Progradational fluvio-deltaic systems tend towards but cannot reach equilibrium, a state in which the longitudinal profile does not change shape and all sediment is bypassed beyond the shoreline. They cannot reach equilibrium because progradation of the shoreline requires aggradation along the longitudinal profile. Therefore progradation provides a negative feedback, unless relative sea level falls at a sufficient rate to cause non-aggradational extension of the longitudinal profile. How closely fluvio-deltaic systems approach equilibrium is dependent on their progradation rate, which is controlled by water depth and downstream allogenic controls, and governs sediment partitioning between the fluvial, deltaic, and marine domains. Here, six analogue models of coastal fluvio-deltaic systems and small prograding shelf margins are examined to better understand the effect of water depth, subsidence, and relative sea-level variations upon longitudinal patterns of sediment partitioning and grain-size distribution that eventually determine large-scale stratigraphic architecture. Fluvio-deltaic systems prograding in relatively deep-water environments are characterized by relatively low progradation rates compared to shallow-water systems. This allows these deeper water systems to approach equilibrium more closely, enabling them to construct less concave and steeper longitudinal profiles that provide low accommodation to fluvial systems. Glacio-eustatic sea-level variations and subsidence modulate the effects of water depth on the longitudinal profile. Systems are closest to equilibrium during falling relative sea level and early lowstand, resulting in efficient sediment transport towards the shoreline at those times. Additionally, the strength of the response to relative sea-level fall differs depending on water depth. In systems prograding into deep water, relative sea-level fall causes higher sediment bypass rates and generates significantly stronger erosion than in shallow-water systems, which increases the probability of incised-valley formation. Water depth in the receiving basin thus forms a first-order control on the sediment partitioning along the longitudinal profile of fluvio-deltaic systems and the shelf clinoform style. It also forms a control on the availability of sand-grade sediment at the shoreline that can potentially be remobilized and redistributed into deeper marine environments. Key findings are subsequently applied to the literature of selected shelf clinoform successions.

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