Topographic index (TI)* takes into account data on catchment area and slope gradient:
Topographic index is a measure of the extent of flow accumulation at the given point of the topographic surface. As catchment area increases and slope gradient decreases, topographic index increases.
Like other combined morphometric variables, topographic index can be derived from a digital elevation model (DEM) by the sequential application of methods for local and nonlocal morphometric characteristics, followed by an arithmetic combination of the results of these calculations.
Example**. A model of topographic index was derived from a DEM of Mount Ararat. CA was calculated by the Martz–de Jong method adapted to spheroidal equal angular grids; G was calculated by the universal spectral analytical method. The model includes 779,401 points (the matrix 1081 x 721); the grid spacing is 1". The vertical exaggeration of the 3D model is 2x. The data processing and modelling were carried out using the software Matlab R2008b and LandLord 4.0.
* Beven, K.J., and Kirkby, M.J., 1979. A physically-based variable contributing area model of basin hydrology. Hydrological Science, 24: 43–69.
** Florinsky, I.V., 2017. An illustrated introduction to general geomorphometry. Progress in Physical Geography, 41: 723–752. doi pdf
For details and other examples, see: