- IDW interpolation, but distance is cost to get to any other site.
v.surf.icw [-r] input=string column=string output=string cost_map=string [friction=float] [layer=integer] [where=string] [post_mask=string] [workers=integer] [--overwrite] [--help] [--verbose] [--quiet] [--ui]
- Use (d^n)*log(d) instead of 1/(d^n) for radial basis function
- Allow output files to overwrite existing files
- Print usage summary
- Verbose module output
- Quiet module output
- Force launching GUI dialog
- input=string [required]
- Name of existing vector points map containing seed data
- column=string [required]
- Column name in points map that contains data values
- output=string [required]
- Name for output raster map
- cost_map=string [required]
- Name of existing raster map containing cost information
- Friction of distance, (the 'n' in 1/d^n)
- Options: 1-6
- Default: 2
- Layer number of data in points map
- Default: 1
- WHERE conditions of SQL query statement without 'where' keyword
- Example: income < 1000 and inhab >= 10000
- Name of existing raster map to be used as post-processing MASK
- Number of parallel processes to launch
- Options: 1-256
- Default: 1
Inverse cost weighting is like inverse distance weighted (IDW) interpolation,
but uses cost
instead of shortest Euclidean distance. In this way
solid barriers and molasses zones may be correctly taken into account.
Input data points do not need to have direct line of sight to each other.
This is interpolation "as the fish swims", not "as the crow flies", and can
see around headlands or across land-bridges without polluting over barriers
which the natural value (or flightless bird) can not cross.
It was initially written to interpolate water chemistry in two parallel
arms of a fjord, but may just as well be used for population abundance
constrained by topography, or in studies of archeologic technology transfer.
In the simplest case, the cost map will just be a mask raster with values
of 1 in areas to interpolate, and NULL in impenetrable areas.
Fancier cost maps can be used, for example, to make it more expensive for
a measured pollutant to diffuse upstream in an estuary, or to make it more
expensive for a stone tool technology to cross waterways.
Since generating cost maps can take a long time, it is recommended to keep
the raster region relatively small and limit the number of starting points
to less than 500.
Higher values of friction will help limit unconstrained boundary
effects at the edges of your coverage, but will incur more of a stepped
transition between sites.
The post_mask, if given, is applied after the interpolation is
complete. A common use for that might be to only present data within
a certain distance (thus confidence) of an actual sampling station.
In that case the r.cost module can be used to create the mask.
This module writes lots of temporary files and so can be rather disk I/O
intensive. If you are running it many times in a big loop you may want to
try setting up a RAM-disk to put the mapset in (on UNIX symlinking back
into the location is ok), or adjust the disk-cache flushing timer to be
slightly longer than one iteration of the script.
To do this on Linux you can tune the
/proc/sys/vm/dirty_expire_centisecs kernel control. The default
is to keep files in memory a maximum of 30 seconds before writing them to
disk, although if you are short on free RAM the kernel may write to disk
long before that timeout is reached.
By default the module will run serially. To run in parallel set the
workers parameter to the desired value (typically the number
of cores in your CPU). Alternatively, if the WORKERS environment
variable is set, the number of concurrent processes will be set at
that number of jobs.
In this example we'll generate some fake island barriers from the
standard North Carolina GRASS dataset, then interpolate a continuous
variable between given point stations. We'll use rainfall, but for the
purposes of the exercise pretend it is a nutrient concentration in our
fake wayerway. Point data stations outside of the current region or
in NULL areas of the cost_map
will be ignored.
# set up a fake sea with islands:
g.region n=276000 s=144500 w=122000 e=338500 res=500
r.mapcalc "pseudo_elev = elev_state_500m - 1100"
r.colors pseudo_elev color=etopo2
r.mapcalc "navigable_mask = if(pseudo_elev < 0, 1, null())"
# pick a data column from the points vector:
v.info -c precip_30ynormals
# run the interpolation:
v.surf.icw input=precip_30ynormals column=annual output=annual_interp.3 \
cost_map=navigable_mask friction=3 --verbose
# equalize colors to show maximum detail:
r.colors -e annual_interp.3 color=bcyr
# display results in a GRASS monitor:
d.vect precip_30ynormals fcolor=red icon=basic/circle
d.legend annual_interp.3 at=48.4,94.8,3.4,6.0
The method was first described in Wing et. al 2004, with further
comments and examples in report 3 of that series, 2005. Ducke and
Rassmann 2010 (in German) describe a novel use of the approach to
study prehistoric movement corridors of early Bronze Age technology
Wing, S.R., M.H.E. Bowman, F. Smith and S.M. Rutger (2004), Analysis
of biodiversity patterns and management decision making processes to
support stewardship of marine resources and biodiversity in Fiordland
- a case study, report 2 of 3, Technical report, Report to the Ministry for
the Environment, New Zealand.
Ducke, B. and K. Rassmann (2010),
Modelling and Interpretation of the Communication
Spaces of the 3rd and Early 2nd Millennium BC in Europe
Using Diversity Gradients
(Modellierung und Interpretation der Kommunikationsräume
des 3. und frühen 2. Jahrtausends v. Chr.),
in Europa mittels Diversitätsgradienten;
Archäologischer Anzeiger 2010/1, pp.239-261
Department of Marine Science,
Dunedin, New Zealand
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