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r.random.surface(1) |
GRASS GIS User's Manual |
r.random.surface(1) |
r.random.surface - Generates random surface(s) with spatial
dependence.
r.random.surface
r.random.surface --help
r.random.surface [-u]
output=string[,string,...] [distance=float]
[exponent=float] [flat=float]
[seed=integer] [high=integer] [--overwrite]
[--help] [--verbose] [--quiet] [--ui]
- -u
-
Uniformly distributed cell values
- --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
- output=string[,string,...] [required]
-
Name for output raster map(s)
- distance=float
-
Maximum distance of spatial correlation (value >= 0.0)
Default: 0.0
- exponent=float
-
Distance decay exponent (value > 0.0)
Default: 1.0
- flat=float
-
Distance filter remains flat before beginning exponent
Default: 0.0
- seed=integer
-
Random seed, default [random]
- high=integer
-
Maximum cell value of distribution
Default: 255
r.random.surface generates a spatially dependent random surface. The
random surface is composed of values representing the deviation from the mean
of the initial random values driving the algorithm. The initial random values
are independent Gaussian random deviates with a mean of 0 and standard
deviation of 1. The initial values are spread over each output map using
filter(s) of diameter distance. The influence of each random value on nearby
cells is determined by a distance decay function based on exponent. If
multiple filters are passed over the output maps, each filter is given a
weight based on the weight inputs. The resulting random surface can have
any mean and variance, but the theoretical mean of an infinitely large
map is 0.0 and a variance of 1.0. Description of the algorithm is in the
NOTES section.
The random surface generated are composed of floating point
numbers, and saved in the category description files of the output map(s).
Cell values are uniformly or normally distributed between 1 and high values
inclusive (determined by whether the -u flag is used). The category
names indicate the average floating point value and the range of floating
point values that each cell value represents.
r.random.surface’s original goal is to generate
random fields for spatial error modeling. A procedure to use
r.random.surface in spatial error modeling is given in the
NOTES section.
- output
-
Random surface(s). The cell values are a random distribution between the low
and high values inclusive. The category values of the output map(s) are in
the form #.# #.# to #.# where each #.# is a floating point number.
The first number is the average of the random values the cell value
represents. The other two numbers are the range of random values for that
cell value. The average mean value of generated output map(s) is 0.
The average variance of map(s) generated is 1. The random values
represent the standard deviation from the mean of that random
surface.
- distance
-
Distance determines the spatial dependence of the output map(s). The
distance value indicates the minimum distance at which two map cells have
no relationship to each other. A distance value of 0.0 indicates that
there is no spatial dependence (i.e., adjacent cell values have no
relationship to each other). As the distance value increases, adjacent
cell values will have values closer to each other. But the range and
distribution of cell values over the output map(s) will remain the same.
Visually, the clumps of lower and higher values gets larger as distance
increases. If multiple values are given, each output map will have
multiple filters, one for each set of distance, exponent, and weight
values.
- exponent
-
Exponent determines the distance decay exponent for a particular filter. The
exponent value(s) have the property of determining the texture of
the random surface. Texture will decrease as the exponent value(s) get
closer to 1.0. Normally, exponent will be 1.0 or less. If there are no
exponent values given, each filter will be given an exponent value of 1.0.
If there is at least one exponent value given, there must be one exponent
value for each distance value.
- flat
-
Flat determines the distance at which the filter.
- weight
-
Weight determines the relative importance of each filter. For example, if
there were two filters driving the algorithm and weight=1.0, 2.0 was given
in the command line: The second filter would be twice as important as the
first filter. If no weight values are given, each filter will be just as
important as the other filters defining the random field. If weight values
exist, there must be a weight value for each filter of the random
field.
- high
-
Specifies the high end of the range of cell values in the output map(s).
Specifying a very large high value will minimize the errors caused
by the random surface’s discretization. The word errors is in
quotes because errors in discretization are often going to cancel each
other out and the spatial statistics are far more sensitive to the initial
independent random deviates than any potential discretization errors.
- seed
-
Specifies the random seed(s), one for each map, that r.random.surface
will use to generate the initial set of random values that the resulting
map is based on. If the random seed is not given, r.random.surface
will get a seed from the process ID number.
While most literature uses the term random field instead of random surface, this
algorithm always generates a surface. Thus, its use of random surface.
r.random.surface builds the random surface using a filter
algorithm smoothing a map of independent random deviates. The size of the
filter is determined by the largest distance of spatial dependence. The
shape of the filter is determined by the distance decay exponent(s), and the
various weights if different sets of spatial parameters are used. The map of
independent random deviates will be as large as the current region PLUS the
extent of the filter. This will eliminate edge effects caused by the
reduction of degrees of freedom. The map of independent random deviates will
ignore the current mask for the same reason.
One of the most important uses for r.random.surface is to
determine how the error inherent in raster maps might effect the analyses
done with those maps.
Generate a random surface (using extent of North Carolina sample dataset):
g.region raster=elevation res=100 -p
r.surf.random output=randomsurf min=10 max=100
# verify distribution
r.univar -e map=randomsurf
Figure: Random surface example (min: 10; max: 100)
With the histogram tool the cell values versus count can be
shown.
Figure: Histogram of random surface example (min: 10; max:
100)
Random Field Software for GRASS by Chuck Ehlschlaeger
As part of my dissertation, I put together several programs that
help GRASS (4.1 and beyond) develop uncertainty models of spatial data. I
hope you find it useful and dependable. The following papers might clarify
their use:
- Ehlschlaeger, C.R., Shortridge, A.M., Goodchild, M.F., 1997. Visualizing
spatial data uncertainty using animation. Computers & Geosciences 23,
387-395. doi:10.1016/S0098-3004(97)00005-8
- Ehlschlaeger, C.R., Shortridge, A.M., 1996. Modeling Uncertainty in
Elevation Data for Geographical Analysis. Proceedings of the 7th
International Symposium on Spatial Data Handling, Delft, Netherlands,
August 1996.
- Ehlschlaeger, C.R., Goodchild, M.F., 1994. Dealing with Uncertainty in
Categorical Coverage Maps: Defining, Visualizing, and Managing Data
Errors. Proceedings, Workshop on Geographic Information Systems at the
Conference on Information and Knowledge Management, Gaithersburg MD,
1994.
- Ehlschlaeger, C.R., Goodchild, M.F., 1994. Uncertainty in Spatial Data:
Defining, Visualizing, and Managing Data Errors. Proceedings,
GIS/LIS’94, pp. 246-253, Phoenix AZ, 1994.
r.random, r.random.cells, r.mapcalc,
r.surf.random
Charles Ehlschlaeger, Michael Goodchild, and Chih-chang Lin; National Center for
Geographic Information and Analysis, University of California, Santa Barbara.
Available at: r.random.surface source code (history)
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