While I was watching the news last month I realized the weather report was basically a discussion of solutions to PDE. In particular, I was paying attention to the hurricane season (which is not yet over) and the case of tropical cyclones.

• all weather is a solution to a partial differential equation. which one is used in weather prediction? This is likely to get very technical I was able to find several models:

  ECMWF, GFS, GFDL, UKMET, HWRF, NOGAPS etc. (as discussed here)

• In a sense I don't really care what the actual PDE just the general shape and qualitative features.

• We are studying the time evolution of some partial differential equation on the two-sphere: $\phi_t:S^2 \to S^2 $ which could be model by some type of random flow

• Observing vortex solutions and in particular we are interested in the location of the center, a "radius" metric of some kind, and a measure of the vorticity (which is a kind of index).

• Locally all hurricanes look about the same. Our prediction is going to be the Minkowski sum of a path and a circle of growing radius: $$ \phi_t \approx \phi_0(t) + t \, S^1 $$ This flow is mildly chaotic as we could predict the flow from one day to the next, but not over weeks or months.

These predictions took hours to achieve by clusters of computers. What enables us to approximate solutions to PDE in this common-sense way without actually solving anything?

9/18

9/25

Final