Introduction

The recent “record breaking” high temperatures recorded in the UK brought attention to the use of such observations within the context of debates on climate change. In many respect the result for unfortunate and caused more heat than light. Single observations of high temperatures are not even particularly good at detecting heat waves. The highest temperature only lasts for a few hours in each day and the physiological impact of heat is complex. Even within a single day the range of temperatures and humidity have to be taken into account. Droughts are the result of prolonged spells of below average rainfall, with or without high temperatures. Temperature is not the only driver of evapotranspiration.

However, this measure has been widely publicised. The previous analysis looked at the rank correlation between years since 1970 and highest recorded temperature for the year. Its interesting to run the same analysis over all the GHCND stations for the northern hemisphere. The function used took the id of the station as input after pulling all the records from GHCND and csv files. This took over 24 hours to run. The function is simple and included for reference in the code chunk below. Only years with almost complete daily records and more than ten years data were used.

f<-function(id)
{
dd<-read.csv(id)
dd %>% filter(element=="TMAX") ->dd
dd$date<-ymd(dd$date)
dd$value<-dd$value/10
dd$year<-year(dd$date)
dd %>% group_by(id,year) %>% summarise(max=max(value),n=n()) %>% filter(year>1969) %>% filter(n>350) ->yrly

d<-data.frame(id=NA,p=NA,r=NA, n=NA,last=NA)

if(length(yrly$year)>10){
a<-cor.test(yrly$year,yrly$max,method="spearman")
d<-data.frame(id=yrly$id[1],p=a$p.value,r=a$estimate, n=length(yrly$year),last=max(yrly$year))
}

d
}

Results

This may not be the most effective way of looking at changes in extreme temperature related to climate change, but it does coincide with the manner in which extreme heat is reported. The mean correlation coefficient over all the stations with records that matched the criteria was 0.083706 , which is not convincing evidence of a general trend. The distribution of the rank correlation coefficient can be looked at using simple histograms

Histograms

All stations

hist(st$r, main="Distribution of rank correlation coeficients", xlab="Rho")

Stations with over thirty years of records since 1990

st %>% filter(n>30) ->stt
hist(stt$r, main="Distribution of rank correlation coeficients",xlab="Rho")

Interpretation of the histograms

The full set of stations shows quite a broad distribution of correlation coefficients, centred just above zero. This is similar when only the significant correlations are considered. Statistical significance tends to be related with sample size, so these will be the stations with more complete records. This does not provide good evidence in favour of using record high temperatures as an indicator of trends in climate. If mean annual temperatures are increasing as a result of slightly warmer winters rather than hotter summers then there would be no real reason to expect much of a trend. Urban heat islands further confound interpretation.

The most surprising result is finding a large number of stations that show a significantly negative coefficient. Some statistically significant negative coefficients would arise by chance if there is no trend at all. However there are too many for that to be the explanation.

Maps

stsp$sig<-ifelse(stsp$p<0.05,"Yes","No")
stsp$rho<-round(stsp$r,3)
stsp$cor<-as.factor(cut(stsp$r,c(-1,0,0.2,0.4,1)))
levels(stsp$cor)<-c("Negative","Very weak","Weak", "Weak to moderate")
st1<-select(stsp,id,name,cor,rho,sig,n)
st1$cor<-as.character(st1$cor)
filter(st1,name !="HIGH MOWTHORPE") ->st1
All_stations <- st1

All stations

mapview(All_stations,zcol="cor")  ->mp
mp@map %>% addFullscreenControl()

Interpretation of the maps

The spatial distribution of the coeficients does show some clustering. Most climate stations in Germany, France and Central Europe do show a significant increasing trend in the ranks of the hottest day of the year. However the significantly negative correlations are also clustered. They are mainly found in central and mid western USA. This is unexpected and may well be a feature of the way the data are collected and the placing of climate stations. However it is still suprising and may merit further research.

On zooming into the area it appears that many of the stations are in the cereal belt and surrounded by extensive cropland. So one possibility is that irrigation and/or the timing of crop planting has led to the surrounding transpiring rather more water during the summer than previously. This would just take the edge of the peak temperature record and could potentially lead to the trend.

Example station with negative correlation USC00234694 Lakeside

To check whether there was any obvious anomaly in the records for the American Mid West I looked at data from some of the stations one by one. Here is one example. There are some missing years, but too few to make a great difference. In this case the record temperature of over 45 degrees was recorded on the 15 July in 1954. Recent years have been well below this. If these data are accurate it would be rather unexpected for a new all time record could be set at this particular station given the current trend. Other stations in this region show similar patterns.

Dygraph of TMAX

dygraph(xts(dd$value,dd$date))

Rank correlation

ggplot(yrly,aes(x=year,y=rank(max))) + geom_point() +geom_smooth(method="lm") +labs(title="Ranked maximum temperatures at Lakeside between 1970 and 2021",y="Rank",x="Year")

Highest daily temperature

ggplot(yrly,aes(x=year,y=max)) + geom_point() +geom_smooth(method="lm") +labs(title="Maximum temperatures at Lakeside between 1970 and 2021",y="TMAX",x="Year")

Example German station with positive correlation GMM00010452 Brounlage

In contrast to the American Mid West, most German stations do show a positive correlation.

Dygraph of TMAX

dygraph(xts(dd$value,dd$date))

Rank correlation

ggplot(yrly,aes(x=year,y=rank(max))) + geom_point() +geom_smooth(method="lm") +labs(title="Ranked maximum temperatures at Braunlage between 1970 and 2021",y="Rank",x="Year")

Highest daily temperature

ggplot(yrly,aes(x=year,y=max)) + geom_point() +geom_smooth(method="lm") +labs(title="Maximum temperatures at Braunlage between 1970 and 2021",y="TMAX",x="Year")

Conclusion

Reporting peak maximum daily temperature as an indicator of climate change is not recommended practice. The correlation between mean annual temperature and the peak is weak, and temporal trends are rather ambiguous. “Cherry picking” of extremes is statistically flawed practice. Even if there is no true trend at all, some stations will show record temperatures during summer warm spells. The negative correlations, if confirmed, may even lead to more divisiveness in the public debate, if they correspond to the “lived experience” of residents of the areas concerned. Reporting that hot days are becoming hotter when people quite correctly don’t notice any effect at all, or even remember hotter days in the past, will only lead to confusion and possible mistrust of the manner in which the media report on the climate.