A "Model" of Climate

Suppose the real climate system is given by a pinball matrix for which we do not know the exact peg positions or the elasticity of the pegs (how far the ball rebounds after hitting a peg). We will try to understand the real climate system by building a matrix that looks as close to the real matrix as we can make it. We use pegs of material that gives rebounds as close as possible to the real matrix.

The trajectory through a given matrix is described by a single set of equations, so by extension, we say that the set of equations and peg positions is the "model" that describes the behavior of the matrix. This "model" can be used to predict the distribution of balls at the bottom (i.e., the climate). We test how well the model works by comparing its predicted results with outcomes from the real matrix. We might find in making this comparison that we need to adjust some constants or compensate for subtle influences (this is called "tuning the model"). This is analogous to using the climate model to predict the characteristics of the present climate. Once we have it working well for a given set of matrix conditions, we should change the real matrix slightly by moving a few pegs slightly (analogous to finding a different real climate, such as an ice-age climate), make comparable changes in the mathematical conditions in the model, and compare model and real outcomes. This is typically done by studying the climate that existed 15,000 years ago during the last ice age (we will discuss later how we get the observed conditions for comparison with model results).

If these "reality checks" prove successful, we feel confident that we can use the model to predict the effects of changing pegs to some configuration for which there are no observed results. This is analogous to making predictions of the effect of changing the "peg" (e.g., equations or conditions) representing increases of greenhouse gases.

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