Growing empirical evidence shows that many geomorphic systems are in transient state or out of equilibrium with respect to the external driving forces. The transient state is often related to the (dis)connectivity of the many constituent parts of geomorphic systems as a result of sediment storage along the sediment flow path from its source to the final sink. The response time of geomorphic systems to external changes is thus depended on the residence time of sediment in various storage compartments. Here, I present a mathematical concept based on reservoir theory to model residence time of sediment using millennial scale sediment budgets. The framework sheds light on the limitation of the sediment delivery ratio, which is often used as a measure of sediment connectivity in geomorphic systems, and provides analytical information on process type, pace of sediment flux and connectivity of storage compartments along the sediment cascade. The application of the reservoir theory to geomorphic systems under agricultural land use show that sediment delivery ratios are linked to the virtual velocity of the eroded sediment, the time since the onset of agricultural land use and the size of the studied basins. With respect to the temporal evolution of sediment storages that temporaryly remove sediment from the conveyor belt, the framework aims to estimate the sediment residence time in storages, which is linked to the effective timescale of disconnectivity. Reanalysis of a long-term empirical sediment budget from Central Europe reveals that the response to agricultural land use, which started ~5000 yrs. BP, is mainly buffered by the long residence time of sediment on hillslopes (in the order of 103 years), which results in a delayed floodplain aggradation. Furthermore, the framework was applied to paraglacial mountain systems that inherit striking evidences of Pleistocene glacial erosion and still recover from the change from glacial to interglacial conditions as a consequence of the reduced lateral and longitudinal connectivity. I show that paraglacial response times of sediment flux in mountain headwater in the Canadian Rocky Mountains range in the order of 100-400 ka. The results indicate that response times at the transition from glacial to interglacial conditions are much longer than the return interval of major glaciations, causing a transient behavior of mountain headwater basins during interglacial periods. The presented reanalysis of millennial-scale sediment budgets of agricultural and mountain geosystems provides an integrative framework to link paleo-environmental reconstructions with the connectivity of transient geomorphic system to external changes.