Looking Under the Cloak of Complexity:
This is a series of articles on models. In this series, I am trying to develop a way to build a foundation for non-scientists to feel comfortable about models and their use in scientific investigation.
Doing Science with Models 1.5: In this series I have used the example of balancing a checkbook to talk about the balance of energy that is at the center of the study of the Earth’s climate. In one of the earlier entries I wrote about the cloak of complexity that obscures climate science, and I made the statement that climate science was, in fact, simple physics (energy balance) but in a complex system. In this entry I want to explore complexity. I will stick to the budget equation for money.
Here again is the budget equation for the amount of money that I have.
Today’s Money = Yesterday’s Money + Money I Get – Money I Spend
The equation looks pretty simple, but … when I first started to think about how to write about models, rather than “Money I Get,” I wrote down “Income.” After I thought about that for a moment, I saw that the Money I Get might come from several places. If I use the model of a 1040 Tax Form, for instance, I might have income, and royalties, and gambling winnings. If I get lucky, I might just find some money. I’ll ignore the various methods of ill-gotten gains. The point is that the Money I Get can come from a number of places. It can get pretty complicated if, say, I have a couple of jobs, get paid for some piecework, sell my jars of homemade pickles, receive vouchers for health insurance, and hurry to collect every penny of Social Security that I can.
Then there is Money I Spend. That should probably have been Money I Get Rid Of, because I might drop some money, get robbed, or lose my retirement investment because I bought into a good-sounding geoengineering project to cool the planet using tunnels in the ocean. Again there are a lot of ways that things can get complex simply by the way I get and the way I get rid of money.
The comparison of the budget equation to the Earth’s climate and climate change is that there are many ways the Earth can gain energy or get rid of energy. Even if you say, “The Earth gets energy only from the Sun,” then if you think about how to count that, there is energy from particles like electrons and protons and there is energy from radiation, like visible light. Then there is that question point of view, are we really interested in how much of that energy reaches some boundary of Earth at the edge of Space, or are we interested in the amount of energy at the Earth’s surface? The answer is, scientifically, both of these places, but for the climate that matters to the humans on the surface of the Earth, we have to know what energy gets to surface of the Earth. So we start to add and subtract: We have the Sun’s energy at the top of the atmosphere minus the energy that goes into charging up the ionosphere minus the energy that breaks up oxygen atoms to make ozone minus the energy reflected back to space by clouds … you get the point. Simply calculating the budget of energy that gets to and goes away from the surface of the Earth is a challenging accounting problem.
Point of View: In the previous blog I wrote about the importance of point of view. What does the stick man on Simple Earth see?
Figure 1: Simple Earth 1: Some basic ingredients of the Earth’s climate.
First, let’s look into his accounts. He has a checking account to pay his utilities and a checking account to buy knitted sweaters for his terriers. There are a couple of savings accounts, retirement accounts, and because of his years as a highly paid scientist, a large mutual fund of ethically based, environmentally sensitive companies. And the end of every month, if there is money left in his utilities account, then he puts half of that into one of his savings accounts and the other half into that account for the terriers’ sweaters.
So let’s think about that transfer. From the point of view of the sweaters-for-terriers account, the transfer from the utilities account is Money the Terriers Get. It is a source of money – production. From the point of view of the utilities account, this is Money the Utilities Spent. From the point of view of the stick man, money is conserved; the total remains the same. Looking at the level of the accountant, the transfers between accounts are losses in one account and gains in another account, but the total worth remains the same.
Bringing it back to the stick man’s climate, he sees energy going from the ocean to the atmosphere (perhaps in a hurricane), energy going from the atmosphere to the land (perhaps blowing over trees), energy going from the ocean to land (surf on the beach), energy going from the atmosphere to ice (melting the glaciers in Glacier National Park). These are all transfers within the accounts of the Earth. When the winds make waves in the Gulf of Mexico, the atmosphere loses energy and the ocean gains an equal amount of energy. We build up more and more complexity, but we are still just balancing a budget.
There is one more source of complexity that I want to explore -Time. Let’s start with credit. One month, a simply fabulous terrier sweater appears on the web, and I charge it on my Usurious Bank credit card. Usurious lets me take years to pay and only charges me 5 percent per month. So now rather than What I Spend happening instantly, I have already spent some of the Money That I (will) Get. Of course, it costs me a little more than the actual money I paid for the terrier sweater; there is that interest rate. Every month, an extra bit of money is added to the debt that I will eventually have to pay.
We add complexity to our accounts by spreading out our income and expenses over time. If I were fortunate enough to lend money and receive interest, then someone else’s debt would look like income to me, but spread out over time. We do this all the time; we invest; we buy on credit; we buy items that we hope will become more valuable, like terrier sweaters of the Hapsburg’.
Where does this element of Time fit into the climate? Everywhere. Energy (heat) and carbon dioxide can stay in the ocean for a long time compared to how long they stay in the atmosphere. How long? That, too, is an issue of complexity, but think about the interest rate in that loan. If the interest rate goes up, it costs you more, and if you pay the same amount every month, then it takes you longer to pay off the debt. If you increase the Time that the atmosphere holds energy (heat) near the surface of the Earth, then it takes a little longer for that energy to get back to Space, to leave the Earth. Therefore, the surface of the Earth is warmer.
We change the transfers between accounts. It still, however, only requires us to balance the budget to understand what is happening.