Digital terrain data are useful for all kinds of applications in digital terrain analysis (DTA). Recently, terrain feature
extraction are generally based on grid DEM because most terrain data are organized in a raster format. Terrain
complexity is very important terrain feature in digital terrain analysis, however, unlike aspect or slope, terrain
complexity is an ambiguous conception that till now no optimal index to quantify it. The traditional terrain complexity
definitiones can be classified as statistical, geometrical and semantic indices, these indices can quantify terrain
complexity to some extent, but can not evaluate some special terrain. This paper wants to seek an optimal Terrain
complexity index (TCI) to evaluate the terrain complexity. The total curvature is a synthesis idex of latitude derivative
fxx, longitude derivative fyy, and diagonal derivative fxy, it is a sound solution to the terrain anisotropy. In order to test
this index, 3 study area with typical terrain of plain, gully, and hill are selected for experimentation, the result shows total
curvature is a sound terrain parameter to evaluate terrain complexity. Terrain complexity is a regional feature, while total
cuvature is a local index, so the statistic (Mean TCI, Maximum TCI and SD TCI) are proper indicator to evaluate terrain
complexity. The derivative of specific points on the mathematic curve is the ratio of the change in the angle of a
tangent that moves over a given arc to the length of the arc, the shorter the arc is, the more arcurate the ratio curvature is.
As to grid DEM, the length of arc can be consier as the DEM resolution. Result shows, the Mean TCI, Maximum TCI
and SD of TCI have strong correlation with DEM resolution according to regression analysis, the R2 is higher than 0.96.