The nonthermal broadening of spectral lines formed in the solar corona is often used to seek the evidence of Alfven waves propagating in the corona. To have a better understanding of the variation of line widths at different altitudes, we measured the line widths of the strong Fe textsc{xii} 192.4, 193.5, and 195.1 mbox{AA} and Fe textsc{xiii} 202.0 mbox{AA} in an off-limb southern coronal hole up to 1.5 $R_odot$ observed by the Extreme Ultraviolet Spectrometer (EIS) on board the textit{Hinode} satellite. We compared our measurements to the predictions from the Alfven Wave Solar Model (AWSoM) and the SPECTRUM module. We found that the Fe textsc{xii} and Fe textsc{xiii} line widths first increase monotonically below 1.1 $R_odot$, and then keep fluctuating between 1.1 and 1.5 $R_odot$. The synthetic line widths of Fe textsc{xii} and Fe textsc{xiii} below 1.3 $R_odot$ are notably lower than the observed ones. We found that the emission from a streamer in the line of sight significantly contaminates the coronal hole line profiles even up to 1.5 $R_odot$ both in observations and simulations. We suggest that either the discrepancy between the observations and simulations is caused by insufficient nonthermal broadening at the streamer in the AWSoM simulation or the observations are less affected by the streamer. Our results emphasize the importance of identifying the origin of the coronal EUV emission in off-limb observations.
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