Fig. 6.

Plume heights as a function of magma discharge rate for a magma with properties identical to those of the 2011 Shinmoe-dake eruptions. Error bar represents the range of plume heights based on the 3D simulations using a magma discharge rate of 1.5 × 10 kg s⁻¹, with the shaded zone representing the relationship between plume height and magma discharge rate based on field observations. The curves are the plume heights as a function of magma discharge rate on the basis of the calculations of the 1D no-wind model (Woods, 1988) and the 1D wind model (Bursik, 2001). In these calculations, we assume that the pressure at the vent is equal to atmospheric pressure and the exit velocity is the sound velocity of the mixture. The volatile content, magma temperature, and initial mixture density are given in Table 1. The solid and dashed curves show the plume heights calculated using the 1D no-wind model with k = 0.10 and with k = 0.07,0.12,0.16, and 0.20, respectively. The dotted curve is the plume height calculated using the 1D wind model with β = 0.7 (Hewett et al., 1971) and k = 0.1.