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The complete three-dimensional structure of the magnetic field withinmolecular clouds has eluded determination despite its high value in determiningcontrolling factors in the star formation process, as it cannot be directlyprobed observationally. Considering that inclination of the magnetic fieldrelative to the plane of sky is one of the major sources of depolarization ofthermal emission from dust in molecular clouds, we propose here a new method toestimate the inclination angle of the cloud-scale magnetic field based on thestatistical properties of the observed polarization fraction. We test thismethod using a series of Monte Carlo experiments, and find that the methodworks well provided that deviations of magnetic field direction from theaveraged values are small. When applied to synthetic observations of numericalsimulations of star-forming clouds, our method gives fairly accuratemeasurements of the mean magnetic field inclination angle (within$10^\circ-25^\circ$), which can further be improved if we restrict ourtechnique to regions of low dispersion in polarization angles ${\cal S}$. Wetested our method on the BLASTPol polarimetric observations of the Vela Cmolecular cloud complex, which suggests that the magnetic field of Vela C has ahigh inclination angle ($\sim 60^\circ$), consistent with previous analyses.

A New Method to Trace Three-dimensional Magnetic Field Structure within Molecular Clouds Using Dust Polarization