We present a study of the infrared (IR) spectra of the (0001) deuterated ice surface based on first-principles molecular dynamics simulations. The computed spectra show a good agreement with available experimental IR measurements. We identified the bonding configurations associated with specific features in the spectra, allowing us to provide a detailed interpretation of IR signals. We computed the spectra of several proton ordered and disordered models of the (0001) surface of ice, and we found that IR spectra do not appear to be a sensitive probe of the microscopic arrangement of protons at ice surfaces.