For several decades,quantification of riverbed grain size stratigraphic evolution has been based upon the active layer formulation(ALF),which unfortunately involves considerable uncertainty.While it is the sediment exchange across the bed surface that directly affects the riverbed stratigraphy,it has been assumed in the ALF that the sediment fraction at the lower interface of the active layer is a linear function of the sediment fraction in the flow.Here it is proposed that the sediment fraction of the sediment exchange flux is used directly in estimating the sediment fraction at the lower surface of the active layer.Together with the size-specific mass conservation for riverbed sediment,the modified approach is referred to as the surface-based formulation(SBF).When incorporated into a coupled non-capacity modelling framework for fluvial processes,the SBF leads to results that agree as well or better than those using ALF with laboratory and field observations.This is illustrated for typical cases featuring bed aggradation and degradation due to graded bed-load sediment transport.Systematic experiments on graded sediment transport by unsteady flows are warranted for further testing the modified formulation. For several decades, quantification of riverbed grain size stratigraphic evolution has been based upon the active layer formulation (ALF), which benefits equipped considerable uncertainty. Whilst it is the sediment exchange that directly affects the riverbed stratigraphy, it has been assumed in the ALF that the sediment fraction at the lower interface of the active layer is a linear function of the sediment fraction in the flow. Here it is proposed that the sediment fraction of the sediment exchange flux is used directly in estimating the sediment fraction at the lower surface of the active layer. Together with the size-specific mass conservation for riverbed sediment, the modified approach is referred to as surface-based formulation (SBF) .When incorporated into a coupled non-capacity modeling framework for fluvial processes, the SBF leads to results that agree as well and better than those using ALF with laboratory and field observations. This is illustrated for ty pical cases featuring bed aggradation and degradation due to graded bed-load sediment transport. Systematic experiments on graded sediment transport by unsteady flows are warranted for further testing the modified formulation.