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The Atacama Desert has been pointed out as one of the places on earth where the highest surface irradiance may occur. This area is characterized by its high altitude, prevalent cloudless conditions and relatively low columns of ozone and water vapor. Aimed at the characterization of the solar spectrum in the Atacama Desert, we carried out in February-March 2015 ground-based measurements of the spectral irradiance (from the ultraviolet to the near infrared) at seven locations that ranged from the city of Antofagasta (on the southern pacific coastline) to the Chajnantor Plateau (5,100 m altitude). Our spectral measurements allowed us to retrieve the total ozone column, the precipitable water, and the aerosol properties at each location. We found that changes in these parameters, as well as the shorter optical path length at high-altitude locations, lead to significant increases in the surface irradiance with the altitude. Our measurements show that, in the range 0-5100 m altitude, surface irradiance increases with the altitude by about 27% in the infrared range, 6% in the visible range, and 20% in the ultraviolet range. Spectral measurements carried out at the Izaa Observatory (Tenerife, Spain), in Hannover (Germany) and in Santiago (Chile), were used for further comparisons.