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.
Pierrehumbert, 2002
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.
Colored curves: Green = Solar constant = 1370 W/m2; Red = 2740 W/m2; blue = 685 W/m2 (values on y-axis are divided by 4 to account for spherical geometry of the Earth and the albedo parametrization described in post). Dashed black lines are two OLR curves for no greenhouse effect (top line) and one with a parametrized greenhouse effect
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.
NCAR CCSM3 depictions of: (a) near surface (2 m) temperature anomalies by month and year over the Arctic Ocean, and (b) latitude by height dependence of zonally-averaged October–March temperature anomalies for 2050–2059. Anomalies are relative to 1979–2007 means. From Serreze et al., 2009
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).
Held and Soden, 2006
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.
Climate Change 
but will help demonstrate claims in part 1 quantitatively, ok
and here is the humongous mass of raw DATA, that you need to do so?
and the ocean is a potential freezer, and the oceanic feedback is poorly understood
if the snowball earth effect as been alterate by some billions of worms
1,200 millions of cubic km of water at 4ºC are to be erased of your
equation
and a statement more logic than this must appear:
It can be shown ?? can?(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.
if you have big upsurges of cold deep ocean water the atmospheric budget is not so simplified..
… But what happens when more cold deep water comes to the surface, disrupting global climatic equilibrium? It tends to reduce the radiation emitted by the Earth to space. The water gains heat as a result.
The ~1.2 K per 3.7 W/m2 climate sensitivity absent feedbacks (besides the Planck response) is an equilibrium value. It doesn’t by itself describe the time it takes to approach equilibrium, or how much internal variability there may be about that equilibrium. The time it takes to approach equilibrium should be proportional to the product of the heat capacity of the system [J/(K*m2)] and the climate sensitivity [K/(W/m2)]
[J/(K*m2)] * [K/(W/m2)] = K*m2*J / (W*K*m2) = s,
divide by 31.5576 million s/year to get years (average with 1 leap year every four years).
though it is a bit more complex than that because the heat capacity available to the climate system depends on the time scale.
Remember that a freeze and thaw through a snowball state is a case of hysteresis. There are a range of solar + greenhouse gas forcing that can support two dramatically different equilibrium climates because the albedo feedback between those equilibria is so large.
But the heat capacity of a sustem is non measured in J/(K*m3)?
Heat capacity per unit area of the Earth will be J/(K*m2), contributions to that from any ‘layer’ can be found by multiplying the heat capacity per unit mass by the density and then by the thickness of that layer (averaged over the globe) (the thickness which exchanges heat with the climate system on the relevant timescale).
Latent heating contributions to the effective heat capacity would be calculated by taking the net mass (per unit area of the globe) that changes phase, per unit change in global average surface temperature (for example, the increase in atmospheric water vapor and decrease in frozen water per K of global warming), and multiplying that by the latent heat per unit mass for that phase change. Generally this is a small contribution; most of the heat capacity of the climate system on relevant timescales is in the ocean and comes from the specific heat of liquid water. The much greater mass of the solid Earth contributes very little on timescales typically relevant to climate change because of the immense time it takes for a thermal perturbation to penetrate even a modest distance through the crust (in other words, the climate system will generally already be very near equilibrium before most of that heat capacity comes into play).
Thanks, a must-read for all students of climate modelling.
Hmm. Is the following correct? As the plants increase the free energy of the isochoric (as determined by gravitation, as meteors increase the mass of earth, the sun decreases by blowing the energy created by the fusion, giving rise to a relatively stable orbit…) system earth, all sorts of things may happen, these are studied in the climate models. It really does not matter whether the chemical potential stored in the fossil fuels is abiogenic or not, using it to extract some transient benefit will increase the local entropy (chaotic behavior of molecules) of the said system. This in turn will occasionally manifest itself as more chaotic behaviour of the system, such as more extreme weather events (now I skipped somethings, didn’t I?) as the isochoricity prevents the materials of the system from escaping the system…
The power chemically stored by photosynthesis is quite small relative to the solar heating and LW and convective cooling, etc, and the heat released by burning fossil fuels is a tiny fraction of that. The much bigger effect of fossil fuel burning comes through the change in CO2 in the atmosphere, which alters the optical properties of the atmosphere, altering the radiative fluxes.
Chris – as usual, your post is very informative on a complex issue. I have a comment on one small part. You state, “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”
That appears to be true on a percentage basis – i.e., with warming, the percent increase in atmospheric precipitable water is greater than the percent increase in evaporation rate. However, on an absolute basis, I expect evaporation increases would exceed increases in atmospheric water. For a kilogram of water to be added to the atmosphere, at least one kilogram must evaporate – presumably more than one kg if at least some of the evaporated water is going to precipitate. For the absolute increase in evaporation to be less than the increase in atmospheric water, precipitation changes would not merely need to be small but would have to have a negative value. As far as I know, warming is not associated with a reduction in absolute precipitation rates but merely with an increase that is small in extent compared with the increase in atmospheric water.
Response: I’m not sure how you would even compare absolute numbers. Evaporation represents a flux of moisture into the atmosphere, which doesn’t even have the same units as the amount of water left behind– chris
Chris – What I had in mine were increases per unit time. The latter could either be a specified interval (e.g., change in evaporation and change in atmospheric water, both expressed as kg/hour) or alternatively, the interval, however long, required for equilibration at a higher temperature. In either case, a certain extra volume of water will have evaporated beyond the baseline volume that would have evaporated at an unchanged temperature, and a certain volume of water will have accumulated in the atmosphere beyond the baseline level that existed before the temperature change.
When I encountered the comparisons on RC and linked articles, I was puzzled (and I guess I still am) as to why comparisons made on a percentage basis had an important physical meaning, or why they should even be expected to be similar. A percentage increase uses a baseline value as a denominator. If the baseline rate of evaporation is very high, then even a small percentage increase can signify a substantial increase over baseline in the volume of water entering the atmosphere. By similar reasoning, if the baseline concentration of atmospheric water is a smaller number, even a modest increase in the volume entering the atmosphere can signify a large percentage change. Your point about units is well taken – evaporation rate and atmospheric concentration involve different units. However, unlike baseline values, changes can be expressed in similar units as I mentioned above.
To return to my puzzlement above, do you see any reason why percentage increases should be expected to be similar, or why it is surprising that they’re not, given that each is so highly dependent on the denominator representing a baseline value?
It makes sense to consider % changes because then you have a sense of how climate will change relative to what it is.
Evaporation and precipitation will both tend to increase as the global average surface temperature increases. Given that the atmospheric water increases, the changes in precipitation will tend to lag those of evaporation, so that evaporation increases first, water builds up in the atmosphere, and then approaches a new equilibrium as precipitation catches up to evaporation. The lag time is very small (I’d guess it would tend to be the residence time of atmospheric water itself, which is on the order of a week) , so with respect to the rate of evaporation and precipitation, they can be assumed to change together without significant error.
One could assume the precipitation has to begin on a higher altitude and with the turbulence (basically a non-directional phenomenon on the scale of troposphere) of the troposphere it takes a bit longer for water to reach there. I’ve no ref’s though.
@ Patrick 027
| September 7, 2010 at 11:33 am | September 9, 2010 at 11:15 pm |
Now I have understood, but I believe that it would be clearer to express the system heat capacity through (J/(Kg*K)/m2). Do you agree?
“The time it takes to approach equilibrium should be proportional … though it is a bit more complex than that because the heat capacity available to the climate system depends on the time scale.”
The used linear relationship seems too much oversimplified. First of all it doesn’t put in evidence that the temperature of equilibrium is reached asymptotically. Indeed, in the simplest case (process of the first order) it is lnT to be a linear function of time and heat capacity. It would be all right only if the timescale is very little and so it’s always justified a series expansion interrupted at the first degree term. But I think it isn’t our case.
J/(K m2) is better; it includes kg via the amount of kg per m2.
The time scale I was refering to was the time scale of exponential decay. For constant climate sensitivity and heat capacity, the system would decay toward equilibrium exponentially (after an instant shift in forcing; for an ongoing linear change in forcing over time, the system would tend to lag the forcing by the same time scale). Yes, that is oversimplified; it wasn’t intended to encompass the full reality. It could work as an approximation.
Suggestion for part 2: it might be helpful to point out (the origin of) the difference between the cloud feedback and the change in cloud forcing.
Chris
“Feedbacks, on the other hand, change only in response to an underlying climate trend and then further modify the radiative budget.”
I find the feedback abstraction could tend to mislead. I will explain via the Temperature-CO2 feedback loop.
Rising Temperatures tend to increase CO2 levels and CO2 levels tend to increase Temperatures hence Temperature-CO2 is a positive feedback loop.
In the unperturbed case it is not logical to pick one component as the forcing and one as the feedback. If Temperature is perturbed (Milankovitch cycles) then it might seem natural to view CO2 as a feedback as it acts to amplify the Temperature variation. If CO2 is perturbed (fossil fuel burning) then it might seem natural to view Temperature as the feedback as it acts to amplify the CO2 variation.
I feel it be important to always view the problem as symetric between the contributing components lest it leads to the “look CO2 lags Temperature during Milankovitch cycles so CO2 doesn’t drive Temperature” arguement.
On the basis that there is a Temperature-CO2 feedback loop I would expect CO2 to lag Temperature when the Temperature is externally driven and for Temperature to lag CO2 when it is the CO2 that is externally driven.
Now if I look at the Cloud-Temperature feedback loop. Which should I take as being externally driven? Probably both.
Now there is a lot of interest in this loop because it is critical in deciding the scale of the climatic sensitivity. At a short timescale it might be that the driver with the largest scale is stochastic cloud variance, in which case short duration experiments might find evidence that Clouds drive Temperature yet fail to find evidence that Temperatures drive Clouds. A long term experiment might find the converse.
Whether I am right or wrong about clouds is not the point. My point being that tagging some variables as forcings and some as feedbacks may tend to encourage a reader to believe that this is a distinction at the system feedback loop level, which I would say it isn’t. I find such attribution tends to blinker one to the possibility of richer system behaviour.
I have a particular interest in the non-CO2 driven, and particualrly the stochastic behaviour, of the climate system, so perhaps I tend to see all “feedbacks” as having a potential for being forcings and forcings such as CO2 as being feedbacks. There is a lot of what one might spercieve as being stochastic noise in the climate system. In the case of the Temperature record the “implied” stochastic flux forcing is large at short timescalse (sub decadal). From that point of view the rest of the system could be viewed as feedbacks to some hypothetical flux forcing.
A non-CO2 centric view, let us say a flux centric view would lead to one notable additional feedback in the “f” term, namely CO2 feedback. Now whereas this might seem irrelevant to present issues, ours is is possibly a rare eventuality. Perhaps for most of historic time CO2, lacking such a strong external driver, would be viewed more as a feedback. It is just this tendency to a happenstance perspective that gives me pause.
A much more general point, and one that few might agree with, is that in an environmental sense, the equlibrium sensitivity is a bit irrelevant. A more important issue being the transient dynamics of the climate system. Here I am thinking of response functions. I for one, do not wish us to find out what the equilibrium climatic sensitivity is. For that would mean that we have waited and seen. I am interested in knowing the short-run (0-100yr) response function is, for that is what will be of material importance in navigating our environment through the eye of the climate needle.
The sensitivity is the time integral of the response function from the perturbation till the infinite future and that is a long time to wait for evidential support. I view the sensitivity as unkowable at any relevant timescale, our chances of narrowing the range of uncertainty significantly before we have reaped whatever we have sown are I suspect remote. Given the long tail, precise knowledge of the sensitivity is unlikely to be of any consequence regarding the global response to emissions in the next 40 or 90 years. At the level of the environmentalist, I simply don’t get the fascination with sensitivity. I am much more interested in climatic responsivity.
Alex