Cost analysis of water and sediment diversions to optimize land building in the Mississippi River delta

[1] Land loss in the Mississippi River delta caused by subsidence and erosion has resulted in habitat loss and increased exposure of settled areas to storm surge risks. There is debate over the most cost-efficient and geomorphologically feasible projects to build land by river diversions, namely, whether a larger number of small, or a lesser number of large, engineered diversions provide the most efficient outcomes. This study uses an optimization framework to identify portfolios of diversions that are efficient for three general restoration objectives: maximize land built, minimize cost, and minimize water diverted. The framework links the following models: (1) a hydraulic water and sediment diversion model that, for a given structural design for a diversion, estimates the volume of water and sediment diverted; (2) a geomorphological land-building model that estimates the amount of land built over a time period, given the volume of water and sediment; and (3) a statistical model of investment cost as a function of diversion depth and width. An efficient portfolio is found by optimizing one objective subject to constraints on achievement of the other two; then by permuting those constraints, we find distinct portfolios that represent trade-offs among the objectives. Although the analysis explores generic relationships among size, cost, and land building (and thus does not consider specific project proposals or locations), the results demonstrate that large-scale land building (>200 km) programs that operate over a time span of 50 years require deep diversions because of the enhanced efficiency of sand extraction per unit water. This conclusion applies whether or not there are significant scale economies or diseconomies associated with wider and deeper diversions.