Thursday, March 15, 2012

Anthropogenic Global Warming

The Anthropogenic Global Warming (AGW) hypothesis states that doubling the CO2 concentration of the Earth's atmosphere will raise the average surface temperature of the Earth by a minimum of 1.5°C, and more likely 3°C.

In our investigation of the absorption and emission of long-wave radiation by the Earth's atmosphere, we calculated that a sudden doubling of CO2 concentration would decrease the power the Earth radiates into space by 6.6 W/m2. We then estimated how much the Earth and its atmosphere would have to warm up in order to restore the heat radiated into space to its original value. We assumed there would be no significant change in cloud cover as a result of the warming, and we applied Stefan's Law to calculate how the heat radiated by the Earth and its atmosphere would increase. We found that the required increase in surface temperature would be around 1.6°C. If there were no change in cloud cover, then the heat arriving from the Sun would remain the same, and we could expect the Earth to warm up by 1.6°C so as to once again arrive at thermal equilibrium.

The AGW hypothesis states that in the event of the Earth warming, changes in cloud cover will be such as to amplify the warming we calculate using Stefan's Law. Here is an extract from today's entry on Global Warming at Wikipedia.

The main positive feedback in the climate system is the water vapor feedback. The main negative feedback is radiative cooling through the Stefan–Boltzmann law, which increases as the fourth power of temperature.

As the Earth warms up, water evaporates more quickly from the oceans. Almost all water that evaporates must turn into clouds before it returns to Earth. Water condensing directly onto grass in the morning is an exception to this rule, but the vast majority of water vapor will return only as rain or snow, and so must first take the form of a cloud.

Clouds absorb long-wave radiation emitted by the Earth's surface, so the Earth cannot radiate its heat directly into space. Instead, the clouds radiate into space and warm the Earth with back radiation. Thus increasing cloud cover means less heat radiated into space for the same surface temperature. This is the positive feedback referred to by the AGW hypothesis. The AGW climate models predict that this positive feedback will amplify the minimum 1.5°C warming caused by CO2 to roughly 3°C. Some say 2°C and other say 4°C, but all agree that the actual warming will be greater than 1.5°C.

We see this positive feedback in our Circulating Cells simulation, version CC11, which simulates the formation of clouds as well as their absorption and emission of long-wave radiation. The graph below shows a close-up of the behavior of the simulation in the neighborhood of its equilibrium point for 350 W/m2 solar power.

The blue line shows how the power that penetrates to the surface of our simulated planet varies with increasing surface temperature. The orange line shows how the total power escaping from our simulated planet increases with surface temperature. These two lines cross at a, where temperature is 288 K and total escaping power is 290 W/m2. Our simulated atmosphere absorbs 50% of long-wave radiation, which is an adequate approximation of our atmosphere with its current concentration of CO2 (roughly 330 ppm).

The green line is the same as the orange line, but displaced down by 6.6 W/m2, which is the amount by which we calculated the total power escaping from the Earth will decrease if we double CO2 concentration (to roughly 660 ppm). Thus the green line tells us the total escaping power at the same temperature if we were to double the CO2 concentration. Point b on the green line is 288 K, and the total escaping power is 283.4 W/m2.

The purple line shows how the total escaping power will increase from b if we assume the cloud cover is constant and use only Stefan's Law to determine the heat radiated into space by the surface and atmosphere. The red line shows the solar power penetrating to the surface if we assume the cloud cover is constant. With constant cloud cover, the penetrating solar power does not change.

The purple and red lines meet at c, which is 289.6 K, or 1.6°C above the previous equilibrium point. Thus our simulation shows us that the warming due to CO2 doubling, if we ignore changes in cloud cover, will be 1.6°C, which is consistent with our previous calculation.

The green line, however, is the simulation's calculation of the total escaping power for increasing surface temperature. We see that the heat radiated into space does not increase as quickly as Stefan's Law would lead us to expect. And the reason for that is precisely the reason quoted by the AGW hypothesis: increasing cloud cover is slowing down the radiation of heat into space. The green line and the red line intersect at d, which is 290.7 K, or 2.7°C above our original equilibrium temperature. This is the new equilibrium temperature of the planet surface if we double CO2 concentration and we assume that there will be no change in the solar power penetrating to the surface while the cloud cover increases.

But the solar power penetrating to the surface must decrease as cloud cover increases. Clouds reflect sunlight. Thick clouds reflect 90% of solar power back into space. Even thin, high clouds reflect 10%. Increasing cloud cover will decrease the solar power penetrating to the surface. That is why our blue line slopes downwards. This is negative feedback, which acts against the positive feedback described by the AGW theory. The blue line shows how the solar power penetrating to the surface decreases as our cloud cover increases.

The blue line and the green line intersect at e, which is the equilibrium point we arrive at after doubling the CO2 concentration and considering both the positive feedback of back-radiation and the negative feedback of solar reflection. The temperature at e is 288.9 K, which is 0.9°C above our original equilibrium temperature.

Thus our simulation shows how the negative feedback generated by clouds dominates their positive feedback, and suggests that the actual warming of the Earth's surface due to a doubling of CO2 will be closer to 0.9°C than the 3°C predicted by the AGW hypothesis.


  1. Thank you. It's great to see the conclusion of your work on this. I've followed it from the beginning and learned a great deal. Do you plan on continuing this line of work?

  2. You are most welcome, and thank you for your attention. It has been an enjoyable pursuit for me. Yes, I plan to continue, at a more relaxed pace, confirming the results of the simulation with other lines of argument, and possibly applying the simulation to the climates of other planets. I also wonder if, by adding surface snow and ice to the simulation, we can discover something about the way the climate switches between ice ages and warm ages, as it appears to do at random over hundreds of thousand of years. If you have any suggestions for what we should work on, I would be very glad to hear them.

  3. Kevan, you were perfectly right, my browser did not work well. I solved the setback coming to your conclusion.

    Congratulations! A very notable effort the yours. You confirm that the total atmospheric water+CO2 feedback is negative and therefore the Earth system is self regulating. No catastrophic runaway then.

    It would be nice if you were applying the simulation to other planets and I think that the need of the evaporation > condensation > rain > re-evaporation cycle obliges you to choose Venus, because Mars is cloudless.

    Allow me an amicable censure, justified by my white hair?

    You have the merit of thinking and arguing about climate like an engineer, but, sorry for you, on back radiation you act like an accountant! Fortunately, the final result does not change and so the yours is still a venial sin. :-)

    With great sympathy.


  4. Welcome back, Michele. I think I know what you mean about back radiation and accounting. I think the approximation of vertical radiation is similar to the assumption of perpendicular field lines within an electrical capacitor. If our array is wide and uniform, the net flux of long-wave radiation is up and down. For this reason and others, I decided that a simple up-down model, with either transparent or opaque clouds, would give us realistic behavior in a simulation with thirty columns of cells.

  5. This from Peter Newnam by e-mail:

    Dear Kevan,

    How about Ole Humlum (climate4you). He presents a measured approach to the issue:

    "The overall reflectance (albedo) of planet Earth is about 30 percent, meaning that about 30 percent of the incoming shortwave solar radiation is radiated back to space. If all clouds were removed, the global albedo would decrease to about 15 percent, and the amount of shortwave energy available for warming the planet surface would increase from 239 W/m2 to 288 W/m2 (Hartmann 1994). However, the longwave radiation would also be affected, with 266 W/m2 being emitted to space, compared to the present 234 W/m2 (Hartmann 1994). The net effect of removing all clouds would therefore still be an increase in net radiation of about 17 W/m2. So the global cloud cover has a clear overall cooling effect on the planet, even though the net effect of high and low clouds are opposite (see figure above). This is not a pure theoretical consideration, but is demonstrated by observations (see diagram below)."