Balancing the Budget:
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.
First, I want to provide an example of model-based science, engineering, and design – the landing of the rover Curiosity on Mars. This effort was reliant upon simulations for the quantitative evaluation of the propulsion of rockets and the drag of the parachute. Computers were programmed to simulate and manage the workflow, the stage separation, and the coordination with the orbiters. The trajectories and orbits were calculated with computer models of the dynamics of objects moving in gravitational fields with atmospheric drag. Observations were made along the way, and they were used to correct errors that were discovered by the discrepancies between model predictions and observations. The validation of these calculations came with a landing on Mars, in a crater, surrounded by steep mountains. A landing where there was one and only one opportunity. A landing, which was the first real-world execution of these quantitative calculations. As best as I can tell the landing was in terrain with characteristics as expected. As best as I can tell, the landing was within a few meters or where the landing was planned. A few meters error – the models were wrong? Useless?
Figure 1: From NASA: “Curiosity Spotted on Parachute by Orbiter: NASA’s Curiosity rover and its parachute were spotted by NASA’s Mars Reconnaissance Orbiter as Curiosity descended to the surface on Aug. 5 PDT (Aug. 6 EDT). The High-Resolution Imaging Science Experiment (HiRISE) camera captured this image of Curiosity while the orbiter was listening to transmissions from the rover. Curiosity and its parachute are in the center of the white box.”
This is rocket science – what is rocket science? Rocket science is classical physics, what most physicists would consider simple physics, in a sequence of steps that in their totality are complex. Simple physics in a complex system – the same as a climate model.
Doing Science with Models 1.3: In the previous entry of this series I introduced the fact that many of the tasks of design, manufacturing, and accounting have been encoded as mathematical models executed by computers. And I made this promise: I will return to this idea of mathematical descriptions of objects later. Here we are.
Let’s start with something intuitive, money. The amount of money that I have today is equal to the amount I had yesterday plus the money I get minus the money I spend. In my class, I maintain that this simple equation
Today’s Money = Yesterday’s Money + Money I Get – Money I Spend
is symbolic of all of the mathematics that is required to have a scientific foundation to understand the Earth’s climate and climate change. This equation is, in a literal sense, a budget equation. Assume Yesterday’s Money is the amount in your checking account, you Get some money from working, and you Spend some money writing checks. From this information, you know the amount of money you have today by addition and subtraction. If you add it all up, and then compare with your bank statement, and you and the bank agree, then the budget balances.
There is a concept of classical physics called the conservation law, described by a conservation equation. The equation for money, above, is a conservation equation: the amount of money is conserved. That is you have a certain amount, and that amount changes either by getting money or spending money. If you don’t get or spend money, then the amount of money remains the same; it is conserved. There is nothing else. If you take a personal point of view, you can say that the money I have today is the money I had yesterday plus the money I produced minus the money I lost.
So I have used the words simple and classical to describe “physics.” One of the primary fields of physics is mechanics, which describes the way things move. This is what Isaac Newton described, and the basic idea is that if there are forces acting on an object with mass, then that object will move in response to those forces. A force we are all familiar with is gravity, which we usually think of as an object falling towards the Earth. This object could be Newton’s proverbial apple, rocks coming down the side of a mountain, or the mass of your body settling on your tired feet as you stand up. If we go back to the landing of the Curiosity rover described above, then when the parachute was slowing the landing module, there was gravity that was resisted by the drag of the atmosphere on the parachute. The study of forces and motions, as described in this paragraph, is called classical physics because it is old and describes the way the everyday objects that we can see move as well, as the way that planets and moons move. Classical stands in contrast with, for example, Einstein’s theory of relativity which is required when observing things that are moving very fast, for example, light.
Now back to the idea of the conservation equation, your checkbook. There are some things that are observed to be conserved. This observed conservation is so strong and so intuitive that we call these conservation laws. There are the laws of conservation of energy, conservation of mass, and conservation of momentum. Momentum describes how an object is moving: its mass, its speed, and its direction. I will start with the conservation of energy.
Let’s imagine that we are sitting out in space, perhaps on Mars, observing the Earth. Then we say
Earth’s energy today = Earth’s energy yesterday + energy gained – energy lost
The total energy of the Earth can be related to the temperature of the Earth. If there is more energy, then it is warmer. The primary way the Earth gains energy is through heating by the Sun. The Earth loses energy by emitting it back to space. If the energy lost is equal to the energy gained, then today’s energy is equal to yesterday’s energy. That is energy is constant, conserved; and, by inference, the temperature remains the same from one day to the next – from one year to the next. That is, the climate is stable. The energy budget is balanced.
The budget equation for your checkbook and the budget equation of the Earth’s energy look the same. Therefore, a model of the Earth’s climate can be viewed as an accountant’s spreadsheet. A climate model is the accounting of the Earth’s energy, and from that accounting, we conclude whether the Earth’s energy, temperature, is constant, increasing, or decreasing.