## Tutorial: Calculate the Topographic Wetness Index from a DTM

### 3. Calculate Slope in Degrees and in Radians

In order to calculate TWI we need the slope in radians. With the raster analysis tools we can calculate the slope in degrees and percentages. So we're first going to calculate the slope in degrees and then convert the values to radians.

1. In the main menu go to

**Raster | Analysis | Slope...**2. In the

*Slope*dialogue choose*dtm_voidfilled*as*Input layer*. Check the box to use the*ZevenbergenThorne formula instead of Horn's one*. The ZevenbergenThorne formula works better with less relief, while we use Horn's formula for steep areas. Choose slopedegrees.tif as output slope layer.3. Click

*Run*.*Close*the dialogue after processing.Because later we're going to calculate the natural logarithm (ln) we need to check if there are pixels with a slope of 0 degrees.

4. Click right on slopedegrees and choose

**Properties**.5. In the

*Layer Properties*dialogue go to the Information tab and check the minumum value (STATISTICS_MINIMUM).In this case the minimum slope is larger than 0, so we can proceed. However, if the minumum slope is 0 you need to do the following steps, that you can also apply to this data, because it will not have any effect.

6. Click

*Cancel*to close the Layer Properties dialogue.7. In the main menu go to

**Raster | Raster Calculator**.8. In the

*Raster Calculator*create the following equation:` ( "slopedegrees@1" <= 0 ) * 1 + ( "slopedegrees@1" > 0 ) * "slopedegrees@1"`

9. Save the result to

*slopedegrees_modified.tif*and click*OK*.To convert from degrees to radians we need to multiply the pixel values by 0.01745

10. Go back to the Raster Calculator and calculate the following equation:

`"slopedegrees_modified@1" * 0.01745`

11. Save the result to

*sloperadians.tif*and click*OK*.12. Style the result from yellow to red.

13. remove the other slope layers.