 Now that we're dealing with an additional degree of freedom, we've now got latitude to deal with. We'll have to do a little bit of geometry. We have to take into account the geometry of Earth's tilt and the variation in incoming solar radiation at the top of the atmosphere as a function of latitude. So all those calculations, the geometry and the distribution of insulation as a function of latitude is calculated in some subroutines, and that is incorporated, of course, into our solution of the one-dimensional energy balance model. So let's actually run that model. It's simply run by me executing the command one dim ebm, one-dimensional energy balance model. Okay, and what it's done, first of all, it calculates the insulation at the top of the atmosphere as a function of latitude, where we, of course, have very high values of solar insulation near the equator, very low values near the pole. And it is now varying the solar constant. We're describing that through a solar multiplier. So it varies the solar constant from 40% larger than its current value, a multiplier of 1.4, all the way to 40% lower than its current value, a multiplier of 0.6, and a multiplier of 1 is the current value of the solar constant. What the red curve shows is what happens to the temperature of the Earth, the average temperature of the Earth, which is constructed by averaging over all the latitude bands, each of which has its own temperature, as you lower the solar constant from a value that's 40% larger than it is today to, let's say, the current day value. By the time you decrease the solar multiplier to the current day value, you get a temperature somewhere in the range of 15 degrees Celsius or so, which we know is, in fact, a pretty reasonable estimate of the average temperature of the Earth. And as we decrease it further, the temperature, of course, decreases, but something very interesting happens. Suddenly, we reach a critical point where the temperature drops quite rapidly. To well below freezing and, of course, continues to drop further as we lower the solar multiplier further. What's happening here is as Earth temperature is getting colder and colder, the latitude zones that are occupied by ice are spreading further and further towards the equator until eventually we reach a point where the entire Earth becomes covered with ice and the albedo plummets dramatically. Sorry, the albedo increases dramatically in Earth's temperature, therefore plummets dramatically. Now we have an ice-covered Earth. As we continue to lower the solar constant, it, of course, continues to cool, but the ice cover isn't changing. We have a frozen Earth. Now what happens if we instead start out with a solar constant that is 40% below the current value and continue to increase it? Well, that's what's shown by the blue curve. And something very interesting happens. As you start with a frozen ice-covered Earth, solar constant 40% lower than today. It, of course, warms as we increase the solar multiplier, but it's still ice-covered, it's still ice-covered, it's still ice-covered, and it actually remains ice-covered and the temperature remains very low. The average temperature of the Earth remains well below zero, all the way until we reach a solar constant of 30% larger than today. At that point, we now suddenly begin to melt away the ice fairly rapidly, and as soon as we do that, Earth's temperature increases very rapidly. Now we have an ice-free Earth and we're back where we begun, and if we increase the solar multiplier to 1.4, we are precisely where we started out.