The Emirates Mars Infrared Spectrometer (EMIRS) instrument onboard the Emirates Mars Mission (EMM) spacecraft relies on a robust retrieval algorithm to obtain dust and water-ice optical depth, surface and lower atmospheric temperatures, and water vapor abundance from thermal-IR spectra. While observations made by EMIRS provide excellent geographic and seasonal/local time coverage, specific measurements might not always be possible. In many cases a single field of view (FOV), or pixel, may contain numerous geologic units, emission angles, and surface temperatures, complicating the retrieval process. To retrieve quantities related to the dynamics of the lower atmosphere with the highest fidelity, it is vital we understand how the uncertainty associated with such retrieved parameters varies at the sub-pixel level. This includes quantifying the minimum number of sub-pixels necessary to reproduce the observed spectral radiance as well as modeling the extent to which forward model parameters vary across a single pixel. Synthetic observations of Mars are constructed by populating modeled footprints with various numbers of randomly distributed sub-pixels, representing different spatial resolution requirements for the EMIRS forward model. Surface temperatures and vertical profiles of atmospheric properties are modeled at the sub-pixel level with top of atmosphere (TOA) radiance, as observed by EMIRS, computed using the Spectral Mapping Atmospheric Radiative Transfer (SMART) code. Resulting synthetic spectra are compared against a truth computation performed at very high spatial resolution to determine the minimum number of computed sub-pixels to accurately model the martian atmosphere to within 0.2 x the Noise Equivalent Spectral Radiance (NESR) of EMIRS. A range of observational and environmental scenarios is investigated to explore the dependence a variety of factors, including emission angle, time of day, and season have on the synthetic spectra. Sensitivity is also assessed in terms of the maximum allowable change in surface temperature within a pixel before noise is introduced to a measurement. Accompanying each synthetic observation are various statistics, allowing for the acquisition of reliable results regardless of viewing geometry, latitude/longitude, season, local time, etc.