| yamamotoKrige {intamap} | R Documentation |
kriging and simulation with alternative kriging variance
Description
ordinary kriging and simulation with an alternative kriging variance
Usage
yamamotoKrige(formula, Obs, newPoints, model, nsim = 0, nmax = 20, maxdist = Inf)Arguments
formula |
formula that defines the dependent variable as a linear model of
independent variables; suppose the dependent variable has name
|
Obs |
|
newPoints |
|
model |
variogram model - of the type that can be found by a call to
|
nsim |
integer; if set to a non-zero value, conditional simulation is used instead of kriging interpolation. For this, sequential Gaussian simulation is used, following a single random path through the data. |
nmax |
for local kriging: the number of nearest observations that should be used for a kriging prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, all observations are used. |
maxdist |
maximum number of neighbours to use in local kriging, defaults to Inf |
Details
The term yamamotoKrige comes from the paper of Yamamoto (2000) where
he suggests using local variance around the kriging estimate (weighted with
the kriging weights) as an alternative kriging variance. This as a
solution to more reliable estimates of the kriging variance also when the
stationarity assumption has been violated. The method was applied by
Skoien et al. (2008), who showed that it can have advantages for cases where the
stationarity assumption behind kriging is violated.
If the number of observations is high, it is recommended have nmax lower.
This is partly because the method relies on positive kriging weights. The method
to do this adds the norm of the largest negative weight to all weights, and rescales.
This tends to smooth the weights, giving a prediction closer to the average if a
too large number of observation locations is used.
Value
Either a Spatial*DataFrame with predictions and prediction variance,
in the columns var1.pred and var1.var, together with the
classical ordinary kriging variance in var1.ok, or simulations with
column names simx where x is the number of the simulation.
Author(s)
Jon Olav Skoien
References
Skoien, J. O., G. B. M. Heuvelink, and E. J. Pebesma. 2008. Unbiased block predictions and exceedance probabilities for environmental thresholds. In: J. Ortiz C. and X. Emery (eds). Proceedings of the eight international geostatistics congress. Santiago, Chile: Gecamin, pp. 831-840.
Yamamoto, J. K. 2000. An alternative measure of the reliability of ordinary kriging estimates. Mathematical Geology, 32 (4), 489-509.
Pebesma, E., Cornford, D., Dubois, G., Heuvelink, G.B.M., Hristopulos, D., Pilz, J., Stohlker, U., Morin, G., Skoien, J.O. INTAMAP: The design and implementation f an interoperable automated interpolation Web Service. Computers and Geosciences 37 (3), 2011.
Examples
library(gstat)
library(automap)
data(sic2004)
coordinates(sic.val) = ~x+y
coordinates(sic.test) = ~x+y
variogramModel = autofitVariogram(joker~1,sic.val)$var_model
newData = yamamotoKrige(joker~1,sic.val,sic.test,variogramModel,nmax = 20)
summary(newData)
plot(sqrt(var1.ok)~var1.pred,newData)
# Kriging variance the same in regions with extreme values
plot(sqrt(var1.var)~var1.pred,newData)
# Kriging standard deviation higher for high predictions (close to extreme values)