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NAME
r.random.surface - Generates random surface(s) with spatial dependence.
KEYWORDS
raster, surface, random
SYNOPSIS
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]
Flags:
-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
Parameters:
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
DESCRIPTION
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.
Detailed parameter description
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.
NOTES
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.
REFERENCES
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
• Modeling Uncertainty in Elevation Data for Geographical Analysis, by Charles R.
Ehlschlaeger, and Ashton M. Shortridge. Proceedings of the 7th International
Symposium on Spatial Data Handling, Delft, Netherlands, August 1996.
• Dealing with Uncertainty in Categorical Coverage Maps: Defining, Visualizing, and
Managing Data Errors, by Charles Ehlschlaeger and Michael Goodchild. Proceedings,
Workshop on Geographic Information Systems at the Conference on Information and
Knowledge Management, Gaithersburg MD, 1994.
• Uncertainty in Spatial Data: Defining, Visualizing, and Managing Data Errors, by
Charles Ehlschlaeger and Michael Goodchild. Proceedings, GIS/LIS’94, pp. 246-253,
Phoenix AZ, 1994.
SEE ALSO
r.random, r.random.cells, r.mapcalc, r.surf.random
AUTHORS
Charles Ehlschlaeger, Michael Goodchild, and Chih-chang Lin; National Center for
Geographic Information and Analysis, University of California, Santa Barbara.
SOURCE CODE
Available at: r.random.surface source code (history)
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