More climate extremes, or simply global warming ?

January 12, 2011
By

(This article was first published on Freakonometrics - Tag - R-english, and kindly contributed to R-bloggers)

In the paper on the heat wave in Paris (mentioned here)
I discussed changes in the distribution of temperature (and
autocorrelation of the time series).

During the workshop on Statistical Methods for Meteorology and
Climate Change
today (here) I
observed that it was still an important question: is climate change
affecting only averages, or does it have an impact on extremes ? And
since I’ve seen nice slides to illustrate that question, I decided to
play again with my dataset to see what could be said about temperature
in Paris.

Recall that data can be downloaded here (daily
temperature of the XXth century).

tmaxparis=read.table("/temperature/TX_SOUID100124.txt",
skip=20,sep=",",header=TRUE)
Dmaxparis=as.Date(as.character(tmaxparis$DATE),"%Y%m%d")
Tmaxparis=as.numeric(tmaxparis$TX)/10
tminparis=read.table("/temperature/TN_SOUID100123.txt",
skip=20,sep=",",header=TRUE)
Dminparis=as.Date(as.character(tminparis$DATE),"%Y%m%d")
Tminparis=as.numeric(tminparis$TN)/10
Tminparis[Tminparis==-999.9]=NA
Tmaxparis[Tmaxparis==-999.9]=NA
annee=trunc(tminparis$DATE/10000)
MIN=tapply(Tminparis,annee,min)
plot(unique(annee),MIN,col="blue",ylim=c(-15,40),xlim=c(1900,2000))
abline(lm(MIN~unique(annee)),col="blue")
abline(lm(Tminparis~unique(Dminparis)),col="blue",lty=2)
annee=trunc(tmaxparis$DATE/10000)
MAX=tapply(Tmaxparis,annee,max)
points(unique(annee),MAX,col="red")
abline(lm(MAX~unique(annee)),col="red")
abline(lm(Tmaxparis~unique(Dmaxparis)),col="red",lty=2)

On the plot below, the dots in red are the annual
maximum temperatures, while the dots in blue are
the annual minimum temperature. The plain line is the regression line
(based on the annual max/min), and the dotted lines represent the
average maximum/minimum daily temperature (to illustrate the global tendency),

It is also possible to look at annual boxplot, and to focus either on
minimas, or on maximas.

annee=trunc(tminparis$DATE/10000)
boxplot(Tminparis~as.factor(annee),ylim=c(-15,10),
xlab="Year",ylab="Temperature",col="blue")
x=boxplot(Tminparis~as.factor(annee),plot=FALSE)
xx=1:length(unique(annee))
points(xx,x$stats[1,],pch=19,col="blue")
abline(lm(x$stats[1,]~xx),col="blue")
annee=trunc(tmaxparis$DATE/10000)
boxplot(Tmaxparis~as.factor(annee),ylim=c(15,40),
xlab="Year",ylab="Temperature",col="red")
x=boxplot(Tmaxparis~as.factor(annee),plot=FALSE)
xx=1:length(unique(annee))
points(xx,x$stats[5,],pch=19,col="red")
abline(lm(x$stats[5,]~xx),col="red")

Plain dots are average temperature below the 5% quantile for minima, or
over the 95% quantile for maxima (again with the regression line),

We can observe an increasing trend on the minimas, but not on the
maximas !
Finally, an alternative is to remember that we focus on annual maximas
and minimas. Thus, Fisher and Tippett theory (mentioned here)
can be used. Here, we fit a GEV distribution on a blog of 10
consecutive years. Recall that the GEV distribution is

http://freakonometrics.blog.free.fr/public/perso/gev1.png
install.packages("evir")
library(evir)
Pmin=Dmin=Pmax=Dmax=matrix(NA,10,3)
for(s in 1:10){
X=MIN[1:10+(s-1)*10]
FIT=gev(-X)
Pmin[s,]=FIT$par.ests
Dmin[s,]=FIT$par.ses
X=MAX[1:10+(s-1)*10]
FIT=gev(X)
Pmax[s,]=FIT$par.ests
Dmax[s,]=FIT$par.ses
}

The location parameter http://freakonometrics.blog.free.fr/public/perso/gev4.png is
the following, with on the left the minimas and on the right the
maximas,

while the scale parameter http://freakonometrics.blog.free.fr/public/perso/gev3.png is

and finally the shape parameter http://freakonometrics.blog.free.fr/public/perso/gev2.png is

On those graphs, it is very difficult to say anything regarding changes
in temperature extremes… And I guess this is a reason why there is still active research on that area…

To leave a comment for the author, please follow the link and comment on his blog: Freakonometrics - Tag - R-english.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , , , , , , , , , , , ,

Comments are closed.