A Box for Fluffy

For one of my classes this week, we started playing with Simile, a box modeling software whose "Evaluation" edition allows for fairly simple models to be built.

A box model is a simplified way of looking at a system, with boxes for reservoirs and fluxes to show what goes into and out of that reservoir. For example, a model of a lake would have a flux of the stream that feeds it going in, as well as one for rain, and would have one going out for evaporation. In complex systems, these are incredibly useful tools, and with software to do the calculations, you can see how a system will behave over time-- they are used to project into the future, and see what is likely to happen.

As with anything that purports to predict the future, there are some caveats. First and foremost, it is based on statistics; you can say that in a hundred years you will have a certain number of major floods, for example, but you can't say when they will happen. Second, a model is only as good as the data you put into it. If you know every single factor that feeds into a model with perfect accuracy, your model will be very, very good. But there are very few cases where that is true.

The first model we worked on was a wonderfully silly little thing involving, to quote the book, a "fairly fragile finicky freshwater fish" named Fluffy. Fluffy has to have flowing water to live, so we were designing a 'tank' for him that had water flowing in through the top and out through a hole in the bottom. If the water level went too low, Fluffy would die. If it got too high, it would run over the top and Fluffy would die. So we created a box model where we could vary the amount of water flowing in, to see where it would reach equilibrium.

For homework, we are working on something a little more complex: global temperture. Our models are going to be much, much simpler than the ones they use to predict climate change. The first one is based solely on the temperature of the oceans, which are, for the purposes of our model, assumed to be evenly distributed on the surface of the earth, at a consistent depth. The only reservoir is Earth's energy, the only inflow is solar radiation, and the only outflow is infrared radiation back out into space. This will remain the same, no matter how complex the model gets. For this model solar radiation doesn't change; in reality, it does. For this model, infrared radiation is based on the temperature of the ocean, which is based on the amount of energy in the Earth reservoir, which is based on solar radiation and infrared radiation into space. As the energy in the system rises, the temperature rises, but as the temperature rises, the amount of heat radiating out rises as well, which lowers the energy of the system. It will reach an equilibrium point.

Unfortunately, I am having trouble with my model; I think I put everything in correctly, but the system did not even out. I'm going to have to work on it some more. It gives me a new appreciation for the models they actually use in science; if I have difficulty with such a simple model, what must it take to make a really complex one work?

On the bright side, every new model that is proposed is better, more accurate than the last. We're getting better at it. And that means our predictions are getting more accurate. And that is always a good thing.