SpatialExtremes (version 1.2-0)

condmap: Produces a conditional 2D map from a fitted max-stable process

Description

Produces a conditional 2D map from a fitted max-stable process.

Usage

condmap(fitted, fix.coord, x, y, marg.cov = NULL, ..., ret.per1 = 100,
ret.per2 = ret.per1, col = terrain.colors(length(x)), plot.contour =
TRUE)

Arguments

fitted

An object of class maxstab. Most often, it will be the output of the function fitmaxstab.

fix.coord

The spatial coordinates of the location from which the conditional quantile is computed.

x,y

Numeric vector defining the grid at which the levels are computed.

marg.cov

A matrix of the (currently only one) marginal covariable value at points x[i], y[j]. See function fitmaxstab.

...

Several arguments to be passed to the link{image} and contour functions.

ret.per1,ret.per2

Numerics giving the return period for which the quantile map is plotted. See details.

col

A list of colors such as that generated by 'rainbow', 'heat.colors', 'topo.colors', 'terrain.colors' or similar functions.

plot.contour

Logical. If TRUE (default), contour lines are added to the plot.

Value

• A plot. Additionally, a list with the details for plotting the map is returned invisibly.

Details

The function solves the following equation:

$$\Pr\left[Z(x_2) > z_2 | Z(x_1) > z_1 \right] = \frac{1}{T_2}$$ where $z_1 = -1 / \log(1 - 1/T_1)$.

In other words, it computes, given that at location $x_1$ we exceed the level $z_1$, the levels which is expected to be exceeded in average every $T_2$ year.

See Also

map, filled.contour, heatmap, heat.colors, topo.colors, terrain.colors, rainbow

Examples

require(RandomFields)

##Define the coordinate of each location
n.site <- 30
locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
colnames(locations) <- c("lon", "lat")

sigma <- matrix(c(4, 1, 1, 3), 2)
sigma.inv <- solve(sigma)
sqrtCinv <- t(chol(sigma.inv))
model <- list(list(model = "gauss", var = 1, aniso = sqrtCinv / 2))

##Simulate a max-stable process - with unit Frechet margins
ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE,
                   model = model, maxstable = "Bool", n = 40)
ms0 <- t(ms0)
ms1 <- ms0

##Now define the spatial model for the GEV parameters
param.loc <- -10 - 4 * locations[,1] + locations[,2]^2
param.scale <- 5 + locations[,1] + locations[,2]^2 / 10
param.shape <- rep(.2, n.site)

##Transform the unit Frechet margins to GEV 
for (i in 1:n.site)
  ms1[,i] <- param.scale[i] * (ms1[,i]^param.shape[i] - 1) /
  param.shape[i] + param.loc[i]

##Define a model for the GEV margins to be fitted
##shape ~ 1 stands for the GEV shape parameter is constant
##over the region
loc.form <- loc ~ lon + I(lat^2)
scale.form <- scale ~ lon + I(lat^2)
shape.form <- shape ~ lat + lon

##  1- Fit a max-stable process
fitted <- fitmaxstab(ms1, locations, "gauss", loc.form, scale.form,
                     shape.form, std.err.type = "none")

condmap(fitted, c(1, 1), seq(0, 10, length = 25), seq(0,10, length =
25))