.g., ¹⁴CO), however, will be mostly removed by dry deposition because of lower solubility.

The atmospheric transport of isotopes was investigated using different models ranging from box, 1D and 2D models, to the most sophisticated 3D global coupled atmosphere–ocean general circulation models (GCM). The zonal and annual mean climatological distribution of ¹⁰Be and ⁷Be was calculated (Heikkilä 2007) using the ECHAM-HAM GCM (Figure 4.16). The ECHAM-HAM GCM treats all relevant processes of isotope transport including advective transport, turbulent mixing, and dry and wet deposition. The simulated isotopes are considered primary particles attached to sulfate aerosols, which means that gravitational sedimentation and solubility are taken into account.

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The altitude–latitude distributions of both isotopes are rather similar despite the substantial difference in decay time. The maximum is observed in the polar lower stratosphere where production by cosmic rays is maximized. The horizontal mixing of ⁷Be with about 50 days of decay time is less effective because the typical timescale of horizontal exchange in the stratosphere is about several years. Therefore, the horizontal gradient of the ⁷Be concentration in the stratosphere is larger than for ¹⁰Be, which is extremely passive in the stratosphere. In the troposphere, the concentrations of the considered isotopes are rather small and almost identical. This fact can be explained by the very fast removal of isotopes by wet deposition. The low abundance of these isotopes in the tropical upper troposphere is explained by intensive convective mixing, which moves up the air from planetary boundary layer with very low ⁷Be and ¹⁰Be concentrations. The stratosphere to troposphere transport is most pronounced over the middle latitudes, where the mixing is enhanced due to meteorological events in the troposphere (see Section 4.3.3). As mentioned in Section 4.3.5, the contribution of dry deposition is not important on a global scale and can be significant only in some specific arid regions, such as Greenland and Antarctica. Because long-lived isotopes (like ¹⁰Be) trapped in the ice cores are of great interest for the reconstruction of past solar activity, their transport to the ice-covered land regions and subsequent deposition there are more important than pure stratospheric transport. Figure 4.17 shows the distribution of ¹⁰Be and ⁷Be in the surface air simulated with ECHAM-HAM GCM (Heikkilä 2007).

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The main features of the ¹⁰Be and ⁷Be geographical distribution are virtually the same; however, the absolute values of ⁷Be concentration are smaller, probably due to stronger decay during the stratosphere to troposphere transport. The maximum values of near-surface concentrations for the both isotopes appear over the middle latitudes, where the stratospheric air masses enter the troposphere. The minimum values are observed over areas with strong precipitation (e.g., Western Pacific) because of enhanced wet deposition and over high latitudes, where the isotopes are lost by decay during rather slow transport from the middle latitudes. Local peaks over North Africa, Saudi Arabia, and Tibet are mostly explained by weak precipitation and intensive transport form the stratosphere; however, the increase of tropospheric isotope production with height can also play some role (some localized spikes appear over the Rocky Mountains and Andes). The surface mixing ratio does not provide information about the origin of the isotope, which is important to properly attribute the observed variability. This information can be extracted from model runs especially designed to elucidate the location where the isotope in the surface air was produced. Such simulations were carried out (Heikkilä et al. 2009) using the ECHAM-HAM GCM, and the obtained results are shown in Figure 4.18.

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This figure demonstrates very localized downward propagation of ¹⁰Be, when about 60% of the produced isotope is deposited in the same latitudinal band. The obtained interhemispheric exchange is also very slow compared to the deposition lifetime: only about 20% of the ¹⁰Be produced in the northern hemisphere propagates to the southern tropical latitudes. The obtained results also show that most of the ¹⁰Be produced in the stratosphere (90%) is deposited outside the polar caps, which are the most interesting locations for studies of the historical variability of solar activity. However, Heikkilä et al. (2009) also stated that the stratospheric source is responsible for about 65% of the total deposition in the polar areas.

Because the stratosphere is the dominant source region for ¹⁰Be in polar surface air, the solar influence on ¹⁰Be production will be imprinted onto polar surface archives. The connection between solar activity and ¹⁰Be deposition in ice can be confirmed using both observations (e.g., Beer et al. 1990; Bard et al. 1997) and models (e.g., Heikkilä et al. 2008), which showed that some of the atmospheric transport variability do not play a dramatic role. Features of atmospheric transport can be illustrated using the simulated response of ¹⁰Be deposition to short-term explosive events on the solar surface. The consequences of one such extreme event in 775 CE was simulated with the chemistry-climate model SOCOL (Sukhodolov et al. 2017). The simulated and measured ¹⁰Be deposition fluxes are depicted in Figure 4.19.

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The simulations were performed using a simplified treatment of wet and dry deposition. In addition, the produced ¹⁰Be was transported without attachment to the sulfur aerosol. The simulated 11 year variability and timing of the ¹⁰Be spike after the event are in good agreement with observations,which confirmed earlier conclusions about the small influence of gravitational sedimentation on the isotope deposition flux (Junge 1963; Lal & Peters 1967), at least in the absence of powerful volcanic eruptions. The mean time for the transport from the stratosphere was estimated as 1–2 years, which is in general agreement with the typical transport time discussed earlier. More accurate estimates of the time for the transport from the stratosphere are difficult because of the uncertainties in the observational data and the many processes involved in the transport and deposition of ¹⁰Be. This problem can be illustrated by comparing the transport time of sulfate aerosol after powerful volcanic eruptions simulated with different models to the measured deposition of the sulfate to ice. The comparison is relevant because of the close connection between ¹⁰Be and sulfate aerosol distribution, transport, and deposition.

Figure 4.20 illustrates the comparison of the observed sulfate deposition over Antarctica and Greenland after the Tambora eruption in 1815 April with four different model results (Marshall et al. 2018). The first traces of enhanced sulfate appear in the observations about six to seven months after the eruption in both locations, which is rather fast considering the distance from the tropics, where the eruption took place. The maximum values of the deposited sulfate are reached after about 1 year in both hemispheres if the second spike after 20 months is not considered. In the MAECHAM5-HAM, model the arrival of enhanced sulfate to the polar regions is even faster (around three to five months), especially for Antarctica. The SOCOL-AER simulation of the sulfate arrival time is similar to the observations, but the shape of the spikes is smoother. Two other models demonstrate rather different behaviors, showing smaller deposition magnitudes and a shift in the time response.

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This example illustrates that model uncertainties in the stratosphere-to-troposphere transport of aerosols remain a challenge. Accurate simulations of the ¹⁰Be atmospheric transport and deposition require further improvements to all relevant model components.

Another problem related to the application of isotopes for the estimation of past solar activity is the influence of atmospheric circulation and deposition parameters. It is well known that greenhouse gases affect the atmospheric temperature and circulation, with implications for the water cycle, convection, and cloud properties. For the recent past, the magnitude of this impact is suggested to be small, in part because the climate changes during the preindustrial period were not too strong. For the distant past and future, the isotope deposition response to climate changes can be estimated only using state-of-the-art models, because of the lack of reliable observations. The Maunder minimum of solar activity and a warmer climate in the future are two interesting cases to consider. The deposition of ¹⁰Be during the Maunder minimum was simulated by Heikkilä et al. (2008) using the ECHAM-HAM model. They introduce a 32% ¹⁰Be production increase for this period and compared the deposition flux increase with this value. For the global mean deposition flux, 8% (1/4 of the production increase) was attributed to a colder climate, weaker stratospheric transport, and a different hydrological cycle. However, Figure 4.21 shows that over Antarctica and Greenland (not shown), the relative increase of ¹⁰Be deposition can exceed 100%, which means that the influence of climate can dominate in case of strong changes in different climate states.

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Because the deposition flux over ice sheets is important for the study of past solar activity, the assumption about the negligible influence of climate change on isotope composition needs to be further investigated. If the emission of greenhouse gases continue above preindustrial levels, the future climate will be warmer and characterized by a stronger meridional circulation (e.g., Li et al. 2008). The response of the ¹⁰Be concentration in snow to climate regime switches was evaluated by Field et al. (2006) using the GISS GCM. They compared present-day simulations with simulations of a warmer climate caused by CO₂ doubling, as well as a simulation with a colder climate during the Younger Dryas. Figure 4.22 illustrates the influence of climate warming on the ¹⁰Be concentration in snow in the polar areas. Intensification of meridional circulation in the stratosphere leads to the faster removal of ¹⁰Be from the production area in the lower stratosphere. Potentially, it could result in tropospheric ¹⁰Be enhancement, but as stated in Field et al. (2006), the intensification of hydrological cycles removes more ¹⁰Be, compensating for the influence of circulation changes. This effect leads to a decrease of ¹⁰Be in snow and more intensive snow accumulation over Antarctica and Greenland by up to 50%. It was concluded in Field et al. (2006) that ¹⁰Be changes due to warmer climate are driven by global-scale changes of the hydrological cycle and not by the changes in local deposition.

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Another interesting aspect of the problem is the influence of volcanic eruptions on the isotope concentration in ice. They can be connected due to the modulation of sulfate aerosol loading by powerful volcanic eruptions leading to changes in the vertical and horizontal transport of isotopes attached to sulfate aerosol particles. These changes could be important because the increased size of aerosol particles after volcanic eruption can substantially intensify downward transport, and their radiative effects can suppress the hydrological cycle (e.g., Grinsted et al. 2007). The correlation between ¹⁰Be and sulfate deposition in the observations was discussed in Baroni et al. (2011, 2019). They found a simultaneous increase of sulfate and ¹⁰Be in cores from two Antarctic sites, Vostok and Concordia, after the powerful volcanic eruptions from Agung and Pinatubo. High-resolution ice-core records from several sites in Antarctica have now been extended back to 887 CE, and among 26 volcanic eruptions studied, 14 have been confirmed to have an increase in ¹⁰Be concentration related to stratospheric volcanic eruptions (Baroni et al. 2019). A detailed explanation of the obtained correlation is difficult to obtain from pure observational data because many processes are involved in the primary signal transformation. The study of the ¹⁰Be deposition response to volcanic eruptions was carried out in Field et al. (2006) using the GISS GCM. In their model, only the influence of the colder climate was considered, because the model was not able to treat gravitational sedimentation and the potential effect of volcanic eruption on ¹⁰Be scavenging. The obtained results showed a small (about 6%) influence of volcanic eruptions on stratosphere–troposphere exchange and the tropospheric concentration of ¹⁰Be. Figure 4.23 illustrates the changes of ¹⁰Be in snow for Antarctica. For this region, the suppressed hydrological cycle leads to lower accumulation rates and reduced wet deposition with almost no changes in dry deposition, resulting in an up to 20% increase of the ¹⁰Be concentration in snow.

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However, a change in accumulation rates would also affect the concentration of other proxies recorded in the snow (e.g., sodium, magnesium which are proxies of marine sources) and no obvious change is observed after volcanic eruptions. The study of 14 volcanic periods from Antarctic ice cores covering the last millennium shows that the increase in ¹⁰Be concentration varies from 14% to 112%. This large range depends upon the volcanic source parameters (amount of SO₂ emitted, altitude reached in the stratosphere, location of the volcano, etc.) and the preservation of the signal in the ice. These results agree with the analysis of observational data by Baroni et al. (2011); however, the description of the involved mechanisms differs. Baroni et al. (2011, 2019) suggested that the large amount of sulfate aerosols formed in the stratosphere on a short timescale after a volcanic eruption would accelerate their sedimentation, dragging ¹⁰Be atoms along in their path. The difference with Field et al. (2006), who claimed that hydrological processes in the troposphere are more important, can be related to the simplified treatment of volcanic aerosol by Field et al. (2006) and needs to be addressed in the future with proper models.

Impact of Stratospheric Volcanic Eruptions

Stratospheric volcanic eruptions can increase the concentration of ¹⁰Be in ice cores by up to 112% (Baroni et al. 2019) over one to three years. On average, the increase in the ¹⁰Be concentration is 56% ± 30% (Baroni et al. 2019), calculated from 14 volcanic periods recorded in different ice cores of the High Antarctic Plateau over the last millennium. For comparison, the 994 CE and the 775 CE SEP events induced, respectively, a 50% and 80%–150% increases in the ¹⁰Be concentration in ice cores from Antarctica and Greenland (Mekhaldi et al. 2015; Miyake et al. 2019, 2015; Sigl et al. 2015). A stratospheric volcanic eruption can therefore reproduce a ¹⁰Be signal mimicking an SEP event. Thus, it is necessary to compare the concentrations of ¹⁰Be and of sulfate, a proxy for volcanic eruptions, in the same ice core, to verify the solar or volcanic origin of a ¹⁰Be peak (see Figure 4.24). Another verification consists in looking at ¹⁴C tree-ring data that are not, a priori, affected by volcanic eruptions. Indeed, the amount of CO₂ emitted by volcanoes is negligible compared to the atmospheric reservoir. It is possible to apply a correction for the volcanic disturbance using the slope of the linear regression between the ¹⁰Be and sulfate concentrations if they were determined from the same samples (red line, Figure 4.24; Baroni et al. 2011).

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The mechanism responsible for the impact of stratospheric volcanic eruption on ¹⁰Be deposition involves the microphysics of aerosols. Volcanic eruptions generate large amounts of sulfate aerosols on a short timescale, accelerating their gravitational sedimentation because of a higher collision rate, making larger aerosols than in nonvolcanic conditions (e.g., Pinto et al. 1989; Timmreck 2012). It would also increase the sedimentation of ¹⁰Be atoms as they attach to aerosols to settle at Earth's surface (Baroni et al. 2011, 2019). However, this is only part of the story—the volcanic imprint is so visible in ¹⁰Be ice-core records because the ¹⁰Be is mostly produced in the polar stratosphere, between 10 km and 15 km altitude (Delaygue et al. 2015; Poluianov et al. 2016) and because the ¹⁰Be snow signal is controlled by stratospheric intrusions even in nonvolcanic conditions, at least on the High Antarctic Plateau. For example, the ¹⁰Be snow/ice signal at Dome C and the South Pole, both located on the High Antarctic Plateau, is controlled by 2%–5% of stratospheric intrusions (Baroni et al. 2019; Hill-Falkenthal et al. 2013; Raisbeck et al. 1981). Any change in the aerosol load in the stratosphere would be seen in ¹⁰Be time series.

Climatic or System Effects

Several studies report "climatic" or "system" effects to explain part of the ¹⁰Be ice-core signal which is not related to modulation of its production in the atmosphere (e.g., Baroni et al. 2011; Beer et al. 1992; Miyake et al. 2019; Pedro et al. 2006, 2011; Winkler et al. 2013).

For example, comparisons are made with the water δ¹⁸O values, which is an indicator of the local temperature that can be related to a change in moisture sources and finally on dry versus wet deposition (see Section 5.3). The cross-correlation coefficient between ¹⁰Be and δ¹⁸O is 0.57 at a high-accumulation-rate site such as Law Dome (Antarctica; Pedro et al. 2006) and 0.32 at a low-accumulation-rate site such as Vostok (Winkler et al. 2013), where dry deposition dominates. This can affect the ¹⁰Be concentration.

A relationship between the concentrations of sodium (Na⁺) and ¹⁰Be has also been observed at several sites in Antarctica, Dome C, Dome Fuji, and Law Dome (Baroni et al. 2011; Miyake et al. 2019; Pedro et al. 2011). Sodium is a sea salt, found as an aerosol particle, originating from the ocean and transported inland in the troposphere. The cross-correlation between the concentrations of ¹⁰Be and Na⁺ over the last 60 years, at Vostok, is 0.51 (Baroni et al. 2011), and a similar value is found at Dome Fuji at the time of the 994 CE event (Figure 4.25; Miyake et al. 2019). The mechanism explaining the relationship between the concentrations of ¹⁰Be and Na⁺ is not yet identified, but at Vostok, both vary according to a cyclicity of a 3–7 year interannual variability. This cyclicity is found in different modes of atmospheric circulation, such as the Antarctic Oscillation, the Antarctic Circumpolar Wave, or the Southern Annular Mode (Baroni et al. 2011). The modulation of atmospheric circulation in the troposphere might explain this relationship, but more investigations are needed in the future.

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However, whatever the mechanism is, it is possible to apply a correction to the ¹⁰Be signal to remove part of the "system effect" (Miyake et al. 2019). Using the linear regression between the normalized concentrations of ¹⁰Be and Na⁺, the relative production variability of ¹⁰Be, called Δ¹⁰Be (Figure 4.25), can be calculated:

$$\begin{eqnarray}&&{\rm{\Delta }}{}^{10}\mathrm{Be}(t)={}^{10}\mathrm{Be}(t)-C\cdot (\mathrm{Na}(t)),\end{eqnarray} \tag{ 4.7 }$$

where ¹⁰Be(t) is the normalized ¹⁰Be concentration at time t, Na(t) is the "normalized Na⁺ concentration," and C(t) is the regression line between the normalized ¹⁰Be and Na⁺ concentrations. This "system effect" correction allowed the strength of the 994 CE event recorded at Dome Fuji (Miyake et al. 2019) to be better emphasized.

Anthropogenic ³⁶Cl from Nuclear Bomb Tests

In natural conditions, ³⁶Cl is produced in the atmosphere through cosmic-ray-induced spallation of ⁴⁰Ar nuclei (Poluianov et al. 2016). Aside from its natural source, anthropogenic ³⁶Cl has also been produced through capture by ³⁵Cl from the sea salt (sodium chloride NaCl) of thermal neutrons emitted during the marine nuclear bomb tests (Bentley et al. 1982; Elmore et al. 1982; Heikkilä et al. 2009) from the 1950s to the 1970s. Other nuclides such as cesium-137 (¹³⁷Cs) or tritium (³H) were mainly produced during atmospheric and ground nuclear tests.

The intensity of these marine nuclear tests made ³⁶Cl reach the stratosphere, mainly in the gaseous form H³⁶Cl (Zerle et al. 1997), then be distributed across the globe, and finally transferred to the troposphere. Consequently, the ³⁶Cl bomb pulse can be observed at all latitudes including Greenland and Antarctica (Figure 4.26; Delmas et al. 2004; Elmore et al. 1982; Heikkilä et al. 2009; Synal et al. 1990).

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Approximately 80 kg of ³⁶Cl were injected into the stratosphere between 1952 and 1971 (Heikkilä et al. 2009; Synal et al. 1990), resulting in a ³⁶Cl flux at low-latitude glaciers of Greenland and Antarctica, 100–1000 times higher than the natural prebomb ³⁶Cl fluxes (Figure 4.26). As a result, SEP events occurring during that time period, such as the hard-spectrum one of 1956 February 23, would be hardly possible to detect. Since the end of the marine nuclear bomb tests, prebomb ³⁶Cl levels have nearly recovered in ice cores, in the 1980s (Elmore et al. 1982; Heikkilä et al. 2009), opening prospects for using³⁶Cl to detect SEPs in the future.

Mobility of ³⁶Cl in the Snowpack

Prebomb ³⁶Cl level has still not recovered in 1998, at Vostok, in Antarctica (Figure 4.27; Delmas et al. 2004). This was explained by the mobility of ³⁶Cl in its gaseous form (H³⁶Cl), in firn, at this low-accumulation site, which was evidenced when comparing ³⁶Cl with ¹³⁷Cs measured in the same snow pit (see Figure 4.27). Even though ¹³⁷Cs was produced during atmospheric nuclear tests and ³⁶Cl was produced during the marine ones, they can be compared because the tests were performed during the same period. Anthropogenic ³⁶Cl peaks should be in phase with those of ¹³⁷Cs identified in 1955 and 1965, but at Vostok, the anthropogenic ³⁶Cl migrates toward the surface. The mobility of ³⁶Cl is not observed at the Dye-3 and NGRIP sites in Greenland and is limited at Berkner Island in Antarctica, where ³⁶Cl deposited as gaseous H³⁶Cl and particulate Na³⁶Cl are both well preserved (see Figure 4.26). This could be explained by the higher accumulation rates for these sites compared to Vostok (Delmas et al. 2004; Heikkilä et al. 2009).

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Low-accumulation sites ($\lt 4\,\mathrm{cm}$ water equivalent/year) are also affected by a significant loss of chlorine during interglacial periods. The loss can be up to 60% or 80% at Dome C and Vostok (Antarctica), respectively (Röthlisberger et al. 2003; Wagnon et al. 1999). This would impact the ³⁶Cl/¹⁰Be ratio used to constrain the energy spectra of SEPs. These peculiarities have to be taken into account for a better interpretation of ³⁶Cl ice-core data.

The Moon has no magnetic field, and therefore its surface is bombarded with the full flux of GCRs and SEPs, as well as solar wind. While more energetic cosmic rays can produce cosmogenic isotopes inside the upper layer of the lunar soil/rock, ions of solar wind can be implanted on the surface. A considerable number of radionuclides have been used to estimate GCR fluxes on the Moon. Radioisotopes in lunar samples that have been measured and that can be used to study SEP fluxes in the past include ²²Na (T_1/2 = 2.6 yr; Fruchter et al. 1976), ³⁹Ar (T_1/2 = 269 yr; Fireman et al. 1970; Stoenner et al. 1970), ¹⁴C (T_1/2 = 5730 yr; Begemann et al. 1972; Boeckl 1972; Jull et al. 1995, 1998), ⁵⁹Ni (T_1/2 = 76,000 yr; Lanzerotti et al. 1973), ⁴¹Ca (T_1/2 = 0.1 Myr; Nishiizumi et al. 1997; Fink et al. 1998), ⁸¹Kr (T_1/2 = 0.2 Myr; Reedy & Marti 1991), ³⁶Cl (t_1/2 = 0.3 Myr; Nishiizumi et al. 1984, 1989), ²⁶Al (T_1/2 = 0.710 Myr; Fruchter et al. 1976; Kohl et al. 1978; Nishiizumi et al. 1984, 2009), ¹⁰Be (T_1/2 = 1.38 Myr; Nishiizumi et al. 1984, 2009), and ⁵³Mn (T_1/2 = 3.7 Myr; Kohl et al. 1978; Nishiizumi et al. 1983; Russ & Emerson 1980). On the Moon, most of these radionuclides such as ¹⁴C and ¹⁰Be are primarily produced in rocks by high-energy spallation reactions on different target elements. SEPs are less energetic, with energies of tens to hundreds of megaelectronvolts, which is still sufficient to induce spallation reactions. They have a variable flux, typically around 100 particles cm⁻² s⁻¹ ($E\gt 10\,\mathrm{MeV}$). Studies of depth profiles in the near surface (<1–2 cm) have been successfully used to derive SEP fluxes in cases where production rates are well known, such as on the lunar surface (Finkel et al. 1971; Fruchter et al. 1976; Fink et al. 1998; Jull et al. 1998; Nishiizumi et al. 2009). Constraints on the temporal variability of the SEP flux have also been determined by comparison of radionuclides with different half-lives (e.g., Nishiizumi et al. 1984; Reedy 1998; Eugster et al. 2006; Nishiizumi et al. 2009; Reedy 2012a).

SEP effects are important in lunar samples, but because SEP effects are rarely observed in meteorites (Nishiizumi et al. 1990, 2014), the cosmogenic nuclide record in lunar samples is unique because they provide a continuous record of GCR and SEP intensities. Lunar cores are very useful in studies of the production of nuclides by GCR particles in planetary surfaces. Lunar samples also contain good records of SEP effects and variations of SEP fluxes in the past (Reedy 1980, 1998; Reedy & Marti 1991).

Cosmogenic isotopes can also be used to identify solar-wind implanted components in lunar rocks, as shown in the case of ¹⁴C (Jull et al. 1995, 2000) and to some extent, ¹⁰Be (Nishiizumi & Caffee 2001).

Generally, lunar rocks and soil-core samples are considered to be excellent recorders of GCR and SEP effects (Reedy et al. 1983; Reedy 1998). Their long residence times on a stable surface integrate the past irradiation of the rocks and core samples. Spallation-produced ¹⁴C, ¹⁰Be and other radionuclides are important for determining solar (SEP) and galactic cosmic-ray production rates. We can do this by comparing flux estimates derived from radioisotopes, which have different half-lives, spanning several orders of magnitude in time (Jull et al. 1998; Fink et al. 1998; Table 4.3).

Without a shielding atmosphere and magnetic field, all charged particles can reach the lunar surface. In addition to galactic and solar energetic particles, discussed in Section 2.2, there is also a population of less energetic (and not always fully ionized) solar wind particles. The solar wind consists of ions entrained in the solar magnetic field, with a flux of protons of 1.6–2 × 10⁸ p cm⁻² s⁻¹ (Geiss et al. 1970). Because the solar wind impinges on the lunar surface most of the time, except when the Moon is in the terrestrial magnetic field (Winglee & Harnett 2007), we expect that these ions should be implanted into lunar surface materials. Such effects have been studied by many researchers for radionuclides such as ¹⁴C (Fireman et al. 1977; Fireman 1978; Jull et al. 1995, 2000), ¹⁰Be (Nishiizumi & Caffee 2001), and noble gases (Wieler 1998). There is also evidence for directly implanted solar ¹⁴C in lunar soil, from either solar wind or solar flares (Fireman et al. 1977; Fireman 1978; Jull et al. 1995, 2000; Lal et al. 2007). The effect of continuous solar-wind implantation and sputtering on the lunar surface also causes the erosion and remobilization of material (Killen & Ip 1999; Wurz et al. 2007). A number of studies have shown that sputtering effects on the lunar surface (e.g., Jull et al. 1980; Kitts et al. 2003) cause compositional changes.

The SEP flux were estimated from recent spacecraft measurements (see Section 2.2.3) and summarized in Table 2.2. As terrestrial cosmogenic data suggest, there have been no SEP events with the fluence ${F}_{30}\gt {10}^{11}\,{\rm{p}}\,{\mathrm{cm}}^{-2}$ over the last 11,000 years see Usoskin et al. (2006) and Usoskin & Kovaltsov (2012).

The first lunar landing occurred on 1969 July 20. The Apollo 11 mission returned some bulk soil samples and rocks. Subsequent Apollo missions between 1969 and 1972 returned about 382 kg of lunar samples in total, including 265.6 kg of rocks (>1 cm; Heiken et al. 1991). Six of the seven missions landed and returned samples from the Moon. One mission, Apollo 13, had to be aborted due to a technical problem. The later missions (Apollo 14–17) were increasingly oriented to the geology of the Moon, and Apollo 17 included a geologist as one of the astronauts (Harrison Schmitt). These are well documented, and there is extensive literature available at https://curator.jsc.nasa.gov/lunar/, which gives detailed information and access to a compendium of information on all lunar samples. Detailed records of astronaut observations and discussions on the lunar surface (Figure 4.28) and sample collection are also available at the Apollo lunar journal site, https://www.hq.nasa.gov/alsj/main.html. There are also some much smaller samples collected as part of the Soviet automatic landers Luna 16, 20, and 24, which collected a total of 321 g of material in three small cores. There was also a fourth lander (Luna 23), but it failed on landing. Detailed information is also available at the NASA lunar sample compendium site, https://curator.jsc.nasa.gov/lunar/lsc/.

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Lunar Cores

Of the 25 cores of lunar soil taken during the Apollo missions, 16 have so far been studied for cosmogenic nuclides. Many of the cores studied show surface disturbance either during sampling or transport. Two types of cores were collected. In all missions, short drive tubes of up to ∼30 cm length were collected, and "double-drive cores" were used for the Apollo 15, 16, and 17 missions (Meyer 2007d), consisting of tubes ∼34 cm long, which coupled together collected up to 68 cm of core (see Figure 4.29). For Apollo 15–17, longer "deep drive cores" were also collected, which were about 242, 224, and 300 cm in length, respectively (Meyer 2007a, 2007b, 2007c). The best core appears to be the Apollo 15 deep-drill core, 15008/7 (Fruchter et al. 1976; Nishiizumi et al. 1984, 1997; Jull et al. 1998), which preserves the best record of solar cosmic-ray signal at the surface. According to Allton & Waltz (1980, p. 1475) "the Apollo 15 drill core was completely filled and its scale is straightforward and accurately represents in situ lunar conditions." Figure 4.29 shows the rather difficult process of setting up the deep-drill core.

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A summary of all lunar cores with references is given in Table 4.4.

Table 4.4.  Lunar Core Samples Recovered During Apollo Missions

Core		Length (cm)	Weight (g)	References and Notes
10004	Single	13.5	44.8	Allton & Waltz (1980)
10005	Single	10	53.4
12026	Single	19.3	101.4
12027	Single	17.4	80
12025/12028	A12 deep drill	41	246.7
12023/12024	A12 core	37 (from trench)		Not in core summary
14210/14211	Double-drive core	40	209.2	14210—full, 14211—not full, only 39.5 g
14220	Single core	16.5	80.7
14230	Single core	12.5	76.7
15007/15008	Double-drive core	56.6	1278.4	Many studies
15009	Single core	30	622
15010/15011	Double-drive core	55	1401.1	Meyer (2007d) shows the complete core
60009/60010	Double-drive tube	65.4	1395.1	Fruchter et al. (1976), Meyer (2007d)
64001/64002	Double	65.6	1336.4	Top 20 cm disturbed (Meyer 2007d)
68001/68002	Double	62.3	1424.2	Binnie et al. (2019)
69001	Single	27	558.4	Unopened (Lofgren 2011)
60001/60007	Deep drill	224 (195 recovered)	1007.6 recovered	Fruchter et al. (1976) (top) 60005 has missing section.
15006/15001	Deep drill	237.2	1333	Fruchter et al. (1976), Meyer (2007c)
76001	Single	34.5	711.6	Jull et al. (1998)
79001/79002	Double drive	51.3	1152.8
70001/70009	Deep drill	300	1368.5	(top) Fruchter et al. (1976), Meyer (2007c)
70012	Single	28	485	Found already open in LRL (Meyer 2009)
73001/73002	Double	56	1239	Unopened (Lofgren 2011)
74001/74002	Double	68.2	1979.2

Note. Apollo Sample Catalogs Index, https://curator.jsc.nasa.gov/lunar/catalogs/index.cfm, Fruchter et al. (1976). LRL denotes Lunar Receiving Laboratory.

The shorter Apollo 15 core 15008/7 (Reedy & Nishiizumi 1998; Jull et al. 1998) as well as the deep-drill core preserve a good record of the SEP component. This can be seen in Figures 4.30 and 4.31. Figure 4.30 shows the deeper profile from the galactic component (GCR) for the 2 m core. A smooth curve of the SEP component in the top 5 g cm⁻² can be seen in Figure 4.31, which shows the top 20 cm of the cores. However, Fruchter et al. (1976) noted that the deep-drill stem (15006) showed disturbance in the top 20 cm for ²⁶Al.

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Apart from the very surface of the Apollo 15 core, Russ et al. (1972) and Pepin et al. (1974) showed that cosmic-ray-produced spallation nuclides are all smooth functions of depth. This indicates that the depositional history of the drill core is coherent and relatively simple. Bogard et al. (1973) and Bogard & Hirsch (1975) found that noble-gas solar-wind components can be documented throughout the length of the core. Bogard et al. (1973) showed that ⁴He and ⁴He/³He were relatively constant. These authors concluded that the Apollo 15 core represents the best sampling of a deep core on the Moon to date.

Disturbed Cores

Lunar Rocks Used for Detailed SEP Studies

A number of lunar rocks have been studied in detail for cosmogenic nuclide records. These samples probably offer the best records of SEP effects, as they are only subjected to low levels of erosion, and the turnover effects evident in cores can be avoided.

Early studies were conducted on rock 12002 from the Apollo 12 site (Finkel et al. 1971), which included short-lived nuclides. In this study, the rock was carefully sliced and external surfaces ground off using a dental tool. The short-lived nuclides suggested high flux rates than longer-lived nuclides. Similar studies were also done in Wahlen et al. (1972) for the large ∼9 kg rock 14321 (known as "Big Bertha"), a clast-rich crystalline matrix breccia. Other measurements have been performed on rock 10017 (Shedlovsky et al. 1970), 14320 (Wahlen et al. 1972) and also rocks 74275, 68815, and 64455. Perhaps the most detailed studies were for rock 64455, a glass-coated impact melt rock that was used for detailed studies of solar cosmic-ray effects (Ryder & Norman 1980; Nishiizumi et al. 2009). The solar-facing surface, which showed micrometeorite impact pits, was used for this study. Detailed studies that refined the flux were conducted for rock 64455 (Nishiizumi et al. 2009). In this study, the rock was ground off with a dental tool in finer fractions than for 12002. The approach used for rock 68815 was to slice different sections (Meyer 2009) at the Johnson Space Center curatorial facility. The most comprehensive series of these studies are those on 68815 (Nishiizumi et al. 1988; Kohl et al. 1978; Rao et al. 1994; Jull et al. 1998). Detailed studies on 68815 show a good record of SEP components of ¹⁴C, ¹⁰Be, ²⁶Al, ³⁶Cl, and ⁵³Mn (Figure 4.32). No SEP ¹⁰Be was observed in 68815, and it was argued (Nishiizumi et al. 1988) that this sets upper limits on SEP, using ¹⁰Be as an indicator of the energy range of the SEP flux. Similar studies have been done for rock 74275 (Fink et al. 1998; Jull et al. 2001), which generally followed the idea of the original 12002 studies (Finkel et al. 1971).

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For rock 64455, Nishiizumi et al. (2009) reported values of flux for $\gt 30\,\mathrm{MeV}$ of J = 24 p cm⁻² s⁻¹ (${R}_{0}=90$ MV) for ²⁶Al, but a higher value of J = 46 p cm⁻² s⁻¹ (with a lower R₀ of 70 MV) for ³⁶Cl. Their values appear to be consistent with other records (shown in the table for this and other rocks) that indicate that the SEP flux is on average higher during the last 0.5–1 Myr, based on results from ¹⁴C (68815; Jull et al. 1998), ³⁶Cl (64455 and 68815; Nishiizumi et al. 1998, 2009), and ⁴¹Ca (74275; Fink et al. 1998). Nishiizumi et al. (2009) argue that the last 0.5 Myr are higher and that there is some effect on ²⁶Al. Fluxes for $\gt 1\,\mathrm{Myr}$ appear to average approximately 24 p cm⁻² s⁻¹ (at least for ∼2 Myr) compared to a higher value of 42–46 p cm⁻² s⁻¹ (Fink et al. 1998; Jull et al. 1998; Nishiizumi et al. 1988, 2009). Rao et al. (1994), also on rock 68815, reached similar conclusions. Because the exposure age of ∼2 Myr for this rock is well established, that study integrates the last 2 Myr. Yaniv & Marti (1981) also measured stopped SEP helium ions in the top millimeter of the lunar rock 68815 (Figure 4.33). Similar studies were also made for rock 74275, but the surface of this rock is angled so that the production rate is reduced by ∼7%–10% (Fink et al. 1998; Jull et al. 2001). The results for this rock have been corrected for geometrical effects that reduce the apparent flux and are in general agreement with earlier studies. A full summary of these estimates from different observations and estimates is given in Table 4.3.

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Stable Nuclides—Noble Gases: Evidence of Exposure Times

Production of isotopes like ¹⁴C, ²⁶Al, or ³⁶Cl in lunar rocks at shallow depths less than several g cm⁻² is mostly defined by SEPs, while deeper layers are sensitive to GCRs. A typical depth dependence of the radiocarbon content in a lunar sample is shown in Figures 4.30 and 4.31. For relatively shallow depths ($\leqslant 5\,{\rm{g}}\,{\mathrm{cm}}^{-2}$), the concentration of ¹⁴C is defined mostly by the flux and spectrum of SEPs, while GCR start dominating the production at larger depths. Thus, measurements of the depth profile of isotope concentrations makes it possible to assess, using appropriate models of the isotope production, the average flux of SEP on the timescale defined by the isotope's lifetime. Earlier estimates of the average SEP flux, based on different isotopes, is shown in Table 4.3, assuming the exponential over rigidity spectral shape of SEPs:

$$\begin{eqnarray}&&J(R)={J}_{0}\cdot \exp \,\left(\frac{-R}{{R}_{0}}\right).\end{eqnarray} \tag{ 4.8 }$$

The estimates were done by finding the values of the spectral parameters J₀ and R₀, which fit best the measured depth profile of the isotope concentration. However, this approach requires an implicit assumption of the spectral shape, the validity of which is not known a priori. As a result, the "effective" energy/rigidity range remains uncertain, and uncertainties of the reconstruction can be hard to define.

Figure 4.34 shows the functions η of the cosmogenic isotope production in lunar samples (see Equation (4.2)). One can see that measurements of cosmogenic isotopes in lunar samples can provide information on SEP only above ∼15 MeV for ²⁶Al, 30 MeV for ³⁶Cl, 40 MeV for ¹⁴C, and 70 MeV for ¹⁰Be. The upper boundary of the SEP spectrum definable from lunar samples is 100–200 MeV. This effective energy range is defined by the ionization losses of protons in the matter and the growing contribution of GCR at depths deeper than ∼5 g cm⁻². Thus, SEP spectra can be reconstructed in a relatively narrow energy band.

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This kind of analysis opens up the possibility to an alternative nonparametric approach, free of a priori assumptions, to reconstruct SEP spectrum from lunar samples, as developed recently by Poluianov et al. (2018). One can see from Figure 4.34 that the most suitable isotope to study SEPs in lunar samples is ²⁶Al, which has the smallest threshold and the highest function η.

The production function of ²⁶Al by protons in a lunar sample is shown in Figure 4.35 for different depths between 0.1 and 3 g cm⁻². One can see that the threshold of isotope production increases with depth. The production grows fast right at the threshold and then gradually declines with energy, staying at nearly the same level. This makes the energy dependence of the production function at a given depth close to that of an ideal integral spectrometer. The ideal integral particle spectrometer is a detector with response directly proportional to the integral flux of primary particles with energy above a threshold E_th, with the response-function being steplike, i.e., zero for energy below E_th, and a constant value above E_th.

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Direct modeling (Poluianov et al. 2018) yields that for each depth below ∼5 g cm⁻², there is an effective energy E_eff defined such that the production of ²⁶Al at this depth is directly proportional (with a high accuracy) to the integral flux of protons with energy above E_eff for every reasonable spectral shape of SEP. This makes it possible to reconstruct, from the point-by-point measured depth profile of the isotope concentration in a lunar sample, the integral SEP spectrum, without any a priori assumptions on the spectral shape. Some examples of such reconstruction by Poluianov et al. (2018) are shown in Figure 4.36. Different colored symbols denote (as specified in the legend) SEP reconstructions based on different lunar samples and bounding assumptions on the not precisely known erosion rate. The full uncertainty range is shown as the gray-hatched stripe. One can see that the reconstruction is very robust for the energy range between 20 and 50 MeV, becoming less certain at higher energies and reaching a factor of ∼3 uncertainty at 80 MeV. We also note that most of earlier parametric estimates of the SEP spectrum from lunar samples agree with the direct reconstruction presented here, within the full range uncertainties of the latter (see details in Poluianov et al. 2018).

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The mean SEP spectrum for the space era (Reedy 2012) is shown in Figure 4.36 as green stars with errors bars (representing the cycle-to-cycle variability). It is interesting to note that the SEP flux during the last solar cycles is totally consistent with the mean flux for the last million years (the green stars are within the gray-hatched area), even though the last 50 year period was characterized by enhanced solar activity (Solanki et al. 2004; Poluianov et al. 2018).

Of course, while lunar samples allow one to assess the spectra of SEP, the time resolution is lost completely, and no individual events can be identified. On the other hand, an integral probability density function (IPDF) can be evaluated within reasonable assumptions, such as the constancy of the IPDF on different timescales, from centennial to millions of years. This was done by Poluianov et al. (2018), who estimated for the Weibull distribution (Weibull 1951) and by combining different data sets (space-era data, cosmogenic isotopes in terrestrial archives, and in lunar samples) the IPDF of the SEP event occurrence on timescales from years to millions of years (Figure 2.16). One can see that different independent data sets, including lunar samples, are consistent with each other.

Unopened Lunar Samples

Lunar Meteorites