Topographic Wetness Index can be expressed as
Ln(a/tanB) based on the idea of Beven and Kirkby (1979)
a is the specific catchment area (a=A/L, catchment area (A)divided by contour length(L))
tanB is the slope
The basic idea here is simple, but as there are multiple ways to calculate both a and tanB, the results of a TWI can vary widely (Qin et al. 2011).
Flow accumulation and catchment area can be calculated, for example by:
D8 (O'Callaghan, J.F. / Mark, D.M. (1984)) D-infinity (Tarboton, D.G. (1997) Triangular Multiple flow direction (Seibert, J. / McGlynn, B. (2007)
algorithms, and there are many other algorithms available too.
Slope is usually calculated as local slope around the pixel (Sorensen et al. 2005). Local slope can also be calculated as minimum, mean and maximum slope around the pixel. Another way to calculate slope is presented by Hjerdt et al. 2004 where slope is calculated to a point d meters below cell center.
Slope is a basic tool in most of the GIS softwares, however the calculation can differ. Here are few examples: ESRI: http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Calculating_slope SAGA: http://sourceforge.net/apps/trac/saga-gis/wiki/Terrain%20Analysis%20-%20Morphometry%20module%20library
As you can see there are many options available to calculate both a and tanB. So, the question is, in practice, which is the proper (best) way to calculate TWI using different these algorithms? Or is there any?
I personally like working in SAGA, mainly because there are a large selection of open source hydrology tools.
P.s. I'm having a hard time to find out exactly how catchment slope is calculated in Saga GIS, and exactly what does it mean here. (Terrain analysis -hydrology: catchment area parallel).
EDITED: Answered by Volker Wichmann from SAGA Forums: "The catchment slope output grid of the Catchment Area (Parallel) module is computed like this: for each cell, the local slope is calculated using the approach of Zevenbergen & Thorne. These slope values are accumulated downslope. Finally, for each cell the accumulated slope values are divided by the derived catchment area of the cell. The unit of the grid are radians."
"The Topographic Wetness Index (TWI) module requires a normal slope grid as input. "
Beven and Kirkby 1979. A physically based variable contributing area model of basin hydrology. Hydrological Sciences Bulletin, 24, pp. 43–69.
Hjerdt et al. 2004. A new topographic index to quantify downslope controls on local drainage. Water Resources Research, 40, W05602, doi:10.1029/2004WR003130.
O'Callaghan, J.F. and Mark, D.M. 1984. The extraction of drainage networks from digital elevation data.Computer Vision, Graphics and Image Processing, 28:323-344
Qin et al. 2011. An approach to computing topographic wetness index based on maximum downslope gradient. Precision Agric 12:32–43.
Seibert, J. and McGlynn, B. 2007. A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models, Water Ressources Research, Vol. 43, W04501
Sorensen et al. 2005. On the calculation of the topographic wetness index: evaluation of different methods based on field observations. Hydrol. Earth Sys. Sci. Discuss., 2, 1807–1834
Tarboton, D.G. 1997. A new method for the determination of flow directions and upslope areas in grid digital elevation models, Water Ressources Research, Vol.33, No.2, p.309-319