We study the interplay of various factors causing vertical grain-size changes in alluvial basins using a simple coupled model for sediment transport and downstream partitioning of grain sizes. The sediment-transport model is based on the linear diffusion equation; by deriving this from first principles we show that the main controls on the diffusivity are water discharge and stream type (braided or single-thread). The grain-size partitioning model is based on the assumption that the deposit is dominated by gravel until all gravel in transport has been exhausted, at which point deposition of the finer fractions begins.
We then examine the response of an alluvial basin to sinusoidal variation in each of four basic governing variables: input sediment flux, subsidence rate, supplied gravel fraction, and diffusivity (controlled mainly by water flux). We find that, except in the case of variable gravel fraction, the form of the basin response depends strongly on the time-scale over which the variation occurs. There is a natural time-scale for any basin, which we call the ‘equilibrium time’, defined as the square of basin length divided by the diffusivity. We define ‘slow’ variations in imposed independent variables as those whose period is long compared with the equilibrium time. We find that slow variation in subsidence produces smoothly cyclic gravel-front migration, with progradation during times of low sedimentation rate, while slow variation in sediment flux produces gravel progradation during times of high sedimentation rate. Slow variation in diffusivity produces no effect. Conversely, we define ‘rapid’ variations as those whose period is short compared with the equilibrium time. Our model results suggest that basins respond strongly to rapid variation in either sediment flux or diffusivity; in both cases, deep proximal unconformities are associated with abrupt gravel progradation. This progradation occurs during times of either low sediment flux or high diffusivity. On the other hand, basin response to variation in subsidence rate gradually diminishes as the time scale becomes short relative to the equilibrium time. Each of the four variables we have considered - input sediment flux, subsidence, gravel fraction, and diffusivity - is associated with a characteristic response pattern. In addition, the time scale of imposed variations relative to the equilibrium time acts in its own right as a fundamental control on the form of the basin response.