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We present a statistical analysis of the gravoturbulent velocity fluctuationsin molecular cloud complexes extracted from our "Cloud Factory" galactic-scaleISM simulation suite. For this purpose, we produce non-LTE $^{12}$CO J=1-0synthetic observations and apply the Principal Component Analysis (PCA)reduction technique on a representative sample of cloud complexes. The velocityfluctuations are self-consistently generated by different physical mechanismsat play in our simulations, which include galactic-scale forces, gasself-gravity, and supernova feedback. The statistical analysis suggests that,even though purely gravitational effects are necessary to reproduce standardobservational laws, they are not sufficient in most cases. We show that theextra injection of energy from supernova explosions plays a key role inestablishing the global turbulent field and the local dynamics and morphologyof molecular clouds. Additionally, we characterise structure function scalingparameters as a result of cloud environmental conditions: some of the complexesare immersed in diffuse (inter-arm) or dense (spiral-arm) environments, andothers are influenced by embedded or external supernovae. In quiescent regions,we obtain time-evolving trajectories of scaling parameters driven bygravitational collapse and supersonic turbulent flows. Our findings suggeststhat a PCA-based statistical study is a robust method to diagnose the physicalmechanisms that drive the gravoturbulent properties of molecular clouds. Also,we present a new open source module, the PCAFACTORY, which smartly performs PCAto extract velocity structure functions from simulated or real data of the ISMin a user-friendly way. Software DOI: 10.5281/zenodo.3822718

The Cloud Factory II: Gravoturbulent Kinematics of Resolved Molecular Clouds in a Galactic Potential