Target CO₂

What is the long term sensitivity to increasing CO₂? What, indeed, does long term sensitivity even mean? Jim Hansen and some colleagues (not including me) have a preprint available that claims that it is around 6ºC based on paleo-climate evidence. Since that is significantly larger than the ‘standard’ climate sensitivity we’ve often talked about, it’s worth looking at in more detail.

We need to start with some definitions. Sensitivity is defined as the global mean surface temperature anomaly response to a doubling of CO₂ with other boundary conditions staying the same. However, depending on what the boundary conditions include, you can get very different numbers. The standard definition (sometimes called the Charney sensitivity), assumes the land surface, ice sheets and atmospheric composition (chemistry and aerosols) stay the same. Hansen’s long term sensitivity (which might be better described as the Earth System sensitivity) allows all of these to vary and feed back on the temperature response. Indeed, one can imagine a whole range of different sensitivities that could be clearly defined by successively including additional feedbacks. The reason why the Earth System sensitivity might be more appropriate is because that determines the eventual consequences of any particular CO₂ stabilization scenario.

Traditionally, the decision to include or exclude a feedback from consideration has been based on the relevant timescales and complexity. The faster a feedback is, the more usual it is to include. Thus, changes in clouds (~hours) or in water vapour (~10 days) are undoubtedly fast and get included as feedbacks in all definitions of the sensitivity. But changes in vegetation (decades to centuries) or in ice sheets (decades(?) to centuries to millennia) are slower and are usually left out. But there are other fast feedbacks that don’t get included in the standard definition for complexity reasons – such as the change in ozone or aerosols (dust and sulphates for instance) which are also affected by patterns of rainfall, water vapour, temperature, soli moisture, transport and clouds (etc.).

Not coincidentally, the Charney sensitivity corresponds exactly to the sensitivity one gets with a standard atmospheric GCM with a simple mixed-layer ocean, while the Earth System sensitivity would correspond to the response in a (as yet non-existent) model that included interactive components for the cryosphere, biosphere, ocean, atmospheric chemistry and aerosols. Intermediate sensitivities could however be assessed using the Earth System models that we do have.

In principal, many of these sensitivities can be deduced from paleo-climate records. What is required is a good enough estimate of the global temperature change and measures of the various forcings. However, there are a few twists in the tale. Firstly, getting ‘good enough’ estimates for global temperatures changes is hard – this has been done well for the last century or so, reasonably for a few centuries earlier, and potentially well enough for the really big changes associated with the glacial-interglacial cycle. While sufficient accuracy in the last few centuries is a couple of tenths of a degree, this is unobtainable for the last glacial maximum or the Pliocene (3 million years ago). However, since the signal is much larger in the earlier periods (many degrees), the signal to noise ratio is similar.

Secondly, although many forcings can be derived from paleo-records (long-lived greenhouse gases from bubbles in the ice cores most notably), many cannot. The distribution of sulphate aerosols even today is somewhat uncertain, and at the last glacial maximum, almost completely unconstrained. This is due in large part to the heterogenity of their distribution and there are similar problems for dust and vegetation. In some sense, it is the availability of suitable forcing records that suggests what kind of sensitivity one can define from the record. A more subtle point is that the ‘efficacy’ of different forcings might vary, especially ones that have very different regional signatures, making it more difficult to add up different terms that might be important at any one time.

Lastly, and by no means leastly, Earth System sensitivity is not stable over geologic time. How much it might vary is very difficult to tell, but for instance, it is clear that from the Pliocene to the Quaternary (the last ~2,5 million years of ice age cycles), the climate has become more sensitive to orbital forcing. It is therefore conceivable (but not proven) that any sensitivity derived from paleo-climate will not (in the end) apply to the future.

We’ve often gone over the Charney sensitivity constraint for the Last Glacial Maximum. There is information about the greenhouse gases (CO₂, CH₄ and N₂O), reconstructions of the ice sheets and vegetation change, and estimates of the dust forcing. A recent estimate of the magnitude of these forcings is around 8 +/- 2 W/m2 (Schneider von Deimling et al, 2006). This implicitly includes other aerosol changes or atmospheric chemistry changes in with the sensitivity (or equivalently, assumes that their changes are negligible). So given a temperature change of about 5 to 6ºC, this gives a Charney sensitivity of around 3ºC (ranging from 1.5 to 6 if you do the uncertainty sums).

Hansen suggests that the dust changes should be considered a fast feedback as well (as could the CH₄ changes?) and that certainly makes sense if vegetation changes are included on the feedback side of the equation. Since all of these LGM forcings are the same sign (i.e. they are all positive feedbacks for the long term temperature change), that implies that the Earth System sensitivity must be larger than the Charney sensitivity on these timescales (and for this current geologic period). So far so good.

Hansen’s first estimate of the Earth System sensitivity is based on an assumption that GHG changes over the long term control the amount of ice. That gives a scaling of 6ºC for a doubling of CO₂. This is however problematic for two reasons; first most of the power of this relationship is derived from when there were large N. American and European ice sheets. It is quite conceivable that, now that we are left with only Greenland and Antarctica, the sensitivity of the temperature to the ice sheets is less. Secondly, it subsumes the very special nature of orbital forcing – extreme regional and seasonal impacts but very little impact on the global mean radiation. Hansen’s estimate assumes that an overall cooling of the same magnitude of the LGM would produce the same extent of ice sheets that was seen then. It may be the case, but it is not a priori obvious that it must be. Hansen rightly acknowledges these issues, and suggests a second constraint based on longer term changes.

Unfortunately, prior to the ice core record, our knowledge of CO₂ changes is much poorer. Thus while it seems likely that CO₂ decreased from the Eocene (~50 million years ago) to the Quaternary through variations related to tectonics, the exact magnitude is uncertain. For reasonable values based on the various estimates, Hansen estimates a ~10 W/m2 forcing change over the Cenozoic from this alone (including a temperature-related CH₄ change). The calculation in the paper is however a little more subtle. Hansen posits that the long term trend in the deep ocean temperature in the early Cenozoic period (before there was substantial ice) was purely due to CO₂ (using the Charney sensitivity). He then plays around with the value of the CO₂ concentration at the initiation of the Antarctic ice sheets (around 34 million years ago) to get the best fit with the CO₂ reconstructions over the whole period. What he ends up with is a critical value of ~425 ppm for initiation of glaciation. To be sure, this is fraught with uncertainties – in the temperature records, the CO₂ reconstructions and the reasonable (but unproven) assumption concerning the dominance of CO₂. However, bottom line is that you really don’t need a big change in CO₂ to end up with a big change in ice sheet extent, and that hence the Earth System sensitivity is high.

So what does this mean for the future? In the short term, not much. Even if this is all correct, these effects are for eventual changes – that might take centuries or millennia to realise. However, even with the (substantial) uncertainties in the calculations and underlying assumptions, the conclusion that the Earth System sensitivity is greater than the Charney sensitivity is probably robust. And that is a concern for any policy based on a stabilization scenario significantly above where we are now.