HADCRUT Global Temperature Anomaly (part 2)

A quick squizz at the latest data with a side order of cogitation.

In the first part of this series we contemplated the fact that a wiggly line on a graph doesn’t do justice to the uncertainty surrounding data collection on a planet that is large in terms of the human scale. We noted the fact that the climatological normal of 1991-2020 had been abandoned in favour of retaining 1961-1990, presumably because the cooler ‘60s give rise to impressive anomalies that support the narrative. We ended up cogitating on two wrinkles, the first indicating that the greenhouse effect can seemingly run out of steam; the second indicating that the HADCRUT5 global temperature anomaly rises several months before atmospheric carbon dioxide rises. I also gently introduced folk to positive feedback in the carbon cycle, whereby a warmer planet will naturally produce more CO2 even without humans. This morning I’ll reveal two more wrinkles, starting with a slice of logic.

A Slice Of Logic

The greenhouse gas theory dictates that temperatures rise as a result of atmospheric carbon dioxide rising. Consequently, temperatures will fall as a result of atmospheric carbon dioxide falling. This much we all understand, but in terms of testing this theory empirically these represent just two of the four possible logic states into which observations may fall. Try this matrix for size…

Enshrined in that matrix are the two statements we have just made, and I have coloured them green because this feels like a cosy, confirmatory colour and is a gentle reminder that carbon dioxide is plant food. There are also two logic states that would prove awkward for the theory if we found empirical evidence of these in the real world. These have been tinted with a dash of pink food colouring, the whole being a Battenberg of impeccable logic.

Chasing The Cake

Let’s now go in search of some data that will enable us to test our logic cake. To keep things simple we will stick to monthly HADCRUT5 anomalies and monthly atmospheric CO2, as measured at Mauna Loa, and derive the month-to-month change in both these quantities for the period Mar 1958 - May 2022). This scatterplot is what comes out of the oven:

Before we get stuck in it is worth noting that the topological structure of this chart matches the topological structure of our colourful Battenberg matrix, with the zero values for each axis defining the four possible logic states. Thus, in the top right-hand corner we have all those data points that confirm the greenhouse theory in terms of the anomaly rising with a rise in CO2. In the bottom left-hand corner we have all those data points that further confirm the theory in terms of the global anomaly decreasing with a decrease in CO2. But that’s not exactly all the data, is it?

We observe a rather large serving of points that fall into the pink contradiction territory. Doing a bean count I find 371 monthly changes that support the greenhouse gas theory and thus the notion of anthropogenic global warming (AGW) and 399 monthly changes that contradict the notion of AGW. This is what they call settled science, apparently. In later newsletters I may well discuss how and why the greenhouse gas theory likely fails in the light of empirical evidence but for now I want to keep things squarely within my bean-counting profession.

Another Prod

There’s nothing worse in the world of baking than a soggy bottom so I decided to cross-check these mind-altering results using ARIMA time series analysis. The idea behind this bit of modelling is simple:

1. Develop a baseline model for the prediction of monthly HADCRUT5 anomalies over the period Mar 1958 - May 2022.

2. Add the Mauna Loa atmospheric CO2 monthly series to the ARIMA model as an independent (predictor) variable.

3. Ascertain whether adding atmospheric CO2 to the model improves predictive performance for the HADCRUT5 global anomaly. AGW declares that it should jolly well do so!

I confess that this was a most enjoyable bit of cookery because I had no idea how my tray bake would turn out as I cranked the stats handle this misty morning. My money was on a statistically significant result for CO2 but with a modest effect size, thus pleasing all parties. A wishy-washy “yes, humans are having an effect but it’s not as big as we thought” sort of thing might go down very well all round, thank you very much!

But it wasn’t to be. In the immortal words of David Walliams on the fabulous Little Britain, “Computer says no”. Herewith the verdict in stark B&W:

That value of 0.185 in the column headed ‘Sig.’ tells us that the monthly series for atmospheric CO2, as measured at the global reference laboratory at Mauna Loa, is not a statistically significant predictor of the HADCRUT5 global anomaly (p=0.185). This shouldn’t come as a shock because we’re now four wrinkles deep into the data with more wrinkles to come! I suspect this is why they have to keep reminding us that the science is settled.

One final slide

One final slide before afternoon tea and biscuits…

Yes, it is one of those infernal cross-correlation plots! We’ve been eyeballing the relationship (lack thereof) between month-on-month changes in atmospheric CO2 and global anomaly on the assumption energy transfer happens pretty much instantly. However, there may be lags of umpteen years before the pattern of CO2 variation imprints on our thermometers so I’ve taken the liberty of rolling out a cross-correlation plot to check for correlations in the differenced annual series out to ±24 years. It is quite clear from the dismal array of coefficients bouncing around within the 95% confidence interval boundary that we haven’t missed any long cycle energy transfers, in which case it is high time to get the…

Kettle on!