Curvature: Computing Profile Curvature, Plan Curvature, and Surface Curvature (Especially for GATE-Geospatial 2022)

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Curvature is a complex terrain derivative to compute. The equation that you use depends on the resolution of your input data, as you must ensure that the curvature results you compute can be distinguished from noise in the data.

Curvature Calculation

The basic principle of curvature calculation, as with slope and aspect, is to pass a moving window over the elevation surface and fit the elevation values to a 6 term polynomial function, the coefficients of which will yield the slope, aspect and curvature of the centre cell of the moving window.

Determine if the surface is upwardly convex or concave. Use windows with a quadratic polynomial equation.

Coefficients A to I can be estimated using the elevation values in window and the grid cell size.

Diagram Shows 3 by 3 Window of an Elevation Grid

Computing Profile Curvature, Plan Curvature, and Surface Curvature

The diagram above represents a window of an elevation grid, with a cell size of 30 meters. This example shows how to compute the profile curvature, plan curvature, and surface curvature at the center cell. The first step is to estimate the coefficients D-H of the quadratic polynomial equation that fits the window:

Where to are elevation values within the window according to the diagram below, and L is the cell size.

Table Shows Elevation Values Within the 3 by 3
  • Profile curvature – estimate along the direction of maximum slope.
    • Profile curvature
  • Plan curvature – estimate across the direction of maximum slope.
    • Plan curvature
  • The curvature is (profile curvature – plan curvature)
    • Curvature

All three measures are based on . The negative curvature value means the surface at the center cell is upwardly concave. The elevation grid above shows the center cell is like a shallow basin surrounded by higher elevations in the neighboring cells.

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