Grain Size-Specific Engelund-Hansen Type Relation for Bed Material Load in Sand-Bed Rivers, With Application to the Mississippi River

Many sand-bed rivers worldwide have been experiencing significant reductions in sediment load over the past several decades. This is one of the causes of river delta drowning worldwide. This problem, however, has not been studied in detail in the context of sediment grain sorting. Considering the good performance of the original Engelund-Hansen relation (OEH) for uniform sediment, and the fact that bulk grain size-specific relations for bed material load that allow for sorting are relatively rare in the case of sand-bed rivers, a grain size-specific Engelund-Hansen type relation (SEH) is proposed in this study based on data from a large flume. We embed both the OEH and the SEH in a one-dimensional river morphodynamic model to simulate the morphodynamic evolution of the middle Mississippi River in response to the upstream cutoff of sediment supply. Simulation results using a single characteristic grain size show that bed material load delivered to the delta reduces only gradually in response to the cutoff of sediment supply, in agreement with previous studies. However, implementing the full grain size distribution of sediment leads to a much faster reduction of bed material load delivered to the delta, because the bed surface coarsens in response to grain sorting. This armoring inhibits the bed degradation that would replenish sediment load along the channel. The bed material load of finer sediment declines more rapidly than that of coarser sediment. The results of this study have practical implications for river delta restoration.