Time series of sediment transport rate in systems as diverse as rivers and rice piles often exhibit correlations across a wide range of temporal scales with a well-defined upper limit (decorrelation time). The source of this generic behavior is storage and release of sediment within the transport system, often due to the presence of a process threshold. On the Earth's surface these complex systems also respond to time-varying environmental forcing that may be natural (e.g., precipitation, sea-level cycles, plate motions) or anthropogenic. Here I analyze temporal records from several sources: clastic deposits on continental margins, shoreline position of an experimental delta, and sediment efflux from a steadily-driven pile of rice. All exhibit a substantial range of scales where transport fluctuations swamp environmental signals. I use cellular models for river delta evolution and rice-pile avalanching to examine the response of sediment transport systems to periodic variations in sediment supply. Results show that imposed cycles with periods smaller than the decorrelation time lose all coherence. Only cycles with periods longer than the decorrelation time are preserved in the time series of transport rate. Stratigraphic and paleo-climatic studies rely on extracting environmental signals from sedimentary deposits. Results of this study suggest that the nonlinear dynamics of sediment transport set a hard lower limit on the temporal range over which such signals may be confidently interpreted. The news is not all bad, however: mathematical and physical models indicate that this limit may be derived fairly easily from a small set of parameters, helping to more rigorously interpret the geologic record.