# Compound Topographic Index

Compound Topographic Index (CTI) (Moore et al. 1991) or "soil wetness" transformation can be used to models aspects of hydrologic systems. CTI is strongly correlated with soil moisture. Thus it can provide indirect information on land cover and agricultural potential. This may be useful when attempting to model ancient environments.

CTI is a steady state wetness index. The CTI is a function of both the slope and the upstream contributing area per unit width orthigonal to the flow direction. CTI was desigined for hillslope catenas. Accumulation numbers in flat areas will be very large and CTI will not be a relevant variable. CTI is highly correlated with several soil attributes such as horizon depth(r=0.55), silt percentage(r=0.61), organic matter content(r=0.57), and phosphorus(r=0.53) (Moore et al. 1993).

CTI is a a secondary topographic attribute, or compound index, that is calculated using a complex of primary topographic attributes (such as slope, aspect). CTI aims to model soil water content (Moore et al 1991:11).

CTI is defined by the following equation: Ln [a/tan ß], where:

• a represents the catchment area per pixel
• ß refers to the slope, in degrees

Areas with low CTI values represent places with small catchments, and steep slopes or hills.

Areas with high CTI values represent places with large catchments, and gentle slopes are depressions or plains.

If the DEM used in calculating CTI has coarse spatial resolution, then it will be important to account for cell size (resolution) of the DEM. For example, SRTM has a cell size of roughly 90m. So, a needs to be converted to As (see 4. below).

Also, the above equation does not specify if slope is expressed in radians or degrees. It may be useful to convert the slope DEM to radians (see 6. below) (Gessler et al. 1995).

Rasters that should be calculated:

1. The DEM used should be assessed for sinks, and if appropriate, the sinks should be filled.
1. I used SRTM 90m dem. In the area I'm interested in, the coast, filling sinks is appropriate because very few are "real", and the ones that are, when filled, should not affect the result of the CTI calculation.
2. Flow direction should be calculated using the filled DEM.
3. Then, flow direction should be used to calculate Flow accumulation.
4. In the above equation, a needs to be converted to As so as to account for DEM resolution. As can be calculated as follows:
1. As = (flow accumulation + 1) * cell size
5. Calculate slope (ß) in degrees.
6. Convert slope (ß) to radians. Do the following:
1. ß * 1.570796)/90
2. the 1.570796 values comes from (pi / 2)
7. Now, run the final equation in the raster calculator:
1. Ln (As / tan ß)

An AML script already exists to calculate CTI, written by Jeffrey Evans and available here: http://arcscripts.esri.com/details.asp?dbid=11863. If using Workstation one can easily run the script. However, there is now limited support for AML scripts in ArcGIS 10 (which is what I'm using). I followed the steps above, calculating steps 4, 6, and 7 pieces separately using the Raster Calculator. However, it produced different (and incorrect) results when compared to the result generated from the AML script run on another machine using Workstation. I am missing something. Creating a Python script to do the above, or a model in Modelbuilder, is something I would like to work on.

References:

Gessler, P.E., Moore, I.D., McKenzie, N.J. and Ryan, P.J. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS, 9(4):421-432.

Moore, I.D., Grayson, R.B. and Ladson, A.R. (1991). Digital Terrain Modelling: A Review of Hydrological, Geomorphological, and Biological Applications. Hydrological Processes, 5:3-30.