Quantitative metrics that describe river deltas and their channel networks

Densely populated river deltas are losing land at an alarming rate and to successfully restore these environments we must understand the details of their morphology. Toward this end we present a set of five metrics that describe delta morphology: (1) the fractal dimension, (2) the distribution of island sizes, (3) the nearest-edge distance, (4) a synthetic distribution of sediment fluxes at the shoreline, and (5) the nourishment area. The nearest-edge distance is the shortest distance to channelized or unchannelized water from a given location on the delta and is analogous to the inverse of drainage density in tributary networks. The nourishment area is the downstream delta area supplied by the sediment coming through a given channel cross section and is analogous to catchment area in tributary networks. As a first step, we apply these metrics to four relatively simple, fluvially dominated delta networks. For all these deltas, the average nearest-edge distances are remarkably constant moving down delta suggesting that the network organizes itself to maintain a consistent distance to the nearest channel. Nourishment area distributions can be predicted from a river mouth bar model of delta growth, and also scale with the width of the channel and with the length of the longest channel, analogous to Hack's law for drainage basins. The four delta channel networks are fractal, but power laws and scale invariance appear to be less pervasive than in tributary networks. Thus, deltas may occupy an advantageous middle ground between complete similarity and complete dissimilarity, where morphologic differences indicate different behavior.