Almost all comments in the press about the IPCC reports start with the remark that global warming has stalled since 2000 (or 1998 … anyway, the last 10, 15 or 20 years). Last year’s IPCC report even mentions this itself. It is the favourite topic of contrarians on the internet.
But is it true?
The datasets used are histrorical surface temperatures, collected by various bodies such as UAH MSU, RSS MSU, GISS, Hadcrut4, NCDC or JMA. I will have a look at the HADCRUT4 data.
This is a gridded dataset of global historical surface temperature anomalies relative to a 1961-1990 reference period. Data are available for each month since January 1850, on a 5 degree grid. The dataset is a collaborative product of the Met Office Hadley Centre and the Climatic Research Unit at the University of East Anglia.
The monthly aggregated data, using the median of all the grid values, are then used as the global surface temperatures. The uncertainties are many: measurement errors, missing grid data, day-night differences, etc. So the data has a confidence interval (that is seldom published. This is how it looks:
I have changed the baseline to 1986-2005,as that is used in the IPCC report of last year. Looks like a lot of noise: the grey’s are the lower and upper bounds of the confidence intervals, the blueish grey the medians, and the red a smoothed 5-year running average by a method called loess (local exponential smoothing). At first sight there is an increase from 1975-2000, after which it flattens out. This is often compared with the predictions by the IPCC, in figures similar to the following:
In the background to the right we see all the runs of the IPCC models. This area is called “likely” by the IPCC: they have at least 66% confidence that the future values will fall within this region. Sceptics say that they do not see any improvement since 1998 .
At first sight they do seem to have a point. Drawing a straight line through the data (a regression line) we see hardly any change since 2000, certainly compared to 1970-2000. But wait, how confident can we be about these lines? This is a very noisy signal, even if we only look at the medians without the uncertainty.
A standard statistical technique to estimate the confidence comes from statistical learning. We use a model (in this case regression), obtain an estimate of the parameters using a “training” set – in this case from 1970-2000 and then see how well the parameters perform on another set, the “test” set, using a measure for the goodness of fit. For a regression, this is obviously the sum of squares. In fact, the mean standard error MSE or its square root called RMSE is used as a standard in statistical learning. Calculating them, we see this result:
For the data in the period 1970-2000 the RMSE for the best fit is 0.14. This prediction works very well for the period 2000-2014, there the fit is even better than in the former period. Of course it is not the best fit, but the difference with the best fit is small.
The big variation in the data causes this. The use of RMSE is all standard theory, but if you feel doubtful about this, “hindcast’ the prediction for a period before 1970, say 1950-1970. There is a big difference!
The R-code is simple for the calculation. You can download the Hadcrut time series from my dropbox. Load the .Rdata – file into R and proceed :
## hc4.median is the time series for the monthly median anomaly st0=1970 h0<-window(hc4.median, start=st0, end=st0+29.999) h1<-window(hc4.median, start=st0+30) train <- data.frame(anomaly=as.numeric(h0), time=as.numeric(time(h0))) test <- data.frame(anomaly=as.numeric(h1), time=as.numeric(time(h1))) l0<-lm(anomaly~time, data=train) test.fit<-predict(l0, newdata=test) sqrt(mean(l0$residuals^2)) ## [1] 0.1362594 sqrt(mean((test.fit-test$anomaly)^2)) ## [1] 0.1211419 l1<-lm(anomaly~time, data=test) sqrt(mean(l1$residuals^2))## [1] 0.1083177