A genetic approach to estimating river bed topography from SWOT observations

River bathymetry plays a key role in estimating river discharge as well as improving our modeling capabilities of fluvial geomorphology. Genetic algorithm techniques can be used to derive river bed topography using only water surface elevations and the corresponding temporal and spatial rates of change. Each river bathymetric estimate, also referred to as a solution, is modeled as a successive collection of cross- sections, also referred to as genes. An initial population of potential solutions is created from solutions comprised of random cross-sections with depths ranging as deep as the surface height to no depth at all. The population is successively evolved by randomly mutating the depths at a random number of cross-sections. The solutions are selected for the next generation by evaluating their individual fitness. Three varieties of fitness tests are applied to each potential solution: Saint-Venant´s 1-D flow equation, flow continuity, and the statistical power-law relationships suggested by Leapold & Maddock[1]. In this manner, an ideal solution is derived.