  The abundance of {\alpha}-elements provides an important fossil signature in
Galactic archaeology to trace the chemical evolution of the different disc
populations. High-precision chemical abundances are crucial to improving our
understanding of the chemodynamical properties present in the Galaxy. However,
deriving precise abundance estimations in the metal-rich disc ([M/H] > 0 dex)
is still challenging. The aim of this paper is to analyse different error
sources affecting magnesium abundance estimations from optical spectra of
metal-rich stars. We derived Mg abundances for 87522 high-resolution spectra of
2210 solar neighbourhood stars from the AMBRE Project. For this purpose, the
GAUGUIN automated abundance estimation procedure was employed. The
normalisation procedure has a strong impact on the derived abundances, with a
clear dependence on the stellar type and the line intensity. For non-saturated
lines, the optimal wavelength domain for the local continuum placement should
be evaluated using a goodness-of-fit criterion, allowing mask-size dependence
with the spectral type. Moreover, for strong saturated lines, applying a narrow
normalisation window reduces the parameter-dependent biases of the abundance
estimate, increasing the line-to-line abundance precision. In addition, working
at large spectral resolutions always leads to better results than at lower
ones. The resulting improvement in the abundance precision makes it possible to
observe both a clear thin-thick disc chemical distinction and a decreasing
trend in the magnesium abundance even at supersolar metallicities. In the era
of precise kinematical and dynamical data, optimising the normalisation
procedures implemented for large spectroscopic stellar surveys would provide a
significant improvement to our understanding of the chemodynamical patterns of
Galactic populations.
