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In a previous paper, we discovered a surprising spectrally-invariant relationship in shortwave spectrometer observations taken by the Atmospheric Radiation Measurement (ARM) program. The relationship suggests that the shortwave spectrum near cloud edges can be determined by a linear combination of zenith radiance spectra of the cloudy and clear regions. Here, using radiative transfer simulations, we study the sensitivity of this relationship to the properties of aerosols and clouds, to the underlying surface type, and to the finite field-of-view (FOV) of the spectrometer. Overall, the relationship is mostly sensitive to cloud properties and has little sensitivity to other factors. At visible wavelengths, the relationship primarily depends on cloud optical depth regardless of cloud phase function, thermodynamic phase and drop size. At water-absorbing wavelengths, the slope of the relationship depends primarily on cloud optical depth; the intercept, by contrast, depends primarily on cloud absorbing and scattering properties, suggesting a new retrieval method for cloud drop effective radius. These results suggest that the spectrally-invariant relationship can be used to infer cloud properties near cloud edges even with insufficient or no knowledge about spectral surface albedo and aerosol properties.