The Millennium Eruption of Changbaishan Tianchi Volcano is VEI 6, not 7

The Millennium Eruption (AD 946–947) of Changbaishan Tianchi Volcano is one of the largest known eruptions in recorded history. With the help of previously published isopachs and distal ash thicknesses, we re-calculate the bulk volume of its distal eruptive product, the B-Tm ash, as 27–62 km3 and the total eruption volume as 40–98 km3. The updated volume estimates are around half of those estimated by previous studies of this seminal eruption. Our work shows that the Millennium Eruption is a VEI-6 eruption, rather than VEI-7 as previously envisaged, and its magnitude is also lower than previously thought. This has implications for regional frequency-magnitude relationships and may also partially explain the limited regional, rather than global, climatic effects of the Millennium Eruption.


Introduction
The Millennium Eruption (ME) of Changbaishan Tianchi Volcano, on the border of China and North Korea, took place in AD 946-947 (Xu et al. 2013;Oppenheimer et al. 2017). Previous works have classified it as a VEI-7 (100 to volumes of other eruptive products are assigned based on the most recent studies.

The B-Tm ash
We have compiled 76 thickness measurements (see Supplementing Document for raw data) of the B-Tm ash from previous works (Fig. 1;Utkin 1977;1989;Machida and Arai 1983;Machida et al. 1990;Machida and Arai 2003;Furukawa and Nanayama 2006;Okuno et al. 2011;Hughes et al. 2013;Chen et al. 2016;Ikehara et al. 2017;Derkachev et al. 2019;Nakanishi et al. 2020;Razjigaeva et al. 2020). Thickness data that are reported to be reworked or contain non-pyroclastic materials are excluded. The B-Tm ash was observed in the west of the volcano as cryptotephra (Sun et al. 2015), which cannot be used for helping isopach construction. Horn and Schmincke (2000) and Machida and Arai (2003) previously constructed two sets of isopachs for the Fig. 1 a, b B-Tm ash isopachs (solid lines; cm) digitized from Horn and Schmincke (2000) and Machida and Arai (2003), respectively. Data sources marked in a. Dashed isopachs in b are constructed in this work; c constructed B-Tm ash extent (solid line) from Machida and Arai (2003) and 1-cm and 0.1-cm isopachs from this work (dashed lines). Crosses are locations with no B-Tm ash observed (Furuta et al. 1986). See Supporting Document for more details on why they are not used to constrain the 0.1-cm isopach constructed in this work B-Tm ash ( Fig. 1a and b). The former set has been used for volume calculation of the B-Tm ash. The latter only has the 10-cm, 5-cm, and > 0-cm isopachs, which are not fully enclosed. They have not been used for volume estimates. The B-Tm ash extent (i.e., the > 0-cm isopach) from Machida and Arai (2003) will not be used here because the B-Tm ash has been found outside this extent: it was found as cryptotephra layer in Lake Kushu, northwest of Hokkaido (Chen et al. 2016) and a thin tephra layer (< 1 mm) in Lake Suigetsu, central Honshu  in Japan (Fig. 1c).
We complete the 10-cm and 5-cm isopachs of Machida and Arai (2003), which have much greater isopach areas (Table 1) than those published in Horn and Schmincke (2000). Additional 1-cm and 0.1-cm isopachs for the B-Tm ash (Fig. 1b and c,and Fig. 2) are also constructed (see Supplementing Document on how the isopachs are constructed) such that they could be combined with isopachs of Machida and Arai (2003) to estimate the maximum volume of the B-Tm ash. The 0.1-cm isopach is constructed with uncertainty. How it would affect the maximum volume estimate will be examined.

Comparing isopachs with thickness measurements
Measured thicknesses of the B-Tm ash do not consistently thin with distance from the vent (Fig. 2). The cause of such a variability is not clear (e.g., varied dispersal patterns and post-depositional processes). It is thus difficult to estimate its volume accurately. Alternatively, if we prove that thicknesses predicted by the isopachs are mostly greater than individual thickness measurements, these isopachs can be used to calculate the maximum volume of the B-Tm ash. We are most interested in the maximum volume here because (1) isopachs of Machida and Arai (2003) have not been used for volume estimate, and they have much greater areas compared to those from Horn and Schmincke (2000); (2) a better-constrained maximum volume of the B-Tm ash could potentially help us confirm or reassign the VEI of the ME as the volume of the B-Tm ash takes up a large portion of the total eruption volume of the ME in previous studies ( Table 2).
We compare thickness measurements of the B-Tm ash with isopachs of Machida and Arai (2003) and the newly constructed 1-cm and 0.1-cm isopachs, and find that within the 1-cm isopach, there are 26, 44, and 4 thickness observations that are consistent, thinner, and thicker, respectively, than thicknesses inferred from the isopachs ( Fig. 2; the other two thickness measurements are outside the 1-cm isopach shown in Fig. 1c). Thickness observations within the 10-cm isopach and north of 42 • N (which corresponds to half of its area) are 3-cm thick or thinner, suggesting that northern halves of the 10-cm and 5-cm isopachs of Machida and Arai (2003) should have much smaller areas. These checks confirm that the isopachs of Machida and Arai (2003) and the newly constructed Table 1 Isopach information of tephra fall deposits of the ME and the tephra from the 1815 Tambora eruption. Blue and red cells: isopach data used for volume calculation of the B-Tm ash. Yellow cells are isopach areas extrapolated based on the 10-cm and 5-cm isopachs assuming a linear relationship in the log(thickness)isopach area plot. Isopach areas measured with the R package "geosphere" (R Core Team, 2017;Hijmans, 2019) 1-cm isopach can be reliably used for the maximum volume estimation of the B-Tm ash.

Volume estimation
Here we use the segmented exponential functions proposed by Fierstein and Nathenson (1992) to estimate the maximum volume of the B-Tm ash (Fig. 4). This method estimates the volume of tephra deposits by segments, and each segment is defined by the available isopachs. The volume within each segment is the volume of a tephra deposit from Isopach A to Isopach B. Exponential thinning is assumed within each segment on the log(thickness)-ispach area plot. This method is chosen because using other methods introduces additional uncertainties in fitting the isopach data to certain types of curves on the log(thickness)-ispach area plot (especially given just four data points), and the results might not represent the maximum estimate. In addition, volume of proximal tephra of the ME will be estimated separately later based on proximal isopachs. One main advantage of other methods (Pyle 1989;Bonadonna and Houghton 2005;Bonadonna and Costa 2012), i.e., the ability to infer the proximal thinning pattern of tephra deposits based on limited isopachs, would not apply to this work.
The volumes of the B-Tm ash calculated from isopachs of Horn and Schmincke (2000) and isopachs published by Machida and Arai (2003) plus our newly constructed ones are 26.66 and 62.48 km 3 , respectively, based on Eq. Extents of a and b correspond to gray and yellow panes in Fig. 1b, respectively. White, blue, and red points correspond to observations that are thinner, consistent, and thicker than thicknesses inferred from the isopachs. Observations masked by the gray box in b are presented in a Table 2 Bulk volumes of different eruptive products of the ME and their sum from this work and previous studies 13 of Fierstein and Nathenson (1992). The one-and twosegment exponential functions of Pyle (1989) and Fierstein and Nathenson (1992) are applied to isopach data of Horn and Schmincke (2000) for better comparison as the same methods were used in their work, and the calculated volumes are 32.99 and 26.69 km 3 , respectively. The two values are within the range of 26.66-62.48 km 3 . It is noted that the reported volumes here include the volume of the proximal ash which is determined based on the distal 10-cm and 5-cm isopachs. In calculating the maximum total eruption volume later, this portion of volume will be replaced by the tephra volume calculated based on the proximal isopachs.
Our uncertainty in constructing the 1-cm and 0.1-cm isopachs has limited influence on the maximum volume estimate. A ±20% variation in both the 1-cm and 0.1-cm isopach areas leads to a ±6.7% (58.29-66.59 km 3 ) variation in calculated maximum volume. A ±20% variation in the 0.1-cm isopach area leads to a ±2.9% (60.70-64.27 km 3 ) variation in calculated maximum volume.

Comparison with previous studies and tephra deposit of the 1815 Tambora eruption
The volume of the B-Tm ash was previously estimated as 63-100 km 3 (Horn and Schmincke 2000). Using the same set of isopachs, our estimated volume is 26.66 km 3 . The estimated maximum volume from this work (62.48 km 3 ) is close to but still below the previous lower limit, and the calculated volumes from our work also include the proximal volume which will be subtracted later in calculating the total eruption volume. Limited information was provided about how the previous volume was calculated, but we notice that with the one-and two-segment exponential functions of Fierstein and Nathenson (1992), using the longest isopach axis of Horn and Schmincke (2000) (Table 1), rather than of the square rooted isopach areas, results in volumes of 92.73 and 81.46 km 3 , respectively. These values are consistent with previous estimate, but overestimate the true volume due to using incorrect data.
Tephra volume of the 1815 Tambora eruption, the most recent VEI-7 eruption, was estimated to be 90-133 km 3 (Self et al. 2004; Kandlbauer and Sparks 2014) using isopach-based methods. The isopach data of the tephra from the Tambora eruption reported in Kandlbauer and Sparks (2014) are compared with those of the B-Tm ash here. For the isopachs of Horn and Schmincke (2000) corresponding to our minimum B-Tm ash volume, their 20-cm and 5-cm isopach areas are 10.3% and 47.1% of those of the 1815 Tambora tephra deposit, respectively ( Table 1). The ratios are 52.9%, 80.5%, and 56.7% for the 20-cm, 5-cm, and 0.1-cm isopachs used for the maximum volume calculation ( Table 1). The comparison confirms that the B-Tm ash volume was overestimated previously. Liu et al. (1998) and Horn and Schmincke (2000) constructed isopachs for total and Phase 1 proximal tephras of the ME, respectively. The two sets lead to volume estimates of 21.66-23.24 km 3 (with the one-and twosegment exponential models) and 4.2 km 3 (Horn and Schmincke 2000), respectively.

Proximal tephra
The isopachs of Liu et al. (1998) are compared with the summed thicknesses of tephra deposits from the ME reported in recent works (Machida et al. 1990;Sun et al. 2017;Pan et al. 2020) at sample sites to the east of the volcano (Fig. 3). Thicknesses of potentially post-ME tephras (due to the dispute over the presence of post-ME eruptions; Wei et al. 2013;Sun et al. 2017;Pan et al. 2017;Pan et al. 2020) are also included as we are more concerned with the maximum thickness. All available observations are at least 50-250 cm thinner than predictions from the isopachs, showing that in the east of the volcano, isopachs of Liu et al. (1998) greatly overestimate the tephra thickness distribution.
We thus use 23.24 km 3 to denote the maximum volume of the proximal ME tephra (i.e., the sum of Phase 1 and 2 volumes). We use 4.2 km 3 and the proximal volume of the B-Tm ash calculated based on isopachs of Horn and Schmincke (2000) to denote minimum volumes of the proximal Phase 1 and 2 tephras, respectively. The latter is adopted because studies have confirmed the presence of Phase 2 tephra close to the vent (Machida et al. 1990;Pan et al. 2017), and tephra thickness tends to have a greater thinning rate in the area close to the vent (Pyle 1989). Horn and Schmincke (2000) estimated that the volume of the ME ignimbrites ranged from 12.3 to 17.5 km 3 (Phase 1: 8.4-11 km 3 ; Phase 2: 3.9-6.5 km 3 ). Zhao et al. (2020) estimated that the volume in China was ∼7 km 3 (Fig. 3), and found that extents of the ignimbrites in China are smaller than those mapped by Horn and Schmincke (2000).

Extra-caldera ignimbrites
Here the maximum extra-caldera ignimbrite volume is assumed to be 13 km 3 , which is the sum of the volume in China (7 km 3 ; Zhao et al. 2020), a quarter (11×0.25 = 2.75 Fig. 3 Proximal ME tephra isopachs (unit: cm) from Liu et al. (1998). Total thicknesses (cm) of ME tephras digitized from recent works are marked with references given. Fall deposits that might be from post-ME eruptions (due to the dispute over the presence of post-ME eruptions) are treated as ME tephras. Inset figure shows the extent of the main figure with reference countries and region labeled km 3 ) of maximum Phase 1 ignimbrite volume estimated by Horn and Schmincke (2000), and half (6.5 × 0.5 = 3.25 km 3 ) of maximum Phase 2 ignimbrite volume estimated by (Horn and Schmincke 2000; Table 2). The latter two denote the assumed Phases 1 and 2 extra-caldera ignimbrite volumes in North Korea because Horn and Schmincke (2000) estimated that Phase 1 ignimbrite covered a half circle area to the north around the vent (Fig. 2 in their  work), which is mostly in China, suggesting that the Phase 1 ignimbrite extent in North Korea must be smaller than a quarter of its total area (the southeast quadrant with respect to the vent is within the North Korean territory); the area ratio of Phase 2 ignimbrite in North Korea is smaller than half of its total area as mapped by Horn and Schmincke (2000). The proposed volume thus maximizes volumes of the ME ignimbrites in North Korea, and takes into account the most recent and more detailed estimate of their volume in China. The minimum extra-caldera ignimbrite volume is assumed to be 9.33 km 3 , which is the estimated volume in China from Zhao et al. (2020) times the inverse of its area ratio (3/4) in China around the volcano.

Intra-caldera ignimbrites
No published studies suggest that a large portion of ignimbrites was preserved within the caldera or indicate significant ponding of ignimbrites during the ME. The intra-caldera ignimbrite volume from the ME has not been considered in previous works. Assigning its value is thus subject to significant uncertainty. No ME ignimbrites can be found at the currently exposed inner caldera wall. Within the caldera and above the caldera lake level, pyroclastic deposits prior to the ME are exposed (Wei et al. 2013). Pyroclastic fall, flow, and surge deposits that were deposited either from or after the ME (Wei et al. 2013) are locally exposed, suggesting that the extent of massive and thick intra-caldera ignimbrites, if present, cannot exceed the caldera lake surface. Here a dummy volume of 4.9 km 3 , the product of the caldera lake surface area (9.8 km 2 ) and an assumed thickness of 500 m, is used to denote the maximum intracaldera ignimbrite volume. The thickness chosen is arbitrary but is considered sufficiently large. We note here that the average depth of the caldera lake today is 213 m. The minimum intra-caldera ignimbrite volume is set to be 0 km 3 , which is a more likely estimate given evidence listed above.

Total volume, VEI, and magnitude of the ME
Minimum and maximum total bulk volumes of the ME are calculated as 40.19 and 97.70 km 3 , respectively, based on volumes assigned for each eruptive product stated above (Table 2). In calculating the maximum, after taking the sum, the double-counted volume of proximal ash and the B-Tm ash is subtracted (Fig. 4c). It is stressed that the volume range is defined based on the minimum and maximum total volumes of the ME, not ± one or two standard deviations from the mean. The maximum volume is estimated based on maximized volumes of all eruptive products of the ME: we have proved that isopachs of the proximal ash and the B-Tm ash used for their maximum volume calculation greatly overestimate their thickness distributions; ignimbrite volumes are also maximized in calculating the maximum total volume, and a dummy volume for intra-caldera ignimbrites, which is highly likely to be a lot greater than their true volume if present, is assumed and included as well. The true total volume of the ME thus has to be a lot smaller than 97.7 km 3 .
One well-accepted total eruption volume of the ME is 96 ± 19 km 3 , which was calculated by assuming a volume range of 63-100 km 3 for the B-Tm ash (Horn and Schmincke 2000), but its volume is updated to 26.66 km 3 based on the same isopachs in this work. We therefore conclude that the ME is a VEI-6 (10-100 km 3 ) eruption, rather than VEI-7 as widely assumed in previous studies.
The magnitude of the ME has been assumed to be 7.4 previously (Hayakawa and Koyama 1998). Estimating its magnitude accurately is difficult because robust data on bulk densities of different eruptive materials are currently not available. We estimate updated magnitude values by somewhat arbitrarily assuming average bulk densities of 1500, 1000, and 600 kg/m 3 . Given the updated maximum volume of 97.7 km 3 , the magnitudes are estimated as 7.2, 7.0, and 6.8; the corresponding values are 6.8, 6.6, and 6.4 if the minimum volume (40.19 km 3 ) is used for calculation. The above calculation suggests that the magnitude of the ME must be lower than 7.4, and its true value lies somewhere in between 6.4 and 7.2.

Significance
The previously estimated eruption volume (∼96-172 km 3 ) has been used in all previous studies on the ME, its eruptive products, and how the eruption interacted with global climate. It is imperative to update the eruption volume of the ME to the more robust and evidence-based estimate of 40.19-97.90 km 3 from this work.
Revising the VEI of the ME from 7 to 6 indicates that there are only two, rather than three, VEI-7 eruptions (i.e., the 1257 Samalas eruption and the 1815 Tambora eruption; Newhall et al. 2018) in the last 2000 years. Our updated eruption volume of the ME also suggests that its magnitude  Horn and Schmincke (2000); b isopach (10-cm and 5-cm) data from Machida and Arai (2003) and the present work (1-cm and 0.1-cm). Tephra volumes in different square roots of isopach area ranges are marked; c: proximal isopach data (orange points and lines) of the ME based on Liu et al. (1998). Green point: the 10-cm B-Tm ash isopach data of Machida and Arai (2003). Green line: the thinning pattern based on 10-cm and 5-cm isopachs of Machida and Arai (2003). Shaded areas correspond to double-counted volumes in calculating the total ME tephra volume. Their volumes are labeled with corresponding colors. All isopach data given in Table 1 is lower than previously thought. These suggest that global magnitude-frequency relationships for the most recent large explosive volcanic eruptions need to be revised.
The ME had limited regional climatic effects, rather than global or hemispheric impact (Xu et al. 2013). Global volcanic aerosol forcing by the ME was smaller than that from the 1815 Tambora eruption (Sigl et al. 2015), although sulfur released from the ME might be greater than the Tambora eruption (Iacovino et al. 2016). These two seemingly conflicted arguments might be partially resolved by our work, which shows that sulfur released from the eruption might be overestimated in previous studies as it was calculated based on a total volume (96 km 3 estimated from (Horn and Schmincke 2000)) that is close to the maximum volume estimated in this work.
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