Large Uncertainties Are Pervasive in Long-Term Frequency-Magnitude Relationships for Volcanoes in Southeast Asia

Frequency-magnitude relationships are a fundamental aspect of volcanic hazard and risk analysis. Typically, frequencies of previously recorded eruptions are used to identify such relationships. This works well for volcanoes that are well-studied, but it can take a long, sustained, and resource intensive research effort to compile complete eruption records. Further, the level of completeness that can be achieved will vary around the world as a function of climatic conditions, eruption style, and duration of written records. Given the importance of understanding hazard and risk for disaster risk reduction, how can frequency-magnitude relationships be determined for volcanoes with little or no eruption records? Analogue models have been used to supplement the eruption records of volcanoes with limited or no recorded eruptions. However, there has been little effort undertaken to compare the agreeability of different approaches to estimating frequency-magnitude relationships using these analogue models. This has implications for volcanic hazard and risk assessment, if different approaches are considered credible, yet yield vastly different estimates. In this work we compare frequency-magnitude relationships for volcanoes in Southeast Asia, a region where eruption records are known to be very incomplete. We do this by first reviewing published frequency-magnitude relationships to evaluate the agreeability between different approaches, and then develop a top-down multi-model Bayesian updating approach to deriving frequency-magnitude relationships for a wide variety of volcanoes in Southeast Asia (n = 176). Our review of published estimates found that there is considerable variability between published eruption probabilities for volcanoes in Southeast Asia. We also found that using different analogue models in the Bayesian analysis can lead to considerably different frequency-magnitude relationships (over an order of magnitude in some cases), highlighting the importance of using multiple models to ensure robust probability estimations are obtained. Sensitivity analysis demonstrated that the choice of model averaging or model combination method can influence the resulting frequency-magnitude estimations, whilst the choice to incorporate or remove uncertain eruption records had modest or no effect. Our findings provide important considerations for estimating frequency-magnitude relationships in volcanic hazard and risk assessments, and a method to combine multiple frequency-magnitude models whilst accounting for uncertainty in our estimations.