Keywords: 
• delta /
• basin water depth /
• geomorphodynamic /
• grade index /
• tank experiment

Abstract: [Objectives] Recent research suggests that the basin water depth as a downstream condition can govern delta morphodynamics. This is because basin water depth affects the subaerial and subaqueous allocation of sediment in the delta. Compared to deep-water deltas, shallow-water deltas have more sediment distribution in the subaerial part. As a result, the aggradation rate of distributary channels in shallow water deltas is higher, making the channel more active in terms of migration and avulsion. Recently, the Grade Index (Gindex) model is proposed to quantitively illustrate this process. [Methods] This paper elaborates the origin, theoretical modeling, experimental validation, and application of the grade index model and discusses its limitations. The grade here refers the graded state of rivers, which means sediment supplied into the river is conveyed without net deposition or net erosion but completely bypassed through the river. The grade index is defined as the ratio of the volume of sediment allocated subaerially to the total volume of sediment input in per unit time. According to its definition, the Gindex is a dimensionless number between 0 and 1. [Results] Theoretical analyses reveal that the Gindex negatively relates to the basin water depth, though also relates to the delta’s geometrical parameters including the radius of the delta plain and the slopes of the topset and foreset. If the basin water is deeper, the Gindex is closer to 0, which means less sediment is deposited subaerially per unit time. As a result, the channel is more stable and closer to the state of grade. Conversely, the Gindex gets closer to 1 with decreasing basin water depth. As a result, the delta plain becomes more aggradational, by which the channel becomes more unstable. The Gindex is able to reflect important geomorphodynamic parameters of the delta such as the rate of progradation, the rate of aggradation, the rate of channel migration, and the timescale of channel avulsion. Each of these parameters can be calculated as the product or quotient between Gindex and their counterparts obtained with negligibly small basin water depth, while the former is determined by the delta’s geometrical parameters and basin water depth and the latter is determined by the delta’s geometrical parameters and total sediment supply rate. This means that for a particular deltaic system with specific geometrical parameters, sediment supply rate and basin water depth, it has theoretical values for the grade index and geomorphodynamic parameters, both of which can be calculated. This speculation has been verified by tank experiments. The Gindex model is derived based on global mass balance of the deltaic system. Local and/or tentative depositional, erosional and dispersal processes such like related to the backwater effect and coastal processes including waves, tides and longshore currents, as well as effects outside of the depositional system (i.e. vegetation, anthropogenic process), are not considered. [Conclusion] So, the grade index model exclusively separates the "contribution" of basin water depth from others in terms of delta morphodynamics. On the one hand, it can reveal the principle of the differentiation of deep-water and shallow-water delta landforms, and on the other hand, it can help to explain the influence of factors other than basin water depth on the evolution of delta landforms. The grade index model has the potential for general application in modern alluvial-deltaic systems, while its application to ancient systems is yet to be explored.