Guest blog by Chris Colose (e-mail: colose-at-wisc.edu)

UPDATE: This is Part 1 of two posts by Chris. Part 2 is here

RealClimate has recently featured a series of posts on the greenhouse effect and troposphere, articulating some of the more important physics of global warming from first principles. It is worthwhile reviewing these elements every so often with different slants just so the broad picture is not lost in the disagreement over details. This post extends on this theme to discuss one of the greatest sources of interest and uncertainty in the physical science of climate change: feedbacks. Feedbacks behave in interesting and often counter-intuitive ways, some of which can only be fully appreciated by mathematical demonstration. The previous posts at RC were criticized for being either too complex or too simple, so this post will feature two parts, with the second part providing some more of the technical details.

Feedbacks are components of the climate system that are constrained by the background climate itself; they don’t cause it to depart from its reference norm on their own, but rather may amplify or dampen some other initial push. These original “pushes” are forcings which are typically radiative in nature (such as adding CO2 to the air) and manifest themselves as a climate change when they are large enough or persistent enough to overcome the large heat capacity of the oceans, and thus change the annual mean radiative energy balance of the Earth. In a broad sense, a feedback means that some fraction of the output is fed back into the input, so the radiative perturbation gets an additional nudge (amplifying the forcing, a positive feedback or damping the forcing, a negative feedback). The major examples such as decline in ice extent in a warmer world, thereby reducing the reflected fraction of incident surface radiation are pretty well known at this point.

Another thought experiment can help to appreciate the implications. When we think about the terrestrial greenhouse effect, it is necessary to distinguish between those gases which condense and then precipitate from the air as solid or liquid rather rapidly (on Earth this substance is water) and those gases which can reside in the atmosphere for a very long time, and whose concentration is not so dependent on the temperature. Once you account for the spectral overlap between the various greenhouse gases and clouds in the sky, it is found that water vapor makes up roughly 50% of the modern greenhouse effect, clouds about 25%, CO2 is 20%, and the remaining gases (primarily methane, ozone, and nitrous oxide) make up the rest (Schmidt et al 2010, in press and a discussion of the paper here). This generally leads to popular claims like ‘water vapor is the most important greenhouse gas’ since it makes up the bulk of the infrared absorption in our atmosphere. This simple picture is incomplete however, since the total water vapor concentration is largely set by temperature and thus the non-condensable, long-lived greenhouse gases (chiefly, CO2) really provide the skeleton by which the greenhouse effect is maintained and what governs its capacity for change. In that sense, water vapor is in large part supported by the other gases and then amplifies their effect significantly.

If you could remove all of the CO2 from our atmosphere, aside from making the planet more efficient at losing its heat to space (thus cooling) you would do a couple of things. First, you’d lose much of the water vapor and cloud greenhouse effect since temperatures would be too cold for them to exist in appreciable amounts. Secondly, you would also get temperatures cold enough to the point where expanding ice cover greatly enhances the surface albedo of the planet and triggers a snowball Earth. This simple picture also holds true as the climate warms today, where it has long been noted that the increase in water vapor content of the upper troposphere should amplify the CO2 signal by a factor of about two.

CO2 concentration itself can act as a feedback to temperature on longer glacial-interglacial timescales in response to changes in ocean dynamics, temperature/salinity, as well as vegetation. It can also be a negative feedback to temperature on still longer timescales, where silicate weathering effects (determined by volcanic output and removal by precipitation) are thought to keep the climate in check over geologic timeframes. Often however, climatologists define some metric CO2 change (such as a doubling) which allows you to ignore the carbon-cycle feedbacks and focus on the ones which alter the radiative balance and temperature further. The principle feedbacks in this category are water vapor responses, surface albedo, cloud, and lapse rate effects.

Feedback behavior

The ultimate constraint on climate change is the Planck radiative feedback, which mandates that a warmer world will radiate more efficiently and therefore provide a cooling effect. For a blackbody, the emission goes like the fourth power of the temperature. So the question of how the other feedbacks behave is really of how they modify the Planck feedback. In order to decide whether a feedback is positive or negative, it is instructive to define a baseline sensitivity value that the climate system would have if no feedbacks operated at all. That is, if we perturb the climate with some forcing, what is the temperature change you would need to have to allow the planet’s energy balance to be satisfied. It can be shown that for every Watt per square meter radiative forcing the climate would warm by about 0.3°C without any other responses. To put this in perspective, it would take about five doublings of CO2 or a 7% increase in the total solar radiation hitting the Earth to produce the magnitude of climate change typical of glacial-to-interglacial transitions. Changes of this sort are well outside the bounds of what is characteristic of proxy records and observations, so this must mean that various feedbacks act to change the temperature much more than 0.3°C for a watt per square meter forcing. In other words, the aggregate effect of feedbacks is to be positive and enhance the so-called climate sensitivity relative to what it would otherwise be. Figure 1 below illustrates this.

The feedback factor is a value that is proportional to the no-feedback sensitivity value. It relates the fraction of the system output that is fed back into the original input, and takes on a value between 0 and 1 for positive feedbacks and less than 0 for negative feedbacks. It also means that the timescale it takes for Earth to reach a new equilibrium value is longer.

Feedback interactions

When multiple feedbacks operate, they can add together in rather odd ways. For instance, you might think that if you take a feedback that doubles the sensitivity to climate and another that halves it, they would cancel and bring you right back to the no-feedback sensitivity. You might also think that two feedbacks which each amplify the original forcing by 50% would add to double the no-feedback sensitivity. In fact, neither of these is the case, and the behavior emerges because multiple feedbacks interact with each other as well. One can imagine that if water vapor and the ice-albedo feedback are operating, the water vapor boost will mean more ice melt, which will mean further warming, more water vapor, still less ice, and so forth. Note that positive feedbacks do not inherently imply a runaway scenario; it just means that the final temperature change is higher than it would have been without the feedback being there.

Aside from just enhancing the temperature signal, the existence of feedbacks is really what allows for significant departures in planetary climate evolution from some reference state. It would not be possible, for example, to cover the whole planet with ice down to the tropics or to boil off Venus’ oceans without feedbacks kicking in and rearranging the climate system to be compatible with a completely new state. Although it is not feasible to trigger a runaway greenhouse like Venus even if we burned all the coal today, it should really be kept in mind that there’s nothing unique about our current climate except that we have adapted to it. It is very readily capable of changing fast and ending up in a completely new regime, and ruling such a scenario out cannot be done with high confidence.

Ice-Albedo feedback

The ice-albedo positive feedback arises because sea ice is less dense than its liquid form, it is more reflective, and the extent is highly sensitive to temperature. Water is somewhat unique in this regard since most solids tend to be denser than their liquid form, causing the ice to sink which would forbid an ice-albedo feedback. This means that if the planet warms the ratio of highly reflective ice to relatively high absorbing ocean and land surfaces will be altered. The key in the modern climate is the seasonality between absorption of solar radiation in the summer and the release of energy from the topmost part of the ocean into the lower atmosphere in the cooler months. Temperatures in the Arctic do not become substantially amplified in the summertime as you might expect in large part because a lot of energy is going into melt or evaporation. However, areas of open ocean water develop earlier in the melt season, raising the heat content of the ocean mixed layer and melting more ice. When the melt season is completed, there’s a lot of open water and heat in the mixed layer and large vertical heat transfer from the ocean to overlying air until the sea ice forms, resulting in a seasonal delay of warming from the radiation absorbed in the summer. This surface amplification of Arctic temperatures has emerged primarily in the autumn and winter and should progress into the spring and summer in the future (Serreze et al., 2009).

Lapse Rate Feedback

Why is the lapse rate (the temperature decline with height) important as a feedback? In the tropics, the temperature lapse rate is largely set by convection to stay near a moist adiabatic profile. In principle, this should decline in a warmer world resulting in the upper atmosphere warming more than the surface. This means that the bulk of the atmosphere radiates to space at a temperature warmer than it would have with no lapse rate change, and emission from warmer layers is more efficient than emission from cooler levels. This provides a negative feedback which partially compensates for the water vapor feedback. Interestingly, the two effects act in tango with each other and so the uncertainty in the water vapor+lapse rate feedback is smaller than the uncertainty in the individual terms.

In the context of anthropogenic global warming, all of these complex feedbacks and interactions end up boiling down to the question of how much warming you get from additional CO2 release into the atmosphere. The most recent IPCC AR4 assessment gives a range of about 2 to 4.5ºC at equilibrium. This is the so-called ‘Charney sensitivity’ which takes into account these fast feedbacks discussed above, as well as clouds which provide the greatest uncertainty in narrowing these estimates.

Estimates of this range have been based on not just GCM results, but constraints from observational data (the seasonal cycle, or volcanic eruptions) as well as the past climate record (Knutti and Hegerl (2008) provide a review). One problem is that high values of sensitivity are more difficult to rule out than low values, and some observations that are good for ruling out the low end do not constrain the high end very well. For example, volcanic eruptions display a non-linear relationship with the equilibrium sensitivity, so the peak in the probability distribution shifts only slightly for larger mean values of sensitivity.

Recently, some studies have expanded on this view to also include ‘slow feedbacks’ such as the response of ice sheets and vegetation that are important on hundreds of year timescales (Lunt et al 2010; Pagani et al 2010). These estimates show that the long-term warming should be even more than the Charney estimates, on the order of about 5°C.