Large explosive volcanic eruptions have far-reaching impacts, significantly varying in their effects. Climate impact is linked to stratospheric sulfur injection, influenced by latitude and timing. Despite detailed models, data for large eruptions remains limited, creating uncertainties. Quantifying magma volume, volatile release, and plume height is crucial for understanding eruption-climate relationships and validating dispersal models. The 946 CE Millennium Eruption (ME) of Paektu volcano offers good constraints on date and climate response, yet its climatic impact appears limited, contrasting with other large eruptions. This study combines tephra fallout thickness measurements with a new ensemble-based, dual-step inversion method using the FALL3D model to constrain eruption magnitude and parameters (mass eruption rate, duration, plume height), modeling the distinct eruption phases. By coupling volume constraints with volatile content data, the study updates estimates of stratospheric volatile release, aiming to explain the limited climatic impact.

The discovery of widespread volcanic ash (tephra) in northern Japan first indicated a recent Paektu eruption. This B-Tm tephra layer has been identified in numerous sequences across East Asia and even as cryptotephra in Greenland ice cores. Glass compositions confirm the tephra's origin from the ME. Paektu's volcanism, fueled by mantle upwelling, comprises three stages: a basaltic shield volcano, an explosive trachytic-rhyolitic stratovolcano, and the Cheonji caldera-forming stage with several large eruptions over the last 80 ka. Radiocarbon dating and historical records pinpoint the ME to 946 CE, with some evidence suggesting a second phase or activity in early 947 CE. Previous studies on proximal ME deposits identified comendite and trachyte phases but disagreed on their proportions. Prior volume estimates for the entire deposit ranged from 40.2 to 97.7 km³ (bulk volume), equating to 17.5 to 42.5 km³ DRE, but didn’t quantify the comendite to trachyte ratio. Proxy climate records show no noticeable changes following the ME, contradicting expectations based on the eruption's apparent magnitude.

This study uses published thickness and compositional data from the ME deposit (>700,000 km²) with a dual-step inversion method to model tephra dispersal from the two phases. A new ensemble-based inversion strategy provides insights into eruption dynamics and magma volume estimations. The first step uses a fast semi-analytical code (PARFIT) to identify suitable wind conditions and ESP ranges for the ensemble-based inversion (FALL3D). Three inverse problems were solved: one each for the comendite and trachyte phases, and one for the total deposit. The weighted least-squares method was used, with tephra load data from >40 km from the vent, where comendite and trachyte fractions were estimated. The first step's results provided input ranges for the second step. In the second step, six ensemble runs (128 members each) were performed with FALL3D-8.2, using best meteorological configurations. The GNC method assimilated observations (23 for each phase) to reconstruct the deposit mass loading. The total deposit was obtained by summing the comendite and trachyte deposits. Statistical indicators (RMSE, bias, MAE, SMAPE) were used to evaluate the results. The optimal configuration minimized the Confidence Ratio and Composite Index, using the total deposit thickness data (83 measurements) for validation. The source term was inverted using the GNC method to obtain the total source term (Equation 1). The cumulative erupted volume and the emission rate were shown (Figure 4). Petrological methods and volatile data were used to estimate total volatile release, considering pre- and syn-eruptive degassing.

The study's dual-step inversion approach revealed that fallout from each phase erupted roughly the same volume of magma: ~7.2 km³ DRE for comendite and ~9.3 km³ DRE for trachyte (with uncertainties). This indicates around 16 km³ of magma was dispersed by fallout (with a range of 7-39 km³), significantly less than previously estimated. Adding previous PDC estimates, the total erupted magma volume is approximately 23 km³ DRE (13-47 km³), representing a M6.7 eruption. Each phase lasted less than a day (~15 and 20 h), with peak mass flow rates around 4 x 10⁸ kg/s, generating plumes reaching ~30-40 km altitude. This suggests near-complete injection of eruptive material, including volatiles, into the stratosphere. Scaled estimates for syn-eruptive sulfur release, considering the new comendite volumes, range from 0.5–2.6 Tg (1.0–5.2 Tg SO₂), without including the trachyte phase. This is consistent with the sulfur load estimated from ice core records and the lack of significant climate impact. The lack of noticeable climate impact suggests low syn-eruptive volatile release, consistent with the estimated sulfur yields, despite not including the trachyte release.

The results address the research question by providing refined estimates of the ME's magnitude and eruption parameters. The similar volumes of comendite and trachyte fallout indicate a complex interplay between magma supply and eruption dynamics. The study shows that eruptions tapping compositionally distinct melts with different volatile histories necessitate understanding the temporal relationship between melt chemistry and dynamics for accurate impact assessment. The limited climatic impact, despite the large volume, highlights the importance of volatile content and injection height in determining climate effects. The high plume height ensured stratospheric injection, but the relatively low sulfur release explains the muted climatic response. Regional impacts from ash deposition, lahars, and gas release were significant. Future studies should focus on obtaining volatile data from the trachyte phase for more precise sulfur release estimates and explore the regional effects of the ME in more detail.

This study presents a novel dual-step inversion method for analyzing large volcanic eruptions, yielding refined estimates of the ME's magma volumes, eruption dynamics, and volatile release. The similar magma volumes of the two phases and the relatively low sulfur release, coupled with high-altitude plume injection, provide a more complete picture of the ME's impact. Future research should focus on obtaining volatile data from the trachyte phase for improved volatile release estimates and examining the regional impacts of the eruption in greater detail.

The study's reliance on published data, including the assumptions made regarding glass shard representation and conversion of shard concentration to thickness, introduces uncertainties. The lack of volatile data for the trachyte phase prevents a comprehensive assessment of total sulfur release. The model's simplifications, particularly concerning proximal deposits and ash aggregation, might affect the accuracy of the results. Additional research is needed to refine the understanding of the trachyte phase's contribution to the overall eruption dynamics and volatile release.