ESTIMATION OF THE OCCURRENCE TIME OF THE Δ14C PEAK IN AD 775 BASED ON THE OXIDATION TIME OF 14C IN THE ATMOSPHERE AND Δ14C VALUES IN SUBANNUAL TREE RINGS

ABSTRACT The 14C peak in AD 775 (M12) has been measured and confirmed globally in several studies since it was first measured in annual tree rings by Miyake et al. (2012). However, M12 data measurements in early- and latewood are limited. This paper presents the Δ14C values in early- and latewood from AD 762–776 Zelkova serrata tree rings from Bangu-dong, Ulsan, South Korea (35°33′N, 129°20′E). The results indicate no early rise in Δ14C values in the latewood of AD 774 in this sample located at mid-latitude. A comparison of the results of this and previous studies suggests latitude dependence (Büntgen et al. 2018); that is, the early rise of Δ14C in AD 774 was not observed at mid-latitudes in South Korea but was observed at high latitudes in Finland. The half-oxidation time of 14C was estimated from a detailed analysis of a small bomb peak in AD 1962. Based on the half-oxidation time, the Δ14C rise in the latewood, but not in the earlywood, of AD 774 in Finland, and the absence of a Δ14C rise in both the early- and latewood of AD 774 in South Korea, the 14C spike was estimated to have been produced from late April to mid-June in AD 774.


INTRODUCTION
Since the discovery of the AD 775 14 C peak (M12) by Miyake (Miyake et al. 2012), M12 has been confirmed, and its potential causes have been investigated by several groups. The potential causes of M12 include a solar proton event (SPE) (Melott and Thomas 2012;Thomas et al. 2013;Usoskin et al. 2013;Jull et al. 2014;Mekhaldi et al. 2015), supernova (Miyake et al. 2012), gamma ray burst (GRB) (Hambaryan and Neuhäuser 2013;Pavlov et al. 2013), and normal periods of low solar activity (Neuhäuser and Neuhäuser 2015). Alone, none of the abovementioned potential causes is sufficient to explain M12, but an SPE seems to have been a primary cause of M12. If M12 was caused by a supernova, there should be a residual candidate supernova in close proximity to the Earth (Miyake et al. 2012). However, no supporting evidence for such a supernova has been found (Stephenson 2015). Supernovae emit high-energy particles and gamma rays. The high-energy particles from supernovae have an abundant energy distribution. Hence, extended arrival times that span a minimum of at least 10 years should be observed (Gehrels et al. 2003;Dee et al. 2017). However, the M12 peak exhibits a sharp 1-2-year increase. Gamma rays from supernovae and GRBs have a very short duration, which implies that a rapidly rising 14 C peak may occur. It has been shown that the M12 concentrations of the cosmogenic isotope 10 Be measured in Antarctic ice were too high to have been produced by a GRB (Usoskin et al. 2013). Although the exact cause of M12 is still disputed, an SPE is considered a possible cause due to the 10 Be/ 36 Cl measured in polar ice cores (Mekhaldi et al. 2015). However, more evidence is required to confirm an SPE as the cause of M12. Moreover, the 14 C peaks in AD 993/994 (Miyake et al. 2013) and 660 BC (Park et al. 2017) are similar to M12 and may have similar explanations.
Under the assumption that an abrupt increase in the production of 14 C led to M12, the aim of this study was to estimate the occurrence time of the abrupt increase in 14 C production based on a comparison of data measured in South Korea and Finland (Uusitalo et al. 2018). The occurrence time of the 14 C spike production estimated by Güttler (Güttler et al. 2015) was between September AD 774 and September AD 775, whereas that obtained by Büntgen (Büntgen et al. 2018) was between June and August of AD 774. These two studies did not include the oxidation time of 14 C in their estimations, so the estimated occurrence times of the abrupt increase in 14 C production are at least a few months late, as the residence time of 14 C ranges from one month to 5 years (Jaffe et al. 1968;Robbins et al. 1968;Weinstock 1969;Weinstock and Niki 1972;Volz et al. 1980;Logan et al. 1981;Brenninkmeijer et al. 1992;Daniel 1999). In this study, we investigated the oxidation time from a detailed analysis of a bomb peak, which differs from the methods used in previous studies. This oxidation time and the early rise in the Δ 14 C values in the latewood of AD 774, one year earlier than the AD 775 timing obtained by other researchers (Uusitalo et al. 2018), was considered to provide an estimate of the occurrence time of the abrupt increase in 14 C production.

MATERIALS AND METHODS
The early-and latewood in tree rings (AD 762-776) of Zelkova serrata C.E. excavated from a burial site at Bangu-dong in Ulsan, South Korea (35°33 0 N, 129°20 0 E) ( were prepared at the Tree-Ring Research Center of Chungbuk National University to provide measurement samples for Δ 14 C analysis ( Figure 2). This burial site is situated in the region of the Asian monsoon; thus, the tree rings were under the influence of the Asian monsoon.
Previous studies have confirmed that the δ 18 O chronology can be used in cross-dating for other tree species (Li et al. 2015;Seo et al. 2017) and applied to areas situated at a distance of approximately 1000 km from the origin (Baker et al. 2015). Based on such findings, the Zelkova tree-ring δ 18 O time series was compared with the Japanese master δ 18 O chronology, which is the mean chronology of three local δ 18 O chronologies from Aomori (Thujopsis dolabrata var. hondae), Akita (Crypomeria Japonica), and Niigata (Zelkova serrata), located in northwest Japan. The Japanese master δ 18 O chronology ranged from AD 502 to 1595. The Zelkova tree-ring δ 18 O time series was cross-dated with the Japanese master δ 18 O chronology and completely overlapped with the Japanese master δ 18 O chronology, so that the first and last tree rings were successfully dated in AD 752 and 861, respectively (Choi 2019). The dating results were decided based on the t-value (4.4), G-value (58%), and correlation coefficients (r = 0.40, p < 0.001) and also the synchronization strength between the Zelkova tree-ring δ 18 O time series and Japanese master δ 18 O chronology.
Zelkova serrata is a genus comprising six species of deciduous trees in the elm family Ulmaceae, which is native to southern Europe and southwest and eastern Asia (Bétrisey et al. 2018;Wikipedia). Early-and latewood from AD 762-776 were treated using the α-cellulose extraction method (Hua et al. 2004). This method removes unwanted mobile materials such as gums, resins, fats, and waxes, leaving the α-cellulose behind. The samples were heated at 80°C for 6 hr in a mixed solution of 120 mL cyclohexane and 60 mL ethanol. The remains were repeatedly rinsed with ethanol and de-ionized water. Thereafter, the samples were treated with 150 mg NaClO 2 and 1 M HCl at 100°C for 1-2 hr. The samples were then treated in a 12% NaOH solution with nitrogen gas bubbling at 60°C. Finally, the samples were neutralized with a 2 M HCl solution for 30 min and dried in an oven at 40°C. An elemental analyzer (EA) was used for combustion to produce CO 2 , which was then reduced to graphite. The 14 C/ 12 C and 13 C/ 12 C ratios of the samples were measured using the 1MV accelerator mass spectrometer (AMS) at the Korea Institute of Geoscience and Mineral Resources in Daejeon, South Korea (Hong et al. 2010). The Δ 14 C values of samples were calculated with oxalic II and background samples older than 100,000 years, Estimation of the Δ 14 C Peak in AD 775 1287 which were measured together with unknown samples. To monitor the counting conditions, known samples (IAEA C7 and C8 reference materials) were measured approximately every 20 samples. Figure 3 shows the Δ 14 C values of the early-and latewood in tree rings between AD 762 and 776. The results confirm the existence of the M12 event and suggest that the height of M12 was approximately 15‰, which is consistent with the results of previous studies (Miyake et al. 2012;Uusitalo et al. 2018). No early rise in Δ 14 C in AD 774 early-or latewood was observed.

Analysis of Δ 14 C from AD 762-776 Early-and Latewood in South Korea
A comparison of our results to those of previous studies (Miyake et al. 2012;Uusitalo et al. 2018) is shown in Figure 4. Although the results from Finland (68.5°N, 28.1°E) show a significant early rise in the latewood of AD 774 (Uusitalo et al. 2018), our results did not identify an early rise in the early-or latewood of AD 774. This comparison shows that the height of the early rise in the latewood in AD 774 was dependent on latitude because the amplitude of M12 increased in accordance with an apparent increase in the latitude of the sampling site (Büntgen et al. 2018). In previous studies (Jull et al. 2014;Büntgen et al. 2018;Uusitalo et al. 2018), the early rise of Δ 14 C in AD 774 was observed at high latitudes in Russia (67.5°N, 70.7°E) and Finland (68.5°N, 28.1°E).

Estimation of the Half-Oxidation Time (HOT) of 14 C Produced in the Troposphere
Of the 14 C emitted by nuclear reactions, 95% is instantaneously oxidized into 14 CO (Pandow et al. 1960;MacKay et al. 1963;Jöckel et al. 2003). The residence time of CO in the atmosphere ranges approximately from 1 to 60 months, as shown in Table 1 (Jaffe et al. 1968;Robbins et al. 1968;Weinstock 1969;Weinstock and Niki 1972;Logan et al. 1981;Volz et al. 1980;Brenninkmeijer et al. 1992;Daniel 1999). The residence time of CO determined in studies from the 1990s, which are relatively recent, tended to be shorter, and CO levels are known to be affected by bacteria in soil (Duggin and Cataldo 1985).   Robbins et al. 1968 Estimation of the Δ 14 C Peak in AD 775 1289 CO in the atmosphere is mainly oxidized into CO 2 , as follows (Volz et al. 1980): The oxidation time of 14 C from nuclear reactions into 14 CO 2 can be used to define the occurrence time of the 14 C spike using Δ 14 C values from tree rings. We attempted to calculate the oxidation time using peak 14 C from the bomb peak (Hua et al. 2013) because M12 can be considered similar to the increase in 14 C due to nuclear testing, or the "bomb peak." The bomb peak (main bomb peak) is a Δ 14 C peak that appeared in AD 1963 at Vermunt, Austria, as a result of nuclear waepon tests (47°N, Levin et al. 1985), but   -December 1961. This led to the conclusion that the initial increase in the small bomb peak measured at Vermunt, Austria, was mostly due to the Russian nuclear tests. From January to August 1962, the USA conducted 70 nuclear tests. However, the site of Figure 5 There is a small bomb peak from October in 1961 to February in 1962 (Levin et al. 1985), and this small bomb peak can be compared to the early rise in M12. The small bomb peak is composed of an initial increase of approximately 100‰ from October 1961 to February 1962, followed by a second increase of approximately 100‰ from March to August 1962; the total height of this small bomb peak was approximately 200‰.
the nuclear tests was situated far from Vermunt, and most of the tests occurred in May-July 1962, and thus were too close to August and too far from Vermunt to have caused the second increase in the small bomb peak.
The observed small bomb peak can be used to estimate the HOT of 14 C in the troposphere. There are two reasons for this. First, we assumed that the small bomb peak (October 1961to February 1962 was only due to high-latitude nuclear tests in Russia; thus, the analysis and assumptions in the estimation of the HOT were relatively straightforward. Second, the initial increase in the small bomb peak occurred in autumn and winter, and was indicated by the 14 C produced in the troposphere due to short dispersion time and absence of a spring seasonal effect; i.e., we can exclude the Brewer-Dobson circulation ("spring mixing" from the stratosphere to the troposphere from May to June). The 14 C dispersion time at similar latitudes was therefore approximately 1-2 weeks, shorter than the HOT, which is known to range from 1 to 60 months (see Table 1). Hence, based on the small bomb peak, it is possible to estimate the HOT from a comparison between the initial increase with its small ratio of 14 C oxidation, and the second increase, with a large ratio of 14 C oxidation.
The height of the initial increase in the small bomb peak was estimated to be 100‰ in February 1962, as shown in Figure 5. The height of the initial increase was overestimated due to the seasonal decrease in Δ 14 C, and this initial increase required 4 months, from the time of the Soviet tests in October 1961 (the middle of a 3-month period of nuclear tests in 1961 in Russia) to February 1962, for the 100‰ increase to be observed. The second increase in the small bomb peak (height of 200‰), from March to August 1962, matched the Brewer-Dobson circulation model and was similar to the bomb peaks in 1963, 1964, and 1965, as shown in Figure 6. The second increase occurred during the time of the normal Brewer-Dobson circulation model. The total 14 C produced by this small bomb peak could potentially increase Δ 14 C to 140‰ (70% of the total height [200‰] of the small bomb peak) for the entire Earth, similar to the main bomb peak (1000‰ at high latitudes and Figure 6 Δ 14 C in atmosphere at Vermunt (Levin et al. 1985). This bomb peak was produced by atmospheric nuclear tests.
Estimation of the Δ 14 C Peak in AD 775 1291 700‰ in the equatorial range, making the average~700‰). The amount of 14 C corresponding to the initial increase in the small bomb peak due to tropospheric dispersion (C sb_T ) was obtained from the following equation, under the assumption that the 14 C production in the troposphere is 30% (Naegler and Levin 2006;Yang et al. 2000) of the total 14 C production (supplementary materials).

C sb T H sb eq
1 e M sb × ln 2 =T 1=2 × C × T 30% 51kg; (1) C The amount of 14 C=‰ 1023 kg 1000‰ (2) (Schimel et al. 1996), where H sb_eq (140‰) represents 70% of the total height (200‰) of the small bomb peak. Similarly to the tendency of the main bomb peak, T (30%) represents the amount of 14 C in the troposphere as a proportion of the total 14 C, M sb (10 months) represents the time required for the total increase in the small bomb peak to occur (October 1961 to August 1962), and T 1/2 (3.8 months) represents the HOT of 14 C.
It was assumed that the 14 C produced in the troposphere by nuclear tests was dispersed at 33.7°N (the lowest latitude of the 14 C dispersion area for 4 months based on the 1.5 years for which the bomb peak was dispersed throughout the Earth; supplementary materials) in February 1962. The amount of Δ 14 C then increased linearly with latitude (as shown in Equation [3] and Table 2), the amount of Δ 14 C could be obtained at each latitude, and the Δ 14 C at 47°N (latitude of Vermunt, H E_1sb_FO ), with full 14 C oxidation, was obtained by equalizing C sb_T (based on an assumption of almost complete 14 C oxidation) with the sum in Table 2 determined from the adjustment of B and C in Equation (3). The oxidation ratio of 14 C for 4 months was obtained using Equation (4) (supplementary materials). (3) where A represents the area from the pole to the specified latitude divided by 10 7 , and B(=492.3) and C(=43.3) are obtained from adjusting to equalize C sb_T with the sum of 14 C in Table 2 (supplementary materials).

* H E_1sb_FO
H 1sb H E 1sb FO 51% 14 C Ox r 14 C oxidation ratio for 4 months ; (4) where H 1sb (100‰) represents the Δ 14 C height of the first increase in the small bomb peak (from October 1961to February 1962, and H E 1sb FO represents the Δ 14 C height of the first increase in the small bomb peak with 14 C full oxidation. The HOT of 14 C was calculated as approximately 3.8 months using iterations of Equation (5) and the calculation procedure presented in the supplementary materials: where T 1sb (4 months) represents the duration of the first increase in the small bomb peak, and 14 C_Ox_r (51%) represents the 14 C oxidation ratio for T 1sb (4 months).
Among the assumptions used during calculation of the HOT, the ratio of 14 C production in the troposphere is sensitive to the value of HOT, so HOTs were recalculated while varying the ratios in the range of 25-35%, as shown in Table 3. HOTs were obtained in the range of 2-7 months and were estimated to be in the range of 1-7 months considering the recalculation and a relatively recent report by Bernninkmeijer et al. (1992).
It can be assumed that the 14 C produced in the troposphere in AD 774 was dispersed to 49.1°N, which is the latitude of the average area between the Finnish and South Korean sampling locations. Given that there was no early rise in Δ 14 C in the latewood of AD 774 in South Korea, as opposed to in Finland, it can also be assumed that Δ 14 C increased linearly with latitude. Based on the HOT of 3.8 months and the above assumptions, Δ 14 C at the sampling location (68.5°N) in Finland (Figure 7) can be calculated by equalizing the sum of 14 C amounts of the latitudes with OR_ 14 CO 2 of Equation (6), similar to obtaining H E 1sb FO (supplementary materials). The calculated Δ 14 C result, shown in Figure 7, can be checked against the " 14 C spike production time" sheet in the supplementary materials. Table 3 HOTs were recalculated with variations of the ratio of 14 C production in the troposphere in the range 25-35%. The HOT of 14 C was calculated to range from 2 to 7 months.
Ratio of 14 C produced in the troposphere (%) HOT (months) 25 2.3 30 3.8 35 6.7 Estimation of the Δ 14 C Peak in AD 775 1293 where 14 C M12 represents the total 14 C produced in M12, Trospos_ratio (30%) represents the proportion of 14 C produced in the troposphere, and T represents the time after the abrupt increase in the production of 14 C.

Estimation of Time of 14 C Spike Production
As shown in Table 4, which gives the Δ 14 C results of Finnish wood, the Δ 14 C increase in earlywood in AD 774 was 2.0 ± 1.2, and that of latewood was 9.7 ± 2.2 (Uusitalo et al. 2018). The Δ 14 C increase of earlywood in AD 774 was calculated from the difference between the amount of 14 C in earlywood in AD 774 and the average Δ 14 C of earlywood from AD 770 to 773, whereas the Δ 14 C increase of latewood in AD 774 was calculated from the difference between the amount of 14 C in latewood in AD 774 and the average Δ 14 C of latewood from AD 770-773.  The onset date of cambium division and the length of the growing season vary from year to year as well as over a longer scale because tree phenology and climate variability (temperature) influence cell production and the calendar dates of early-and latewood formation. However, the tree ring width (TRW) of 2000-year tree rings does not show summer temperatures in Finland (Esper et al. 2012) or certain other trends. Thus, although estimation from cambium division and xylem formation can still result in errors due to phenology and climate variability, we can attempt to estimate the onset times of early-and latewood, as well as the end time of latewood, of a Scots pine tree from AD 775 based on their times in recent Scots pine trees. The onset time of the earlywood of a Scots pine tree used for the measurement of M12 was June 11 ± 5; the onset time of latewood was July 10 ± 5, and the end time of latewood was August 26 ± 9 (Seo et al. 2010(Seo et al. , 2011Cuny et al. 2015; supplementary materials). The onset time of earlywood of the Scots pine tree was defined as the onset time of the radial growth of earlywood; the onset time of latewood was defined as the onset time of the radial growth of latewood (Seo et al. 2010(Seo et al. , 2011. However, the end time of latewood was defined as the sum of the end time of the radial growth of latewood and the time lag (27 days) between the woody biomass production and xylem size increase (radial growth) in the boreal region, as woody biomass production proceeds after the end time of the xylem size increase (Seo et al. 2010(Seo et al. , 2011Cuny et al. 2015).
The time required for trees to absorb CO 2 from the air via photosynthesis and produce tree ring tissue via metabolism is approximately one month (Grootes et al. 1989). Air mixing and the oxidation of 14 C in the troposphere occur simultaneously; however, the oxidation of 14 C proceeds at a significantly slower rate. Although the rate of air mixing between different latitudes is slower, the air mixing times at the sampling location in Finland and similar latitudes were considered negligible due to westerly winds. The Δ 14 C in the early-and latewood periods in Finland (Figure 7) noted in the preceding paragraph were calculated under the assumptions of a linear increase in Δ 14 C with an increase in latitude (supplementary materials), HOT, and a one-month delay between photosynthesis and metabolism. The Volz et al. 1980; χ 2 values were obtained from the difference (divided by measurement error) between the Δ 14 C values of early-and latewood in Finland and the calculated Δ 14 C values.
where m represents a Δ 14 C measurement in Finland, c represents a Δ 14 C calculation, σ represents the error of Δ 14 C measurements in Finland, E represents early wood, and L represents late wood.
The occurrence time of the abrupt increase in 14 C production was approximately mid-May (5.3 months) from a minimum χ 2 value of 0.56. Although the occurrence time of the 14 C spike obtained by Güttler et al. (2015) was between September AD 774 and September AD 775, and that by Büntgen et al. (2018) was between June and August of AD 774, the calculation in this study yielded an occurrence time of approximately mid-May (5.3 months) in AD 774, i.e., a few months earlier than the estimation by Büntgen. This difference can be attributed to the consideration of the oxidation times of 14 C in this study.
The value of HOT can vary from 1 to 6 months due to variation in the amount of 14 C produced in the troposphere. The month of the abrupt increase in 14 C with the lowest χ 2 value for each HOT is presented in Table 5. This result indicates that the occurrence time of the abrupt increase in production of 14 C was from late April to mid-June in AD 774. This is still a few Estimation of the Δ 14 C Peak in AD 775 1295 months earlier than the estimation by Büntgen (Büntgen et al. 2018) and 10 months earlier than that made by Güttler (Güttler et al. 2015). These differences are mainly due to the lack of consideration of 14 C oxidation time.

CONCLUSION
We measured Δ 14 C values for the early-and latewood tree rings of Zelkova serrata from AD 762-776 at Bangu-dong, Ulsan, South Korea, confirming the presence of M12 in a South Korean tree.
A comparison of the results obtained in this study and those from previous studies suggests that, in addition to the latitude dependence of the highest Δ 14 C values of M12 (Büntgen et al. 2018), the height of the early rise in Δ 14 C in AD 774 also varied according to latitude; we did not see an identifiable early rise in Δ 14 C in either the early-or latewood of AD 774 in South Korea, whereas a notable early rise in Δ 14 C in the latewood of AD 774 was observed at high latitudes (Finland).
The HOT of 14 C produced in the air could be estimated by a detailed analysis of a small bomb peak from October AD 1961 to August AD 1962. The HOT of 14 C was calculated to range from 2 to 7 months, based on analysis of a small bomb peak similar to M12 for the calculation of HOT, whereas the residence time of CO was estimated from sources and sinks of CO, although the residence time of CO and HOT were almost the same. From the estimated values of HOT, including another recent estimate (1 month, Brenninkmeijer et al. 1992;Daniel 1999), and a comparison of Δ 14 C values calculated and measured in the early-and latewood periods in Finland, the occurrence time of the abrupt increase in 14 C production was estimated to have occurred sometime during the period of late April to mid-June in AD 774.