Potential Impact of Tonga Volcano Eruption on Global Mean Surface Air Temperature

1.   Basic physics

In volcano-related climate change research, rather than the eruption intensity, the aerosol optical depth and associated radiative forcing are the most important physical variables, which are most closely related to the sulfates released into the stratosphere by the eruption. When a vol-cano erupts, it injects a large amount of sulfurous gases into the stratosphere, mainly SO₂ and sometimes H₂S. These gases react with OH and H₂O to generate sulfate aerosols in a few weeks, which will take months or even years to subside to the earth’s surface. Sulfate aerosols in the air strongly reflect solar radiation, decreasing solar radiation reaching the surface, which is the main reason for global cooling after the volcanic eruption.

Based on the relationship given in Shi (2007), the global sulfate aerosol radiative forcing in the stratosphere ( $\Delta F$) is related to the global mean aerosol optical thickness (τ) as follows,

If τ is in some way known, we can thus obtain the $\Delta F$ caused by volcanic eruption [note that Eq. (1) only applies to cases with small τ].

The linearized global energy balance equation can be written as,

where $\Delta R$ represents the imbalance of radiation at the top of the atmosphere (TOA) and $\Delta {T_{\rm s}}$ represents the change in global mean surface air temperature. The climate sensitivity parameter α, equal to the reciprocal of the climate feedback parameter, describes the steady-state global warming per unit increase in radiative forcing (Gregory and Andrews, 2016). When TOA radiation reaches equilibrium ( $\Delta R = 0$), $\Delta {T_{\rm s}}$ can be calculated as (Shi, 2007),

For historical volcanic eruptions, α is empirically set as −0.3 in unit of (W m⁻² °C⁻¹)⁻¹. For current and new eruptions, according to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR6), the very likely value range of the climate feedback parameter is −1.81 to −0.51 (best estimate −1.16) (Forster et al., 2021), i.e., the value of climate sensitivity parameter α is −1.961 to −0.552 (best estimate −0.862).

In sum, according to Eqs. (1)–(3),τ is the critical variable for estimating $\Delta {T_{\rm s}}$.

2.   A historical case—El Chichón (1982)

The explosive eruption of El Chichón in Mexico in 1982 produced a great deal of sulfate aerosols that had a substantial influence on the global climate, especially in the Northern Hemisphere (NH), and significantly cooled the earth. Taking El Chichón eruption with more related observational data for a reference in this work, we first estimate its impact on global mean surface air temperature and validate our result with observations.

Figure 1 shows the aerosol optical thickness τ at the 0.55-μm wavelength corresponding to six different volcanic indices for the NH and Southern Hemisphere (SH) in the past 150 years. The volcanic indices are used to describe the relative strength of past volcanic activities (Robock and Free, 1995), which include dust veil index (DVI), Mitchell index, volcanic explosivity index (VEI), Sato index, Khmelevtsov index, and ice core volcanic index (IVI) (Table 1). They are linked to aerosol mass, τ, and other properties of aerosols from volcanic eruption.

According to Fig. 1, we estimate that the global mean τ generated by the El Chichón eruption is approximately 0.0325. When α is assumed to be −0.3 (W m⁻² °C⁻¹)⁻¹, based on Eqs. (1) and (3), the $\Delta F$ caused by the El Chichón eruption is −0.975 W m⁻², and the T_s decreases by 0.2925°C (Table 2), which is well consistent with the observational result of 0.3°C (Hofmann, 1987).

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Fig  1.  Aerosol optical thickness (τ) at the 0.55-μm wavelength in association with six different volcanic indices for the (a) Northern and (b) Southern Hemispheres in the past 150 years [from Robock and Free (1995)]. The zoomed-in panels on the right show details of the relationship during the 1982 El Chichón eruption.

Table  1.  Indices of past volcanic eruptions (Robock, 2000; Shi, 2007)

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Name	Base unit	How it was calculated	Reference
Dust veil index (DVI)	Krakatau = 1000	Sapper (1917, 1927), sunsets, eruption, and radiation observations	Lamb (1970, 1977, 1983)
Mitchell	Aerosol mass	Based on H. H. Lamb (personal communication, 1970)	Mitchell (1970)
Volcanic explosivity index (VEI)	Krakatau = 6	Explosivity, from geologic and historical reports	Newhall and Self (1982)Simkin et al. (1981)Simkin and Siebert (1994)
Sato	τ (λ = 0.55 μm)	Mitchell (1970), radiation and satellite observations	Sato et al. (1993)
Ice core volcanic index (IVI)	τ (λ = 0.55 μm)	Average of ice core acidity or sulfate measurements	Robock and Free (1995, 1996)
Note: τ represents aerosol optical thickness; λ represents wavelength; and Krakatau denotes the volcano that erupted in 1883 in Indonesia, whose strength is used as a base reference for DVI and VEI.

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Here is how τ = 0.0325 for El Chichón eruption is derived. According to Figs. 1a, b, by zooming in (as shown in the right panels), we obtain the values of τ corresponding to DVI, Mitchell, Sato, and IVI indices in the NH and SH, and calculate the global mean τ as the average of the NH and SH values (Table 3). Considering that the curves of VEI and Khmelevtsov indices are overlapped with those of the other four indices (see the zoomed-in panels of Fig. 1 on the right), we also give the maximum and minimum τ values corresponding to the six indices, and calculate $\Delta {T_{\rm s}}$ based on Eqs. (1) and (3) (Table 3). As shown in Table 3, compared with the observation from Hofmann (1987), $\Delta {T_{\rm s}}$ would be underestimated or overestimated if we only used one index to estimate τ. Only when the average τ from Sato and IVI (namely 0.0325) is used, is $\Delta {T_{\rm s}}$ the closest to the observation (Hofmann, 1987). Therefore, we set τ = 0.0325 as the global mean stratospheric aerosol optical thickness caused by the El Chichón eruption in this work.

3.   Impact of Tonga eruption (2022)

We estimate that the Tonga eruption intensity represented by VEI is approximately level 5, based on the criteria for VEI estimation (Table 4) and the indices of past volcanic activities (Table 1). This level is equivalent to the El Chichón eruption in 1982. According to the media reports and data released so far, we obtain that the amount of SO₂ sent into the stratosphere by the Tonga eruption is 0.4 million tons, which is 5.7% of the El Chichón eruption (7 million tons). Therefore, we estimate that the global mean τ caused by the Tonga eruption is about 0.0019 in proportion. We then calculate that the resulting stratospheric $\Delta F$ is about −0.057 W m⁻² according to Eq. (1), and we estimate that the T_s will decrease by 0.0315–0.1118°C in the 1–2 years following the Tonga eruption based on Eq. (3), given the α range from the IPCC AR6. The corresponding results are listed in Table 2 in comparison with the El Chichón eruption.

Additionally, according to the range of τ from the six indices (bottom row of Table 3) and the best estimate of α = −0.862 (W m⁻² °C⁻¹)⁻¹, which are set as references without observational constraint, the probable range of $\Delta {T_{\rm s}}$ is calculated as −0.1290 to −0.0280°C for Tonga eruption.

Table  2.  Estimates of aerosol optical thickness (τ), radiative forcing (ΔF), and surface air temperature change (ΔT_s) caused by volcanic eruptions of El Chichón (1982) and Tonga (2022, three scenarios)

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Volcanic eruption	τ	ΔF (W m−2)	α (W m−2 °C−1)−1	ΔTs (°C)
El Chichón (1982)	0.0325	−0.9750	−0.3	−0.2925
Tonga (2022) (present scenario)	0.0019	−0.0570	−1.961 to −0.552	−0.1118 to −0.0315
Tonga continues to emit 0.4 million tons of SO2 (future scenario)	0.0038	−0.1140	−1.961 to −0.552	−0.2235 to −0.0630
Tonga continues to emit 0.8 million tons of SO2 (future scenario)	0.0057	−0.1710	−1.961 to −0.552	−0.3353 to −0.0945

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Table  3.  Manual estimation of aerosol optical thickness (τ) according to Fig. 1, and the calculated [based on Eqs. (1) and (3)] ΔT_s caused by El Chichón eruption [α = −0.3 (W m ⁻² °C⁻¹)⁻¹]

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Volcanic index	τ	ΔTs (°C)
DVI	0.0875	−0.7875
Mitchell index	0.0605	−0.5445
Sato index	0.0460	−0.4140
IVI	0.0190	−0.1710
Average of Sato and IVI	0.0325	−0.2925
Six indices	0.0190–0.0875	−0.7875 to −0.1710

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Table  4.  Criteria for estimation of volcanic explosivity index (VEI) (Newhall and Self, 1982; Shi, 2007)

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Criterion	VEI
	0	1	2	3	4	5	6	7	8
Description	Non-explosive	Small	Moderate	Moderate– large	Large	<---------------------Very large---------------------->
Volume of ejection (m3)	< 104 (I)	104–106 (II–III)	106–107 (IV)	107–108 (V)	108–109 (VI)	109–1010 (VII)	1010–1011 (VIII)	1011–1012 (IX)	> 1012 (X)
Column height (km)	< 0.1	0.1–1	1–5	3–15	10–25	> 25	> 25	> 25	> 25
Qualitative description	< “Gentle, effusive” >		<---------“Explosive”--------->		<-----------“Cataclysmic, paroxysmal, colossal” --------------->
				<------------------------------ “Severe, violent, terrific”----------------------------->
Classification		<---“Strombolian”--->			<----------------------------“Plinian” ------------------------------>
	<-----“Hawaiian”----->		<---------------“Vulcanian” --------------->			<-------------------“Ultraplinian” ----------------->
Duration (h) of continuous blast	< 1	< 1	< 1		> 12	> 12	> 12	> 12	> 12
			1–6	1–6	1–6
				6–12	6–12	6–12
CAVW max explosivity	Lava flows	<---------------------------------------------Explosion or nuee ardente----------------------------------------------->
		<---------------------------------Phreatic-------------------------------->
	<Dome or mudflow>
Tropospheric injection	Negligible	Minor	Moderate	<---------------------------------------Substantial------------------------------------>
Stratospheric injection	<-----------------None----------------->			Possible	Definite	<--------------------Significant-------------------->
Note: CAVW refers to Catalog of Active Volcanoes of the World.

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4.   Conclusions and discussion

To sum up, the Tonga volcanic eruption has a VEI of about 5, and its intensity is similar to the El Chichón eruption in 1982. However, the stratospheric aerosol radiative forcing caused by the Tonga eruption is only −0.057 W m⁻², and the global average surface temperature will decrease by about 0.0315–0.1118°C in the next 1–2 years. The Tonga eruption will slightly slow down the global warming in a short period of time, but it will not change the global warming trend in the long run.

Based on the relevant information available so far and the quantitative estimates in this study, we conclude that the impact of the Tonga eruption on global warming is much smaller than the El Chichón eruption in 1982. The aerosol radiative forcing generated by the Tonga eruption is only 5.7% of the El Chichón eruption, and the surface temperature change caused by the former is only 11%–37% of the latter. In addition, we find out that the aerosol radiative forcing resulted from the Tonga eruption is only 1.5% of current greenhouse gas forcing (3.84 W m⁻²) assessed in IPCC AR6 (Forster et al., 2021). Therefore, we infer that the Tonga eruption in the SH has a minor effect on global warming trend in the future. However, if Tonga volcano erupts with the same or even twice the intensity once more in the near future, that is, it continues to inject 0.4 or 0.8 million tons of SO₂ into the stratosphere, it will have a significant influence on glo-bal warming, equal to the effect of the El Chichón eruption. Combined with the high climate sensitivity at present (Zhang et al., 2022), the impact caused by the Tonga eruption may exceed the El Chichón eruption, and our estimates show that the global surface air temperature will be reduced by up to 0.2235 or 0.3353°C if Tonga volcano continues to erupt in the near future (Table 2).

Considering the possible scenarios of future volcanic eruptions, we summarize and further propose a generalized approach, as shown in Fig. 2, for predicting and estimating volcanic eruption induced global mean surface air temperature change. This simple approach is based on the simplified radiation equilibrium of the earth system. It can be easily applied to quickly and quantitatively assess the climatic effect of any future volcanic eruptions.

It should be noted that the method used in this study can only estimate the stratospheric aerosol radiative forcing caused by volcanic eruption and the resulting global mean surface air temperature change in the next 1–2 years. More complex models are needed to analyze quantitative effects of volcanic eruption on atmospheric temperature, precipitation, atmospheric circulation, and so on at other temporal (such as months and seasons) and spatial scales (such as different regions).

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Fig  2.  Flow chart for estimating $\Delta {T_{\rm s}}$ caused by a future volcanic eruption.

Acknowledgments. We would like to thank Dr. Wei Ke from the Institute of Atmospheric Physics of Chinese Academy of Sciences for his helpful comments.