Landform Classification Slopecurvature Calculator
Compute landform classification slope–curvature using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Landform = f(slope, profile_curvature, plan_curvature); TWI = ln(a / tan(slope))
Profile curvature measures slope change downslope, plan curvature measures contour curvature, TWI combines contributing area with slope.
Worked Examples
Example 1: Convergent Footslope
Problem:Slope 12 deg, profile curvature +0.008, plan curvature +0.005, elevation 720 m, 30 m cell.
Solution:Slope: Strongly Sloping\nProfile: Concave\nPlan: Convergent\nLandform: Convergent Footslope\nTWI = ln(900/tan(12)) = 8.350
Result:Convergent Footslope | Strongly Sloping | TWI: 8.350
Example 2: Divergent Shoulder
Problem:Slope 22 deg, profile -0.012, plan -0.004, elevation 1450 m, 10 m cell.
Solution:Slope: Steeply Sloping\nProfile: Convex\nPlan: Divergent\nLandform: Divergent Shoulder\nTWI = ln(100/tan(22)) = 5.512
Result:Divergent Shoulder | Steeply Sloping | TWI: 5.512
Frequently Asked Questions
What is landform classification based on slope and curvature?
Landform classification based on slope and curvature is a geomorphometric approach that categorizes terrain into distinct landform elements using quantitative measurements from digital elevation models. The method combines slope steepness with profile curvature in the downslope direction and plan curvature across the slope. Originally developed by Pennock in 1987 and expanded by Dikau in 1989, this classification identifies elements such as shoulders, backslopes, footslopes, and level surfaces. Each element has characteristic hydrological behavior controlling soil development and erosion.
How are the nine basic landform elements defined?
The nine elements arise from combining three slope positions with three plan curvature classes. Shoulder slopes have convex profile curvature and can be convergent, planar, or divergent. Backslopes have near-linear profile and similarly vary in plan. Footslopes have concave profile curvature in three plan variants. Convergent footslopes accumulate the most water forming saturated zones. Divergent shoulders are the driest positions where runoff disperses rapidly. This provides a systematic framework for soil-landscape modeling and precision agriculture.
What DEM resolution is needed for accurate classification?
The required DEM resolution depends on the landform feature scale and application. For hillslope-scale classification, grid cells of 5 to 30 meters are typically appropriate. Coarser resolutions above 90 meters smooth out terrain details and merge distinct elements. High-resolution LiDAR DEMs at 1 to 5 meters capture micro-topography but may introduce noise requiring smoothing. The relationship between resolution and curvature values is nonlinear, so classification thresholds must be adjusted when resolution changes.
What software tools perform automated landform classification?
SAGA GIS offers dedicated modules for slope-curvature landform classification following Dikau and Pennock approaches. GRASS GIS provides curvature computation through r.slope.aspect and classification through r.mapcalc. ArcGIS Pro supports curvature analysis through Spatial Analyst with custom model builders for full classification. WhiteboxTools includes efficient algorithms for terrain derivatives from large DEMs. R packages including RSAGA and terra provide scripting environments for batch processing multiple basins with reproducible workflows.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy