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The principal goal of the NASA Terrestrial Planet Finder (TPF) and European Space Agency's Darwin mission concepts is to directly detect and characterize extrasolar terrestrial (Earthsized) planets. This first generation of instruments is expected to provide disk-averaged spectra with modest spectral resolution and signal-to-noise. Here we use a spatially and spectrally resolved model of a Mars-like planet to study the detectability of a planet's surface and atmospheric properties from disk-averaged spectra. We explore the detectability as a function of spectral resolution and wavelength range, for both the proposed visible coronograph (TPFC) and mid-infrared interferometer (TPF-I/Darwin) architectures. At the core of our model is a spectrum-resolving (line-by-line) atmospheric/surface radiative transfer model. This model uses observational data as input to generate a database of spatially resolved synthetic spectra for a range of illumination conditions and viewing geometries. The model was validated against spectra recorded by the Mars Global Surveyor-Thermal Emission Spectrometer and the Mariner 9-Infrared Interferometer Spectrometer. Results presented here include disk-averaged synthetic spectra, light curves, and the spectral variability at visible and mid-infrared wavelengths for Mars as a function of viewing angle, illumination, and season. We also considered the differences in the spectral appearance of an increasingly ice-covered Mars, as a function of spectral resolution, signal-to-noise and integration time for both TPF-C and TPFI/ Darwin.