Plume height, volume, and classification of explosive volcanic eruptions based on the Weibull function

The Weibull distribution between volume and square root of isopach area has been recently introduced for determining volume of tephra deposits, which is crucial to the assessment of the magnitude and hazards of explosive volcanoes. We show how the decay of the size of the largest lithics with the square root of isopleth area can also be well described using a Weibull function and how plume height correlates strongly with corresponding Weibull parameters. Variations of median grain size (Md phi) values with square root of area of the associated contours can be, similarly, well fitted with a Weibull function. Weibull parameters, derived for both the thinning of tephra deposits and the decrease of grain size (both maximum lithic diameter and Md phi), with a proxy for the distance from vent (e.g., square root of isoline areas) can be combined to classify the style of explosive volcanic eruptions. Accounting for the uncertainty in the derivation of eruptive parameters (e.g., plume height and volume of tephra deposits) is crucial to any classification of eruptive style and hazard assessment. Considering a typical uncertainty of 20 % for the determination of plume height, a new eruption classification scheme based on selected Weibull parameters is proposed. Ultraplinian, Plinian, Subplinian, and small-moderate explosive eruptions are defined on the ground of plume height and mass eruption rate. Overall, the Weibull fitting represents a versatile and reliable strategy for the estimation of both the volume of tephra deposits and the height of volcanic plumes and for the classification of eruptive style. Nonetheless, due to the typically large uncertainties (mainly due to availability of data, compilation of isopach and isopleth maps, and discrepancies from empirical best fits), plume height, volume, and magnitude of explosive eruptions cannot be considered as absolute values, regardless of the technique used. It is important that various empirical and analytical methods are applied in order to assess such an uncertainty.