So the naked planet model is an energy balance model. We have energy coming in at some rate, and energy flowing out at a rate, which depends on the temperature of the planet. So the temperature and the heat content are related to each other by means of the heat capacity. Which is how many jewels it takes to raise the temperature of one square meter of the surface by one degree kelvin. And that number depends on the water depth, because the water is the sort of heat sink. So if we change this value to smaller value, you'll see the heat capacity change. Because I'm calculating the heat capacity as a function of the water depth. The incoming energy is from sunlight, and the albedo reflective energy is lost sort of off the top. And then outgoing is epsilon sigma T to the fourth. So you can calculate, at any given temperature, what the heat flux out will be. The way this works is that you want to keep track of the heat content of the planet. So you start out at a temperature of zero, the heat content will be zero. But then you have heat coming in and heat, not so much heat going out. And so you need to calculate how many joules of energy per square meter there are in that column, after a timestep of a certain duration. And once you have the heat content, you can calculate what the temperature is each timestep. You have to be careful about the length of the timestep. Because if you take a timestep that's too short for the water depth, it will become numerically unstable and blow up, very exciting. So what we do here is make the timestep shorter, let's try 50 years. That's better but, it's still looking a little jittery there. So, right, right, ten years and oh, you can't see the time scale is changing there so. If we change the timestep, we get the same number of time steps. But, each one goes longer so the number of years is longer. So now if we look at the Python script for this, we see it's very short. We define parameters up top. In both cases, it's real important to keep close track of the units. So I just have comments here for units. In the spreadsheet I have actual cells that I use to put units in just to keep it. It's much easier to debug if you can kind of keep it straight. And then, here is a loop that goes through the timesteps. And here are some plotting lines that use this Python library matplotlib to make the plot that we see.