The grade index model as a rationale for autogenic nonequilibrium responses of deltaic clinoform to relative sea-level rise

Grade index (G(index)) is a dimensionless number given as the volume-in-unit-time ratio of subaerial allocation to both subaerial and subaqueous allocations of sediment supplied to a delta from upstream. It was originally proposed for understanding the effect of basin water depth on the morphodynamics of delta distributary channels under stationary relative sea level. We here examine how rising relative sea level modulates the G(index), using geometrical reasoning and numerical simulations. We find that the grade index model can account for autoretreat of the deltaic shoreline, autodrowning of the whole system, and autobreak of the deltaic sedimentation, all of which are the consequences of autogenic nonequilibrium responses to steadily rising relative sea level. The regressive-to-transgressive threshold (i.e. the onset of autoretreat) is crossed when the delta plain's dimensionless basal area (A(t*)) encounters a critical value that is expressed in terms of G(index): regression and transgression are sustained when A(t*) is below and above the threshold, respectively. The mode of transgression depends on the slope conditions. If the hinterland slope (gamma) is steeper than the foreset slope (beta), both A(t*) and G(index) decrease as the relative sea-level rises. Eventually, the depositional system experiences autodrowning when A(t*) = G(index) = 0. If gamma < beta; on the other hand, both A(t*) and G(index) increase. This latter slope condition eventually causes autobreak of the deltaic sedimentation, afterward of which A(t*) = G(index) = 1. The grade index model is useful for interpreting and predicting the stratigraphic responses of natural deltaic clinoforms in conditions of rising relative sea level.