Development of an Inverse Plume Model for Mass Eruption Rate in Unsteady Conditions

Following volcanic eruptions, forecasters need accurate estimates of mass eruption rate (MER) to appropriately predict the downstream effects. Most analyses use simple correlations or models based on large eruptions at steady conditions, even though many volcanoes feature significant unsteadiness. To address this, a superposition model is developed based on a technique used for spray injection applications, which predicts plume height as a function of the time-varying exit velocity. This model can be inverted, providing estimates of MER using field observations of a plume. The model parameters are optimized using laboratory data for plumes with physically relevant exit profiles and Reynolds numbers, resulting in predictions that agree to within 10% of measured exit velocities. The model performance is examined using historic eruptions with well-documented unsteadiness, again providing MER estimates of the correct order of magnitude. This method can provide a rapid alternative for real-time forecasting of small, unsteady eruptions.