Disambiguating Flat Spots in Digital Elevation Models

We consider Digital Elevation Models (DEMs) encoded as regular grids of discrete elevation data samples. When the terrain's slope is low relative to the dataset's vertical resolution, the DEM may contain flat spots: connected areas where all points share the same elevation. Flat spots can hinder certain analyses, such as topological characterization or drainage network computations. We discuss the application of Morse-Smale theory to grids and the disambiguation of flat spots. Specifically, we show how to characterize the topology of flat spots and symbolically perturb their elevation data to make the DEM compatible with Morse-Smale theory while preserving its topological properties. Our approach applies equivalently to three different surface models derived from the DEM grid: the step model, the bilinear model, and a piecewise-linear model based on the quincunx lattice.