Relative elevation model (REM) of Birch Creek, a tributary to the Yukon River, Alaska, USA. (NW to the left)
Topographic data are often represented in the form of a digital elevation model (DEM), where an elevation value is defined at each pixel in a rectangular grid. Spatially, the grid is defined with respect to a local (or geographic) coordinate system, and elevation values are given with respect to a particular datum (typically sea level).
Because rivers flow downhill, DEMs of river corridors will always have a decreasing trend in elevations from the upper headwater streams down to an outlet such as an ocean or terminal basin. Superimposed on this overall trend are smaller-scale topographic variations in the river corridor. These fluctuations in topography interact with the river hydraulics, which in turn control where sediment moves, thus adjusting the topography and creating a feedback process between topography and hydraulics (see: river morphodynamics).
In fluvial geomorphology (the study of the physical shape/structure of rivers), the topography of a river corridor can provide valuable insights regarding the processes that govern the evolution of the river over time. For example, low points adjacent to the main channel are often abandoned, creating relic channels in meandering rivers. One technique used to study these topographic variations is the creation of a relative elevation model, or REM. An REM is created by removing the overall downward trend in river elevation, leaving behind the local fluctuations in topography relative to the river. REMs serve as a simple (and often aesthetically pleasing) means to visualize river corridors and floodplains. REMs have also been used in applications such as machine learning models to predict river substrate size classes
An example river centerline elevation profile (top) and the residual relative elevations (bottom) after removing the large-scale trend in slope. This detrending for the lower Yuba River was originally developed to study river landform sequences.
Detrending a DEM to create an REM involves three main steps:
While the overall method is typically the same, there are several different ways of accomplishing each step in the process of producing a REM. The river centerline used can be manually drawn, or it can be explicitly calculated with more complex topographic methods such as least cost path analysis or flow accumulation. A channel cross-section sampling can also be used as an alternative approach. Depending on whether the topographic data covers the river bathymetry (e.g. sonar or green lidar) or not (near infrared lidar), the river elevation sampled will either correspond to the river bed elevation or water surface elevation, respectively. Detrending can also be based on a functional fit of bed elevations in order to emphasize in-channel topographic fluctuations. Interpolation methods used to determine the nearest river elevation across the DEM include nearest neighbor, inverse distance weighting, Kriging, and others. Each of these methods has their own parameters that can lead to differing results in the final output. Consequently, producing REMs is typically a manual, iterative process.
Generating REMs usually takes some manual steps and iteration in order to generate a good looking final product. The gold standard are the tutorials produced by Daniel Coe of the Washington Geological Survey.
Although for optimum cartographic presentation, manual intervention is required, the OpenTopography team is always interested in automating data processing to the greatest extent possible. Thus, we're happy to announce a new Python package that automates REM creation from nothing but an input DEM. The methods used by this package are outlined below.
The Milk River in Montana, USA.
To start creating your own REMs, download a DEM from OpenTopography and install the RiverREM Python package
The RiverREM package was developed by Kenneth Larrieu during summer 2022, with support from OpenTopography, and the UNAVCO Student Internship Program. See the RiverREM Github repository for more information.
Beaver Creek, a tributary to the Yukon River, Alaska, USA.
Neches River, Texas, USA. (North to the left)
The Dirty Devil River in Utah, USA.