[1] No genetic model can explain the variability in distributary network pattern on modern deltas. Here we derive scaling relationships for two processes known to create distributary channels and, with these laws, construct a simple model for distributary network evolution. The first process is mouth-bar deposition at the shoreline and subsequent channel bifurcation; the second is avulsionthe wholesale abandonment of a channel in favor of a new path. The former creates relatively small networks with power-law distributions of channel length; the latter generates relatively few, backwater-scale distributaries.

We present a model of sedimentation in a subsiding fluvio-deltaic basin with steady sediment supply and unsteady base level. We demonstrate that mass transfer in a fluvio-deltaic basin is analogous to heat transfer in a generalized Stefan problem, where the basin's shoreline represents the phase front. We obtain a numerical solution to the governing equations for sediment transport and deposition in this system via an extension of a deforming-grid technique from the phase-change literature. Through modification of the heat-balance integral method, we also develop a semi-analytical solution, which agrees well with the numerical solution. We construct a space of dimensionless groups for the basin and perform a systematic exploration of this space to illustrate the influence of each group on the shoreline trajectory. Our model results suggest that all subsiding fluvio-deltaic basins exhibit a standard autoretreat shoreline trajectory in which a brief period of shoreline advance is followed by an extended period of shoreline retreat. Base-level cycling produces a shoreline response that varies relative to the autoretreat signal. Contrary to previous studies, we fail to observe either a strong phase shift between shoreline and base level or a pronounced attenuation of the amplitude of shoreline response as the frequency of base-level cycling decreases. However, the amplitude of shoreline response to base-level cycling is a function of the basin's age.

[1] Experimentally determined shoreline migration rates show high-frequency autogenic variability superimposed on low-frequency allogenic shoreline responses induced by eustatic base level change. This variability persists even when the shoreline migration is averaged laterally, indicating time variation in total sediment discharge reaching the shoreline. The magnitude of autogenic variability in shoreline migration rate changes by roughly a factor of 3 depending on the shoreline migration direction: It is strongest during transgression, when the shoreline is on average migrating against the mean sediment flow, and weakest during regression, when the shoreline is migrating with the mean sediment flow. We propose that this time variation is due to overall sediment storage and release in the fluvial system. We use a one-dimensional geometric model to model the autogenic signals observed in the experiment. The model uses small periodic changes in the fluvial slope to represent the effects of storage and release of supplied sediment due to intrinsic variation in the transport efficiency of the fluvial system. The periodic pulses of sediment discharge to the shoreline required in the model to explain the variations in shoreline migration can exceed by an order of magnitude the mean allogenic sediment discharge. The slope variability required in the model to explain the autogenic shoreline signals is 1-4% of the mean slope. This is well within the range of observed variability in depositional fluvial slopes. We propose that at least part of this observed variability is real; that is, the long-profile slope of a depositional river system may have an intrinsic ''elasticity'' of a few percent of its mean value, even under steady forcing. Autogenic slope variation of this magnitude could readily produce parasequence-scale deposits in the stratigraphic record.