  The nonthermal broadening of spectral lines formed in the solar corona is
often used to seek the evidence of Alfv\'en 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 Alfv\'en 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.
