Planet Earth/2d. Daisy World and the Solar Energy Cycle

Incoming Solar Radiation from the Sun
Since 1978, NASA has employed a series of satellites that measure the amount of incoming solar radiation from the sun, measured as irradiance which is the amount of radiant flux received by a surface. The newest instrument NASA has deployed is the Total and Spectral Solar Irradiance Sensor-1 (TSIS-1) that was installed on the International Space Station in 2017. Since then, it has measured Earth’s solar irradiance at nearly a precise constant of 1,360.7 watts per meter2 which is known as the solar constant. This is equivalent to 23 60‑watt light bulbs arranged on a 1‑meter square title on the ceiling, or 1.36 kW per square meter of ceiling space.

To imagine lighting a 50 square meter room with the power of the sun’s irradiation for a single 12-hour day, would be 816 kW/hr, and cost about $110 a day on average, dependent on the local cost of electricity. Imagining this spread out over the surface of the Earth and it would cost 1,098 trillion dollars a day. That is a huge amount of energy striking the Earth, but not all of this energy makes it through the atmosphere, as much of the energy (up to 90%) gets absorbed or reflected back into space as the light interacts with gas particles in the atmosphere, with much of that solar irradiation getting reflected back into outer space. When Earth is viewed from Saturn, it appears like a bright star. This light is caused by the reflected light from the sun’s light striking Earth. Like a small shiny mirror left high on a giant mountain. This is why other planets in the Solar system appear to shine brightly in the night sky, they are reflecting sunlight back to Earth, and are not generating their own light source. This reflection of light is called albedo. A pure mirrored surface reflecting all light will have an albedo close to 1, while a pure black surface (a black body radiator) will have an albedo of 0, indicating all the light energy will be absorbed by its surface. This is why you get hot in a black shirt compared to a white shirt on sunny days, since the black shirt will absorb more of the sun’s light. All other surfaces will be somewhere along this range. Clouds typically have an albedo between 0.40 and 0.80, indicating between 40 and 80% of the sun’s light is reflected back into outer space. Open ocean water however, has an albedo of only 0.06, with only 6% of the light reflected back into outer space. However, if the water becomes frozen, ice has an albedo closer to white clouds, between 0.50 and 0.70.

The Young Faint Sun Paradox
In 1972, Carl Sagan and George Mullen published a paper in Science assessing the surface temperatures of Mars and Earth through time. They discussed a quandary regarding the early history of Earth’s surface temperatures. If the sun’s radiation was less than today’s solar radiation (say only 70%) would this not have caused Earth to have been a frozen planet for much of its early history? Geological evidence supports a liquid ocean early in Earth’s history, yet if the solar irradiation was much fainter than today, sea ice would have become more common with its higher albedo, spread across more of the surface area of the planet. The fainter solar irradiation would have been reflected back into space, resulting in Earth being locked up in ice, and completely frozen.

The faint sun paradox can be solved if, however, Earth had a different atmosphere than today that allowed more incoming solar irradiation at shorter wavelengths and blocked more outgoing solar irradiation at longer wavelengths.

An analogy of this would be a person working at a low-end job making $100 a week, but only spending $25, while another person working at a high-end job making $500 a week, but spending $450. The low-end worker would net $75 in savings a week, while the high-end worker will net only $50 in savings in a week. Indeed, geological evidence indicates that the early atmosphere of Earth lacked oxygen, which blocks incoming solar irradiation via an ozone layer, and contained abundant amounts of carbon dioxide which blocks long wave-length solar irradiation within the infra-red spectrum from leaving the Earth. Thus, more light was coming in, and less was leaving, resulting in a net warmer world than expected from just the total solar irradiation, which was fainter.

Daisy World
In 1983 after receiving heavy criticism for his concept of a Gaia Hypothesis, James Lovelock teamed up with Andrew Watson, an atmospheric scientist and global modeler to build a simple computer model to simulate how a simplified planet could regulate surface temperature through a dynamic negative feedback system to adjust to changes in solar irradiation. This model became known as the Daisy World model. The modeled planet contains only two types of life: black daisies with an albedo of 0, and white daisies with an albedo of 1, with a gray ground surface with an albedo of 0.5. Black daisies absorb all the incoming light, while white daisies reflect all the incoming light back into space. There is no atmosphere in the Daisy World, so we do not have to worry about absorption and reflection of light above the surface of the simple planet. As solar irradiation increases, black daisies become more abundant as they are able to absorb more of the sun’s energy, and quickly they become the prevalent life form of the planet. Since the planet is warming due to its surface having a lower albedo, quickly it becomes a hotter planet, which causes the white daisies to grow in abundance. As they do so, the world starts to reflect more of the sun light back into space, cooling the planet. Over time, the surface temperatures of the planet will reach an equilibrium and stabilize, so that it does not vary much despite changes in the amount of solar irradiation increasing. As the sun’s irradiation increases, it will be matched by an increase abundance of white daisies over black ones. Eventually, solar irradiation will increase to a point where white daisies are unable to survive on the hot portions of the planet, and they begin to die, revealing more of the gray surface of the planet, which absorbs half the light’s energy. As a result, the planet quickly starts to absorb more light, and quickly heats up, killing off all the daises and leaving a barren gray planet. The Daisy World illustrates how a planet can reach a dynamic equilibrium in regard to surface temperatures and how there are limits or tipping points in regard to these negative feedback systems. Such a simple model is extremely powerful in documenting how a self-regulating system works and the limitations of such regulating systems. Scientists, since this model was introduced in 1983, have greatly expanded the complexity of Daisy World models, by adding atmospheres, oceans and differing life forms, but ultimately, they all reveal a similar pattern of stabilization followed by a sudden collapse.

Water World
The Daisy World invokes some mental gymnastics as it ascribes life forms to a planet, but we can model an equally simple life-less planet; one more similar to an early Earth. A water world with a weak atmosphere. Just like the 1995 sci-fi action movie starring Kevin Costner, the Water World is just open ocean and contains no land. The surface of the ocean water has a low albedo of 0.06, which absorbs most of the incoming solar irradiation. As the sun’s solar irradiation increases and the surface temperatures of the Water World begin to heat up, the water reaches high enough temperatures that it begins to evaporate into a gas, resulting in an atmosphere of water, and with increasing temperatures, the atmosphere begins to form white clouds. These white clouds have a high albedo of 0.80 meaning more of the solar irradiation is reflected back into space before it can reach the ocean’s surface, and the planet begins to cool. Hence, just like in the Daisy World, the Water World can become a self-regulating system with an extended period of equilibrium. However, there is a very narrow tolerance here, because if the Water World gets too cooled down, then sea ice will form. Ice on the surface of the ocean with a high albedo of 0.70 is a positive feedback, meaning that if ice begins to cover the oceans, it will cause the Water World to cool down, which causes more ice to form on the surface of the Earth. In a Water World model, the collapse is toward a planet locked in ice—a Frozen World. There is evidence that early in Earth’s own history, the entire planet turned into a giant snow ball. With ever increasing solar irradiation a Frozen World will remain frozen, until the solar irradiation is high enough to begin to melt the ice to overcome the enhanced albedo of its frozen surface.

The world, at this point will quickly and suddenly return to a Water World again, although if solar irradiation continues to increase the oceans will eventually evaporate, despite increasing cloud cover and higher albedo, leaving behind dry land with an extremely thick heavy water atmosphere of clouds. Note that a heavy atmosphere of water clouds will trap more of the outgoing long-wave infra-red radiation, resulting in a positive feedback. The Water World will eventually become a hot Cloud World.



Examples of both very cold Frozen Worlds and very hot Cloud Worlds exist in the Solar System. Europa, one of the four Galilean moons of Jupiter is an example of Frozen World, with a permeant albedo of 0.67. The surface of Europa is locked under thick ice sheets. The moon orbits the giant planet of Jupiter which pulls and tugs on its ice-covered surface, producing gigantic cracks and fissures on the moon’s icy surface with an estimated average surface temperature of −171.15° Celsius or 102 on the Kelvin scale.

Venus, the second planet from the Sun is an example of a Cloud World, with its thick atmosphere, which traps the sun’s irradiation. In fact, the surface of Venus is the hottest place in the Solar System, besides the Sun, with a surface temperature of 462° Celsius or 737 on the Kelvin scale, nearly hot enough to melt rock, and this is despite an albedo slightly higher than that of Europa of around 0.69 to 0.76.

The Solar System contains both end states of Water Worlds, and Earth appears to be balanced in an ideal Energy Cycle, but as these simple computer models predict, Earth is not immune from these changes and can quickly tip into either a cold Frozen World like Europa or extremely hot Cloud World like Venus. Ultimately, as the sun increases its solar radiation with its eventual expansion, a more likely scenario for Earth is a Cloud World, and you just have to look at Venus to imagine the long-term very hot future of planet Earth.