(This article was first published on

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).
**Freakonometrics - Tag - R-english**, and kindly contributed to R-bloggers)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)

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")

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

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

}

while the scale parameter is

and finally the shape parameter 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

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