Considering the mathematics of planet earth, one tends to think first of direct applications of mathematics to areas like climate modeling. But MPE is a diverse subject, with respect to both applications and the mathematics itself. This was driven home to me at the recent SIAM Conference on Dynamical Systems in Snowbird, Utah, when I attended a session on “Supermodeling Climate.”
The application is simple enough to describe. There are about twenty global climate models, each differing slightly from the others in their handling of the subgrid physics. Typical codes discussed in the session have grid points spaced about 100 kilometers apart in the horizontal directions and about 40 vertical layers in the atmosphere. While the codes reach some general consensus on overall trends, they can differ in the specific values produced. The question is whether the models or codes could be combined in a way that would produce a more accurate result.
Perhaps one approach for thinking about this is to consider something familiar to anyone who watches summer weather forecasts in the U.S. – hurricane predictions. Weather forecasters often show a half-dozen different projected tracks for a hurricane – each based on a different model or computer code. Simply averaging the spatial locations at each time step would make little sense.
While climate models or computer codes are completely different from weather models used to predict hurricanes, the problems are similar. It isn’t sufficient to average the results of the computer runs. But perhaps an intelligent way could be found to combine the computer codes so that they would produce a more accurate result with a smaller band of uncertainty.
In the field of dynamical systems, it is known that chaotic systems can synchronize. The session that I attended considered whether researchers could couple models by taking a “synchronization view” of data assimilation. This involves dynamically adjusting coupling coefficients between models.
While the goal is to attempt this for climate models, work to date has focused on lower-order models (like the Lorenz system). If successful, this could lead to a new way of combining various models to obtain more accurate and reliable predictions. It’s one of many examples of mathematics finding useful applications in areas not originally envisioned.
More generally, “interactive ensembles” of different global climate models, using inter-model data assimilation, can produce more accurate results. An active area of research is how to best do this.
Society for Industrial and Applied Mathematics (SIAM)