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Reconstructions of volcanic aerosol radiative forcing are required to understand past climate variability. Currently, reconstructions of pre‐20th century volcanic forcing are derived from sulfate concentrations measured in polar ice cores, mainly using a relationship between the average ice‐sheet sulfate deposition and stratospheric sulfate aerosol burden based on a single explosive eruption—the 1991 eruption of Mt. Pinatubo. Here we estimate volcanic radiative forcings and associated uncertainty ranges from ice‐core sulfate records of eight of the largest bipolar deposition signals in the last 2,500 years using statistical emulation of a perturbed parameter ensemble of aerosol‐climate model simulations of explosive eruptions. Extensive sampling of different combinations of eruption source parameters using the emulators reveals that a very wide range of eruptions in different seasons with different sulfur dioxide emissions, eruption latitudes, and emission altitudes produce ice‐sheet sulfate deposition consistent with ice‐core records. Consequently, we find a large range in the volcanic forcing that can be directly attributed to the unknown eruption source parameters. We estimate that the uncertainty in volcanic forcing caused by many plausible eruption realizations leads to uncertainties in the global mean surface cooling of around 1°C for the largest unidentified historical eruptions. Our emulators are available online (https://cemac.github.io/volcanic-forcing-deposition) where eruption realizations for given ice‐sheet sulfate depositions can be explored. Plain Language Summary: Explosive volcanic eruptions inject sulfur into the atmosphere, forming sulfate particles that reflect sunlight and cause surface cooling. To understand past climate variability it is important to quantify the climate effects of historical eruptions. However, there are no direct observations of the sulfur emissions and cooling from eruptions that occurred hundreds of years ago, and volcanic climate effects must be inferred from indirect measurements. Volcanic sulfate is deposited onto Earth's surface and can be found in layers of polar ice. Ice‐core sulfate records are used to identify the occurrence of past eruptions, and the size of the sulfate signals is used to estimate the amount of sulfate that was present in the atmosphere and consequently the climatic effect of the eruption. We explored the uncertainty in this calculation by using climate model simulations and novel statistics to infer the properties of eruptions that could lead to sulfate deposition that matches that from ice‐core records. We found there are many eruption scenarios that could lead to the same polar sulfate deposition but have different resulting magnitudes of surface cooling. Consequently, there is a large uncertainty in the climatic effect of historical eruptions, which affects our understanding of past climate variability. Key Points: We use an aerosol‐climate model and statistical emulation to find eruption source parameters from eight bipolar sulfate deposition signalsPlausible eruptions have a wide range in sulfur dioxide emissions and latitude, and consequently, a large range in radiative forcingResulting uncertainties in global mean surface cooling for the largest unidentified historical eruptions are on the order of 1°C [ABSTRACT FROM AUTHOR]

Using volcanic sulfur dioxide emissions in an aerosol‐climate model, we derive a time series of global‐mean volcanic effective radiative forcing (ERF) from 1979 to 2015. For 2005–2015, we calculate a global multiannual mean volcanic ERF of −0.08 W/m2 relative to the volcanically quiescent 1999–2002 period, due to a high frequency of small‐to‐moderate‐magnitude explosive eruptions after 2004. For eruptions of large magnitude such as 1991 Mt. Pinatubo, our model‐simulated volcanic ERF, which accounts for rapid adjustments including aerosol perturbations of clouds, is less negative than that reported in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) that only accounted for stratospheric temperature adjustments. We find that, when rapid adjustments are considered, the relation between volcanic forcing and volcanic stratospheric optical depth (SAOD) is 13–21% weaker than reported in IPCC AR5 for large‐magnitude eruptions. Further, our analysis of the recurrence frequency of eruptions reveals that sulfur‐rich small‐to‐moderate‐magnitude eruptions with column heights ≥10 km occur frequently, with periods of volcanic quiescence being statistically rare. Small‐to‐moderate‐magnitude eruptions should therefore be included in climate model simulations, given the >50% chance of one or two eruptions to occur in any given year. Not all of these eruptions affect the stratospheric aerosol budget, but those that do increase the nonvolcanic background SAOD by ~0.004 on average, contributing ~50% to the total SAOD in the absence of large‐magnitude eruptions. This equates to a volcanic ERF of about −0.10 W/m2, which is about two thirds of the ERF from ozone changes induced by ozone‐depleting substances. Plain Language Summary: We calculate the climatic effects of explosive volcanic eruptions between 1979 and 2015 using a more complex climate model simulation than has been used previously. This includes many of the chemical and physical processes that lead to the formation of volcanic aerosol. Volcanic aerosols are tiny airborne particles that are important for Earth's climate because they reflect sunlight and trap thermal infrared radiative energy. In line with previous studies, we find that the most powerful eruptions between 1979 and 2015 had a substantial cooling effect. However, we calculate that their effect on climate is about 20% weaker than previous estimates used by the Intergovernmental Panel on Climate Change (IPCC). In our model simulation this is mainly a result of the volcanic aerosol particles affecting ice clouds, making these clouds less transparent. We also find that it is very rare to have a period with relatively few notable explosive eruptions as was the case during 1996–2002. Furthermore, eruptions of small‐to‐moderate size occur frequently and decrease the transparency of the stratosphere by as much as all nonvolcanic sources of aerosol particles combined. These small‐sized volcanic eruptions therefore cause a small but noticeable surface cooling and so should be included in climate model simulations, which is rarely done. Key Points: Small‐magnitude eruptions caused a global‐mean ERF of −0.08 W/m2 during 2005–2015 relative to the volcanically quiescent 1999–2002 periodIn our model rapid adjustments act to reduce the total volcanic forcing per unit SAOD change by 13–21% for large‐magnitude eruptionsOn average, frequent small‐magnitude eruptions increase the nonvolcanic background SAOD by 0.004, equating to a volcanic ERF of −0.10 W/m2 [ABSTRACT FROM AUTHOR]