Welcome back today we're going to discuss one of the what I think of as one of the most fascinating episodes in earth's history snowball earth. A period of time when the earth was completely covered with snow and ice. In doing this we're going to use a lot of the ideas we developed in the previous lecture, where we talked about energy balance. Energy flowing in from the sun. A form of visible light being radiated the infrared, and to see how we understand episodes like Snowball Earth in terms of energy balance. Looking ahead to the next lecture, which is now then going to apply these ideas to Venus and Mars. And look at how we could understand the history of those planets. But let's start first here on Earth today. We're going to begin by talking about albedo and what we call the Faint Sun problem. I want to introduce the idea of stable and unstable equilibria and look at how feedback can drive instability or keep things stable. And then finally turn back to the Earth and look at Snowball Earth and it's evolution. Let me remind you what we talked about last. When we look at energy flowing into the planet, we have energy coming from the sun. The energy coming from the sun is going to depend on the temperature of the sun. How big the star, the sun is, the temperature of the star, and the radius of the star, and it's distance. A hotter star will emit more radiation, a bigger star will emit more radiation, on the other hand one that's further away will heat a planet less. A very important term. In the amount of energy that reaches the surfaces for heating the planet is the albedo. If the the albedo is large, a lot of the sunlight that hits the surface is reflected back. If the albedo is low, the albedos zero, paint the planet completely black. All the energy that comes in is absorbed and goes to heating the planet. The flux in will be balanced over time by the flux out. The energy that goes into heating the planet surface is then radiated in the infrared. And the amount of radiation will go as the temperature of the planet to the fourth plow, power. Another important term that we talked about in the last lecture, was the optical depth of the atmosphere. If a lot of the energy radiated from the surface in the infrared. Is absorbed by water, carbon dioxide, methane in the atmosphere. That acts as a greenhouse and keeps the heat in and reduces the efficiency of radiation. We quantify that in our simple model by what we call the optical depth which we symbolize by the Greek letter Tau. The larger Tau is, the more radiation is kept in and it serves as a blanket that keeps the planet warmer. By increasing Tau, we decrease the amount of energy that gets out, so the planet temperature has to be higher for this term to balance this term. And in this equation here we have equated these two terms, solved for the planet temperature. And let me again just remind you of the dependencies here. The star is hotter, the planets hotter, more energy reaches the star, the planet. The star is bigger. A planet's hotter. Further away it's colder and now lets look at the terms that depend upon the properties of the planet itself. If the planet's surface has a higher albedo, so it reflects back more light the planet will be cooler. On the other hand, if the planets atmosphere has a lot of gases that absorb infrared radiation. Gases like water, carbon dioxide, methane, that increases the opacity. More carbon dioxide, more methane, the hotter the planet will be. In this, set of equations, and in our model, that we're using to describe the planet, this is a very simple model. We're describing the planet as having a single temperature everywhere. Having, being carried by a a single type of material, it's always covered by dirt or water or snow. A more complete model would be a three dimensional model of course. Where we worry about the energy flow across the surface, the winds, the effect of waves and water. But that's far beyond what we can write down on a single piece of paper here. And, is beyond the scope of what we hope to cover in the class, but this simple model as we'll see is powerful enough. To, be able to express a lot of the key ideas in the evolution of our own planet. And will give us a framework for thinking about other planets, first in our solar system. And then beyond as we move on in the course. Let's talk about different materials with different levels of reflectivity. Asphalt's very black. It has a very small albedo. Most of the light that hits asphalt is absorbed and goes into heat. And those of you who've stood on asphalt at a sunny day, realize that it gets very hot as it absorbs a lot of light. On the other hand, snow is highly reflective. Much of the visible light that hits snow, bounces right back up. Desert or dry land is about in the middle, about thirty to forty percent of the light that hits its surface reflects back and the rest is absorbed. I want to contrast the difference in albedos. Between ice and snow, and liquid water. Liquid water in an ocean is quite dark. A lot of the light that hits the ocean, 90% of it, since 10% bounces back, goes into heat. So a planet that's covered in water will absorb most of the light from the sun. When we look at the different planets, in our solar system some of the moons, there's an enormous range, in albedos. The moon, and Mercury are dark. While we see the moon in the night sky as a bright seemingly white object, it is only 12% of the sun's radiation that hits the moon that reflects back. That we see in reflected sunlight when we see moonlight in the night sky 88%. The difference between 1 and 1.2 of the light that strikes the moon is absorbed and goes into heating the moon. Venus is quite bright, .7. Albedo of .7 means that 70% of the light strikes Venus' surface, Venus' cloud layer, bounces back and is visible to us. The most reflective planet Enceladus or moon. Enceladus. Is a snow covered moon of Saturn. It is a remarkably bright planet in moon. It just reflects lots and lots of light. The earth averaged over the whole planet. Has an albedo, of about 0.367. So it absorbs, about 60 odd percent, of the light that strikes it. The rest reflects off. And, as we'll discuss in this lecture, the Earths albedo varies a great deal from place to place. As we mentioned just a few moments ago, the snow is very reflective. Ocean, forest, absorb a great deal of the light that strikes them. This will lead to different temperatures depending on, what the planets surface is covered by. A planet covered with forest, has a low albedo. It absorbs most of the light that strikes it from it's star. A planet covered with snow or a moon like Enceledus, has a very high albedo. It reflects most of the light that hits it. Another way of representing this equilibrium, between heat. Coming and heat going out, energy in and energy out, is a plot like this. Where would I show on this plot are two lines. This line here is the flux in, this, in this case here, the flux in, in my forest covered planet. So I'm plotting here flux in versus planet temperature. And since the planet temperature doesn't enter into this equation regardless of what the planet temperature is. When I express it this way the flux in is just a constant. The flux out goes as the planet temperature to the 4th power. So what's plotted with this curve, is the flux out the amount radiated by the planet as a function of the planets temperature. A hotter planet radiates more, a cooler planet radiates less. The equilibrium is where these two curves cross. Then the flux in balances the flux out. We set these two equal to each other. And that gives us the planet temperature, which for these values is about. A bit less than 300 degrees Kelvin, or pretty comfortable there on the warm side planet. With a mean temperature right here. On the other hand, if the planet was covered mostly by snow. The albedo is quite high. This term here the albedo's high is smaller that means the flux in is smaller that makes the two curves cross here. And for a snow covered planet, the equilibrium temperature is lower. Now, we should step back and think about when we're going to have a snow covered planet and when we're going to have a forest covered planet. A planet that's hot, is going to be covered with forest. A planet that's cold is going to be covered with snow. So, you know we need to. When we include that effect, we'll have have to make the planet's surface depend upon temperature. Now let's apply this graph as a way of understanding how the solution depends upon the properties of the star and the properties of the planet. It's another way of understanding this equation graphically. So today the surface temperature of our sun is about 5700 degrees. The early sun was colder. As stars evolve their composition changes. As they convert hydrogen to helium. And as they evolve and get older, they get warmer. Our current models of stellar evolution. These are model, we actually have a fair amount of faith in because they successfully reproduce properties of stars we see through our galaxy. Suggest that the early sun. Say three, four billion years ago was about eight percent colder than the sun today. Because the sun was eight percent colder and recall that the flux goes to the stars temperature to the fourth power. The energy coming from the sun hitting the earth was only 70% of what we get from the sun today. It's what's called the faint sun problem. We have a much colder sun. The sun's flux goes down from its value today, to a smaller value in the past. When we equate the flux in. To the flux out, this implies a much lower temperature. A temperature so cold that we would expect, based on that temperature, that there wouldn't be liquid water on the planet. It'd be cold enough that the planet became snow-covered. And once it becomes snow covered. As we discuss, the albedo goes up, that makes it even colder. So, one of the things that geologists studying the history of the earth struggle with. Is trying to understand why the early earth was as warm and as comfortable as it is today in many ways. The early earth had lots of liquid water. And was a good place for life. The way that we think we understand this, is if we look at this equation we can see that there are different terms that can balance out. Well the star's temperature for the early Earth was lower. We think that the optical depth, the amount of gas in the atmosphere, was higher. The early Earth did not have photosynthetic plants. Because of that, there probably was a higher abundance of carbon dioxide and perhaps methane in the atmosphere. Carbon dioxide and methane. Our greenhouse gasses. They raise the optical depth, they make the planet hotter. While, today we're concerned about the greenhouse gasses making the earth hotter than it is now. If we were around 3 billion years ago, we'd be grateful for this greenhouse effect because the greenhouse effect. Balanced out, the colder temperature of the sun's surface. Now, you can look at this equation and see how you can use this to, you know, ask questions. When you go to create a planet towards the end of the course, how you might want to put your planet in the habitable zone. You can balance, the albedo, the optical depth, the distance of the planet from the star. And choose values so that the planet's temperature at its surface is warm enough to have liquid water but not too hot to be covered with steam. And you can see that there's several different factors that's going to determine the habitability of a planet. This is why when we detect planets around other stars and just know the property of the star. And the distance between the star and the planet that's not really enough information. To be confident that we know whether a planet is habitable or not. Now let me turn and break at this point and have you think about this question. And then come back and rejoin me in a moment.
