Reconstruction of eruption column dynamics on the basis of grain size of tephra fall deposits 1. Methods

Two inversion methods are developed to reconstruct eruption column dynamics from granulometric data of Plinian deposits. They are based on the steady tephra dispersal model from umbrella clouds which spread as gravity current s. The methods provide (1) expansion rate of an umbrella cloud, (2) grain-s ize distribution at the top of the eruption column, and (3) total amount of ejecta including very fine particles which are extensively dispersed in th e atmosphere. The first quantity is correlated to the magma discharge rate. The second quantity provides information about sorting processes during co lumn rise, and hence, about deceleration in the "gas thrust region" of the eruption column and the timing of column collapse. The third quantity, toge ther with the estimated magma discharge rate, provides the effective durati on of the eruption. The two methods are based on the same dispersal model b ut use different averaging. Combining the two methods can provide additiona l information about eruption dynamics, such as minor flow structures of the umbrella cloud and fluctuations of eruption rate. The methods are applicab le to large-scale eruptions where the radial expansion velocity of the umbr ella cloud exceeds wind velocity. The applicability of the methods is teste d from the viewpoint of comparison with real-time observations in the compa nion paper (paper 2).