Rivers as ribbons in time: a novel lens for quantifying channel movement from remote sensing data

The lateral migration of river channels is an important control on the evolution of alluvial fans, deltas, and floodplains. Lateral migration consists of gradual riverbank migration and abrupt shifts in location when new channels are created by cutoffs and avulsions. Most existing frameworks can easily measure bank migration, while shifts in position are not considered. When yearly records of rivers are stacked together along the time axis they form a ribbon-like manifold where the width of the ribbon is the persistence of the channel in time, and twists and deformations of the ribbon are created by bank migration. Shifts appear as tears in the ribbon as the channel moves to a new position. We compute a weighted, nearest neighbor graph using all the points that define the manifold in space-time. The weights of this graph are Markovian transition probabilities of a point moving to another point in time. These probabilities are defined by applying a fixed-width gaussian kernel to each pair of points on the manifold. The movement of a point in the river through time is then simulated as an ensemble of Markovian random walks weighted by these transition probabilities. The average endpoint of a random walk in time gives an estimate for how long a migrating river has persisted since the time of the starting point of the random walk. If all the points that define the ribbon-like manifold are considered, this gives a measure of the time duration of the river channel (the width of the ribbon) that is insensitive to the amount of bank migration the channel has undergone. The variance between the starting and ending locations of the river is a proxy for the amount of bank migration that has occurred during the time span in question. Shifts are detectable by branches in the data with markedly lower time durations than the parent branch (the ribbon splits or tears and is less wide along an avulsing segment). We present the results of this analysis for the rivers of the Andean foreland basins to highlight the potential of the analysis to detect and quantify channel shifts and gradual bank migrations at the basin scale.