Improving on mass flow rate estimates of volcanic eruptions

We introduce a novel analytical expression that allows for fast assessment of mass flow rate of both vertically-rising and bent-over volcanic plumes as a function of their height, while first order physical insight is maintained. This relationship is compared with a one-dimensional plume model to demonstrate its flexibility and then validated with observations of the 1980 Mount St. Helens and of the 2010 Eyjafjallajökull eruptions. The influence of wind on the dynamics of volcanic plumes is quantified by a new dimensionless parameter (Π) and it is shown how even vertically-rising plumes, such as the one associated with the Mount St. Helens 1980 eruption, can be significantly affected by strong wind. Comparison between a one-dimensional model and the analytical equation gives anR2-value of 0.88, while existing expressions give negativeR2-values due to their inability to adapt to different source and atmospheric conditions. Therefore, this new expression has important implications both for current strategies of real-time forecasting of ash transport in the atmosphere and for the characterization of explosive eruptions based on the study of tephra deposits. In addition, this work provides a framework for the application of more complete three-dimensional numerical models as it greatly reduces the parameter space that needs to be explored