Thickening Clouds

As we describe in Solar Increase, we warmed up our simulated planet by increasing the incoming solar power by 10 W/m² every two thousand hours of simulated time. Starting from an initial value of 100 W/m², we increased the solar power to 1200 W/m² over the course of three weeks of our own time, which corresponds to the passage of over a million hours of simulated time. During the course of the simulation, we recorded the state of the atmospheric array every twenty hours, and these recordings constitute our measurements of the simulated atmosphere during the course of our simulated experiment.

In our pervious post we observed that some properties of the atmosphere, such as penetrating power, fluctuated greatly from one measurement to the next. In order to reduce the influence of these fluctuations, we took the average of the last 500 hours of measurements at each value of incoming solar power, and so obtained a value for each property at each solar power. The graph below shows how some of these properties vary with solar power.



Surface temperature increases hardly at all from 800 W/m² to 1200 W/m², and yet cloud cover increases steadily. How can it be that cloud cover increases when the surface temperature, which drives evaporation, hardly increases at all?

In our simulated evaporation cycle, precipitation beings with the formation of snow in air below temperature Tf_droplets. We have this parameter set to 268 K, which is five degrees below the freezing point of water. When solar power reaches 800 W/m², the average temperature of the tropopause has reached 268 K. Snow can form only in the colder clouds of the tropopause, and nowhere below the tropopause. Each time we increase the solar power, the surface temperature at first warms a little, but within a few hundred hours, this warming reaches the tropopause, where it further slows snow formation, and increases the cloud depth. With more sunlight being reflected back into space, the surface cools again until it is hardly warmer than it started. For solar powers greater than 800 W/m², an increase of 100 W/m² causes a substantial increase in cloud depth (roughly 0.5 mm), a slight increase in tropopause temperature (roughly 1 K), and an increase in surface temperature too small for us to detect (less than 0.3 K).

This profound suppression of warming by our simulation is not, however, a good representation of what would happen in the Earth's atmosphere. In our simulation, gas cells that contain clouds cannot rise above our top row of cells, so there is a limit to how much they can cool down. In the Earth's atmosphere, clouds can rise as far as they need to in order to cool down and produce snow rapidly. Thus our simulation is no longer realistic once its tropopause approaches the melting point of ice. We will therefore concentrate our attention upon the behavior of the simulation for solar powers less than 600 W/m², for which our simulated tropopause is well below the temperature required for the rapid formation of snow.

Solar Increase Continued

Today we continue our previous post without any preamble. The graph below shows how our simulated atmosphere warms up as we increase the solar power from one hundred to twelve hundred Watts per square meter. The green line shows how we increased the solar power over the course of twelve simulated years. The blue line shows how the power penetrating to the surface varied with time. The red line is the average temperature of the air resting upon the surface of our simulated planet.



At first, when the sky is clear, the solar power and the penetrating power are equal. But when the solar power reaches 300 W/m² clouds form and the penetrating power drops below the solar power. As solar power increases from 600 W/m² to 1200 W/m², fluctuations in the penetrating power double in their extent, but the average penetrating power appears to remain unchanged. The negative feedback generated by the evaporation cycle is so powerful that the surface air temperature increases by only a few degrees while we double the solar power.

The following screen shot shows the state of the simulation after two thousand hours at 1210 W/m². You can download this state as a text file SIC_1210W and load it into CC11 to watch the vigorous formation of clouds and descent of precipitation.



We now have the data we need to plot graphs of surface temperature and other properties of the simulation versus solar power.

Solar Increase

In our previous post we cooled down our simulated atmosphere by reducing the incoming solar power to 100 W/m². We gave the simulation plenty of time to reach equilibrium, and it arrived at the state RC_100W. The sky is clear. All the Sun's power penetrates to the surface. The surface temperature is −50°C.

We started CC11 from this equilibrium state. We increased the solar power to 110 W/m². After two thousand hours of simulated time, we increased the solar power to 130 W/m². We ran for another two thousand hours of simulated time, after which we increased the solar power again. The program performs the solar Increases automatically, so we were able to walk away from the computer and let the simulation run on its own.

The following graph shows surface temperature and solar power plotted against simulation time in weeks. The purpose of this plot is to determine if our simulation reaches equilibrium at each value of solar power.



Below 270 K, we see see the surface temperature is still increasing two thousand hours after the increases in solar power. Perhaps ten thousand hours at each step would be enough. But we are faced with a practical problem of execution time: it took one full week for us to obtain the graph above, with a computer dedicated to the job running continuously.

Once the surface temperature gets above 270 K, however, the evaporation cycle starts up and we see the effects of negative feedback. The changes that result from increases in solar power are markedly smaller and they establish themselves more quickly. Thus our program of solar Increase appears to be gradual enough for temperatures above 270 K, and these are the temperatures we are most interested in.

The following figure shows the equilibrium state of the atmosphere with 490 W/m² solar power. The running simulation shows vigorous cloud formation and precipitation. You can view this for yourself by downloading CC11, loading state SI_490 into the program, setting Q_sun to 490 in the configuration panel, and pressing Run.



By next week, we hope to have obtained the equilibrium state of our simulation for solar powers 100 W/m² all the way up to 900 W/m².

A Big Chill

In Negative Feeback, we increased our simulation's incoming solar power from 200 W/m² to 400 W/m² and saw the surface warm by only a 5°C. It turned out that the increasing solar power was almost entirely compensated for by an increase in cloud thickness, so that the power penetrating to the surface remained almost constant. We now ask ourselves, what will happen if we drop the solar power all the way down to 100 W/m²? Will our Radiating Clouds be able to stop the world from cooling?

We started our Circulating Cells program (CC11) in its equilibrium state for 350 W/m² solar power (RC_14000hr), and reduced the solar power to 100 W/m². The following graph shows surface air temperature and atmospheric cloud depth for the first five hundred hours.



In the first ten hours, the surface temperature drops by a few degrees. This is what we might expect during one of Earth's nights. After three hundred hours, the surface temperature has dropped to −5°C and there are hardly any clouds left in the sky. The following graph shows the world cooling down to a new, clear-sky equilibrium of −50°C. The graph also shows the solar power penetrating to the surface. Once the sky clears, the penetration is exactly equal to 100 W/m². We saved the final state of the atmosphere in RC_100W.



We conclude that 100 W/m² is insufficient solar power to warm the Earth above the freezing point of water, and therefore insufficient solar power to generate the cycle of evaporation and precipitation that stabilizes our climate.