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
Best Answer
According to this R-sig-Geo forum question, it seems the
Close gapstool uses the Nearest Neighbour interpolation method. The following is quoted from the webpage (emphasis mine):