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The flow of magma in a volcanic conduit and the flow of the mixture of gas, solid and liquid through a Plinian eruption column are highly complex physical processes governed by a large number of mechanisms operating at different spatial and temporal scales. Nevertheless, under certain conditions, steady-state homogeneous fluid mechanical models provide volcanologists with leading order approximations of such complex phenomena. These types of models, for conduit flow (Wilson et al. 1980; Buresti Casarosa 1989; Mastin 1995; Woods 1995) and for Plinian eruption columns (Wilson et al. 1978; Sparks 1986; Wilson Walker 1987; Woods 1988, 1995) are welldeveloped in the volcanological literature and help volcanologists to gain insight into the important parameters governing real volcanic eruptions. A good knowledge of these parameters is essential not only in characterizing ancient eruptions but also in improving forecasts of future eruptions. This parameter exploration is usually accomplished through a parametric sensitivity analysis, in which the sensitivity of the models to various changes in parameter values is studied. A parametric sensitivity analysis can also be used to determine how well output parameters, such as eruption column height, can be determined from input parameter ranges that are poorly constrained, and to investigate the originof shapes of parameter distributions observed in nature (e.g. log-normal distributions of eruption column heights). This can be accomplished by introducing input parameters in conduit and eruption column models as probability density functions.

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