Roughness & Texture
Roughness & Texture measures the grain of the surface rather than its shape. Two hillsides can have the same average slope while one is a smooth grass field and the other a boulder field. These six tools capture that difference, in a single number per cell.
Roughness is used as a habitat descriptor in ecology, as a proxy for geology and erosion history, as a trafficability measure, and as a way of detecting where a surface model still carries vegetation noise.
Start here
Section titled “Start here”Ruggedness Index
Section titled “Ruggedness Index”The classic and the easiest to explain. Riley’s Terrain Ruggedness Index sums the squared elevation differences between a cell and its eight neighbours, then takes the square root. Low values are smooth plains, high values are broken mountain terrain.
It is expressed in the same unit as your elevations, so it can be compared between areas as long as the resolution is the same. Change the resolution and the numbers change with it.
Standard Deviation Of Slope
Section titled “Standard Deviation Of Slope”Roughness expressed as the variability of slope within a moving window. A uniform 30 degree hillside has a low value, a hillside broken by gullies has a high one, even though both average the same steepness.
Often preferred over the raw elevation based indices because it separates the grain from the overall inclination.
Spherical Std Dev Of Normals
Section titled “Spherical Std Dev Of Normals”The most refined of the three. It measures how much the surface normals, the little arrows perpendicular to the ground, disagree with each other in a neighbourhood. Perfectly flat or perfectly tilted planes give zero, however steep they are. Only genuine irregularity raises the value.
This is the measure to use when comparing roughness across areas of very different steepness.
All the tools
Section titled “All the tools”| Tool | What it does |
|---|---|
| Ruggedness Index | Riley’s TRI, from the squared elevation differences with the eight neighbours. |
| Standard Deviation Of Slope | Local variability of slope within a moving window. |
| Spherical Std Dev Of Normals | Spread of surface normal directions in a neighbourhood, independent of overall tilt. |
| Average Normal Vector Angular Deviation | Mean angle between the original surface normals and a smoothed version of them. |
| Circular Variance Of Aspect | Variability of aspect in a moving window, handling its circular nature correctly. |
| Edge Density | Density of breaks in slope, from angular differences between neighbouring normals. |
Resolution decides the answer. Roughness measured on a 1 metre model describes boulders and furrows. The same index on a 30 metre model describes hills. Say which resolution you used whenever you report a roughness value.
Vegetation looks rough. On a surface model that still includes trees, the roughest areas will be the woods. Run Remove Off Terrain Objects or Smooth Vegetation Residual in General first if you want the roughness of the ground.
A multiscale variant exists. See Multiscale Roughness in Multiscale Signatures when the size of the roughness matters as much as its amount.