At first, data points are checked for identical points and points that are closer to each other than given dmin are removed. Parameters wmult and zmult allow user to re-scale the w-values and z-values for sites (useful e.g. for transformation of elevations given in feet to meters, so that the proper values of gradient and curvatures can be computed).
Regularized spline with tension is used for the interpolation. The tension parameter tunes the character of the resulting volume from thin plate to membrane. Higher values of tension parameter reduce the overshoots that can appear in volumes with rapid change of gradient. For noisy data, it is possible to define a smoothing parameter, smooth. With the smoothing parameter set to zero (smooth=0) the resulting volume passes exactly through the data points.
User can define a raster file named maskmap, which will be used as a mask. The interpolation is skipped for 3-dimensional cells whose 2-dimensional projection has zero value in mask. Zero values will be assigned to these cells in all output grid3 files.
If the number of given points is greater than 400, segmented processing is used. The region is split into 3-dimensional "box" segments, each having less than segmax points and interpolation is performed on each segment of the region. To ensure the smooth connection of segments the interpolation function for each segment is computed using the points in given segment and the points in its neighborhood. The minimum number of points taken for interpolation is controlled by npmin , the value of which must be larger than segmax and less than 400. This limit of 400 was selected to ensure the numerical stability and efficiency of the algorithm.
s.vol.rst uses regularized spline with tension for interpolation from point data (as described in Mitasova and Mitas, submitted to Mathematical Geology.). The implementation has an improved segmentation procedure based on Oct-trees which enhances the efficiency for large data sets.
Topographic parameters are computed directly from the interpolation function so that the important relationships between these parameters are preserved. Original values of curvatures are multiplied by 100000, to conform with GRASS integer raster files. Therefore any curvature lower than 0.00001 will be zero.
The program gives warning when significant overshoots appear and higher tension should be used. However, with tension too high the resulting volume changes its behavior to membrane( rubber sheet stretched over the data points resulting in a peak in each given point and everywhere else the volume goes rapidly to trend). With smoothing parameter greater than zero the volume will not pass through the data points and the higher the parameter the closer the volume will be to the trend. For theory on smoothing with splines see Talmi and Gilat, 1977 or Wahba, 1990.
If a visible connection of segments appears, the program should be rerun with higher npmin to get more points from the neighborhood of given segment.
If the number of points in a site file is less then 400, segmax should be set to 400 so that segmentation is not performed when it is not necessary.
The program gives warning when user wants to interpolate outside the "box" given by minimum and maximum coordinates in site file, zoom into the area where the points are is suggested in this case.
For large data sets (thousands of data points) it is suggested to zoom into a smaller representative area and test whether the parameters chosen (e.g. defaults) are appropriate.
The user must run g.region before the program to set the region for interpolation.
Mitasova H., Mitas L., Brown W.M., D.P. Gerdes, I. Kosinovsky, Baker, T.1995 Modeling spatially and temporally distributed phenomena: New methods and tools for GRASS GIS. International Journal of GIS, 9 (4), special issue on Integrating GIS and Environmental modeling, 433-446.
Mitas L., Brown W. M., Mitasova H., 1997, Role of dynamic cartography in simulations of landscape processes based on multi-variate fields. Computers and Geosciences, Vol. 23, No. 4, pp. 437-446 (includes CDROM and WWW: www.elsevier.nl/locate/cgvis)
Helena Mitasova, Lubos Mitas, Bill Brown, Irina Kosinovsky, Terry Baker, Dave Gerdes (1994): Multidimensionaö interpolation and visualization in GRASS GIS