## CLiMate And Weather

What is the difference between climate and weather? It is intuitively clear what the weather is—it is the day-to-day state of the atmosphere at some location, usually with particular reference to such things as temperature, windiness, and precipitation. It is also intuitively clear that when we speak of climate we wish to average out all these day-to-day fluctuations and refer to some kind of average of the weather. But what precisely? There is no ideal definition of climate, but a useful working notion is that climate is the statistics of the weather—the mean, the standard deviation, and so forth. However, this notion slightly begs the question of how we calculate the statistics—how do we take the mean, for example? And if climate is a time average of the weather, then how can climate have any temporal variability?

Although it is rather fanciful, it is useful to envision a thought experiment in which we take the ensemble average of the weather. Thus, we envision a large number of identical planet Earths, forced the same way, but each one started out in a slightly different way so that each has different weather. We could then unambiguously define the climate to be the average, along with other relevant statistical quantities like the variance, over the ensemble of planet Earths. If the forcing were to change, perhaps because the C02 levels in the planets were to increase, then the climate of the ensemble would also change.

The problem with this definition is that it is not practical, there is no such ensemble in reality. However, we can try to take our average in such a way that it mimics the ensemble average as closely as possible, and this way of proceeding will be useful to the extent that the weather and climate have different time- and space scales. We could then define climate as the average of the weather over a time period long enough so that weather fluctuations are averaged out but variability on longer timescales is still allowed. Weather typically varies on timescales of a few days to a few weeks, so that we might define climate as the average weather over time periods longer than a month, say. In practice, this time period is too short for many purposes because the monthly average temperature still fluctuates considerably, and a more common definition takes the climate to be the average (along with other statistical quantities) over a period of a few years, with the precise averaging period depending on what quantity is of interest. We might choose to take the average over a particular time of year—only over the winter months, for example, and so obtain a winter climatology. If we are interested in how climate varies across ice ages, then averaging over a period of centuries or even millennia might be appropriate, but if we are interested in whether climate changed over the course of the twentieth century, a much shorter period is obviously more appropriate.

The moral of the above discussion is that, although it is useful to think of the climate as some kind of average, there is no compact single definition of climate that is useful and appropriate for all purposes, and we are often better served by talking about the climate with reference to a particular timescale. Climate varies on more than one timescale—indeed, there may be no timescale on which we can say there is no climate variation.

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