| Trend surfaces Trend surfaces are developed by fitting low-order polynomial
functions of the location variables, and then evaluating the resulting
model over a grid of points. The smoothness of the resulting
surface is controlled by the order of the polynomial. This
analysis can be conveniently done using the
spatial library of Venebles
and Ripley
# use Venables and Ripley
spatial library
library(spatial)
x <- ortann$longitude
y <- ortann$latitude
z <- ortann$elevation
oldpar <- par(mfrow = c(2, 2))
# second-order trend surface
ctrl.data <- data.frame(x, y, z)
fit.sfc2 <- surf.ls(2, ctrl.data)
interp.sfc2 <- trmat(fit.sfc2, -124.5000, -116.8333, 42.0000, 46.1667,
30)
plot(latitude ~ longitude, main="second-order", type="n")
contour(interp.sfc2, add=T)
points(latitude ~ longitude)
# third-order trend surface
ctrl.data <- data.frame(x, y, z)
fit.sfc3 <- surf.ls(3, ctrl.data)
interp.sfc3 <- trmat(fit.sfc3, -124.5000, -116.8333, 42.0000, 46.1667,
30)
plot(latitude ~ longitude, main="third-order", type="n")
contour(interp.sfc3, add=T)
points(latitude ~ longitude)
# fourth-order trend surface
ctrl.data <- data.frame(x, y, z)
fit.sfc4 <- surf.ls(4, ctrl.data)
interp.sfc4 <- trmat(fit.sfc4, -124.5000, -116.8333, 42.0000, 46.1667,
30)
plot(latitude ~ longitude, main="fourth-order", type="n")
contour(interp.sfc4, add=T)
points(latitude ~ longitude)
# fifth-order trend surface
ctrl.data <- data.frame(x, y, z)
fit.sfc5 <- surf.ls(5, ctrl.data)
interp.sfc5 <- trmat(fit.sfc5, -124.5000, -116.8333, 42.0000, 46.1667,
30)
plot(latitude ~ longitude, main="fifth-order", type="n")
contour(interp.sfc5, add=T)
points(latitude ~ longitude)
par(oldpar)
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