# OR/14/051 Appendix 2 - Interpolation functions

 Whitbread, K. 2014. The geomorphic impact of road construction: a case study of the A9 in Scotland. British Geological Survey Internal Report, OR/14/051.

The interpolation functions used to derive a ‘pre-road’ DTM were Inverse Distance Weighting (IDW), spline and triangulation. Details of the functions are as follows:

Inverse Distance Weighting (IDW): attributes each target raster cell an elevation value based on a weighted combination the surrounding points; points at greater distance from the target have less influence on the value. The degree to which a point is influenced by surrounding points was modelled as a power function of the inverse of the distance from the point of interest using factors of 1.5, 2 and 3. A search radius of 12 surrounding points was used to calculate each output cell value.

Regularised spline: this process defines the surface elevation between known points using a mathematical function that minimises the surface curvature. A default weighting of 0.1 and a search radius of 12 points were used for local approximation.

Triangulation: this procedure defines a surface through linear triangulation between sets of three known points. Triangulation was done in GSI3D by generating an envelope of the DTM and using the ‘add scattered data points function’ prior to triangulating the 3D surface. GSI3D assumes that the surface is a geological unit and thus automatically calculates two surfaces representing the ‘top’ and ‘base’ of a geological unit during the triangulation. The top surface is clipped to the modern DTM and is therefore the triangulated representation of the modern ground surface. The base surface is not clipped to the DTM and represents the estimated pre-road ground surface.

Both the IDW and spline interpolations honour all the data present in the clipped DTM and therefore match the original DTM in the non-clipped areas. The re-interpolated DTMs were compared directly with the original DTM to estimate the ground surface change along the road route. For the triangulated DTM, the top and base TINs were exported from GSI3D as asci grids and compared against each other in ARC GIS.