
224 Computing in Geographic Information Systems
12.7 Curvature
The rate of change of slope i.e. the first order derivative of the slope or the
second order derivative of DTM gives the curvature of the Earth’s surface.
Generally curvature describes the terrain surface in terms of how convex,
concave or plane the surface is with respect to its surroundings. Curvature
is computed using the second order partial derivatives as given by equation
12.17.
Curvature =
s
(
∂
2
Z
∂X
2
)
2
+ (
∂
2
Z
∂Y
2
)
2
(12.17)
The curvature of a particular point in the grid of DEM can also be computed
using the Hessian function as given in Chapter 6 and its subsequent inter-
pretation with resp ...