# SAGA tool 'Relative Heights and Slope Positions' - What do results tell me?

I am currently trying to get in morphometry, using the SRTM 30m DEM. I was recommended to test the SAGA mudule 'Relative Heights and Slope Positions' (http://www.saga-gis.org/saga_module_doc/2.1.3/ta_morphometry_14.html) in QGIS. It runs smoothly and I have first results, but I am a bit lost in understanding what results tell me. Does anybody of you have expert knowledge to explain what the following mean?

• Slope height (values ~0-700)
• Valley depth (values ~0-600)
• Normalized height (values ~0-1)
• Standardized height (values ~0-3000)
• Mid slope position (values ~-0,00001-1)

Input options w, t and e are also not clear to me.

If anybody of you has an idea or an idea where to find information, I would be very happy.

• There is paper which explains some of the terms you describe (nomarlized/standardized heights and mid slope positions). Hope this helps a little. Commented Jul 13, 2015 at 10:25
• Thank you very much! One of the authors is also the module developer. I already contacted him on Research Gate. Great help from your side. Commented Jul 13, 2015 at 12:54
• Most welcome buddy but it seems you did all the work in contacting the developer, kudos! Perhaps you could post what you learnt as an answer so that it could help those in similar situations? :) Commented Jul 13, 2015 at 13:00
• Yes, definitely will do that as soon as I get an answer :) Commented Jul 13, 2015 at 14:16

Now, the answer from the developers of the tool, who kindly allowed me to forward the answer here. I translate and do my best to reproduce what I learnt from Dr. Conrad:

The only expected input-dataset is the DEM. The tool runs an interative procedure which works with relative relief-position. The same procedure is used to calculate - the vertical distance below a terrain culmination (peak, ridge,...) - distance above the terrain minima (valley, depression,...). This is in the first step based on a drainage-oriented calculation of vertical distances ( based on Freeman, T.G.,1991: Calculating catchment area with divergent flow based on a regular grid. Computers and Geoscience, Bd. 17, 3, 413-422. [hope this is the correct publication]) and is afterwards refined iteratively to eliminate effects of watersheds.

Options W, T, E control the iterative process: 'W: The parameter weights the influence of catchment size on relative elevation (inversely proportional). T: The parameter controls the amount by which a maximum in the neighbourhood of a cell is taken over into the cell (considering the local slope between the cells). The smaller 't' and/or the smaller the slope, the more of the maximum value is taken over into the cell. This results in a greater generalization/smoothing of the result. The greater 't' and/or the higher the slope, the less is taken over into the cell and the result will show a more irregular pattern caused by small changes in elevation between the cells. E: The parameter controls the position of relative height maxima as a function of slope.'

After determination of relevant distances (below/ above), these are used to calculate standardized elevation (0= low; 1= top) and based on that we receive standardized elevation and mid slope position.

Reference: - Boehner, J. and Selige, T. (2006): Spatial prediction of soil attributes using terrain analysis and climate regionalisation. In: Boehner, J., McCloy, K.R., Strobl, J. [Ed.]: SAGA - Analysis and Modelling Applications, Goettinger Geographische Abhandlungen, Goettingen: 13-28. (find this online on the saga homepage)

To cite saga: Conrad, O., Bechtel, B., Bock, M., Dietrich, H., Fischer, E., Gerlitz, L., Wehberg, J., Wichmann, V., and Böhner, J.: System for Automated Geoscientific Analyses (SAGA) v. 2.1.4, Geosci. Model Dev., 8, 1991-2007, doi:10.5194/gmd-8-1991-2015, 2015. Available online for free http://www.geosci-model-dev.net/8/1991/2015/gmd-8-1991-2015.html

• +1, great for coming back and posting this from the developers! Commented Aug 10, 2015 at 12:15

Your answer is great, but I had some difficulty interpreting the use of the t parameter. The SAGA discussion forum has a similar explanation, with further explanation by the developers on what t does. In case of trouble with that link, I wanted to include it here (too long to put in a comment):

I will try to provide an explanation, based on how Jürgen Böhner explained it to me. The parameter "t" controls the amount by which a maximum in the neighbourhood of a cell is taken over into the cell (considering the slope between the cells). The smaller "t" and/or the smaller the slope, the more of the maximum value is taken over into the cell. You can observe this by a greater generalization/smoothing of the result. The greater "t" and/or the higher the slope, the less is taken over into the cell and you will observe a more irregular pattern caused by small changes in elevation between the cells.

Consider a flat and broad valley bottom. There are typically some cells on the valley bottom which are just a little bit higher (a few centimetres) than their surrounding cells. These cells would have only themselves as catchment area and not the whole catchment of the valley side. This "noise" in the DEM is hydrologically irrelevant but would cause a very high spatial variation of the computed values which is not observable in nature (a small elevation difference of 1cm would not cause a "dry" soil column at this position).

As you already have read Böhner & Selige (2006), have a look at equation 01. It shows the same principle, here with catchment area calculation for the SAGA Wetness Index. The parameter "t" is fixed here (15). So simply exchange 15 by "t" in the equation and you have the formula used by the "Relative Heights and Slope Positions" tool to determine the amount by which a maximum from the neighbourhood is taken over into the currently processed cell.