The Condition of Eruption Column Collapse: 1. A Reference Model Based on Analytical Solutions

The critical condition at which an eruption column collapses to generate a pyroclastic flow (the column collapse condition) generally depends on magmatic properties, crater shape (radius, depth, and opening angle), and the magma supply rate through the volcanic conduit. Here we propose a reference model for the column collapse condition based on analytical solutions of a one-dimensional (1-D) eruption column model and a quasi-1-D conduit flow model, which considers the effects of the crater. In the reference model, the column collapse condition is expressed by a single surface in a dimensionless parameter space related to magma discharge rate, magma supply rate (per unit area) at the crater base, and the ratio of the cross-sectional areas at the top and base of the crater. The dependence of the column collapse condition on magmatic properties is included in the normalization factors of these dimensionless parameters. Previous criteria for the column collapse condition, which were based on the relationship between water content and magma discharge rate and that between magma discharge rate and crater radius, are regarded as part of, or a projection of, the present reference model. The reference model provides a framework for a comprehensive analysis of the diverse scenarios resulting in column collapse during explosive eruptions.