In honor of the National Research Council of the National Academies committee to study “Surface Temperature Reconstructions for the Past 1,000-2,000 Years” meeting at this moment, I offer my own climate reconstruction based on the methods blessed by dendroclimatology. The graph below shows reconstructed temperature anomolies over 2000 years, with the surface temperature measurements from 1850 from CRU as black dots, the individual series in blue and the climate reconstruction in black. I think you can see the similarity to other published reconstructions (see here), particularly the prominent ‘hockey-stick’ shape, the cooler temperatures around the 1500s and the Medieval Warm Period around the 1000s. What data did I use? Completely random sequences. Reconstruction methods from dendroclimatology will generate plausible climate reconstructions even on random numbers!
The steps to construction were as follows:
- Generate 100 sequences of 2000 random numbers with long term persistant (LTP) stochastic process.
- Select sequences with a positive correlation with CRU.
- Average the selected series.
The series show a ‘hockey-stick’ pattern due to step 2 – only those random series correlating with temperatures are selected. This step is analogous to only using trees with positive correlation with temperatures. Outside the range of the calibration temperatures the average of the series reverts to the mean value of the random numbers, which in this case is the chosen zero value of the calibration temperatures. This leads to an upward drift in values back through time. The maximum value is entirely arbitrary. Base the anomolies around a different zero value, and the MWP will go higher or lower. LTP is necessary because a similar set of i.i.d. series would be very unlikely to have members that correlate significantly with the CRU temperatures. Around 5% of LTP series were significant in this case due to ‘spurious correlation’.
Here is an attempt at describing the logical implications of this. This demonstration does not necessarily falsify the results of climatic reconstruction using tree-rings. If we take the theory of tree-ring reconstructions as a finding P and C where P is the premise and C is the conclusion, falsification would be a finding like P not C, that is, that using real tree ring data leads to a temperature reconstruction that is in disagreement with reality. Demonstrating the same results with random numbers is a finding like Q and C, essentially an alternative theory for generating the same conclusions. What one would also need is to prove is that P is equivalent Q, that tree-rings series are essentially indistinguishable from random numbers generated from stochastic series with LTP say. Alternatively, to counter the claim that climate reconstructions from tree-rings are based on random numbers, one should show the reconstruction is not be generated from a random series. The data from the calibration period could not be used, as it is already a biased sample. Also, coherence between series would not provide support for P not equivalent Q either, due to spatial correlations between the series.