Two of the most widely observed co-eruptive volcanic phenomena - ground deformation and volcanic outgassing - are fundamentally linked via the mechanism of magma degassing and the development of compressibility, which controls how the volume of magma changes in response to a change in pressure. Here we use thermodynamic models (constrained by petrological data) to reconstruct volatile exsolution and the consequent changes in magma properties. Co-eruptive SO2 degassing fluxes may be predicted from the mole fraction of exsolved SO2 that develops in magma whilst stored prior to eruption and during decompression. Co-eruptive surface deformation may be predicted given estimates of erupted volume and the ratio between chamber compressibility and magma compressibility. We conduct sensitivity tests to assess how varying magma volatile content, crustal properties, and chamber geometry may affect co-eruptive deformation and degassing. We find that magmatic H2O content has the most impact on both SO2 flux and volume change (normalised for erupted volumes). Our findings have general implications for typical arc and ocean island volcanic systems. The higher magmatic water content of arc basalts leads to a high pre-eruptive exsolved volatile content, making the magma more compressible than ocean island eruptions. Syn-eruptive gas fluxes are overall higher for arc eruptions, although SO2 fluxes are similar for both settings (SO2 flux for ocean island basalt eruptions is dominated by decompressional degassing). Our models are consistent with observation: deformation has been detected at 48% of ocean island eruptions (16/33) during the satellite era (2005-2020), but only 11% of arc basalt eruptions (7/61).

In order to reconcile petrological and geophysical observations in the temporal domain, the uncertainties of diffusion timescales need to be rigorously assessed. Here we present a new diffusion chronometry method: Diffusion chronometry using Finite Elements and Nested Sampling (DFENS). This method combines a finite element numerical model with a nested sampling Bayesian inversion meaning the uncertainties of the parameters that contribute to diffusion timescale estimates can be rigorously assessed, and that observations from multiple elements can be used to better constrain a single timescale. By accounting for the covariance in uncertainty structure in the diffusion parameters, estimates on timescale uncertainties can be reduced by a factor of 2 over assuming that these parameters are independent of each other. We applied the DFENS method to the products of the Skuggafjöll eruption from the Bárðarbunga volcanic system in Iceland, which contains zoned macrocrysts of olivine and plagioclase that record a shared magmatic history. Olivine and plagioclase provide consistent pre-eruptive mixing and mush disaggregation timescales of less than 1 year. The DFENS method goes some way to improving our ability to rigorously address the uncertainties of diffusion timescales, but efforts still need to be made to understand other systematic sources of uncertainty such as crystal morphology, appropriate choice of diffusion coefficients, growth, and the petrological context of diffusion timescales.