  Using high-resolution ground-based transmission spectroscopy to probe
exoplanetary atmospheres is difficult due to the inherent telluric
contamination from absorption in Earth's atmosphere. A variety of methods have
previously been used to remove telluric features in the optical regime and
calculate the planetary transmission spectrum. In this paper we present and
compare two such methods, specifically focusing on Na detections using
high-resolution optical transmission spectra: (1) calculating the telluric
absorption empirically based on the airmass, and (2) using a model of the
Earth's transmission spectrum. We test these methods on the transmission
spectrum of the hot Jupiter HD 189733 b using archival data obtained with the
HARPS spectrograph during three transits. Using models for Centre-to-Limb
Variation and the Rossiter-McLaughlin effect, spurious signals which are
imprinted within the transmission spectrum are reduced. We find that correcting
tellurics with an atmospheric model of the Earth is more robust and produces
consistent results when applied to data from different nights with changing
atmospheric conditions. We confirm the detection of sodium in the atmosphere of
HD 189733 b, with doublet line contrasts of -0.64 $\pm$ 0.07 % (D2) and -0.53
$\pm$ 0.07 % (D1). The average line contrast corresponds to an effective
photosphere in the Na line located around 1.13 R$_p$. We also confirm an
overall blueshift of the line centroids corresponding to net atmospheric
eastward winds with a speed of 1.8 $\pm$ 1.2 km/s. Our study highlights the
importance of accurate telluric removal for consistent and reliable
characterisation of exoplanetary atmospheres using high-resolution transmission
spectroscopy.
