The time history of magma withdrawal through a central vent from a flat-roofed chamber strongly stratified in density and viscosity has been numerically modeled. Important parameters include the geometry of the reservoir; the initial vertical compositional profile; the ratio of viscous, inertial, and gravitational forces; and the basal normal stress driving the eruption. Finite critical stresses in the range 102 to 106 Pa are required to initiate and maintain an eruption. The composition-time history of erupted magma depends strongly on the reservoir/conduit width (A) such that large A increases (1) the time interval during which mixed magma is erupted, (2) the steady-state time (ts), defined as the time at which the composition of erupted magma is within 1% of the initial basal composition, and (3) the fraction of silicic magma trapped within the chamber. Steady-state times increase by a factor of two as the viscosity contrast increases from 1 to 102, and they become independent of viscosity variations for contrasts > 104. It is possible to distinguish continuous from discontinuous (i.e., layered) pre-eruptive gradients within chambers by comparing synthesized and measured geochemical stratigraphic sections for particular pyroclastic flow deposits. A mechanism for the generation of compositional gaps in ignimbrites following either a short eruption hiatus or an abrupt increase or decrease of the discharge during an otherwise quasi-steady eruption is quantitatively predicted. Most important, a compositional gap or a series of gaps within a pyroclastic deposit does not necessarily mean that one existed within the chamber before the eruption. It is impossible to invert stratigraphically controlled geochemical data to obtain in situ chamber compositional structure if one does not have detailed information regarding the location of vents and the variation of magma discharge with time during a pyroclastic eruption.