The control of volcanic column heights by eruption energetics and dynamics

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Abstract
The height reached by a volcanic eruption column, together with the atmospheric wind regime, controls the dispersal of tephra. Column height is itself a function of vent radius, gas exit velocity, gas content of eruption products, and efficiency of conversion of thermal energy contained in juvenile material to potential and kinetic energy during the entrainment of atmospheric air. Different heights will be attained for the same total energy release depending on the style of the eruption: a discrete exptosion produces a transient plume, whereas a prolonged release of material forms a maintained plume. A maintained eruption plume will also be formed if discrete explosions occur within a few minutes of one another, and eruptions producing large volumes of tephra commonly lead to maintained plume formation. Observed eruption columns from eight eruptions with cloud heights in the range 2–45 km and volume rates of magma production in the range 10 to 2.3 × 105 m3/s are compared with predicted values deduced from theoretical relationships for fluid convection. Theoretical model heights were calculated in two ways: first, for a wide range of eruptive conditions by using a dynamic model of eruption column formation and second, by using a theoretical formula relating height to rate of thermal energy release. Results from the two calculations were found to agree well and furthermore showed satisfactory agreement with the eight observations. Expected cloud heights can be usefully expressed as a function of heat release rate, expressed as the equivalent volume eruption rate of magma, for three different values of the efficiency of heat use. The results imply that many eruptions involve highly efficient use of the released heat, which indicates that the particle sizes in these eruptions are sufficiently small to allow rapid heat transfer to air entrained into the column. For certain combinations of vent radius, gas exit velocity, and gas content, column collapse to form pyroclastic flows should occur. Cloud heights have been calculated for a wide range of permutations of these parameters corresponding to the onset of collapse. The maximum theoretical height expected for a stable maintained plume is about 55 km, corresponding to a volume eruption rate of 1.1 × 106 m3/s.