Reply to Gualda & Ghiorso Comment on ‘A Metamodel for Crustal Magmatism: Phase Equilibria of Giant Ignimbrites’

We welcome the opportunity to clarify issues raised by Gualda & Ghiorso (G&G, hereafter) on our 2010 paper, ‘A metamodel for crustal magmatism: phase equilibria of giant ignimbrites’. Voluminous (V 100^1000 km) explosive eruption of silicic magma, accompanied by eruption columns that may empty into the stratosphere, has environmental consequences of planetary significance and represents an important mechanism for the growth of continental crust. Understanding the origin and evolution of silicic volcanic systems is hence critically important. We have described quantitatively (Fowler et al., 2007; Fowler & Spera, 2008; Fowler & Spera, 2010) how cooling and crystallization and/or assimilation can lead inherently to destabilization and eruption of several well-known magmatic systems. Fig. 15e (Fowler & Spera, 2010) summarizes the lithostatic pressure, melt fraction, and initial wt. % H2O conditions that may lead to destabilization. One contentious point raised by G&G concerns our thermal timescale estimate for evolution of the Long Valley magmatic system culminating in the Bishop Tuff eruption (G&G support a shorter timescale). The other deals with the compatibility of our conclusions with data from BishopTuff minerals, melt inclusions, and pumice. Regarding our timescale estimates for development of Long Valley rhyolitic liquids from a mafic liquid parent, we described (Fowler et al., 2007; Fowler & Spera, 2010) a scale analysis aimed at providing a system thermal lifetime estimate for a particular set of initial conditions and configuration: cooling of a fixed mafic magma mass, assuming closed-system behaviour (no thermal or mass recharge), a simple magma body shape, a fixed heat flux, and eruption of some fraction of differentiated magma formed by fractional crystallization. As opposed to a scale analysis, a proper thermal model would necessarily include computation of conjugate heat transfer rates across a magma body^host-rock boundary zone. For a particular system, such a thermal model should account for the threedimensional magma body geometry (size, shape, and depth), the time history of magma recharge (very difficult to gauge without real-time geodetic data; e.g. Lundgren et al., 2003), host-rock thermophysical properties (notably thermal conductivity and permeability structure, including anisotropy; e.g. Rosenberg & Spera, 1990), the regional stress field (an important feedback to permeability and, hence, heat transfer), and detailed crustal stratigraphy. Sufficient spatial resolution (of the order of 10m) would be required, based on conjugate heat transfer zone thickness. Initial conditions, generally unknown, would also need to be specified. Computation of such a model is extremely challenging, requiring a great deal of focused effort. We have not made this calculation (neither have G&G) because there are so many uncertain quantities as to render any ‘detailed’ model as uncertain as the simple scaling estimate embodied in equation (1) of Fowler &