The Structure and Dynamics of a River Delta are Related Through its Nourishment Area, Suggesting Optimality

Scaling relations in tributary network geomorphology are well understood with respect to optimality. However, the scaling relations between structure and dynamics in distributary network geomorphology are less well understood. This is primarily due to the fact that nourishment area boundaries are difficult to map compared to tributary network catchment area boundaries. Furthermore, most previous work has focused either on the distributary channel networks or the delta’s partitioning of discharge. Here we show that, on the Wax Lake Delta (WLD) in Louisiana, the asymmetry in nourishment areas and downstream nourishment boundary width (∏) at a channel bifurcation, acts as a control upon the partitioning of discharge thereby influencing delta dynamics. We found that relationships between nourishment width, channel width, nourishment area, and discharge can be adequately described by power law functions. Linear power law relationships between discharge and nourishment width show demonstrate a link between a channel network’s structure and dynamics. This confirms that individual channel structure is a function of the dynamical competition amongst channels for unchannelized nourishment width and therefore individual channels cannot be considered independently. The uniformity of flux across the downstream nourishment boundary demonstrates the optimality of distribution of water and sediment flux across the unchannelized delta front and suggests self-regulation of the channel structure to achieve maximum entropy of the system. Leave one out cross validation shows that discharge can be predicted with increased accuracy using nourishment width compared to predictions using channel width. This empirically derived scaling relationship will allow for more accurate prediction of discharge partitioning using remote sensing and has important implications for delta geomorphology. These relationships have potential use in future monitoring and management of deltas