Stars are not hydrostatic spheres and their atmospheric layers are not in local thermodynamic equilibrium. Inferring stellar surface abundances from such 1D+LTE models is subject to significant biases. We are now at a stage of maturity of quantitative stellar spectroscopy where these classical assumptions can be superseded by physically realistic modelling. However, doing so for hundreds of thousands or even millions of stellar spectra (as produced by the current and upcoming large spectroscopic surveys around the world) remains a challenge. The other challenge lies in the connection between the inferred surface abundances and the composition of the star as a whole. Stars evolve through different stages and internal mixing will alter the surface composition of specific, sometimes of all, elements. We know the effects at play, but cannot generally model them from first principles in the framework of quasi-hydrostatic stellar-evolution models. Inferring accurate birth-cloud compositions as input for chemical-evolution models thus remains challenging.
Andreas Korn (2025) studied this question.