The sensitivity of fluvial systems to tectonic and climatic boundary conditions allows us to use the geomorphic and stratigraphic records as quantitative archives of past climatic and tectonic conditions. Thus, fluvial terraces that form on alluvial fans and floodplains as well as the rate of sediment export to oceanic and continental basins are commonly used to reconstruct paleoenvironments. However, we currently lack a systematic and quantitative understanding of the transient evolution of fluvial systems and their associated sediment storage and release in response to changes in base level, water input, and sediment input. Such knowledge is necessary to quantify past environmental change from terrace records or sedimentary deposits and to disentangle the multiple possible causes for terrace formation and sediment deposition. Here, we use a set of seven physical experiments to explore terrace formation and sediment export from a single, braided channel that is perturbed by changes in upstream water discharge or sediment supply, or through downstream base-level fall. Each perturbation differently affects (1) the geometry of terraces and channels, (2) the timing of terrace cutting, and (3) the transient response of sediment export from the basin. In general, an increase in water discharge leads to near-instantaneous channel incision across the entire fluvial system and consequent local terrace cutting, thus preserving the initial channel slope on terrace surfaces, and it also produces a transient increase in sediment export from the system. In contrast, a decreased upstream sediment-supply rate may result in longer lag times before terrace cutting, leading to terrace slopes that differ from the initial channel slope, and also lagged responses in sediment export. Finally, downstream base-level fall triggers the upstream propagation of a diffuse knickzone, forming terraces with upstream-decreasing ages. The slope of terraces triggered by base-level fall mimics that of the newly adjusted active channel, whereas slopes of terraces triggered by a decrease in upstream sediment discharge or an increase in upstream water discharge are steeper compared to the new equilibrium channel. By combining fill-terrace records with constraints on sediment export, we can distinguish among environmental perturbations that would otherwise remain unresolved when using just one of these records.