In August 2008 an unmonitored, largely unstudied Aleutian volcano, Kasatochi, erupted catastrophically. Here we use seismic data to infer the height of large eruptive columns such as those of Kasatochi based on a combination of existing fluid and solid mechanical models. In so doing, we propose a connection between a common, observable, short-period seismic wave amplitude to the physics of an eruptive column. To construct a combined model, we estimate the mass ejection rate of material from the vent on the basis of the plume height, assuming that the height is controlled by thermal buoyancy for a continuous plume. Using the estimated mass ejection rate, we then derive the equivalent vertical force on the Earth through a momentum balance. Finally, we calculate the far-field surface waves resulting from the vertical force. The model performs well for recent eruptions of Kasatochi and Augustine volcanoes if v, the velocity of material exiting the vent, is 120-230 m s^-1. The consistency between the seismically inferred and measured plume heights indicates that in these cases the far-field ~1 s seismic energy radiated by fluctuating flow in the volcanic jet during the eruption is a useful indicator of overall mass ejection rates. Thus, use of the model holds promise for characterizing eruptions and evaluating ash hazards to aircraft in real time on the basis of far-field short-period seismic data. This study emphasizes the need for better measurements of eruptive plume heights and a more detailed understanding of the full spectrum of seismic energy radiated coeruptively.