So far in Uncertainty Wednesday we have mostly built up concepts and ideas, with only one extended example.  Given the two massive hurricanes Harvey and Irma, the weather received a lot of attention, including the question to what extent the occurrence and/or severity of these storms lets us draw any conclusions about climate change. For that reason we will spend the next few Uncertainty Wednesdays looking at the weather using the ideas and concepts from the series. 

First, let’s put weather in the context of our framework, which consists of reality, explanations and observations. The reality in question is the complete state of the Earth’s atmosphere. The first thing to note here is that the atmosphere is not a closed system. It receives energy from outside (as a first approximation entirely from the sun, albeit much of that via heat radiated back by the Earth’s surface) and its mix of gases changes due to processes here on earth, such as photosynthesis and the burning of fossil fuels.

Second, let’s not that our set of observations about the state of the atmosphere and of the energy providing and gas changing processes is small relative to the scale of the system. This stands in sharp contrast to the many smaller examples used throughout the series where the system had only two states and we have a signal with two values. Here we have a system with a great many possible states and we have a lot less signal (e.g., measurement of say air pressure). It is also important to note though that how much signal we have available, has dramatically increased over time through technology, such as satellite imaging.

Third, weather is a classically deterministic system. Albeit one with explanations we do not fully understand. There as some explanations that are quite simple and well understood, such as air flowing from areas of high air pressure to low pressure causing wind. We also understand for instance how air above land and water heats up differentially also causing wind to form. But explanations for other phenomena, such as what goes into cloud formation and when clouds begin to rain, are less complete and less well understood.

Fourth, weather is a chaotic system as described in the introduction to the framework. As we saw there, small differences in observations will lead us to large differences in predictions about the future, especially the further out the future is.

Something that follows pretty much immediately from all of the above is: as we get more observations (and better computers for crunching them) our weather forecasts will get better. Here is a graph from an article that appeared in Nature which beautifully summarizes this:

We can see that forecasts have gotten much better between 1981and 2015 with a 3 day forecast (blue lines at top) going from about 80% accuracy to about 97.5% accuracy. We also see that accuracy drops off dramatically as the forecasts go further out and even though we se a big improvement in 10 day forecasts (grey lines at bottom), they are still pretty bad and have leveled out around 40% accuracy. Something else the chart shows is the convergence between Northern and Southern Hemisphere forecasts. Whereas the overall improvement is the sum of both better observations and better models, the convergence is largely the result of much better southern hemisphere data in the satellite age.