An algorithm for treating flat areas and depressions in digital elevation models using linear interpolation

Digital elevation model (DEM) data are essential to hydrological applications and have been widely used to calculate a variety of useful topographic characteristics, e.g., slope, flow direction, flow accumulation area, stream channel network, topographic index, and others. Except for slope, none of the other topographic characteristics can be calculated until the flow direction at each pixel within a DEM is determined. However, flow direction cannot be accurately calculated until depressions and flat areas within a DEM have been rectified. This is a routine problem in hydrologic modeling, because virtually all DEMs contain flat and sink pixels, both real and artifactual, that if left untreated will prevent accurate simulation of hydrologic flow paths. Although a number of algorithms are available for rectifying flat and sink pixels in DEM data, treatment of flat areas and depressions and calculation of flow direction remain problematic for reasons of complexity and uncertainty. A new algorithm that effectively rectifies flat and sink pixels was developed and tested. The approach is to use linear interpolation between low elevation grid cells on the edge of each flat area or depression defined as outlets and higher elevation grid cells on the opposite side defined as inflow pixels. The implementation requires an iterative solution to accommodate the irregular geometry of flat areas or depressions and exceptions that arise. Linear interpolation across flat areas or depressions provides a natural way to scale elevation adjustments based on the vertical scale of the surrounding topography, thereby avoiding the addition or subtraction of arbitrary small numbers that we regard as a disadvantage in some prior techniques. Tests for two virtual terrains and one real terrain show that our algorithm effectively rectifies flat areas and depressions, even in low‐relief terrain, and produces realistic patterns of flow accumulation and extracted channel networks.