The vibration response of a structure from ambient excitation is measured and used to estimate the modal parameters in Operational Modal Analysis (OMA). Subspace-based system identification allows the accurate estimation of the modal parameters (natural frequencies, damping ratios, mode shapes) from output-only measurements, amongst others with data-driven methods like the Unweighted Principal Component (UPC) algorithm. Due to unknown excitation, measurement noise and finite measurements, all modal parameter estimates are inherently afflicted by uncertainty. The information on their uncertainty is most relevant to assess the quality of the modal parameter estimates, or when comparing modal parameters from different datasets. Previously, a method for variance estimation has been developed for the covariance-driven subspace identification. In this paper, we present an extension of this method for the variance computation of modal parameters for the UPC subspace algorithm. Developing the sensitivities of the modal parameters with respect to the output covariances, the uncertainty is propagated from the measurements to the modal parameters from UPC in a rigorous way. The resulting variance expressions are easy to evaluate and computationally tractable when using an efficient implementation. In a second step, the uncertainty information of the stabilization diagram is used to extract appropriately weighted global mode estimates and their variance. The method is applied to experimental data from the Z24 Bridge.