Update: I have recently done a guest post on feedbacks at RealClimate. Part 1 is similar, but not the same as this post. I will not be doing a Part two on this site, instead it will be over at RC.
In light of recent attempts to describe the physics of climate change from first principles and in an accessible way (see Rasmus’ recent posts at RealClimate on the greenhouse effect and the troposphere) (also , here and here) it is worthwhile reviewing one of the greatest uncertainties surrounding climate change science and future predictions in a similar fashion: climate sensitivity and feedbacks. Feedbacks can behave in odd and counter-intuitive ways, some of which require some mathematics to really appreciate. In order to help facilitate an understanding for those who receive information at different levels of understanding, this will be a 2-part endeavor, where part 2 will be the more ‘technical version’ which may not necessarily be for everyone but will help demonstrate claims in part 1 quantitatively.
The most simple climate model features a globally-averaged outlook with a planet in radiative equilibrium (where the sunlight absorbed by a planet must equal the outgoing infrared radiation lost). This is the fundamental boundary condition that all planets must satisfy on long-term timescales, except in the case of gaseous planets where internal heating from gravitational contraction can also be significant. We also allow the troposphere of a planet to convect in order to establish a lapse rate (temperature decrease with altitude) somewhere near an appropriate adiabatic lapse rate (the lapse rate is set by convection in the tropics to stay near a moist adiabat, the controls in the mid-latitudes are a bit more complicated but usually the atmosphere is always somewhere between ~6 and 10 K / km decrease with height).
From here, climate scientists distinguish between radiative forcings and feedbacks, both of which involve various agents that can alter the global-mean radiative budget (and thus temperature) of a planet.
A forcing is a change in some variable that alters the planetary energy budget (e.g., sunlight, CO2, volcanic eruptions) by modifying the incoming sunlight, the ratio of absorbed to reflected sunlight, or by changing the rate of outgoing longwave radiation to space; however, forcings themselves can be considered to be independent of the current climate (e.g., the sun doesn’t really care what is happening on Earth, and aside from possible subtle effects of an ice sheets weight on the land surface or something like that, volcanic eruptions don’t really care what the current climate is like either). Radiative forcings will be expressed as a surface temperature change only if they are large enough or persistent enough to overcome the large heat capacity of the ocean.
Feedbacks, on the other hand, change only in response to an underlying climate trend and then further modify the radiative budget. This can amplify the initial forcing (positive feedback) or dampen it (negative feedback). The distinction also depends on the timescale; greenhouse gases for instance are generally feedbacks over millennia since the carbon cycle can easily be perturbed, by say, orbital changes while fossil fuel combustion is clearly a much faster process and is external to the climate system.
The most important feedback in the present-day climate is the nearly exponential increase in the water vapor mixing ratio in the upper atmosphere with global warming (which scales with the Clausius-Clapeyron relation to the extent relative humidity is conserved). Water vapor is a feedback since it is also a good greenhouse gas, yet the processes of evaporation, condensation, and precipitation occur on timescales of days to weeks and are highly temperature dependent. In informal terms, we say that a warmer atmosphere can ‘hold’ more water vapor. Caution should taken in popular and ill-defined statements like ‘water vapor is the most important greenhouse gas’ because while it is the largest single source of infrared opacity in the atmosphere (contributing to about 50% of the infrared absorption) the skeleton of the greenhouse effect is provided by CO2, CH4, and other such non-condensable greenhouse gases that do not precipitate from the atmosphere under Earthlike conditions. If you could remove all the water vapor and clouds from the atmosphere, the non-condensable greenhouse gases would be able to support a temperature nearly 10 K above the baseline “effective temperature” of 255 K that the Earth would have with no greenhouse effect (assuming constant albedo in all of this). However, removing all of the CO2 would also make you lose most of the water vapor feedback and substantially increase the surface albedo as the climate cooled, resulting in a collapse of the terrestrial greenhouse effect and a temperature even colder than the 255 K effective temperature. The distinction between forcing and feedback is therefore not merely semantics, it’s a fundamental difference in how geologists look at the basic causes of geologic timescale climate shifts (which is ultimately provided by CO2 mostly, probably methane on early Earth, and competing with the greenhouse effect on geologic timescales is a gradually brightening sun which has gone up by ~25% in luminosity since Earth’s formation) versus those factors which amplify the climate shifts and allow the magnitude of the past climate trends (and variability) to be explained.
Note also that the water vapor concentration typically increases more rapidly than evaporation or precipitation, an effect manifested as an increase in the mean residence time of a water vapor molecule in the atmosphere and a decrease in the rate of exchange between water in the lower atmosphere and the upper atmosphere (this is most readily detected in observations as a weakening of the tropical Walker circulation).
It is sometimes assumed that net positive feedbacks imply an unstable system, perhaps one that runs away until the Earth became as hot as the sun itself. To see why this need not be the case, at least in the climatological notion of a feedback, it is instructive to consider a scenario in which there are no feedbacks operating and the only global temperature change came through the applied radiative forcing. In this case, once the temperature changes the only thing that can restore the planet back to radiative equilibrium is the changed outgoing infrared energy (in the strict sense, this is a feedback, but climate scientists usually don’t group it with other feedbacks since it’s a pre-requisite to coming back to equilibrium). It can be shown (see part 2) that in this case the planet will warm or cool by about 0.27 °C for every W/m2 radiative forcing. In practice, the value is a bit higher than this owing to the fact that the atmosphere absorbs some finite amount of radiation, so with the 3.7 W/m2 forcing you get from a doubling of CO2 the result is a ~1.2°C temperature rise. The no-feedback response is obviously not an observable quantity since it is unphysical, but the precise magnitude will differ very little amongst various radiation models or methods used, and is due to different atmospheric properties (such as cloud treatment) and independent of the land surface physics.
Whether a feedback is positive or negative is defined relative to this ~0.30-0.31°C/(W/m2) baseline, the so-called ‘Planck response’. You can think of positive feedbacks as a series of gains where each gain is smaller than the last, so the series eventually converges without running away, yet still allowing a temperature change to exceed the Planck-only case. This is what is most relevant for modern-day Earth, but it is not inevitable. If the solar radiation absorbed by the planet is sufficiently high, it is possible that the temperature increase via the greenhouse effect from water vapor overcomes its ability to condense out when the pressure is high. Greenhouse gases effectively make a plot of the outgoing long wave radiation (OLR) vs. temperature more linear than the T4 dependence from the Stefan-Boltzmann law. If the optical depth due to water vapor is sufficiently deep it is possible for the OLR to be completely decoupled from the surface temperature (See figure) , something commonly known as the Simpson-Kombayashi-Ingersoll (SKI) limit after its discoverers. In the event that the absorbed solar radiation exceeds this threshold, the Earth will heat up and the OLR will not be able to increase in order for equilibrium to be established. In this case, the planet becomes incompatible with oceans and the runaway greenhouse process begins.
This runaway process is not something that can happen on Earth anytime soon. Evidence from past climates and GCM results indicate the actual temperature change will be the Planck response amplified by a factor of anywhere between 2 and 4, which implies a system where positive feedbacks are predominant over negative ones. To introduce another term, we can thus say the climate sensitivity (the ratio of the temperature change to the forcing) is higher than it otherwise would be.
Interaction of Feedbacks
When multiple feedbacks are present, they can add and interact in very strange ways. If you have two positive feedbacks for instance, each of which enhance the no-feedback sensitivity by an extra 50%, they will combine to enhance the no-feedack case by 300%! As another example, you may think that if you take a positive feedback which doubles the no-feedback temperature change, then take a negative feedback which halves the no-feedback temperature change, and add them together the net result will bring you right back to the Planck-only response. This is not actually the case, and the departure from intuition grows as the magnitudes of the feedbacks grow. The key here is that feedbacks work off of each other, so if you have two positive feedbacks of the same size, you can’t just multiply by 2 to get the total, since they will reinforce each other and further amplify the initial forcing.
Feedbacks can also allow two planets with the same solar insolation and the same greenhouse effect to have two radically different climates depending on the history it took to get to that point. Suppose we accept that the albedo of Earth is dependent upon temperature, which is the case as the ratio of highly reflective ice/snow extent to highly absorbing ocean/land extent changes in time. Cloud cover also plays a role.
Figure 2 shows three colored plots; the green line corresponds to a solar insolation value of S0=1370 W/m2 (with the blue and red lines, half and double that, already weighed by the ¼ geometrical cross-section factor) with a parametrized albedo that is bounded between 0.2 (warm climate) and 0.6 (cold climate) and is linearly interpolated between those values between T=263 and 283 K. The dashed black lines are the OLR curves for a no-greenhouse scenario (top curve) and one in which the greenhouse effect forces the planet to radiate at 60% efficiency for some given temperature. Where the curves intersect corresponds to a possible climate state. Note that the 0.5* S0 case is always locked in a cold-snowball regime with this greenhouse effect. For the modern solar insolation value, only the greenhouse effect scenario is consistent with a stable, warm climate. With no greenhouse effect the Earth would be in a snowball state. The 2* S0 scenario is always in the warm state however. Note however that because of the ice-albedo feedback, the ‘snowball planet’ case is a plausible mathematical solution with current solar and greenhouse parameters. If the Earth were magically thrown into a snowball state, it would not escape unless the greenhouse effect became substantially stronger or we waited for millions of years for the sun to brighten enough.
The key to understanding the ice-albedo feedback in the present day climate is the seasonality between absorbed solar radiation in the warm months and the release of heat by the ocean to the atmosphere in the cold months. Specifically, low-albedo open water will develop earlier in the melt season, and these areas will strongly absorb incoming sunlight. In the summer itself, there isn’t much surface-air amplification owing to a lot of energy being dedicated to melt or evaporation rather than temperature increase. At the close of the melt season, there is now higher heat content in the ocean mixed layer and a delay of sea ice formation in the cold months, increasing the vertical heat flux from the water to overlying air. This effect becomes more pronounced as the sea ice extent declines over the decades. Cloud cover also matters for the surface albedo feedback since they can efficiently scatter radiation and limit the effect of changed ice extent at the underlying surface, but also by enhancing downwelling infrared energy to the surface. The following figure shows how surface-air temperature anomalies evolve as a function of season over the next century, with a substantial summer and spring signal not emerging until later on, and an already Autumn amplification emerging.
The strength of Earth’s greenhouse is also sensitive to the strength of the lapse rate, going to zero greenhouse effect in an isothermal atmosphere where the surface temperature is equal to the emission temperature. It is expected that in the tropics, the moist adiabatic profile will shift toward warmer values so that the upper atmosphere warms more than the surface, thus reducing stability. The changed lapse rate is a feedback since now the bulk of the atmosphere radiates to space at a temperature warmer than it otherwise would have, which provides a cooling effect than can partially offset the water vapor feedback (or a warming effect that offsets a cooling water vapor feedback if the climate is in a cooling trend).
Cloud changes are also a feedback since they modulate the flow of energy on both the incoming and outgoing side of the energy budget. Because both of those terms make up very large effects of opposite magnitude, they nearly cancel in the present-day climate but small errors in the relative effects can lead to large implications for climate sensitivity. It is well accepted that cloud feedbacks make up the bulk of uncertainty amongst the feedbacks in estimates of climate sensitivity, particularly on the shortwave side (which is dominated by low clouds that control the albedo more than other kinds). The longwave component of the cloud feedback is generally always positive in models.
I will try to make Part 2 available within the week or so…stay tuned.