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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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