Landform Classification Slopecurvature Calculator

Slope-curvature landform classification rests on a simple idea: the two curvatures of a hillslope predict what water does there, and what water does determines soil, erosion, and stability. Profile curvature, the second derivative of elevation along the line of steepest descent, controls whether flow accelerates or decelerates; plan curvature, measured across the slope, controls whether flow converges or spreads. Crossing three profile states with three plan states yields the nine-element scheme of shoulders, backslopes, and footslopes in convergent, planar, and divergent variants. This tool applies a curvature threshold of 0.001 per meter to separate curved from linear, and treats anything under 2 degrees as a level surface, which is a common convention for 10 to 30 m grids. Realistic curvature magnitudes for natural terrain fall between about -0.05 and +0.05 per meter, so the 0.001 cutoff is deliberately tight. Three limitations matter. Sign conventions differ between software packages, and ArcGIS in particular reports curvature scaled by a factor of 100, so raw values must be checked before thresholds are applied. Curvature is strongly resolution dependent because second derivatives scale roughly with the inverse square of cell size, meaning a class boundary calibrated on a 30 m DEM will misclassify a 1 m LiDAR surface. Finally, the boundaries themselves are conventions, not natural breaks, so the same hillslope can shift class under a defensible alternative threshold.

The vocabulary came before the arithmetic. Robert Ruhe, working on Iowa hillslopes and publishing through the 1960s and 1970s, formalized the summit, shoulder, backslope, footslope, and toeslope sequence as a way of describing where soils sit on a slope, extending a tradition of qualitative hillslope segmentation that ran back through G. K. Gilbert. Ian Evans at Durham University supplied the quantitative half during the 1970s by defining general geomorphometry around altitude, slope, aspect, and the profile and plan curvatures, computed by fitting surfaces to gridded elevation data. The two strands were joined in 1987, when Dan Pennock, Bernie Zebarth, and Eddy de Jong published in Geoderma a classification of hummocky terrain in Saskatchewan that used measured slope, profile curvature, and plan curvature to assign landform elements and then showed those elements predicted soil properties and salinity patterns. Richard Dikau extended the approach in 1989 to derive relief units from digital elevation models across broader landscapes. Through the 1990s the method migrated into GIS as raster processing became routine, and it now underpins digital soil mapping and terrain-based landslide susceptibility work, where convergent hollows with convex profiles are consistently identified as initiation sites for shallow failures.