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A fully physical retrieval scheme for land surface emissivity spectra is presented, which applies to high spectral resolution infrared observations from satellite sensors. The surface emissivity spectrum is represented with a suitably truncated Principal Component Analysis (PCA) transform and PCA scores are simultaneously retrieved with surface temperature and atmospheric parameters. The retrieval methodology has been developed within the general framework of Optimal Estimation and, in this context, is the first physical scheme based on a PCA representation of the emissivity spectrum. The scheme has been applied to IASI (Infrared Atmospheric Sounder Interferometer) and the retrieved emissivities have been validated with in situ observations acquired during a field experiment carried out in 2017 at Gobabeb (Namib desert) validation station. It has been found that the retrieved emissivity spectra are independent of background information and in good agreement with in situ observations.