Volcanic ash concentrations in the plume from Sakurajima volcano in Japan are observed from airplanes equipped with optical particle counters and GPS tracking devices. The volcano emits several puffs a day. The puffs are also recorded by the Sakurajima Volcanological Observatory. High concentrations are observed in the puffs and fallout driven by vertical air current, called streak fallout. Puffs dispersion is analyzed by the classical diffusion-advection method and a new gravitational dispersion method. The fluid mechanic of the gravitational dispersion, streak fallout, and classical diffusion-advection theory is described in three separate appendices together with methods to find the time gravitational dispersion constant and the diffusion coefficient from satellite photos. The diffusion-advection equation may be used to scale volcanic eruptions so the same eruption plumes can be scaled to constant flux and wind conditions or two eruptions can be scaled to each other. The dispersion analyses show that dispersion of volcanic plumes does not follow either theories completely. It is most likely diffusion in the interface of the plume and the ambient air, together with gravitational flattening of the plumes core. This means larger boundary concentration gradients and smaller diffusion coefficients than state of the art methods can predict. 1. Introduction Airborne observations of volcanic ash concentrations with optical particle counters and GPS tracking have recently been taken in use to study volcanic plumes [1–7]. Three campaigns of airborne observations of volcanic ash and gas content of the plume from the Sakurajima volcano in Japan were performed in 2013, in cooperation between the Universities of Kyoto, University of Iceland, and University of Applied Sciences in Düsseldorf, Germany. The Sakurajima volcano has been in constant eruption since 1955; it does not emit a continuous plume but produces a series of explosion puffs, sometimes many each day [8]. The preliminary results of the first campaign were described in presentations to the IAVCEI conference July 2013 in Kagoshima, Japan [9–12]. The staggering economic disaster [13, 14], inflicted upon the aviation industry by the Eyjafjallaj？kull eruption in 2010 and the Grimsv？tn eruption in 2011, made clear the importance of ash cloud predictions. These events sparked the research program that produced the Sakurajima campaigns. It is hoped they may help to increase the accuracy of ash cloud predictions. Ash cloud predictions make use of point source atmospheric dispersion models, for the simulation
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