Using high-resolution ground-based transmission spectroscopy to probe exoplanetary atmospheres is difficult due to the inherent telluric contamination from absorption in Earths 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 Earths 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.
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