Transfer functions facilitate the volumetric data visualization by assigning optical properties to various data features and scalar values. Automation of transfer function specifications still remains a challenge in volume rendering. This paper presents an approach for automating transfer function generations by utilizing topological attributes derived from the contour tree of a volume. The contour tree acts as a visual index to volume segments, and captures associated topological attributes involved in volumetric data. A residue flow model based on Darcy's Law is employed to control distributions of opacity between branches of the contour tree. Topological attributes are also used to control color selection in a perceptual color space and create harmonic color transfer functions. The generated transfer functions can depict inclusion relationship between structures and maximize opacity and color differences between them. The proposed approach allows efficient automation of transfer function generations, and exploration on the data to be carried out based on controlling of opacity residue flow rate instead of complex low-level transfer function parameter adjustments. Experiments on various data sets demonstrate the practical use of our approach in transfer function generations.