The control of volcanic column heights by eruption energetics and dynamics

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 explosion 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 l0 to 2.3 X l05 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 X 1tY m3/s.

A multidisciplinary effort to assign realistic source parameters to models of volcanic ash-cloud transport and dispersion during eruptions

“…Theoretical studies (Morton et al, 1956) indicate that H T should increase with the fourth root of eruption rate, and empirical compilations (Settle, 1978;Sparks et al, 1997, Chapter 5;Wilson et al, 1978) roughly follow this relationship Figure 1 plots plume height H T or H U (km) versus average eruption rate for the eruptions in Table 1.…”

“…The observations from which these numbers were extracted are detailed in an accompanying document (Mastin et al, in preparation). Some entries were also compiled by previous authors (Carey and Sigurdsson, 1989;Sparks et al, 1997, Table 5.1; Wilson et al, 1978). Our compilation includes only events of the past century or so, excludes one from previous tables (Bezymianny, 1956) that is now known not to have produced a Plinian column (Belousov et al, 2007), and added some (e.g.…”

Transport of SO2 by explosive volcanism on Venus

“…All of the first-order models of buoyant volcanic plume dynamics [Wilson et al, 1978 and that no mass is lost as a result of sedimentation or rainout.…”

Volcanic eruption plume top topography and heights as determined from photoclinometric analysis of satellite data

“…A major outcome of the early modeling work was the demonstration that the maximum height to which a plume will rise is determined almost completely by the mass eruption rate of magma from the vent [Settle, 1978;Wilson et al, 1978]; it is the single most important parameter controlling the dispersal of particles, aerosols and gases and is the most useful quantity to know in any investigation of a plume's eruptive history and likely future behavior. Conversely, knowledge of the height of an eruption plume provides important information on the magma eruption rate.…”

“…Progressively more detailed theoretical models of plume rise [Morton et al, 1956;Wilson, 1976;Wilson et al, 1978;Sparks, 1986;Wilson and Walker, 1987;Woods, 1988;Glaze et al, 1997] have shown that the development of eruption plumes is generally a complex process. Despite evidence that the ash and gas components of some plumes may separate, ultimately rising to different altitudes [Holasek et al, 1996b;Seftor et al, 1997], all of these models assume well-mixed plumes where the ash and gas rise confluently.…”