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Predictions for the heights and downwind trajectories of volcanic plumes using integral models are critical for the assessment of risks and climate impacts of explosive eruptions but are strongly influenced by parameterizations for turbulent entrainment. We compare four popular parameterizations using small scale laboratory experiments spanning the large range of dynamical regimes in which volcanic eruptions occur. We reduce uncertainties on the wind entrainment coefficient.. which quantifies the contribution of wind-driven radial velocity shear to entrainment and is a major source of uncertainty for predicting plume height. We show that models better predict plume trajectories if (i) beta is constant or increases with the plume buoyancy to momentum flux ratio and (ii) the superposition of the axial and radial velocity shear contributions to the turbulent entrainment is quadratic rather than linear. Our results have important implications for predicting the heights and likelihood of collapse of volcanic columns.

Plain Language Summary One-dimensional models of volcanic plumes can predict whether a volcanic column will collapse and produce devastating pyroclastic flows or rise as a buoyant plume. In this case, 1-D models can predict the height at which the volcanic plume will inject gases and ash, which is critical to make predictions for the climate impact of an eruption, as well as to assess ash fallout hazard. In these models, the mixing between the plume and the ambient atmosphere is parameterized. Uncertainties on this parameterization are very large and undermine all model predictions, such as the height a volcanic plume. In this study, we use small-scale laboratory experiments to improve constraints on the most used parameterizations for mixing between a volcanic plume and the atmosphere. The experimental data set used spans the large range of dynamical regimes in which explosive volcanic eruptions occur. Our result significantly reduce uncertainties for predicting (i) under which conditions an eruptive column will collapse and produce pyroclastic flows and (ii) what eruption magnitude is required for a volcanic plume to reach the stratosphere (the higher part of the atmosphere) and significantly reduce Earth's surface temperature.