Global Climate Data

We downloaded this data set from the Carbon Dioxide Information Analysis Center at Oak Ridge National Laboratory (http://cdiac.ESD.ORNL.GOV/ftp/ndp020). As in Wahba and Luo (1996), we use the averages of winter (December, January and February) temperatures in 1981 from $n=690$ stations (Wahba and Luo (1996) used $n=725$ stations). The data also contains geological locations of these stations in terms of longitude (long.degree) and latitude (lat.degree). We use this data set to illustrate how to fit a spline on the sphere. We first made the following transformations: $\mbox{\tt long}=\mbox{\tt long.degree}*\pi/180+\pi$ and $\mbox{\tt lat}=\mbox{\tt lat.degree}*\pi/180$. Then $0 \le \mbox{\tt long} \le 2\pi$ and $-\pi/2 \le \mbox{lat} \le \pi/2$.

> attach(climate)
> climate.fit <- ssr(temp~1, rk=sphere(cbind(long,lat)), data=climate)	
> climate.fit
Smoothing spline regression fit by GCV method
Call: ssr(formula = temp ~ 1, rk = sphere(cbind(long, lat)), data = climate)

GCV estimate(s) of smoothing parameter(s) : 1.293621e-05 
Equivalent Degrees of Freedom (DF):  210.993 
Estimate of sigma:  2.270291 

Number of Observations: 690 

> long.grid <- seq(0,2*pi,len=60)
> lat.grid <- seq(-pi/2,pi/2,len=60)
> p.climate <- predict(climate.fit,expand.grid(long=long.grid,lat=lat.grid))

The contour plot of the predicted values is shown in Figure .

Figure: Contour plot of global average Winter temperature in 1981.