Estimating the volume of tephra deposits: A new simple strategy

Volume determination of tephra deposits is necessary to the characterization of active volcanoes, with obvious implications for environmental and climatic impact, estimation of magma-production rate, long-term hazard assessments and forecasting of future eruptions. Several methods have been proposed that mainly include the integrations of various deposit-thinning relationships and the inversion of field observations using computational models. Regardless of their strong dependence on tephra-deposit exposure, empirical integrations of deposit-thinning trends still represent the most widely adopted strategy due to their practical and fast application. The choice of best-fitting trends (e.g., exponential and power-law thinning on semi-log plots) has been subject of lively debate because they are all characterized by various advantages and disadvantages. We propose a new empirical method that is based on the Weibull distribution and shows a better agreement with observed data reconciling the debate on the use of the exponential versus power-law methods. Nonetheless, we also show that all empirical methods used to derive erupted volume based on integration of deposit thinning strongly depend on the available data and are affected by various degrees of uncertainties. Application of various empirical and analytical methods can help to assess the associated uncertainties