Doug Keenan has written a long essay on the “Statistical Analyses of Surface Temperatures in the IPCC Fifth Assessment Report” that Anthony Watts has seen fit to link to from WUWT.
The essay claims to evaluate the IPCC claim that the temperature increase in the instrumental record is statistically significant. The reader is advised that “No background in statistics is required.”, which is sort of true as there are no statistical analyses in the essay and no equations, but mainly false, because the reader cannot evaluate the veracity of Keenan’s claims, and is instead forced to rely on his authority. The essay is however stuffed will irrelevant digressions, for example into radiocarbon dating (which I will look at later), and irrelevant details of Parliamentary questions asked by a Lord.
Keenan’s basic claim is that the model the IPCC use to test if the temperature trend is significant is not appropriate. The IPCC use a linear model that allows the residuals to be autocorrelated. Keenan argues that a driftless ARIMA (3,1,0) model is more appropriate and a better fit to the data. This is exactly the same argument that I showed to be specious earlier this year. Keenan ignores this post and the follow-up posts.
To recap, the ARIMA(3,1,0) model is not a stationary model, that is, the expected value of the mean changes with time and the 1 indicates the number of differencing steps needed to make the model stationary. The differencing step removes the trend in the temperature data.
Non-stationary models are not physically plausible descriptions of global temperature. Temperature cannot simply drift up and down without violating the laws of thermodynamics. When it gets hot, heat loss by radiation increases, something has to provide that energy.
Non-stationary models also cannot be reconciled with what is known about Earth’s climate from palaeoclimatic archives. For example, syntheses of palaeoclimatic data show that the early Holocene was globally <1°C warmer. In contrast, simulations of an ARIMA(3,1,0) model give wild, physically impossible, fluctuations.
Further, I showed that the choice between a linear model with autocorrelation and Keenan’s ARIMA(3,1,0) model is extremely sensitive to deviations from a linear trend in the temperature data. Indeed, even if an arbitrarily large trend is added to the temperature data, the deviations from the linear trend in the instrumental data are sufficient such that the meaningless ARIMA(3,1,0) model is apparently best.
Had I the time and inclination, I could test whether climate model output for the instrumental period is better fitted by a linear trend or ARIMA(3,1,0) model. I confidently predict that the ARIMA(3,1,0) model will appear to be better even in model output where we precisely know the forcing and the model physics.
Keenan is savaging a straw man. Nobody believes that a linear trend is a full description of climate change over the instrumental period. Climate forcings do not increase linearly with time, so it would be absurd to expect global temperature to. The linear trend model is simply a quick test of whether temperature is increasing. Replacing an oversimplified but informative model with a physically meaningless model is not progress.