Cloud feedback

A cloud feedback is a climate change feedback where some aspects of cloud characteristics (e.g. cloud cover, composition or height) are altered due to climate change, and these changes then further affect the Earth’s energy balance.^[1]: 2224 On their own, clouds are already an important part of the climate system, as they consist of liquid droplets and ice particles, which absorb infrared radiation and reflect visible solar radiation.^[2] Clouds at low altitudes have a stronger cooling effect, and those at high altitudes have a stronger warming effect. Altogether, clouds make the Earth cooler than it would have been without them.^[3]: 1022

During daytime, clouds scatter incoming shortwave radiation from the Sun due to their albedo, which results in substantial cooling

Clouds also absorb longwave radiation from the Earth's surface and reemit it back. This effect is often weaker than the albedo cooling, but it is active day and night

If climate change causes low-level cloud cover to become more widespread, then these clouds will increase planetary albedo and contribute to cooling, making the overall cloud feedback negative (one that slows down the warming). Vice versa, if they change in such a way that their warming effect increases relative to their cooling effect then the net cloud feedback, then the net cloud feedback will be positive and accelerate the warming, as clouds will be less reflective and trap more heat in the atmosphere.^[2]

There are many mechanisms by which cloud feedbacks occur. Most substantially, evidence points to climate change causing high clouds to rise in altitude (a positive feedback), the coverage of tropical low clouds to reduce (a positive feedback) and polar low clouds to become more reflective (a negative feedback).^[4] Aside from cloud responses to human-induced warming through greenhouse gases, the interaction of clouds with aerosol particles is known to affect cloud reflectivity,^[5][6] and may modulate the strength of cloud feedbacks.^[7] Cloud feedback processes have been represented in every major climate model from the 1980s onwards.^[8][9][10] Observations and climate model results now provide high confidence that the overall cloud feedback on climate change is positive.^[11]: 95

Cloud feedbacks are estimated using both observational data and climate models. Uncertainty in both these aspects - for example, incomplete observational data or uncertainty in the representation of processes in models mean that cloud feedback estimates differ substantially between models. Thus, models can simulate cloud feedback as very positive or only weakly positive, and these disagreements are the main reason why climate models can have substantial differences in transient climate response and climate sensitivity.^[3]: 975 In particular, a minority of the Coupled Model Intercomparison Project Phase 6 (CMIP6) models have made headlines before the publication of the IPCC Sixth Assessment Report (AR6) due to their high estimates of equilibrium climate sensitivity (ECS).^[12][13] This had occurred because they estimated cloud feedback as highly positive.^[14][15] Although those particular models were soon found to contradict both observations and paleoclimate evidence,^[16][17] it is suggested to be problematic if ruling out these 'hot' models solely based on ECS^[18] and care should be taken when weighting climate model ensembles by temperature alone.^[19]

One reason why constraining cloud feedbacks has been difficult is because humans affect clouds in another major way besides the warming from greenhouse gases. Small atmospheric sulfate particles, or aerosols, are generated due to the same sulfur-heavy air pollution which also causes acid rain, but they are also very reflective, to the point their concentrations in the atmosphere cause reductions in visible sunlight known as global dimming.^[20] These particles affect the clouds in multiple ways, mostly making them more reflective through aerosol-cloud interactions. This means that changes in clouds caused by aerosols can be confused for an evidence of negative cloud feedback, and separating the two effects has been difficult.^[21]

How clouds affect radiation and climate feedback

Details of how clouds interact with shortwave and longwave radiation at different atmospheric heights^[22]

Clouds have two major effects on the Earth's energy budget. Firstly, they reflect shortwave radiation from sunlight back to space due to their high albedo - a cooling effect for the Earth. Secondly, the condensed and frozen water contained inside them absorbs longwave radiation emitted by the Earth's surface. Clouds themselves also emit longwave radiation, both towards the surface and to space. Clouds are usually colder than the surface, so that they emit less energy upward. The net longwave effect is that the presence of clouds reduces the radiation emitted to space, i.e. a warming effect.^[23]

In meteorology, the difference in the radiation budget caused by clouds, relative to cloud-free conditions, is described as the cloud radiative effect (CRE).^[24] This is also sometimes referred to as cloud radiative forcing (CRF).^[25] However, since cloud changes are not normally considered an external forcing of climate, CRE is the most commonly used term.

This can be described by the equation

${\displaystyle CRE=R_{all-sky}-R_{clear-sky}}$

Where CRE is cloud radiative effect (W m^-2), R_all-sky is the radiation flux (W m^-2) under actual sky conditions, and R_clear-sky is a hypothetical radiation flux (W m^-2) computed for the identical temperature and moisture conditions but omitting the optical effects of clouds.^[26]

Cloud feedback is one of a number of climate feedbacks. Cloud feedback sums up the influence of all aspects of the cloud field on radiation, weighted by the sensitivity of each aspect to global average temperature change. In equation form,

${\displaystyle \lambda _{cloud}=\Sigma {\frac {\partial N}{\partial x_{cloud}}}{\frac {\partial x_{cloud}}{\partial T}}}$

where N is the Earth's net radiation (W m^-2), ${\displaystyle x_{cloud}}$ is the change in some aspect or characteristic of cloudiness (e.g. cloud cover, thickness, particle sizes, height), and T is the global mean near-surface air temperature (K).^[27]

Attribution of individual atmospheric component contributions to the greenhouse effect, separated into feedback and forcing categories (NASA)

On a hypothetical cloud-free Earth, water vapor would contribute 67% and CO₂ 24% of the greenhouse effect keeping the planet warmer than it would be without an atmosphere. In actual (all-sky) conditions, clouds contribute 25%, and their screening effect lowers the vapor and CO₂ contributions to 50% and 19% respectively.^[28] According to 1990 estimates, the presence of clouds reduces the outgoing longwave radiation by about 31 W/m². However, it also increases the global albedo from 15% to 30%, and this reduces the amount of solar radiation absorbed by the Earth by about 44 W/m². Thus, the observed global population of clouds contributes a net cooling of about 13 W/m².^[29] If all clouds were removed with all else remaining the same, the Earth would lose this much cooling and the global temperatures would increase.^[3]: 1022

Climate change increases the amount of water vapor in the atmosphere due to the Clausius–Clapeyron relation, in what is known as the water-vapor feedback.^[30] It also affects a range of cloud properties, such as their height, the typical distribution throughout the atmosphere, and cloud microphysics, such as the amount of water droplets held, all of which then affect clouds' radiative forcing.^[3]: 1023 Differences in those properties change the role of clouds in the Earth's energy budget. The name cloud feedback refers to this relationship between climate change, cloud properties, and clouds' radiative forcing.^[1]: 2224 Clouds also affect the magnitude of internally generated climate variability.^[31][32]

Cloud feedback mechanisms

Tropical Marine Low-Cloud Feedback

Tropical marine low clouds are of the cumulus and stratocumulus cloud types. The feedback of low clouds primarily arises from effects on shortwave radiation. Multiple lines of evidence, including global climate models, observations and high resolution process modelling, agree that the tropical low cloud feedback is likely positive.^[33]

High clouds

Examples of cloud feedback

High clouds in the tropics

High cloud feedback is defined as the change in radiative flux due to the response of high altitude clouds to warming.^[34] High clouds refer to clouds with a top pressure lower than 440 hPa (i.e. cloud tops above ~6500m) and include cirrus type clouds as well as cumulonimbus.^[35] The high cloud feedback is one part of the total cloud feedback which is an important variable in the climate system.^[34] The cloud feedback is the reason for a large part of the uncertainty in today's climate models and has a larger intermodel spread than any other radiative feedback.^[36]

The cloud feedback, and therefore also the high cloud feedback, has a longwave and a shortwave part which are summed up to get the total feedback. In the current climate the CRE is positive in the longwave and negative in the shortwave regime.^[37] The longwave part includes the interaction of the clouds with the longwave radiation coming from the earths surface. The longwave feedback is dominated by the altitude and temperature of the cloud top, leading currently to a positive feedback.^[34][38] The shortwave CRE on the other hand include the interaction of the clouds with the shortwave radiation coming directly from the sun. The shortwave feedback is dominated by cloud amount and the optical thickness leading currently to a weak negative shortwave feedback.^[34] Since the feedback strengths are depending on temperature, it is not clear that the longwave part will stay positive and the shortwave part negative as our climate changes.^[34]

For high clouds the feedback is currently positive in total, as the shortwave feedback is near zero and the longwave feedback is positive.^[34] It is together with the mid-level cloud feedback a larger contributor to the total cloud feedback than low clouds.^[36]

The calculation and modeling of high cloud feedback states a challenge and is an active field of research.^[34]

Physical Background

The high cloud feedback describes the change of radiation at the top of the atmosphere that is due to a change of high cloud properties.^[34]

A negative feedback reduces the effect of a forcing back towards an equilibrium state. The shortwave part of the high cloud feedback is negative, but very close to zero.^[34] It can be influenced e.g. by changes in the reflection of solar radiation by the high cloud tops and their amount.^[34] A positive feedback amplifies the effect of a forcing. The longwave part of the high cloud feedback is positive.^[34] This is due to the increased reduction of outgoing longwave radiation with rising temperatures, triggered by the changing amount of high clouds that absorb and reflect the terrestrial radiation.^[34] The total high cloud feedback is the sum of the longwave and shortwave feedback and is positive.^[37]

The high cloud properties which mainly influence the high cloud feedback are the cloud area fraction, the cloud top height and the optical depth.^[34] These cloud attributes, and therefore also the cloud feedback, are not spatially homogeneous.^[34] Hence the cloud feedback is mostly expressed as a global mean.^[34]

The cloud feedback is quantified by measuring the difference of the radiative flux between all-sky (with clouds) and clear-sky (without clouds).^[34] It remains a challenge to model the various radiative interactions and their effects on clouds without introducing biases or unwanted dependencies.^[36] To gain insight to the connections between a feedback parameter and a cloud property, the model would have to realistically represent all the physical processes influencing the clouds.^[36] Because of the coarse resolution of most climate models, they need to rely on cloud parameterizations, which brings about large uncertainties.^[36]

Longwave Feedback

The total longwave (LW) part of the high cloud feedback is positive.^[36] Contributions to the LW feedback stem from changes in cloud altitude, optical depth and cloud amount.

Cloud Altitude

The longwave feedback is dominated by the positive cloud altitude feedback^[38] which is mainly found in the tropics with the mechanisms being identical in the extra tropics.^[34] The LW radiation emitted by the high cloud tops is proportional to the temperature at the cloud top.^[34] The altitude of the high clouds changes with rising temperatures, due to the following mechanisms:^[34] Higher temperatures on the surface force the moisture to rise, which is fundamentally described by the Clausius Clapeyron equation.^[34][38] The altitude at which the radiative cooling is still effective is closely tied to the humidity and rises equally.^[34][38] The altitude, at which the radiative cooling becomes inefficient due to a lack of moisture, then determines the detrainment height of deep convection due to the mass conservation.^[34][38] The cloud top height therefore strongly depends on the surface temperature.^[34]

There are three theories on how the altitude and thus temperature depends on surface warming.^[34] The FAT (Fixed Anvil Temperature) hypothesis argues, that the isotherms shift upwards with global warming and the temperature at the cloud top stays therefore constant.^[39] This results in a positive feedback, since no more radiation is emitted while the surface temperature is rising.^[39] According to the FAT hypothesis this leads to a feedback of 0,27 W m${\displaystyle ^{-2}}$ K${\displaystyle ^{-1}}$.^[38] The second hypothesis called PHAT (Proportionally Higher Anvil Temperature) claims a smaller cloud feedback of 0.20 W m${\displaystyle ^{-2}}$ K${\displaystyle ^{-1}}$,^[38] due to a slight warming of the cloud tops which agrees better with observations.^[38] The static stability increases with higher surface temperatures in the upper troposphere and lets the clouds shift slightly to warmer temperatures.^[34] The third hypothesis is FAP (Fixed Anvil Pressure) which assumes a constant cloud top pressure with a warming climate, as if the cloud top does not move upwards.^[38] This results in a negative LW feedback, which does not agree with observations.^[38] It can be used to calculate the impact of the cloud height change on the LW feedback.^[38] Most models agree with the PHAT hypothesis which also agrees the most with observations.^[38]

Optical Depth

The optical depth feedback is determined by the increasing optical depth of the high clouds with rising temperatures.^[40] The optical depth increases the LW emission of the cloud, so that the contribution of the optical depth to the LW feedback is positive.^[40] At the same time, the shortwave contribution of increasing optical depth is negative and, because it is larger than the LW component, dominates. The overall optical depth feedback for high clouds is just below zero.^[34]

Cloud Amount

The area fraction of high clouds is also an important part of the LW feedback. A decrease in the area fraction would lead to a more negative feedback.^[34] Two mechanisms can lead to a decrease in the area fraction and therefore a negative feedback.^[34] The warming at the surface decreases the moist adiabat which leads to a decrease of the clear sky subsidence.^[41] Since the convective mass flux has to be equal to the clear sky subsidence it decreases as well and with it potentially the cloud area fraction.^[41] Another argument for a smaller area fraction is that the self-aggregation of clouds increases at higher temperatures.^[34] This would lead to smaller convective areas and larger dry areas which increase the radiative longwave cooling, resulting in a negative feedback.^[34] How the area fraction will change is however a topic of ongoing research and discussion.^[34] Since the area fraction of high clouds in models is sensitive, among others to cloud micro physics,^[34] there are also models which predict an increase in high cloud area fraction^[38] which would lead to a positive feedback.

Shortwave Feedback

The total shortwave (SW) part of the high cloud feedback is negative.

The impact of cloud area fraction on the shortwave feedback with warming is a topic of discussion, similar to the LW feedback.^[36] The SW high cloud feedback depends on the shot cloud area fraction due to its control of SW reflection. With a larger cloud area fraction more solar radiation can be reflected.^[38] A decreasing cloud fraction would lead to a positive SW feedback.^[36] It was found that the high cloud SW feedback is anticorrelated to the lapse rate feedback (the change of the temperature profile of the atmosphere with warming) which influences the cloud coverage.^[38] Therefore the high cloud SW feedback could be computed together with the lapse rate feedback to simplify the calculations in climate models. It is important to note, that this is a topic of ongoing discussion.^[38]

The impact of the cloud height and optical thickness on the SW feedback is negative. A higher optical thickness due to warming, changes fore example the cloud particle size and density which then changes the reflectivity of the cloud and therefore impacts the SW feedback.^[34]

Challenges

It is difficult to detect the reason for a change in the SW and LW radiation due to cloud feedback, because there are a lot of cloud responses which could be the cause for a specific radiation feedback.^[36] Furthermore is it difficult to not count in clear sky effects.^[36] There are techniques to decompose the cloud feedbacks in models and their triggers in detail by showing the cloud fraction as a function of cloud-top pressure and the optical depth of the cloud. In the GCM, which are mostly used, the main challenge is the parametrization of clouds, especially in coarse-resolution models. The characteristics of clouds need to be parametrized in such a way, that the different feedbacks and physical interactions are as correct as possible in order to decrease the uncertainty of the models.^[36]

Another challenge when dealing with (high) cloud feedbacks, is that the LW and SW part often cancel each other out, so that only a small total feedback is left.^[36] The positive and negative feedback parts are not neglectable, since they can change independent of one another with rising temperature.^[36]

Possible break-up of equatorial stratocumulus clouds

See also: Tipping points in the climate system

In 2019, a study employed a large eddy simulation model to estimate that equatorial stratocumulus clouds could break up and scatter when CO₂ levels rise above 1,200 ppm (almost three times higher than the current levels, and over 4 times greater than the preindustrial levels). The study estimated that this would cause a surface warming of about 8 °C (14 °F) globally and 10 °C (18 °F) in the subtropics, which would be in addition to at least 4 °C (7.2 °F) already caused by such CO₂ concentrations. In addition, stratocumulus clouds would not reform until the CO₂ concentrations drop to a much lower level.^[42] It was suggested that this finding could help explain past episodes of unusually rapid warming such as Paleocene-Eocene Thermal Maximum.^[43] In 2020, further work from the same authors revealed that in their large eddy simulation, this tipping point cannot be stopped with solar radiation modification: in a hypothetical scenario where very high CO₂ emissions continue for a long time but are offset with extensive solar radiation modification, the break-up of stratocumulus clouds is simply delayed until CO₂ concentrations hit 1,700 ppm, at which point it would still cause around 5 °C (9.0 °F) of unavoidable warming.^[44]

However, because large eddy simulation models are simpler and smaller-scale than the general circulation models used for climate projections, with limited representation of atmospheric processes like subsidence, this finding is currently considered speculative.^[45] Other scientists say that the model used in that study unrealistically extrapolates the behavior of small cloud areas onto all cloud decks, and that it is incapable of simulating anything other than a rapid transition, with some comparing it to "a knob with two settings".^[46] Additionally, CO₂ concentrations would only reach 1,200 ppm if the world follows Representative Concentration Pathway 8.5, which represents the highest possible greenhouse gas emission scenario and involves a massive expansion of coal infrastructure. In that case, 1,200 ppm would be passed shortly after 2100.^[45]

Representation in climate models

Examples of some effects of global warming that can amplify (positive feedbacks) or reduce (negative feedbacks) global warming^[47]

Climate models have represented clouds and cloud processes for a very long time. Cloud feedback was already a standard feature in climate models designed in the 1980s.^[8][9][10] However, the physics of clouds are very complex, so models often represent various types of clouds in different ways, and even small variations between models can lead to significant changes in temperature and precipitation response.^[9] Climate scientists devote a lot of effort to resolving this issue. This includes the Cloud Feedback Model Intercomparison Project (CFMIP), where models simulate cloud processes under different conditions and their output is compared with the observational data. (AR6 WG1, Ch1, 223) When the Intergovernmental Panel on Climate Change had published its Sixth Assessment Report (AR6) in 2021, the uncertainty range regarding cloud feedback strength became 50% smaller since the time of the AR5 in 2014.^[11]: 95

Tropical clouds are known to have a cooling effect, but it is uncertain whether it would become stronger or weaker in the future^[22]

Remaining uncertainty about cloud feedbacks in IPCC Sixth Assessment Report^[3]: 975

Feedback	Direction	Confidence
High-cloud altitude feedback	Positive	High
Tropical high-cloud amount feedback	Negative	Low
Subtropical marine low-cloud feedback	Positive	High
Land cloud feedback	Positive	Low
Mid-latitude cloud amount feedback	Positive	Medium
Extratropical cloud optical depth feedback	Small negative	Medium
Arctic cloud feedback	Small positive	Low
Net cloud feedback	Positive	High

This happened because of major improvements in the understanding of cloud behaviour over the subtropical oceans. As the result, there was high confidence that the overall cloud feedback is positive (contributes to warming).^[11]: 95 The AR6 value for cloud feedback is +0.42 [–0.10 to 0.94] W m–2 per every 1 °C (1.8 °F) in warming. This estimate is derived from multiple lines of evidence, including both models and observations.^[11]: 95 The tropical high-cloud amount feedback is the main remaining area for improvement. The only way total cloud feedback may still be slightly negative is if either this feedback, or the optical depth feedback in the Southern Ocean clouds is suddenly found to be "extremely large"; the probability of that is considered to be below 10%.^[3]: 975 As of 2024, most recent observations from the CALIPSO satellite instead indicate that the tropical cloud feedback is very weak.^[48][22]

In spite of these improvements, clouds remain the least well-understood climate feedback, and they are the main reason why models estimate differing values for equilibrium climate sensitivity (ECS). ECS is an estimate of long-term (multi-century) warming in response to a doubling in CO₂-equivalent greenhouse gas concentrations: if the future emissions are not low, it also becomes the most important factor for determining 21st century temperatures.^[11]: 95 In general, the current generation of gold-standard climate models, CMIP6, operates with larger climate sensitivity than the previous generation, and this is largely because cloud feedback is about 20% more positive than it was in CMIP5.^{[11]: 93 [14]}

However, the median cloud feedback is only slightly larger in CMIP6 than it was in CMIP5;^[11]: 95 the average is so much higher only because several "hot" models have much stronger cloud feedback and higher sensitivity than the rest.^{[11]: 93 [49]} Those models have a sensitivity of 5 °C (41 °F) and their presence had increased the median model sensitivity from 3.2 °C (37.8 °F) in CMIP5 to 3.7 °C (38.7 °F) in CMIP6.^[15] These model results had attracted considerable attention when they were first published in 2019, as they would have meant faster and more severe warming if they were accurate.^[12][13] It was soon found that the output of those "hot" models is inconsistent with both observations and paleoclimate evidence, so the consensus AR6 value for cloud feedback is smaller than the mean model output alone. The best estimate of climate sensitivity in AR6 is at 3 °C (37 °F), as this is in a better agreement with observations and paleoclimate findings.^{[11]: 93 [16][17]}

Role of aerosol and aerosol-cloud interaction

Air pollution, including from large-scale land clearing, has substantially increased the presence of aerosols in the atmosphere when compared to the preindustrial background levels. Different types of particles have different effects, and there is a variety of interactions in different atmospheric layers. Overall, they provide cooling, but complexity makes the exact strength of cooling very difficult to estimate.^[50]

Atmospheric aerosols—fine particles suspended in the air—affect cloud formation and properties, which also alters their impact on climate. While some aerosols, such as black carbon particles, make the clouds darker and thus contribute to warming,^[51] by far the strongest effect is from sulfates, which increase the number of cloud droplets, making the clouds more reflective, and helping them cool the climate more. These influences of aerosols on clouds are aerosol indirect effects, of which the famous one are the Twomey effect^[52] and the Albrecht effect^[53] through aerosols acting as cloud condensation nuclei (CCN). Less well understood indirect effects of aerosols are on the formation of ice, through variation in concentrations and types of ice nucleating particles. Aerosols also have an indirect effect on liquid water path, and determining it involves computationally heavy continuous calculations of evaporation and condensation within clouds. Climate models generally assume that aerosols increase liquid water path, which makes the clouds even more reflective.^[21] However, satellite observations taken in 2010s suggested that aerosols decreased liquid water path instead, and in 2018, this was reproduced in a model which integrated more complex cloud microphysics.^[54] Yet, 2019 research found that earlier satellite observations were biased by failing to account for the thickest, most water-heavy clouds naturally raining more and shedding more particulates: very strong aerosol cooling was seen when comparing clouds of the same thickness.^[55]

Moreover, large-scale observations can be confounded by changes in other atmospheric factors, like humidity: i.e. it was found that while post-1980 improvements in air quality would have reduced the number of clouds over the East Coast of the United States by around 20%, this was offset by the increase in relative humidity caused by atmospheric response to AMOC slowdown.^[56] Similarly, while the initial research looking at sulfates from the 2014–2015 eruption of Bárðarbunga found that they caused no change in liquid water path,^[57] it was later suggested that this finding was confounded by counteracting changes in humidity.^[56]

Visible ship tracks in the Northern Pacific, on 4 March 2009

To avoid confounders, many observations of aerosol effects focus on ship tracks, but post-2020 research found that visible ship tracks are a poor proxy for other clouds, and estimates derived from them overestimate aerosol cooling by as much as 200%.^[58] At the same time, other research found that the majority of ship tracks are "invisible" to satellites, meaning that the earlier research had underestimated aerosol cooling by overlooking them.^[59] Finally, 2023 research indicates that all climate models have underestimated sulfur emissions from volcanoes which occur in the background, outside of major eruptions, and so had consequently overestimated the cooling provided by anthropogenic aerosols, especially in the Arctic climate.^[60]

Early 2010s estimates of past and future anthropogenic global sulfur dioxide emissions, including the Representative Concentration Pathways. While no climate change scenario may reach Maximum Feasible Reductions (MFRs), all assume steep declines from today's levels. By 2019, sulfate emission reductions were confirmed to proceed at a very fast rate.^[61]

Estimates of how much aerosols affect cloud cooling are very important, because the amount of sulfate aerosols in the air had undergone dramatic changes in the recent decades. First, it had increased greatly from the 1950s to 1980s, largely due to the widespread burning of sulfur-heavy coal, which caused an observable reduction in visible sunlight that had been described as global dimming.^[20][62] Then, it started to decline substantially from the 1990s onwards and is expected to continue to decline in the future, due to the measures to combat acid rain and other impacts of air pollution.^[63] Consequently, the aerosols provided a considerable cooling effect which counteracted or "masked" some of the greenhouse effect from human emissions, and this effect had been declining as well, which contributed to acceleration of climate change.^[64]

Climate models do account for the presence of aerosols and their recent and future decline in their projections, and typically estimate that the cooling they provide in 2020s is similar to the warming from human-added atmospheric methane, meaning that simultaneous reductions in both would effectively cancel each other out.^[65] However, the existing uncertainty about aerosol-cloud interactions likewise introduces uncertainty into models, particularly when concerning predictions of changes in weather events over the regions with a poorer historical record of atmospheric observations.^{[66][62][67][68]} See also

• Cloud formation
• Earth's energy budget
• Fixed anvil temperature hypothesis