## NAME

r.fillnulls.py - Fills no-data areas in raster maps using spline interpolation.

## KEYWORDS

raster, surface, elevation, interpolation, splines, no-data filling

## SYNOPSIS

r.fillnulls.py
r.fillnulls.py --help
r.fillnulls.py input=name output=name method=string [tension=float] [smooth=float] [edge=integer] [npmin=integer] [segmax=integer] [lambda=float] [memory=integer] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

### Flags:

--overwrite
  Allow output files to overwrite existing files
--help
  Print usage summary
--verbose
  Verbose module output
--quiet
  Quiet module output
--ui
  Force launching GUI dialog

### Parameters:

input=name [required]
  Name of input raster map
output=name [required]
  Name for output raster map
method=string [required]
  Interpolation method to use
  Options: bilinear, bicubic, rst
  Default: rst
tension=float
  Spline tension parameter
  Default: 40.
smooth=float
  Spline smoothing parameter
  Default: 0.1
edge=integer
  Width of hole edge used for interpolation (in cells)
  Options: 2-100
  Default: 3
npmin=integer
  Minimum number of points for approximation in a segment (>segmax)
  Options: 2-10000
  Default: 600
segmax=integer
  Maximum number of points in a segment
  Options: 2-10000
  Default: 300
lambda=float
  Tykhonov regularization parameter (affects smoothing)
  Used in bilinear and bicubic spline interpolation
  Default: 0.01
memory=integer
  Maximum memory to be used (in MB)
  Cache size for raster rows
  Default: 300

## DESCRIPTION

r.fillnulls fills NULL pixels (no data areas) in input raster map and stores filled data to a new output raster map. The fill areas are interpolated from the no data area boundaries buffer using v.surf.rst regularized spline interpolation with tension (method=rst) or r.resamp.bspline cubic or linear spline interpolation with Tykhonov regularization.

## NOTES

Each area boundary buffer is set to three times the map resolution to get nominally three points around the edge. This way the algorithm interpolates into the hole with a trained slope and curvature at the edges, in order to avoid that such a flat plane is generated in a hole. The width of edge area can be adjusted by changing the edge parameter.

During the interpolation following warning may occur when using the RST method:

`Warning: strip exists with insufficient data
Warning: taking too long to find points for interpolation--please change the region to area where your points are`

This warning is generated if large data holes exist within the surface. As the idea of r.fillnulls is to fill such holes, the user may ignore the warning. The interpolation will be continued. However, the user may pay attention to below notes.

If interpolation fails, temporary raster and vector maps are left in place to allow unfilled map hole (NULL area) identification and manual repair.

When using the default RST method, the algorithm is based on v.surf.rst regularized splines with tension interpolation module which interpolates the raster cell values for NULL data areas from the boundary values of the NULL data area. An eventual raster MASK is respected during the NULL data area(s) filling. The interpolated values are patched into the NULL data area(s) of the input map and saved into a new raster map. Otherwise, either the linear or cubic spline interpolation with Tykhonov regularization can be selected (based on r.resamp.bspline).

## WARNING

Depending on the shape of the NULL data area(s) problems may occur due to an insufficient number of input cell values for the interpolation process. Most problems will occur if a NULL data area reaches a large amount of the map boundary. The user will have to carefully check the result using r.mapcalc (generating a difference map to the input map and applying the "differences" color table with r.colors) and/or to query individual cell values.

RST method stores temporary maps on hard disk. It will require at least as much free space as one extra input raster map takes.

## EXAMPLE

In this example, the SRTM elevation map in the North Carolina sample dataset location is filtered for outlier elevation values; missing pixels are then re-interpolated to obtain a complete elevation map:

    g.region raster=elev_srtm_30m -p
    d.mon wx0
    d.histogram elev_srtm_30m

    # remove SRTM outliers, i.e. SRTM below 50m (esp. lakes), leading to no data areas
    r.mapcalc "elev_srtm_30m_filt = if(elev_srtm_30m < 50.0, null(), elev_srtm_30m)"
    d.histogram elev_srtm_30m_filt
    d.rast elev_srtm_30m_filt

    # using the default RST method to fill these holes in DEM
    r.fillnulls input=elev_srtm_30m_filt output=elev_srtm_30m_rst tension=20

    # using the bilinear method to fill these holes in DEM
    r.fillnulls input=elev_srtm_30m_filt output=elev_srtm_30m_bilin method=bilinear

    d.histogram elev_srtm_30m_rst
    d.rast elev_srtm_30m_rst

    d.erase
    d.histogram elev_srtm_30m_bilin
    d.rast elev_srtm_30m_bilin

    r.mapcalc "diff_rst_bilin = elev_srtm_30m_rst - elev_srtm_30m_bilin"
    r.colors diff_rst_bilin color=differences

    r.univar -e diff_rst_bilin
    d.erase
    d.rast diff_rst_bilin
    d.legend diff_rst_bilin

## 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, pp.481-492
- 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.
- Mitasova H. and Mitas L. 1993: Interpolation by Regularized Spline with Tension: I. Theory and Implementation, Mathematical Geology 25, 641-655.
- Mitasova H. and Hofierka L. 1993: Interpolation by Regularized Spline with Tension: II. Application to Terrain Modeling and Surface Geometry Analysis, Mathematical Geology 25, 657-667.

## SEE ALSO

r.fill.dir, r.mapcalc, r.resamp.bspline, v.surf.rst

## AUTHORS

Markus Neteler, University of Hannover and Fondazione Edmund Mach
Improvement by Hamish Bowman, NZ

## SOURCE CODE

Available at: r.fillnulls source code (history)

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