r.random.surface(1grass) GRASS GIS User's Manual r.random.surface(1grass)
NAME
r.random.surface - Generates random surface(s) with spatial depen-
dence.
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 ini-
tial 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 float-
ing point values that each cell value represents.
r.random.surface’s original goal is to generate random fields for spa-
tial error modeling. A procedure to use r.random.surface in spatial er-
ror modeling is given in the NOTES section.
Detailed parameter description
output
Random surface(s). The cell values are a random distribution be-
tween 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 de-
viation 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 out-
put 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 expo-
nent 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 exam-
ple, 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 val-
ues 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 can-
cel each other out and the spatial statistics are far more sensi-
tive to the initial independent random deviates than any potential
discretization errors.
seed
Specifies the random seed(s), one for each map, that r.random.sur-
face 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.ran-
dom.surface will get a seed from the process ID number.
NOTES
While most literature uses the term random field instead of random sur-
face, this algorithm always generates a surface. Thus, its use of ran-
dom 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 re-
gion 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.
EXAMPLE
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)
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. Comput-
ers & Geosciences 23, 387-395.
doi:10.1016/S0098-3004(97)00005-8
• Ehlschlaeger, C.R., Shortridge, A.M., 1996. Modeling Uncer-
tainty 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 Uncer-
tainty in Categorical Coverage Maps: Defining, Visualizing, and
Managing Data Errors. Proceedings, Workshop on Geographic In-
formation Systems at the Conference on Information and Knowl-
edge Management, Gaithersburg MD, 1994.
• Ehlschlaeger, C.R., Goodchild, M.F., 1994. Uncertainty in Spa-
tial Data: Defining, Visualizing, and Managing Data Errors.
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 Califor-
nia, Santa Barbara.
SOURCE CODE
Available at: r.random.surface source code (history)
Accessed: unknown
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