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Turbulence plays a major role in the formation and evolution of molecularclouds. The problem is that turbulent velocities are convolved with the densityof an observed region. To correct for this convolution, we investigate therelation between the turbulence spectrum of model clouds, and the statistics oftheir synthetic observations obtained from Principal Component Analysis (PCA).We apply PCA to spectral maps generated from simulated density and velocityfields, obtained from hydrodynamic simulations of supersonic turbulence, andfrom fractional Brownian motion fields with varying velocity, density spectra,and density dispersion. We examine the dependence of the slope of the PCAstructure function, alpha_PCA, on intermittency, on the turbulence velocity(beta_v) and density (beta_n) spectral indexes, and on density dispersion. Wefind that PCA is insensitive to beta_n and to the log-density dispersionsigma_s, provided sigma_s < 2. For sigma_s>2, alpha_PCA increases with sigma_sdue to the intermittent sampling of the velocity field by the density field.The PCA calibration also depends on intermittency. We derive a PCA calibrationbased on fBms with sigma_s<2 and apply it to 367 CO spectral maps of molecularclouds in the Galactic Ring Survey. The average slope of the PCA structurefunction, <alpha_PCA>=0.62\pm0.2, is consistent with the hydrodynamicsimulations and leads to a turbulence velocity exponent <beta_v>=2.06\pm0.6 fora non-intermittent, low density dispersion flow. Accounting for intermittencyand density dispersion, the coincidence between the PCA slope of the GRS cloudsand the hydrodynamic simulations suggests beta_v~1.9, consistent with bothBurgers and compressible intermittent turbulence.

The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-Dependent PCA Calibration