Alluvial stratigraphic records are notoriously incomplete. All stratigraphic sections within sedimentary basins experience varying episodes of erosion and geomorphic stasis during their accumulation. This has detrimental effects on the completeness of paleoclimatic and paleobiologic records. Here we evaluate the resultant stratigraphic incompleteness using a physical experiment with self-organized vertical scales of topography and lateral scales of geomorphic stasis. First, we document how stratigraphic completeness improves as the temporal discretization interval coarsens, and show that the primary cause of the missing time shifts from stasis to erosion as the discretization is coarsened. Second, we demonstrate that the debilitating effect of finer temporal resolution can be predictably offset by compositing records across a wider area, and present a new two-dimensional formulation of stratigraphic completeness. These findings imply systematic shifts in taphonomic preservation, and by extension, the quality of paleobiologic and paleoclimatic proxy records.