rtopSim function

Spatial simulation of data with spatial support

rtopSim will conditionally or unconditionally simulate data with areal support. This function should be seen as experimental, some issues are described below.

## S3 method for class 'rtop'
rtopSim(object, varMatUpdate = FALSE, beta = NA, 
      largeFirst = TRUE, replace = FALSE, params = list(), 
      dump = NULL, debug.level, ...) 
## Default S3 method:
rtopSim(object = NULL, predictionLocations,
    varMatObs,  varMatPredObs, varMatPred, variogramModel, ...)

Arguments

• object: object of class rtop or SpatialPolygonsDataFrame or sf (st_sf) or NULL

• varMatUpdate: logical; if TRUE, also existing variance matrices will be recomputed, if FALSE, only missing variance matrices will be computed, see also varMat

• 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 rtop package, set in getRtopParams. The argument params can also be used for the other methods, through the ...-argument.

• 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.

• debug.level: logical that controls some output, will override the object parameters

• predictionLocations: SpatialPolygons or SpatialPolygonsDataFrame

  or sf-object with locations for simulations.

• varMatObs: covariance matrix of possible observations, where diagonal must consist of internal variance, typically generated from call to varMat

• varMatPredObs: covariance matrix between possible observation locations and simulation locations, typically generated from call to varMat

• varMatPred: covariance matrix between simulation locations, typically generated from a call to varMat

• variogramModel: a variogram model of type rtopVariogramModel

• ...: possible modification of the object parameters or default parameters.

Returns

If called with SpatialPolygons or sf as predictionLocations and either

SpatialPolygonsDataFrame, sf or NULL for observations, the function returns a

SpatialPolygonsDataFrame or sf with simulations at the locations defined in

predictionLocations

If called with an rtop-object, the function returns the same object with the simulations added to the object.

Details

This function can do constrained or unconstrained simulation for areas. The simplest way of calling the function is with an rtop-object that contains the fitted variogram model and all the other necessary data (see createRtopObject or rtop-package). 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.

References

Skoien J. O., R. Merz, and G. Bloschl. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10:277-287, 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.

Author(s)

Jon Olav Skoien

Examples

# The following command will download  the complete example data set
# downloadRtopExampleData() 

rpath = system.file("extdata",package="rtop")
library(sf)
observations = st_read(rpath, "observations")
predictionLocations = st_read(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, formulaString = "obs~1")

# 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)

summary(data.frame(rtopObj10$simulations))
summary(data.frame(rtopObj12$simulations))