The usefulness of satellite multi-sensor precipitation (SMP) and other satellite-informed precipitation products in water resources modeling can be hindered by substantial errors which vary considerably with spatiotemporal scale. One approach to cope with these errors is by combining SMPs with ensemble generation methods, such that each ensemble member reflects one plausible realization of the true—but unknown—precipitation. This requires replicating the spatiotemporal autocorrelation structure of SMP errors. The climatology of this structure is unknown for most locations due to a lack of ground reference observations, while the unique anisotropy and nonstationarity within any particular precipitation system limit the relevance of this climataology to the depiction of error in individual storm systems. Characterizing and simulating this autocorrelation across spatiotemporal scales has thus been called a grand challenge within the precipitation community. We introduce the Space-Time Rainfall Error and Autocorrelation Model (STREAM), which combines anisotropic and nonstationary SMP spatiotemporal correlation structures with a pixel-scale precipitation error model to stochastically generate ensemble precipitation fields that resemble “ground truth” precipitation. We generate STREAM precipitation ensembles at high resolution (1-hour, 0.1˚) with minimal reliance on ground-reference data, and evaluate these ensembles at multiple scales. STREAM ensembles consistently “bracket” ground-truth observations and replicate the autocorrelation structure of ground-truth precipitation fields. STREAM is compatible with pixel-scale error/uncertainty formulations beyond those presented here, and could be applied globally to other precipitation sources such as numerical weather predictions or “blended” products. In combination with recent work in SMP uncertainty characterization, STREAM could be run without any ground data.