We use Principal Component Analysis ( PCA ) to study the gas dynamics in numerical simulations of typical MCs .
Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry .
We model the CO line emission in a post-processing step using a 3D radiative transfer code .
We consider mean number densities n _ { 0 } = 30 , 100 , 300 cm ^ { -3 } that span the range of values typical for MCs in the solar neighbourhood and investigate the slope \alpha _ { \text { PCA } } of the pseudo structure function computed by PCA for several components : the total density , H _ { 2 } density , ^ { 12 } CO density , ^ { 12 } CO J = 1 \rightarrow 0 intensity and ^ { 13 } CO J = 1 \rightarrow 0 intensity .
We estimate power-law indices \alpha _ { \text { PCA } } for different chemical species that range from 0.5 to 0.9 , in good agreement with observations , and demonstrate that optical depth effects can influence the PCA .
We show that when the PCA succeeds , the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as \approx \pm 0.1 .
The method can fail if the CO distribution is very intermittent , e.g .
in low-density clouds where CO is confined to small fragments .