Global Sensitivity Analysis (GSA) has long been recognized as an indispensable tool for model analysis. GSA has been extensively used for model simplification, identifiability analysis, and diagnostic tests, among others. Nevertheless, computationally efficient methodologies are sorely needed for GSA, not only to reduce the computational overhead, but also to improve the quality and robustness of the results. This is especially the case for process-based hydrologic models, as their simulation time is often too high and is typically beyond the availability for a comprehensive GSA. We overcome this computational barrier by developing an efficient variance-based sensitivity analysis using copulas. Our data-driven method, called VISCOUS, approximates the joint probability density function of the given set of input-output pairs using Gaussian mixture copula to provide a given-data estimation of the sensitivity indices. This enables our method to identify dominant hydrologic factors by recycling pre-computed set of model evaluations or existing input-output data, and thus avoids augmenting the computational cost. We used two hydrologic models of increasing complexity (HBV and VIC) to assess the performance of the proposed method. Our results confirm that VISCOUS and the original variance-based method can detect similar important and unimportant factors. However, while being robust, our method can substantially reduce the computational cost. The results here are particularly significant for, though not limited to, process-based models with many uncertain parameters, large domain size, and high spatial and temporal resolution.