Phase equilibrium modelling" in today's metamorphic and igneous petrology commonly refers to pseudosection calculations, using one of THERMOCALC, Perple_X or Theriak-Domino. The calculation of pseudosections (Powell, Holland & Worley 1998 J Metam Geol 16 577) is a method of thermobarometry by forward modelling. It evolved in the late 1990s from multiple-reaction thermobarometry, an inverse approach that applied the power of internally-consistent datasets to the more traditional single-reaction approach to thermometry and barometry.
A primary reason for developing the pseudosection approach was to show what large uncertainties afflict thermobarometry, as derived from the modelling of the equilibrium. But the uncertainties are far from transparent to the user. There is a good reason for that - the structure of the uncertainties is sufficiently complicated that the developers struggle with how to frame it, too. A new tool in THERMOCALC, currently in development, should move us forward with this.
If the discussion of uncertainty in thermobarometry is difficult, the problem looks even harder once we consider recent efforts to combine phase equilibrium modelling with other computational disciplines in the Earth Sciences. While there are no straightforward answers, there are important concepts that we should be aware of.
In today's talk I will give an overview of the uncertainties challenge from a model developer's perspective.