Grain-size variation of tephra derived from volcanic umbrella clouds

Abstract

The relationships among the thickness and grain-size of tephra-fall deposits and the volumetric flow rate of their source umbrella clouds are analytically obtained. The logarithm of the ratio of the probability distribution function based on grain size (InR _f) in fall deposits at two localities from the vent (r ₁ and r ₂, respectively) has a linear relationship with the particle-settling velocity, v, as: In

$$1n R_f = - \frac{{\pi (r_2^2 - r_1^2 ) \nu }}{Q} + 1n A,$$

where Q is the volumetric flow rate of the umbrella cloud and A is a constant for a given pair of localities. The volumetric flow rate of the umbrella cloud can be estimated from granulometric data using this formula. Generally, the thickness-distance relationship of tephra-fall deposits depends on the initial grain-size distribution and the volumetric flow rate of the umbrella cloud. The empirical relationship of the exponential thinning behaviour can be extrapolated towards infinite distance only for a specific initial grain size which is similar to a log-normal distribution with σ_φ=2.5, otherwise it holds only in a limited range of distances. In applying these results to the 1991 eruption of Mt. Pinatubo, it is shown that the volumetric flow rate of the umbrella cloud during the climactic phase of 15 June was approximately 5x10¹⁰ m³/s, which is fairly consistent with the expansion rate of the umbrella cloud observed in the satellite images.