Guest post by Bo Christiansen: On temperature reconstructions, past climate variability, hockey sticks and hockey teams

Bo Christiansen from the Danish Meteorological Institute works actively on the development of statistical methods for climate reconstructions, a field of intense debate in the past few years. Hopefully we will enter a phase in which scientific debates remain .. well, in the scientific realm. Enjoy his post.

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.

Fig 1. Pseudo-proxy experiments with seven different reconstruction methods. The black curve is the NH mean temperature, the target which we hope the reconstructions will catch. But this is not the case: All reconstructions underestimate the pre-industrial temperature level as well as the amplitude of the low-frequency variability. Note that the reconstructions are very good in the last 100 years which have been used for calibration. The three panels differ in the strength of the variability of the target. From Christiansen et al. 2009.

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.

It is important to note the two different kinds of errors which are examples of what is known in statistics as ensemble bias and ensemble variance. While the variance may be minimized by taken the average over many reconstructions the same is not true for the bias. Thus, all the reconstruction methods in our study gave biased estimations of the low-frequency variability. We now see the fallacy of the 'hockey team' reasoning mentioned above; if all reconstruction methods underestimate the low-frequency variability then considering an ensemble of reconstructions will not be helpful.
The question that arises now is if the systematic underestimation of low-frequency variability can be avoided. Based on an idea by Anders Moberg and theoretical considerations I formulated a new reconstruction method, LOC, which is based on simple regression between the proxies and the local temperatures to which the proxy is expected to respond. To avoid the loss of low-frequency variance it is important to use the proxy as the dependent variable and the temperature as the independent variable. When the local temperatures have been reconstructed the NH mean is found by averaging. Pseudo-proxy studies (Fig. 2) confirms that the low-frequency variability is not underestimated with this method. However, the new reconstruction method will overestimate the amplitude of high-frequency variability. This is the price we must pay; we can not totally remove the influence of the noise but we can shift it from low to high frequencies. The influence of the noise on the high-frequency variability can be reduced by averaging over many independent proxies or by smoothing in time. 

Fig. 2 Pseudo-proxy experiment showing the ability of the new method (LOC, blue curve) to reconstruct the low-frequency variability of the target (black curve). Here the target has been designed to include a past warm period. This past warm period is well reconstructed by the new method but not by the two versions of the ReEM method. From Christiansen 2010.

 I have applied the new reconstruction method, LOC, to a set of 14 decadally smoothed proxies which are relatively homogeneously geographically distributed over the extra-tropical NH. This compilation of proxies was used in the reconstruction by Hegerl et al. 2007.  The proxies cover the period 1505-1960, the calibration period is 1880-1960, and observed temperatures are from HadCRUT2v.  The result is shown in Fig. 3 together with eight previous reconstructions.  The new reconstruction has a much larger variability than the previous reconstructions and reports much colder past temperatures. Whereas previous reconstructions hardly reach temperatures below -0.6 K the LOC reconstruction has a minimum of around -1.5 K.  Regarding the shape of the low-frequency variability the new reconstruction agrees with the majority of the previous reconstructions in the relative cold temperatures in the 17th century and in the middle of the 19th century as well as in the relative warm temperatures in the end of the 18th century. I consider these real world results mainly as an illustration of the potential of the new method as reconstruction based on decadally resolved proxies are not particularly robust due to small number of degrees of freedom. Work is in progress to apply the new method to an annual resolved and more comprehensive proxy compilation. 

Fig. 3 The new real-world reconstruction (thick black curve) shown together with some previous reconstructions. All reconstructions are decadally smoothed and centered to zero mean in the 1880-1960 period. From Christiansen 2010.

Where does all this lead us? It is very likely that the NH mean temperature has shown much larger past variability than caught by previous reconstructions. We cannot from these reconstructions conclude that the previous 50-year period has been unique in the context of the last 500-1000 years. A larger variability in the past suggests a larger sensitivity of the climate system. The climate sensitivity is a measure how how much the surface temperature changes given a specified forcing. A larger climate sensitivity could mean that the estimates of the future climate changes due to increased levels of green-house gases are underestimated.