We describe a simple deterministic model for the dispersion of particulate ash which has been ejected into the atmosphere by a volcanic eruption. In our model the atmosphere is divided into a series of horizontal layers within which the physical parameters involved are constant. This is an effective way to allow for the changing behaviour of the particulate ash and atmospheric flow with height whilst retaining simplicity. From our model we construct an analytical expression for the final

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... which could be incorporated within hazard assessment projections. In particular we show how to allow for variation with height of dispersion (caused by turbulence due to the wind) and settling speed (affected by the agglomeration and fragmentation of particles).