## NAME

r.resamp.rst - reinterpolates and computes topographic analysis from input raster file to a new raster file (possibly with different resolution) using regularized spline with tension and smoothing.
(GRASS Raster Program)

## SYNOPSIS

r.resamp.rst
r.resamp.rst help
r.resamp.rst [-r] [-d] [-t] input = name ew_res = val ns_res = val elev = name [slope = name] [aspect = name] [pcurv = name] [tcurv = name] [mcurv = name] [smooth = name] [maskmap = name] [overlap = val] [zmult = val] [tension = val]

## DESCRIPTION

r.resamp.rst
This program reinterpolates the values a from given raster file named input to a new raster file named elev. If -r flag is specified, all zero elevations in input file are treated as elevations, otherwise they are ignored. Reinterpolation (resampling) is done to higher, same or lower resolution which is specified by parameters ew_res and ns_res. All resulting raster files are created for the given region (which might be different from the header of the input raster file). As an option, simultaneously with interpolation, topographic parameters slope, aspect, profile curvature (measured in the direction of steepest slope), tangential curvature (measured in the direction of a tangent to contour line) or mean curvature are computed and saved as raster files as specified by the options slope, aspect, pcurv, tcurv, mcurv respectively. If -d flag is set the program outputs partial derivatives fx,fy,fxx, fxy,fyy instead of slope, aspect and curvatures.

For noisy data, it is possible to define spatially variable smoothing by prividing a raster file smooth containing smoothing parameters. With the smoothing parameter set to zero (smooth is not given or contains zero data), the resulting surface 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 cells which have zero value in mask. Zero values will be assigned to these cells in all output raster files. Parameter zmult allows the user to rescale the z-values (useful, e.g., for transformation of elevations given in feet to meters, so that the proper values of slopes and curvatures can be computed).

Regularized spline with tension is used for the interpolation. The tension parameter tunes the character of the resulting surface from thin plate to membrane. Higher values of tension parameter reduce the overshoots that can appear in surfaces with rapid change of gradient. The flag -t can be set to use "dnorm independent tension". The interpolation is performed for overlaping rectangular segments. The user can define the width of overlap (in number of cells) by option overlap.

## OPTIONS

The user can run this program either interactively or non-interactively. The program will be run non-interactively if the user specifies program arguments and flag settings on the command line using the form:

r.resamp.rst [-r] [-d] [-t] input = name ew_res = val ns_res = val elev = name [slope = name] [aspect = name] [pcurv = name] [tcurv = name] [mcurv = name] [smooth = name] [maskmap = name] [overlap = val] [ zmult = val ] [tension = val]

Alternatively, the user can simply type r.resamp.rst on the command line without program arguments. In this case, the user will be prompted for parameter values and flag settings using the standard GRASS parser interface described in the manual entry for parser .

Flags

-r Indicates that zeroes in input map represent elevation.

-d Output partial derivatives instead of aspect, slope and curvatures

Parameters:

input =name
Use the existing site file name as input.

ew_res = val
Set desired east-west resolution to val .

ns_res = val
Set desired north-south resolution to val .

elev = name
Output elevation values to raster file named name .

slope = name
Output slope or fx values to raster file named name .

aspect = name
Output aspect or fy values to raster file named name .

pcurv = name
Output profile curvature or fxx values to raster file named name .

tcurv=name
Output tangential curvature values or fyy to raster file named name .

mcurv=name
Output mean curvature values or fxy to raster file named name
.
smooth=name
18 Set smoothing parameter from file name .

maskmap=name
Use the existing raster file name as a mask.

overlap =val
Use overlap val cells to get additional points for interpolation for a given segment. Default value is 3.

zmult =val
Convert z-values using conversion factor val . Default value is 1.

tension = val
Set tension to val .

## NOTES

r.resamp.rst uses regularized spline with tension for interpolation (as described in Mitasova and Mitas, 1993). Region is temporarily changed while writing output files with desired resolution. Topographic parameters are computed the same way as in s.surf.rst. (See also Mitasova and Hofierka, 1993) Raster file smooth should contain variable smoothing parameters that can be derived from errors, slope, etc. using r.mapcalc. The program gives warning when significant overshoots appear and higher tension should be used. However, with tension too high the resulting surface changes its behavior to membrane (rubber sheet stretched over the data points resulting in a peak or pit in each given point and everywhere else the surface goes rapidly to trend). Smoothing can also be used to reduce the overshoots. When overshoots occure the resulting elev file will have white color in the locations of overshoots since the color table for the output file is the same as colortable for raster input file.The program checks the numerical stability of the algorithm by computation of values in given points, and prints the maximum difference found into the history file of raster map elev . Increase in tension is suggested if the difference is unacceptable. For computation with smoothing set to 0 this difference should be 0. With smoothing parameter greater than zero the surface will not pass through the data points and the higher the parameter the closer the surface will be to the trend.

The program writes the values of parameters used in computation into the comment part of the history file elev as well as the following values which help to evaluate the results and choose the suitable parameters: minimum and maximum z values in the data file (zmin_data, zmax_data) and in the interpolated raster map (zmin_int, zmax_int), maximum difference between the given and interpolated z value in a given point (errtotal), rescaling parameter used for normalization (dnorm), which influences the tension. The program gives warning when the user wants to interpolate outside the region given by the header of the input raster file, zooming into the area where the points are is suggested in this case. When a mask is used, the program takes all points in the given region for interpolation, including those in the area which is masked out, to ensure proper interpolation along the border of the mask. It therefore does not mask out the data points; if this is desirable, it must be done outside r.resamp.rst .

## SEE ALSO

g.region, r.resample, r.surf.contour, s.surf.rst

## AUTHORS

Original version of program (in FORTRAN):
Lubos Mitas, NCSA, University of Illinois at Urbana Champaign, Il
Helena Mitasova, US Army CERL, Champaign, Illinois

Modified program (translated to C, adapted for GRASS , segmentation procedure):
Irina Kosinovsky, US Army CERL .
Dave Gerdes, US Army CERL .

## REFERENCES

Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley, M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Information Systems: Principles, Techniques, Management and Applications, Wiley, 481-492.

Mitasova, H. and Mitas, L., 1993. Interpolation by regularized spline with tension: I. Theory and implementation, Mathematical Geology No.25 p.641-656.

Mitasova, H. and Hofierka, L., 1993. Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis, Mathematical Geology No.25 p.657-667.

Talmi, A. and Gilat, G., 1977. Method for smooth approximation of data, Journal of Computational Physics , 23, pp 93-123.

Wahba, G., 1990. Spline models for observational data, CNMS-NSF Regional Conference series in applied mathematics, 59, SIAM, Philadelphia, Pennsylvania.

Last changed: $Date: 2002/01/25 05:45:34 $