Spatial simulation of data with spatial support
Description
rtopSim will conditionally or unconditionally simulate data with areal support. This function should be seen as experimental, some issues are described below.
Usage
1 2 3 4 5 6 7 8 
Arguments
object 
object of class 
varMatUpdate 
logical; if TRUE, also existing variance matrices will
be recomputed, if FALSE, only missing variance matrices will be computed,
see also 
beta 
The expected mean of the data, for unconditional simulations 
largeFirst 
Although the simulation method follows a random path around the predictionLocations, simulating the largest area first will assure that the true mean of the simulated values will be closer to beta 
replace 
logical; if observation locations are also present as predictions, should they be replaced? This is particularly when doing conditional simulations for a set of observations with uncertainty. 
params 
a set of parameters, used to modify the standard parameters for
the 
dump 
file name for saving the updated object, after adding variance matrices. Useful if there are problems with the simulation, particularly if it for some reason crashes. 
predictionLocations 

varMatObs 
covariance matrix of possible observations, where diagonal must consist
of internal variance, typically generated from call
to 
varMatPredObs 
covariance matrix between possible observation locations and
simulation locations, typically generated from call
to 
varMatPred 
covariance matrix between simulation locations, typically generated
from a call to 
variogramModel 
a variogram model of type 
... 
possible modification of the object parameters or default parameters. 
Details
This function can do constrained or unconstrained simulation for areas.
The simplest way of calling the function is with an rtopobject that
contains the fitted variogram model and all the other necessary data (see
createRtopObject
or rtoppackage
). rtopSim
is the only function in rtop
which does not need observations.
However, a variogram model is still necessary to perform simulations.
The arguments beta
and largeFirst
are only used for unconditional simulations.
The function is still in an experimental stage, and might change in the future. There are some issues with the current implementation:
Numerical issues can in some cases give negative estimation variances, which will result in an invalid distribution for the simulation. This will result in simulated NA values for these locations.
The variability of simulated values for small areas (such as small headwater catchments) will be relatively high based on the statistical uncertainty. This could be overestimated compared to the uncertainty which is possible based on rainfall.
Value
If called with SpatialPolygons
as predictionLocations
and either
SpatialPolygonsDataFrame
or NULL
for
observations, the function returns a
SpatialPolygonsDataFrame
with simulations at the
locations defined in
predictionLocations
If called with an rtopobject, the function returns the same object with the simulations added to the object.
Author(s)
Jon Olav Skoien
References
Skoien J. O., R. Merz, and G. Bloschl. Topkriging  geostatistics on stream networks. Hydrology and Earth System Sciences, 10:277287, 2006.
Skoien, J. O., Bloschl, G., Laaha, G., Pebesma, E., Parajka, J., Viglione, A., 2014. Rtop: An R package for interpolation of data with a variable spatial support, with an example from river networks. Computers & Geosciences, 67.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41  ## Not run:
library(rgdal)
# The following command will download the complete example data set
# downloadRtopExampleData()
rpath = system.file("extdata",package="rtop")
observations = readOGR(rpath,"observations")
predictionLocations = readOGR(rpath,"predictionLocations")
# Setting some parameters; nclus > 1 will start a cluster with nclus
# workers for parallel processing
params = list(gDist = TRUE, cloud = FALSE, nclus = 1, rresol = 25)
# Create a column with the specific runoff:
observations$obs = observations$QSUMMER_OB/observations$AREASQKM
# Build an object
rtopObj = createRtopObject(observations, predictionLocations,
params = params)
# Fit a variogram (function also creates it)
rtopObj = rtopFitVariogram(rtopObj)
# Conditional simulations for two new locations
rtopObj10 = rtopSim(rtopObj, nsim = 5)
rtopObj11 = rtopObj
# Unconditional simulation at the observation locations
# (These are moved to the predictionLocations)
rtopObj11$predictionLocations = rtopObj11$observations
rtopObj11$observations = NULL
# Setting varMatUpdate to TRUE, to make sure that covariance
# matrices are recomputed
rtopObj12 = rtopSim(rtopObj11, nsim = 10, beta = 0.01,
varMatUpdate = TRUE)
rtopObj10$simulations@data
rtopObj12$simulations@data
## End(Not run)
