Why do I get negative values for the topographic position index (TPI)?

Question

I run into issues, when trying to calculate the topographic position index (TPI). I get values ranging from -13 to 17. And the resulting layer looks a bit odd, too:

If I understand it correctly, this index should range from 1-10 (Poster of TPI-creator)

My DEM as a resolution of 30m and I used the default values fo the Tpi-Tool. I'm running QGIS 3.16.3 in Windows 10 and I tried to use "SAGA > Terrain Analysis - morphometry > Topographic position index (tpi)" from the toolbox. (I also tried "GDAL > Raster analysis > Topographic Position Index (TPI)", resulting in values ranging from -80-70ish). I made sure I have the right projection assigned to my DEM. I also made sure there are no holes or anything in the DEM.

It gives me the error message:

The following layers were not correctly generated.
• C:/Users/xxxx/AppData/Local/Temp/processing_flYZSV/1abd3e1d82594e88b04d28cd346343e3/TPI.sdat
You can check the 'Log Messages Panel' in QGIS main window to find more information about the execution of the algorithm.

However, in the log-panel I can't find something helpful:

021-04-16T17:31:35     INFO    SAGA execution commands
   ta_morphometry "Topographic Position Index (TPI)" -DEM "C:/Users/xxxxx/AppData/Local/Temp/processing_flYZSV/10afe001939746859ef23972335147d5/DEM30mSavaSofia.sgrd" -STANDARD true -RADIUS_MIN 0.0 -RADIUS_MAX 100.0 -DW_WEIGHTING 0 -DW_IDW_POWER 1 -DW_IDW_OFFSET true -DW_BANDWIDTH 75.0 -TPI "C:/Users/xxxx/AppData/Local/Temp/processing_flYZSV/642542ca03774ce59275236d376a8fc0/TPI.sdat"
2021-04-16T17:32:00     INFO    SAGA execution console output

   D:\xxxx>set SAGA=C:/OSGEO4~1/apps\saga-ltr
   D:\xxxx>set SAGA_MLB=C:/OSGEO4~1/apps\saga-ltr\modules
       D:\xxxx>PATH=C:\OSGEO4~1\apps\qgis\bin;C:\OSGEO4~1\apps\Python37;C:\OSGEO4~1\apps\Python37\Scripts;C:\OSGEO4~1\apps\qt5\bin;C:\OSGEO4~1\bin;C:\WINDOWS\system32;C:\WINDOWS;C:\WINDOWS\system32\WBem;C:\OSGEO4~1\apps\Python37\lib\site-packages\pywin32_system32;C:\OSGEO4~1\apps\Python37\lib\site-packages\numpy\.libs;;C:/OSGEO4~1/apps\saga-ltr;C:/OSGEO4~1/apps\saga-ltr\modules
             
   D:\xxxx>call saga_cmd ta_morphometry "Topographic Position Index (TPI)" -DEM "C:/Users/xxxx/AppData/Local/Temp/processing_flYZSV/10afe001939746859ef23972335147d5/DEM30mSavaSofia.sgrd" -STANDARD true -RADIUS_MIN 0.0 -RADIUS_MAX 100.0 -DW_WEIGHTING 0 -DW_IDW_POWER 1 -DW_IDW_OFFSET true -DW_BANDWIDTH 75.0 -TPI "C:/Users/xxxx/AppData/Local/Temp/processing_flYZSV/642542ca03774ce59275236d376a8fc0/TPI.sdat"
   ____________________________

   ##### ## ##### ##
   ### ### ## ###
   ### # ## ## #### # ##
   ### ##### ## # #####
   ##### # ## ##### # ##
   ____________________________
     
   SAGA Version: 2.3.2 (64 bit)
   ____________________________
   library path: C:\OSGEO4~1\apps\saga-ltr\modules\
   library name: ta_morphometry
   library : Morphometry
   tool : Topographic Position Index (TPI)
   author : O.Conrad (c) 2011
   processors : 8 [8]
   ____________________________
     
   Load grid: C:/Users/xxxx/AppData/Local/Temp/processing_flYZSV/10afe001939746859ef23972335147d5/DEM30mSavaSofia.sgrd...
     
   Parameters
     
   Grid system: 30.284487; 5718x 5048y; 231561.120511x 8322967.608079y
   Elevation: DEM30mSavaSofia
   Topographic Position Index: Topographic Position Index
   Standardize: yes
   Radius: 0.000000; 100.000000
   Weighting Function: no distance weighting
     
   D:\xxxx>exit

So I wonder, what could be the cause? And what else could I try?

PS: I'm sorry I don't know how to attach sample data, otherwise I would do.

Answer 1

As @Spacedman and @Jeffrey Evans pointed out, it is indeed correct to get netative values for the TPI.

The result I however expected from the poster was a TPI based land classification as can be seen here (a screenshot from said poster).

There's a good post describing how the different TPI and TRI based land-classifications look here.

And this post describes well how the TPI is calculated.

In the end, it turned out, I had just used the wrong tool for what I expected: Instead of using:

Processing Toolbox > SAGA > Terrain analysis - Morphometry > Topographic position index (tpi)

I should have used:

Processing Toolbox > SAGA > Terrain analysis - Morphometry > Tpi based landform classification

One has to search for "tpi" not for "topographic position index" in the toolbox's search field in order to finde the later one, which I was not aware of.

As @Jeffrey Evans pointed out there's a classification and comparison between 2 TPI-layers at different scales necessary as an intermediate step.

This results in the following raster: