Last Uncertainty Wednesday I introduced how think about weather using the concepts we have developed in this series. We saw that our improved data collection and ability to process more complicated weather models has given us significantly improved predictions. We also learned that because of the chaotic nature of weather, despite our massive progress on short term forecasts we still do quite poorly for forecasts that go out further than a week.

Now a key question that we asked throughout this series is what we can learn about the reality of weather from the signals that we observe. Of particular interest here is the question whether the observations should us make more less inclined to believe in climate change, a topic that I have also covered extensively here on Continuations.

To get started on that we need to draw a distinction between weather and climate. The first sentence of the Wikipedia entry on climate provides an interesting approach here:

Climate is the statistics of weather over long periods of time.

The key words here is the “statistics” of weather. What is a statistic? It is a summary of observations, such as a minimum, or a maximum, or a total, or an average, or a variance.  

The weather is the temperature, rainfall, humidity, etc. on a given date and time. There is past weather, current weather and forecasts of future weather. The climate would then be summaries of these observations over longer periods of time. These periods don’t need to be contiguous. For instance, you could take the minimum, maximum and average temperatures for the month of July in New York City using data from July for say the last 10 years (or the last 100 years). 

So the weather are the raw observations and the climate are statistics computed from those raw observations? So the climate is simply a summary of the weather? That seems, well, not a very useful definition of climate.

The weakness of this definition is the result of a problem which I alluded to in my post about expected value, where I warned against confusing the sample mean with the expected value of the probability distribution.  A better definition of climate would be as follows:

Climate is the probability distribution of possible weather events.

The statistics of weather are supposed to help us understand what that probability distribution is.  With this definition, climate change becomes a shift in the probability distribution of weather events. And we begin to understand that inferring whether such a shift has indeed occurred is quite tricky. We have a bunch of hot years in a row. Is that just “dumb luck” (sort of like losing the coin toss at five matches in a row)? Or is it that the distribution has changed (the referee is tossing a biased coin)?  

Next Uncertainty Wednesday we will dig deeper into the relation between the sample mean and expected value using the context of weather and climate.