Is the volume-frequency distribution of eruptions a power-law? Accounting for volume uncertainty in modeling the size distribution of volcanic eruptions

Abstract. Forecasting the size of a future volcanic eruption in densely populated areas is a key aspect of volcanic hazard and risk assessment. Estimates of the next eruption's size for both long- and short-term forecasts are typically based on the sizes of past events. Using the erupted volume as a proxy for eruptive size, forecasts are often obtained from the sampling of a power-law distribution. Notwithstanding, the distribution of the measured/inferred erupted volume of past eruptions often appears markedly different from a power-law. Here, we consider how the uncertainty on the volume of past eruptions may affect the shape of a hypothetical power-law distribution. The goal is to understand if the distribution of real data is compatible with an Exponentially Modified Gaussian distribution (EMG) that includes both the power-law and the uncertainty on the observed volumes. We apply this method to two large high-risk calderas, Campi Flegrei, Italy, and Taupo, New Zealand, but it can be potentially applied to any volcano. We find that the EMG distribution provides a good statistical fit to both volcanoes' eruptive records, supporting the use of a power-law distribution for forecasting the volume of the next eruption.