Addendum to “A Mistake with Repercussions”

1. What are “pseudo-proxies” and why are they useful?

Our only information from before the “instrumental period” (the period from which we have systematic measurements with thermometers, starting around 1850) comes from proxy records of climate (like tree rings, ice cores, corals, sediments, pollen etc.). Therefore it is important to know what the available kind and distribution of proxy records can tell us about quantities that we care about (like changes in the average temperature of the northern hemisphere). A typical question is: what accuracy for the northern hemisphere temperature can one expect, given the available number and spatial distribution of proxies? How much uncertainty arises from the non-climatic ‘noise’ in these records? How do the different methods for combining the proxies compare? And so on…

If there was sufficient length of good instrumental data, then we would be able to answer these questions simply by comparing measurements with proxy records. But the instrumental record is short – after all this is the prime reason why we have to rely on proxies.

Enter the virtual world of climate models. This world may not exactly match the real world – but within this world, we have complete information about any changes in climate. Recently a number of simulations using different models have been made for the last 1000 years. These simulations can be used as a numerical laboratory in which we can test the reconstruction methods and assess their potential limitations, by pretending to derive proxy records of the model climate, called “pseudo-proxies”.

The first stage is to designate points in the model where you want to derive a proxy record. A good idea is to take the same points on the globe that are used for a real proxy reconstruction – then you can test, e.g., how good this particular spatial coverage is for capturing the hemispheric mean. Secondly, you need to determine what is recorded in your pseudo-proxy. This can be simple or it can be complicated. The simplest is to assume that the pseudo-proxies depend on local temperature (which is known in the model world, of course), plus some non-climatic noise (this is the approach taken by von Storch et al.). This could be significantly more complicated if desired – the pseudo-proxy could be dependent on precipitation as well, or on more sophisticated climate metrics (such as growing degree days for tree rings for instance).

However, there are a few caveats that one needs to be aware of. First, the climate field reconstruction (CFR) methods (like MBH98 and more recently the RegEM methodology in Rutherford et al, 2005) rely on the observed tele-connections between local processes recorded in the proxies and large-scale climate patterns. For instance, a precipitation record that is influenced by ENSO contains information about ENSO and hence regional temperatures, even if it is not locally reflecting temperature changes. If the climate model has different tele-connections from the real world, or a different balance of different sources of variability (ENSO vs. NAO etc.), the cross-correlations of the pseudo-proxies to the large scale patterns might be different. Since the models that we are discussing do not tend to have very realistic ENSO variability, this is a significant point. Secondly, all the CFR methods implicitly rely on the stationarity of some aspects of climate variability over the modern period compared to the last 1000 years (specifically that the patterns of variability are not hugely different over the last 150 years than they are in the previous 850 years). There is no hard evidence that this isn’t the case (as it might be over the glacial period for instance), but the same must be true in the model as well. If there is an important cause of variability in the model that is not operating in the calibration/verification period, then that could cause problems. Large climate drifts in the beginning of the simulation might fall into that category (see below).

2. Spot the error

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