The spectral-difference algorithm of Barker and Marshak for inferring optical depth τ of broken clouds has been shown numerically to be potentially useful. Their method estimates cloud-base reflectance and τ using spectral radiometric measurements made at the surface at two judiciously chosen wavelengths. Here it is subject to sensitivity tests that address the impacts of two ubiquitous sources of potential error: instrument noise and presence of aerosol. Experiments are conducted using a Monte Carlo photon transport model, cloud-resolving model data, and surface albedo data from satellite observations. The objective is to analyze the consistency between inherent and retrieved values of τ. Increasing instrument noise, especially if uncorrelated at both wavelengths, decreases retrieved cloud fraction and increases retrieved mean τ. As with all methods that seek to infer τ using passive radiometry, the presence of aerosol requires that threshold values be set in order to discriminate between cloudy and cloud-free columns. A technique for estimating thresholds for cloudy columns is discussed and demonstrated. Finally, it was found that surface type and mean inherent τ play major roles in defining retrieval accuracy.