Representations of Meandering River Planforms

The planform geometries of meandering single-channel rivers are commonly represented and studied using Cartesian coordinates. A major limitation of the use of this coordinate system is that more than one y coordinate may exist for a given x coordinate, which prohibits the use of functional representations of the river channel. For a function \(f:X \to Y\) to be valid, within a set \(X\) , each element must map exactly to one element within a set \(Y\) . We present three transformations that give functional alternatives to Cartesian representations of river planforms and apply them to six river reaches within the Miramichi River watershed in New Brunswick, Canada. Through the application of these transformations and discussion of the results, we show that the amplitude-based approach is generally not recommended due to potential loss of information and the non-reversible nature of the process. Instead, transformations based on the channel direction (azimuth) and radius of curvature are recommended for general use.