# Topographic Wetness Index (TWI)

The Topographic Wetness Index (TWI), also called Compound Topographic Index (CTI), is a steady-state wetness index. In some areas, TWI has been shown in some study areas to predict solum depth (i.e., Gessler et al., 1995). It involves the upslope contributing area (a), a slope raster, and a couple of geometric functions. The value of a for each cell in the output raster (the CTI raster) is the value in a flow accumulation raster for the corresponding DEM. Higher CTI values represent drainage depressions, lower values represent crests and ridges.

Things to consider carefully: FlowAcc and Slope. How you calculate each will strongly affect TWI values. Catchment area (flow accumulation) can be calculated at least 3 ways (i.e., D8, D-infinity, Triangular multiple flow). Slope calculations also can take different forms (i.e., “local slope” of a pixel, max or min slope generated using a small neighborhood around each pixel, etc.). See referenced articles.

CTI = ln(a/tan B)
a = Upstream contributing area in m2, filename = FLOWACC
B = Slope raster, filename = SLOPE

ArcGIS Instructions

** Check these links for specific forum comments and general info **

1. In Spatial Analyst, create a flow direction raster from a filled, projected DEM (use meters or feet as units).

2. Create flow accumulation raster from flow direction raster. This finds the upslope contributing area for each pixel. Ouput filename = FLOWACC.

3. Create slope raster from the DEM. Ouput filename = SLOPE

4.) In Raster Calculator (Spatial Analyst > Map Algebra > Raster Calculator), create this equation:

Ln((“FLOWACC”*900) / Tan(“SLOPE”))

Note: “FLOWACC” and “SLOPE” are the names of the rasters created in steps 1-3.

5. Normalize (standardize) output values.

6. Categorize value ranges. See references for examples of how this has been done by others.

Or try this…

cellsize of the raster dem = 30
fd = flowdirection(dem)
sca = flowaccumulation(fd)
slope = ( slope(dem) * 1.570796 ) / 90
tan_slp = con( slope > 0, tan(slope), 0.001 )
sca_scaled = ( sca + 1 ) * cellsize
cti = ln ( sca_scaled / tan_slp )

Or this…

Ln(“fac” / Tan(“slope” / DEG180/3.141592)
…where “DEG” is a constant that equals 180/pi, or 180/3.141592
…where “fac” is flow accumulation raster
…where “slope” is slope raster

Or this for CTI…

Normalize (standardize) the CTI values to the highest value in order to obtain the probability (values between 0 and 1). Normalizing/Standardizing is simply scaling a set of values to a small, more interpretable range (i.e., between 1 and 10 or 0 and 1).

A map of dominant runoff process results from a CTI analysis. Map categories are No runoff, Saturation Excess, and Infiltration Excess with corresponding percent area values for each. High CTI values (normalized, data range: 0 to 1) indicate areas more likely (higher probability) to drain by saturated excess flow. Threshold values for classifying areas where saturation excess overland flow will occur, though based on empirical soil properties, are 0.6 and above (Leh et al., 2008). Values between 0.5 and 24 were obtained by Stichbury et al. (2010). Modify threshold values for your study area.

Stichbury Version of CTI Model
A weighted CTI model was developed using CTI, NDSI (snow cover), and a snow-weighted flow accumulation, to generate a final weighted CTI output.

Gessler’s regression model (Gessler et al., 1995) for predicting the environmental variable, solum depth, from TWI in a 100km2 study area located in the Murray-Darling River basin of SE Australia (Ordovician metasediments):
Solumn Depth = -57.95 + 12.83 x plan_curvature + 21.46 x TWI

See Leh and Chaubey (2009), Figs 4 and 5 for map display and unit styles.
See Stichbury et al. (2010) for figures and data presentation.
See post called ‘Normalize Data in Excel’. Two simple examples are shown there.

Normalizing involves these steps:
– Identify minimum value in dataset. Label it A. Ex: 25
– Identify maximum value in dataset. Label it B. Ex: 75
– Identify min and max values in the normalized range of your choice. Ex: 1 and 10, respectively.
– Set these to be: 1=a, 10=b.
– The normalized value of any value x in the dataset is calculated:

a + (x-A)(b-a) / (B-A)

Note: The CTI calculation involves substituting the Max for the more commonly used Mean. The change is made to the formula in one of the steps: =MAX(A1:Ax) instead of =AVERAGE(A1:Ax).

Refs:
Beven & Kirkby (1979) A physically based variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24, p. 43–69
Hjerdt et al. (2004) A new topographic index to quantify downslope controls on local drainage. Water Resources Res. v.40
O’Callaghan, J.F.; Mark, D.M. 1984. The extraction of drainage networks from digital elevation data, Computer Vision, Graphics and Image Processing v. 28, p. 323-344
Qin et al. (2011) An approach to computing topographic wetness index based on maximum downslope gradient, Precision Agriculture v. 12, p. 32–43
Seibert, J.; McGlynn, B. (2007) A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models, Water Resources Research v. 43
Sorensen et al. (2005) On the calculation of the topographic wetness index: evaluation of different methods based on field observations. Hydrol Earth Systems Science Discussions v. 2, p. 1807–1834

Tarboton, D.G. 1997. A new method for the determination of flow directions and upslope areas in grid digital elevation models, Water Resources Research v.33, p. 309-319
Chapman, G.A. et al. (2004) Using soil landscape mapping for on-site sewage risk assessment, in ‘Proceedings of SuperSoil 2004 Conference, Australian and NZ Societies of Soil Science Conference’. University of Sydney
Evans, J. (2003) Compound topographic index script, http://arcscripts.esri.com
Gessler, P.E.; Moore, I.D., McKenzie N.J., Ryan P.J. (1995) International Journal of GIS 9, p. 421-432
Moore I.D., Lewis A., Gallant J.C. (1993), Terrain attributes: estimation methods and scale effects, in A.J. Jakeman et al. (editors): Modelling change in environmental systems, p. 189-214
Leh et al. (2008)
Leh and Chaubey (2009)
R Wiki, http://rwiki.sciviews.org/doku.php?id=guides:tutorials:hydrological_data_analysis:dta
Stichbury, G., Brabyn, T.G., Green, A., Cary, C. (2011) Polar Research 30
USGS Work on Elevation Derivatives: http://edna.usgs.gov/Edna/datalayers/cti.asp
Wilson, J.P., Gallant, J.C. (2000) Secondary topographic attributes, in Wilson and Gallant (editors) ‘Terrain analysis: principles and applications’, p. 87-131
Yang et al. (2007) Australian Journal of Soil Research 45
http://www.mssanz.org.au/modsim05/papers/yang_x.pdf
http://www.biomedsearch.com/article/Delineating-soil-landscape-facets-from/174059452.html