Upon seeing liquid water at the bottom of a glass of crushed ice, most people would understand that the melting ice will not stop melting unless the temperature is reduced below freezing. The Greenland ice sheet has lost 5500 billion tons of water since 2000. It now occasionally rains even where the ice is thickest. Greenland ice is melting and it will not stop melting because Greenland temperatures are not decreasing. The earth’s energy imbalance with the sun is increasing. If heat were being added to the atmosphere at a steady rate, then global temperature would only be increasing at a constant rate. It is not. Heat is being added at an increasing rate. The earth has been and is warming at an accelerating rate.  This is the opposite of what is needed to stop climate change.     

Will clouds save us? It seems reasonable that higher evaporation rates from a warming climate would produce more clouds and that more clouds would resist further warming by reflecting more of incoming solar radiation. Another idea, originally proposed by the MIT professor Richard Lindzen, is that warming sea surface would concentrate tropical convection and reduce the type of clouds (Cirrus) that block infrared radiation from the earth. Either effect, i.e. reflecting more sunlight or allowing more thermal radiation to escape, would provide negative feedback to oppose global warming. NASA CERES satellites have provided measurements relevant to these two hypotheses. They have monitored Earth’s reflected short wave and emitted long wave radiation for both “all sky” and “clear sky” conditions since the year 2000. The “clear sky” condition means no clouds, so the effect of clouds can be inferred.

Albedo

The fraction of short-wave solar radiation reflected by the earth is called the albedo. A higher albedo means a brighter, but cooler, planet because what is not reflected is absorbed and heats the planet. The albedo for both “all sky” and “clear sky,” i.e. no clouds, conditions are shown below.

The albedo of “all sky” condition is 85% higher (brighter) than the “clear sky” condition. The albedo of clouds varies widely from 0.1 and 0.9, depending on density. This data indicates that on average the albedo of clouds is higher than the average albedo of earth surfaces. Clouds keep the earth cooler, but do they help reduce current warming? If a warming earth created more clouds of similar albedo, then “all sky” albedo should increase. However, albedo for both “all sky” and “clear sky” conditions has decreased since 2000. Below is the 12 month running averages of each divided by albedo in year 2000 to show the relative decrease.  

The decline in clear-sky albedo may reflect reduced surface reflectivity-such as less or dirtier ice-or a decrease in atmospheric aerosols. Aerosols are suspended particles that scatter incoming solar radiation back into space, contributing to earth’s reflectivity. However, the observed decrease decline in all-sky albedo has been relatively steeper than that of clear sky albedo, suggesting either a reduction in over all cloud coverage or a shift to less reflective clouds. For instance, if average cloud albedo remained constant at 0.36, the measured drop in all-sky albedo would imply that cloud cover decreased from 67.1 % in 2000 to 64.7% by the end of 2024.   The idea that an increase in clouds would counteract global warming is contradicted. Although the earth warmed since 2000, albedo has not increased. The effectiveness of clouds to reflect solar radiation has decreased.    

Effective Emissivity

The influence of clouds on Earth’s energy balance can be seen in their effect on effective emissivity, defined as the ratio of emitted longwave thermal radiation to the product of the Stefan-Boltzmann constant and global temperature raised to the fourth power. This ratio provides a measure of the greenhouse effect’s strength. Here is the effective emissivity for both clear-sky and all-sky conditions since 2000. Average global surface measurements were from Climate Reanalyzer.

Interestingly, all-sky effective emissivity is about 10% lower than clear-sky emissivity, meaning that clouds tend to enhance the greenhouse effect by trapping outgoing infrared radiation. Despite this, both all-sky and clear-sky emissivity have been declining since 2000, indicating an overall strengthening of the greenhouse effect.  See the relative running average for both below.

The decline in all-sky emissivity has been less steep than the decline in clear-sky emissivity—implying that clouds have partially offset the worsening greenhouse effect.

Clouds form around aerosols, which act as nucleation sites for water vapor. A reduction in atmospheric aerosols could be limiting cloud formation. Another contributing factor may be a shift in cloud type, as suggested by Lindzen’s “iris hypothesis,” in which warming reduces high cirrus cloud coverage and allows more thermal radiation to escape.

Combined Factor

The overall radiative effect of clouds can be assessed using the combined factor: the inverse of emissivity multiplied by one minus albedo. This combined factor represents how clouds influence both incoming solar reflection and outgoing thermal radiation.

The all-sky combined factor is about 6% lower than the clear-sky value, indicating that, on balance, clouds exert a cooling influence on the planet. The relative running average for both is shown below.

Both all-sky and clear-sky combined factors have been increasing since 2000, with all-sky rising slightly faster. This suggests that while clouds have slightly weakened their cooling role by reflecting less sunlight (reduced albedo), they have also helped to mitigate the strengthening greenhouse effect. Overall, these opposing changes in cloud behavior have nearly canceled each other out in terms of their net effect on global warming. In other words, the overall effect of clouds has been near neutral. Clouds are not saving us from global warming.

Seasonal Variation from Running Average

Without comment, here are the seasonal variations of albedo, effective emissivity, and combined factor.

The Paris Agreement of Dec. 2015

Several posts in Open Mind argue that the Paris Accord goals are unsatisfactory. For one, there is too much uncertainty in the pre industrial global temperature to use it as a basis. A better basis would be the best estimate of global temperature from a well characterized recent time frame such in 2015, the year of the Paris Agreement, or 1951 to 1980.  Another problem, however, is that global temperature is affected by the sun. Humans have no control of the sun.  A better climate metric would imply something over which humans have an influence.

This post explores alternate metrics, all based on comparing the earth, a very complicated planet, to a simple, hypothetical planet with the same rotation and orbit as earth, but with no atmosphere and with a black surface.

The reason to compare earth to a black planet is that the temperature of a black planet and its radiation energy budget can be easily calculated. If a black planet had a global temperature, T_BP, then the energy it would be radiating per unit area and unit time ( radiant exitance) would be given by the Sefan-Boltzmann Law.

where σ is the Stefan-Boltzmann constant and ETR is the magnitude of the emitted thermal radiation. The temperature, T, is in units of absolute temperature. A black planet would absorb all incoming solar energy. At equilibrium the ETR of a black planet would be equal to the incoming solar flux, IN. The equilibrium temperature of a black planet would be given by

Earth’s mean global temperature is complicated. It depends on the incoming solar flux and on conditions on earth that can be affected by human activity.   I define the black planet ratio, BPR, as

Note that this definition of BPR depends on how global temperature is measured or defined.  Here I will use the global mean surface air temperature at a height of 2 meters.

Conditions on Earth

The earth is not black. Plus, it has an atmosphere with clouds, aerosols, and a greenhouse effect. Since the year 2000 NASA has been using the CERES satellite and other instrument systems that “precisely track changes in Earth’s radiation budget with remarkable precision and accuracy.” CERES publishes the following parameters:

IN = Incoming solar flux

ETR = Emitted Thermal Radiation, Top of the atmosphere long wave flux – all sky

ASR = Absorbed Solar Radiation, (Incoming Solar flux) minus (Top of the atmosphere short wave flux – all sky)

Note two radiations emanating from earth. The radiation emanating from earth is not just heat radiation. The earth also reflects, i.e. does not absorb, nearly one third of the incoming solar radiation. The CERES scientists can separate the two components because reflected solar radiation has a much higher energy or shorter wave length than does the heat radiation. The absorbed solar radiation, ASR, equals the incoming flux minus the reflected short-wave flux. The earth’s reflectivity or albedo, α, can be defined by the following relation

The reflectivity of the earth depends on what is on the surface. Ice and snow are more reflective than water or forest. It also depends on what is in the atmosphere. Clouds and aerosols are more reflective than clear sky.  

The much longer wave radiation, ETR, is the emitted flux due to the earth’s heat. Just as for a black planet, it is proportional to the fourth power of global mean surface temperature, but the proportionality constant is less than the Stefan-Boltzmann constant. As shown below, the ratio of the earth’s ETR to that of a hypothetical black planet at the same temperature can be used to estimate how hot the earth will get, if all current conditions, including ASR, remain the same. In other words that ratio, ε, call it the earth’s effective emissivity, can be used to estimate the earth’s temperature set point.

The following shows ASR and ETR since 2000. (See Earth’s Energy Imbalance Chart in Global Temperature Report for 2023 posted by Robert Rohde.)

At equilibrium the emitted thermal radiation, ETR, will equal the absorbed solar radiation, ASR. If the emissivity ratio remains the same, then  

or, simplifying,

This is a powerful result because it directly shows that if the earth is in energy balance (emitted flux equals absorbed flux), the equilibrium temperature is equal to the current temperature. When the absorbed flux is greater than the emitted flux, the equilibrium temperature must be higher, and the earth will warm. The equilibrium temperature is where the earth is headed, but it is not necessarily the final temperature. There are feedback processes that could change the set point, either amplifying or counteracting the warming. Changes in earth’s energy budget – whether from increased greenhouse gases, changes in albedo, or other factors – will lead to changes in global temperature. The following graph shows how the equilibrium temperature has compared to global temperature since the year 2000. For global temperature I used the 2-meter surface temperature estimates of ECMWF Reanalysis version 5 (ERA5) from the Climate Reanalyzer web site. The global temperature and the CERES earth energy parameters have large seasonal dependencies. One way to avoid the large swings is to only plot yearly averages. Another method, one used by Robert Rhode, is to plot the one year moving average. Here is the 1 year moving average of global temperature from 1940 and the equilibrium temperature from 2000 to the present. There is a range of suggested values for preindustrial temperature. One, for example, is 0.87°C less than the average global temperature between 2006 and 2015. For this I calculate it as 286.7°K.

Equilibrium Temperature

Note that in the year 2000 the equilibrium temperature was only slightly higher than global temperature. Even though the planet was warming, it was close to being in equilibrium. Since then, the gap between the current temperature and equilibrium temperature has gradually increased by about 0.15°C per decade until in 2024 the gap is about 0.4°C. The earth cannot keep up with the rapidity of the changes. It is analogous to cooking a turkey. When the set point of the oven is increased quickly the temperature of the turkey goes up, but how fast it goes up depends on the size of the turkey. The equilibrium temperature is like the oven set point. The earth’s climate system is a very big turkey. It has a large heat capacitance, so it takes time. The graph shows that global temperature now is close to 1.5°C above preindustrial levels. The equilibrium temperature, however, has exceeded the 1.5°C goal since 2016. Just one year after the Paris Agreement the earth’s set point exceeded the goal.    

Comparing the equilibrium temperature with the previously defined Black Planet temperature, one gets

or, substituting the definitions for ε and α,

In summary

And

Arguably, BPR_eq is a better metric for a climate accord than global temperature.  It only depends on conditions on earth and directly indicates what factors need to be controlled to “set” the global temperature that will meet our goals. The following graph shows BPR since 1941 and BPR_eq since 2000. Again, all values are one year moving averages.  

  

 

Also shown in the graph is how BPR correlates (very well) with atmospheric CO_2.. This is essentially the same information as the first graph except that now it indicates the two controlling parameters, namely α and ε. BPR_eq is the earth’s set point. When the incoming solar flux, IN, is factored in, BPR_eq gives the earth’s set point.

Assuming an average value for IN, BPR_eq is well above the 1.5°C goal. Given current conditions, it is inevitable that 1.5°C will soon be exceeded.

It’s interesting to see by how much BPR_eq and the individual parameters which contribute to it have changed since 2000. The next graph shows BPR_eq, (1-α), and (1/ε) relative to their values in 2000.

The (1/ε) factor is a measure of the greenhouse effect. Since 2000 it has increased by 0.531%. The (1-α) factor is a measure of how much of the incoming solar energy is absorbed. In the same period, it has increased by 0.791%. The combined effect, namely BPR_eq , has increased by 1.33%. At least since 2000, the amount of heat being absorbed, the (1-α) factor, has been increasing faster than the amount of heat being retained by the extra greenhouse effect, the (1/ε) factor. The earth is reflecting less radiation. This could be due to less ice coverage or to fewer aerosols. Some causes are discussed in this reference by J. Hansen, et. al. Uh-Oh. Now What?

Seasonal Variation

In the previous graphs the seasonal variation was suppressed by plotting the 12-month running average. All the previous parameters, namely T, BPR, α, and ε show large seasonal variations. Climate scientists worry about a 1.5°C to 2°C change in global temperature from the beginning of the industrial period in 1760. Yet the 2-meter global air temperature varies by about 4°C every year from a minimum in mid-January to a maximum at the end of July! That is a huge change! 

Here is the 2-meter global air temperature for 2024.

Why does mean global temperature peak in the summer? The next graph compares the seasonal variation of the 2-meter global temperature, T, to the forth power with the incoming solar flux, IN. The earth’s orbit is an ellipse with a small eccentricity of about 0.0167. Incoming solar should be at a minimum when the earth is farthest from the sun, which is about July 5.

Incoming solar precisely follows the inverse square of the distance to the sun. One would think that global temperature would follow the seasonal dependence of the solar flux. It shows the opposite trend. Global temperature peaks when the earth is farthest from the sun. The seasonal variation of α and ε may help explain why. The following graph shows that variation.

The reflectivity or albedo, α, has a strong seasonal dependence with two peaks, the larger peak in December and January, the smaller peak in April and May. The emissivity factor, ε, has a smaller seasonal variation. Higher reflectivity means cooler temperature. Lower reflectivity means hotter temperature. This makes sense. In January the earth is tilted to expose more of reflective snow of Antarctica to the sun. In June Antarctica is tilted away. See two images of the earth from the DSCOVR satellite below. The first is from Jan. 15. The second is from June 28. By eye, the first image has higher average brightness. The southern hemisphere, which is tilted toward the sun in January, has more ocean. More ocean may mean more clouds.

In conclusion, I estimate that we reached a “setpoint” temperature of 1.5°C above preindustrial in 2018. We are well on our way to reaching a “setpoint,” i.e. a point of no return, of 2.0°C by 2032.