Space-time Covariance Models
Here, a collection of implemented space-time models is given.
Stationary space-time models
Here, most of the models are composed models (operators).
Note that in space-time modelling the argument proj may also take the values "space" for the projection on the space
and "time" for the projection onto the time axis.
| separable models | are easily constructed using
+, *,
and proj, see also the example below
|
RMave |
space-time moving average model |
RMcoxisham |
Cox-Isham model |
RMcurlfree |
curlfree (spatial) field (stationary and anisotropic) |
RMdivfree |
divergence free (spatial) vector-valued field (stationary and anisotropic) |
RMgennsst |
generalization of Gneiting's non-separable space-time model |
RMiaco |
non-separable space-time model |
RMmastein |
Ma-Stein model |
RMnsst |
Gneiting's non-separable space-time model |
RMstein |
Stein's non-separable space-time model |
RMstp |
Single temporal process |
RMtbm |
Turning bands operator |
Alexander Malinowski; Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., Space-Time Processes and Challenges Related to Environmental Problems. New York: Springer.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again ## multiplicative separable model with exponential model in space ## and Gaussian in time model <- RMexp(proj = "space") * RMgauss(proj = "time") x <- T <- seq(0, 10, 0.1) z <- RFsimulate(model, x=x, T=T) plot(z) ## additive separable model with exponential model in space ## and Gaussian in time. The structure is getting rather simple, ## see the function stopifnot below model <- RMexp(proj = "space") + RMgauss(proj = "time") x <- T <- seq(0, 10, 0.1) z <- RFsimulate(model, x=x, T=T) stopifnot(sum(abs(apply(apply(z, 1, diff), 1, diff))) < 1e-14) plot(z)
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