Bo Christiansen Variance loss
Posted by Jeff Id on July 27, 2010
This is a repost from Eduardo Zorita’s blog, regarding a paper produced by Bo Christiansen which analyzed variance loss in climate reconstructions. It’s a science post so keep all comments/questions on that topic or face the red heat laser of doom.
Mann 07 made the claim that RegEM didn’t create variance loss and alleged proof using pseudoproxies. This was of course ‘proven’ false here recently with a few simple posts and the ‘difference of opinion’ was identified in the artificially trendless noise added to the mannian pseudoproxies.
This is a very ‘hot’ field in climatology because the reasonable scientists have finally recognized the math issue that I found obvious literally within moments of reading my first hockey stick paper at CA. I’m not that smart BTW, so why is it that Mann can find every excuse to miss the point?
Anyway, I read the pre-print of this paper but if someone can send a non-paywall copy of the final version, I would appreciate it. There is a cool equation in the pre-print which would make a fun post by itself.
This paper again demonstrates what I consider the primary reason for unprecedentedness and repeatability of so many hockey stick proxy papers. Remember, the primary defense of the hockey sticks is that so many have reproduced the result. The reason is twofold. At CA Steve has focused on unique proxies – they are unique, here, we have focused on math.
BTW, I doubt any of these scientists are as skeptical of other AGW claims as some of us are so don’t attach some of the tAV fare to them. That doesn’t mean that they don’t do good, honest and open science - don’t lump their fine work in with the opinions of those of us who are outsiders.
Guest post by Bo Christiansen: On temperature reconstructions, past climate variability, hockey sticks and hockey teams
Anthropogenic emissions of greenhouse gases – in particular CO2 and methane – change the radiative properties of the atmosphere and thereby impose a tendency of heating at the surface of the Earth. In the past the Earths temperature has varied both due to external forcings such as the volcanic eruptions, changes in the sun, and due to internal variability in the climate system. Much effort has in recent years been made to understand and project man-made climate change. In this context the past climate is an important resource for climate science as it provides us with valuable information about how the climate responds to forcings. It also provides a validation target for climate models, although paleoclimate modelling is still in its infancy. It should be obvious that we need to understand the past climate variability before we can confidently predict the future.
Unfortunately, we do not have systematic instrumental measurements of the surface temperature much further back than the mid-19th century. Further back in time we must rely of proxy data. The climate proxies include tree rings, corals, lake and marine sediment cores, terrestrial bore-hole temperatures, and documentary archives. Common to all these sources is that they include a climate signal but that this signal is polluted by noise (basically all non-climatic influences such as fires, diseases etc.). From these different noisy proxies information such as the global mean surface temperature is sought extracted. A famous and pioneering example is the work by Mann et al. 1998, in which the mean NH temperature is relatively constant with a weak decreasing rend from 1400-1900 followed by a sharp rise in industrial times – the so-called “hockey stick”. There has been much debate about this reconstruction, and its robustness has been questioned (see e.g.). However, some other reconstructions have shown similar shape and this has encouraged some to talk about the ‘hockey team’ (e.g., here). This partial agreement between different reconstructions has also led to statements such as ‘It is very likely that average Northern Hemisphere temperatures during the second half of the 20th century were higher than for any other 50-year period in the last 500 years’ by the IPCC. That different reconstructions show a ‘hockey stick’ would increase its credibility unless the different reconstructions all shared the same problems. We shall see below that this is unfortunately the case. All proxies are infected with noise. To extract the climate signal – here the NH mean temperature – from a large set of noisy proxies different mathematical methods have been used. They are all, however, based on variants of linear regression. The model is trained or calibrated by using the last period where we have access to both proxies and instrumental data. This calibration period is typically the last 100 years. When the model has been trained it is used to estimate the NH mean temperature in the past (the reconstruction period) where only the proxies are known. To test such methods it is useful to apply them to long simulations from climate models. Like in the real-world situation we split the total period into a calibration period and a reconstruction period. But here we know the NH mean temperature also in the reconstruction period which can therefor be compared with the reconstruction. The proxies are generated by adding noise to the local temperatures from the climate model. The model based scheme decried above is known as the ‘pseudo-proxy’ approach and can be used to evaluate a large number of aspects of the reconstruction methods; how the different methods compare, how sensitive they are to the number of proxies, etc. Inspired by previous pseudo-proxy studies we decided to systematically study the skills of seven different reconstruction methods. We included both methods that directly reconstruct the NH mean temperature and methods that first reconstruct the geographical distributed temperatures, The method used by Mann et al. 1998 was included as well as two versions of the RegEM method later used by this group. Perhaps surprisingly the main conclusion was that all the reconstruction methods severely underestimate the amplitude of low-frequency variability and trends (Fig. 1). Many of the methods could reproduce the NH temperature in the calibration period to great detail but still failed to get the low-frequency variability in the reconstruction period right. We also found that all reconstructions methods has a large element of stochasticity; for different realization of the noise or the underlying temperature field the reconstructions are different. We believe this might partly explain why some previous pseudo-proxy studies have reached different conclusions.