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In this paper, we propose a novel out-of-core volume rendering algorithm for large time-varying fields. Exploring temporal and spatial coherences has been an important direction for speeding up the rendering of time-varying data. Previously, there were techniques that hierarchically partition both the time and space domains into a data structure so as to re-use some results from the previous time step in multiresolution rendering; however, it has not been studied on which domain should be partitioned first to obtain a better re-use rate. We address this open question, and show both theoretically and experimentally that partitioning the time domain first is better. We call the resulting structure (a binary time tree as the primary structure and an octree as the secondary structure) the space-partitioning time (SPT) tree. Typically, our SPT-tree rendering has a higher level of details, a higher re-use rate, and runs faster. In addition, we devise a novel cut-finding algorithm to facilitate efficient out-of-core volume rendering using our SPT tree, we develop a novel out-of-core preprocessing algorithm to build our SPT tree I/O-efficiently, and we propose modified error metrics with a theoretical guarantee of a monotonicity property that is desirable for the tree search. The experiments on datasets as large as 25 GB using a PC with only 2 GB of RAM demonstrated the efficacy of our new approach.