Thermal structure of a gas-permeable lava dome and timescale separation in its response to perturbation

The thermal boundary layer at the surface of a volcanic lava dome is investigated through a continuum model of the thermodynamic advection-diffusion processes resulting from magmatic gas flow through the dome matrix. The magmatic gas mass flux, porosity, and permeability of the rock are identified as key parameters. New, theoretical, nonlinear steady state thermal profiles are reported, which give a realistic surface temperature of 210°C for a region of lava dome surface through which a gas flux of 3.5 × 10?3 kg s?1 m?2 passes. This contrasts favorably with earlier purely diffusive thermal models, which cool too quickly. Results are presented for time-dependent perturbations of the steady states as a response to changes in surface pressure, a sudden rockfall from the lava dome surface, and a change in the magmatic gas mass flux at depth. Together with a generalized analysis using the method of multiple scales, this identifies two characteristic timescales associated with the thermal evolution of a dome carapace: a short timescale of several minutes, over which the magmatic gas mass flux, density, and pressure change to a new quasi-steady state and a longer timescale of several days, over which the thermal profile changes to a new equilibrium distribution. Over the longer timescale, the dynamic properties of the dome continue to evolve, but only in slavish response to the ongoing temperature evolution. In light of this timescale separation, the use of surface temperature measurements to infer changes in the magmatic gas flux for use in volcanic hazard prediction is discussed.