\subsection{Tracing Column Density with Different Tracers}
To estimate the turbulent energy of the Ophiuchus cloud, we first estimate its physical properties, including density and temperature. Various tracers have been used in deriving the column density of the molecular gas. For star forming regions like the Ophiuchus, people often use three tracers: near-infrared extinction, mid/far-infrared dust thermal emission, and molecular line emission as proxies for the molecular gas. However, as noted in \citet{Goodman_2009}, since none of these three tracers are the result of physical processes directly related to the dominant component of the molecular gas, which is H$_2$, one has to be extremely careful when choosing a tracer and when comparing measurements from one with another. Following the analysis done in \citet{Goodman_2009}, we examine the distributions of column densities derived from these tracers for the Ophiuchus cloud.

As described in \S 3, we use the 2MASS-based extinction map, the IRIS data, the Herschel data and the FCRAO observation of $^{12}$CO/$^{13}$CO line emission in our analysis. Fig. 2 shows the column density maps based on these tracers, given in units of equivalent V-band magnitude.