We use a thermal model with large-scale surface roughness to study the effects of topography and roughness on thermal infrared spectra of planetary surfaces. We study a range of roughness values, illumination geometries, and viewing geometries and find that surface roughness can strongly alter the slope of a thermal infrared spectrum, especially for large solar incidence angles. This roughness-induced slope in the spectrum can shift the location of the Christiansen frequency and should be removed in order to study the mineralogy and other surface properties. The effect is minimized for viewing near zero phase angle. This makes it possible to measure large-scale roughness by comparing thermal infrared spectra taken near zero phase angle with those taken at a large solar incidence angle and nonzero phase angle. Changes in apparent emissivity with wavelength in the thermal infrared due to roughness are calculated for Clementine longwave-infrared images of the Moon. These roughness-induced spectral slopes observed for the Moon are 5% between 5 and 8 microns for regions of moderate topography.