The Compound Topographic Index (CTI; also called Topographic Wetness Index) 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.
CTI = ln(a/tan B)
a = Upstream contributing area in m2, filename = FLOWACC
B = Slope raster, filename = SLOPE
1. In Spatial Analyst, create a flow direction raster from a filled, projected DEM.
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.
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).
Beven and Kirkby (1979)
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) Soil-landscape modeling and spatial prediction of soil attributes. 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, Spatial modelling of wetness for the Antarctic Dry Valleys, 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) Using compound topographic index to delineate soil landscape facets from DEMs for comprehensive coastal assessment, Australian Journal of Soil Research 45