What Is Climate? Really?

A post at RealClimate introduces a new app, which enables the user to take a detailed look at climate data. It also raises the age-old and oft confusing issue, just what is “climate” anyway? I’ll begin the new year with my own definition, in the hope that I can impart to all the knowledge of what climate really is.


The RealClimate post author (Rasmus Benestad) defines it this way:


For many people, “climate” may seem to be an abstract concept. I have had many conversations about climate, and then realised that people often have different interpretations. In my mind, climate is the same as weather statistics (which I realise can be quite abstract to many).


Frankly, I consider that a damn good definition, essentially the same as my own:


Climate is the probability density function of weather.

The catchy way I like to say it is:


Climate is the odds. Weather is the roll of the dice.

I notice that both Rasmus Benestad and I can (and probably have more than once) write “weather statitstics” to mean the full probability structure: the odds, all the odds, and nothing but the odds — then be surprised because someone thinks that it “implies average weather.” Not an idiot, mind you, but someone who knows that climate change is so much more than just a change of the average, maybe is even keenly aware of how the change in extreme events is one of the crucial aspects. What we have here, is failure to communicate.

Because a reader objects, saying


To my mind you fell at the first fence. You wrote:
“In my mind, climate is the same as weather statistics (which I realise can be quite abstract to many).”

to me that implies average weather, which is what most meteorologist believe. But the dangers of climate change are not that the temperature will rise by 1.5C on average. The danger is from the more extreme events caused by the temperature rise, which will lead to wild fires and heat waves. The average rise in sea level of 10cm will not flood many places. It is the the storm surges 10cm higher which will cause disaster, just as it did in New Orleans. If sea level had only risen by the average, New Orleans would never have been flooded.

I don’t agree that weather statistics “implies average weather” to the exclusion of “the more extreme events.” I think it specifically includes the entire change of probabilities, which is why we call it “weather statistics” rather than just “average weather.” Certainly the average is the most prominent, one could even say most important, single statistic, but there are lots and lots of others which capture those extreme events.

But when intelligent people equate “weather statistics” with “average weather,” we can have failure to communicate. We need to stop calling it “weather statistics” and use a better description. The one I like is, “the odds” — it’s much friendlier and more familiar than “probability density function.”


The association of climate change with a change of the average, may be rooted in the fact that the most common (and probably easiest) way to show that climate has changed, is to show a change in the average that’s more than just random fluctuation. That’s because if the odds don’t change then the mean value won’t change. Just can’t happen. A change in the average which is “statistically significant” reveals a change in the mean, and a change in the mean, means somehow the odds have changed, which is exactly what climate change is.

And it’s so easy to show a change in the mean. The classic case is yearly global average temperature anomaly (I’ll use the data from NASA):

The change in average value is definitely statistically significant, and visually, it packs quite a punch. The world is getting hotter.

But, as has been emphasized and repeated, the change in the average isn’t the only aspect of climate change — it’s just one of the most obvious.


If climate is some abstract notion of “statistics” beyond just the average, if it’s a “probability density function” which is another name for “the odds” (by which I mean, all the odds for every possibility), then what does it really look like? To put it in more sensible terms, how can we show it in a way which conveys all the odds, not just the averages?

I think such views have to be tailored to what is being studied. Consider, for instance, the daily high temperature in the city of Moscow, Russia during the month of July, and begin by looking for a change in the average. I can average the high temperatures over the entire month of July, for each and every July from 1949 through 2017, and get this:

The red line is a trend estimate, and it is statistically significant (there are other ways to estimate the trend which also confirm its statistical significance). This means that the trend is not flat, i.e. the average is changing in a statistically significant way so the actual mean value is changing. Hence the odds are changing, and voila, we have climate change.

But that’s just the average. We can look at all the probabilities, for all possibilities, using something called a histogram.

We begin by dividing the range of temperatures into slots, or “bins”; I chose bins 1°C wide each. Then we count how often the value is within each bin. Finally, we divide by the total number of days we’ve observed to estimate the probability that the daily high temperature in Moscow during July will be within that bin. We can plot all these estimates in a bar graph, to show the histogram.

These are just estimates mind you, and the histogram itself is an estimate of the probability density function (i.e., the odds). It’s what climate is.

The smooth solid blue line is another estimate of the probability density function, using the same data. It assumes that the data follow the normal probability distribution (the familiar “bell curve” probability function), which indeed it does very closely. This too is only an estimate (perhaps an even better estimate than the histogram itself).

There’s climate! But it doesn’t show us climate change like the graph of monthly averages for each year did. How might we get that onto a graph like this?

One thing we can do is split the available data into two pieces: everything before the year 2000, and everything since. Then we can make a histogram (and a smooth line) for each piece separately, and plot them on the same graph (pre-2000 in blue, post-2000 in red):

This succeeds in showing the details of climate (at least as far as daily high temperature is concerned), and how it has changed between the last few decades and the half-century before that.

In my opinion, this graph is quite effective. It makes clear that the average has changed, but it also highlights that the odds of extreme events have changed dramatically. Days at 30°C or above (damn hot by Moscow standards) are now twice as common as they used to be. Days at 35°C and above, which used to be practically unheard-of, are now an uncommon but regular occurence.

The graph is also visually stimulating (in my opinion) and makes good use of color (quite eye-catching I think). I have no idea how the color-blind might be hampered by it.


Climate change denial is on its death-bed. That’s not because of the savvy messaging skillz of scientists and advocates, but because of the onslaught of climate-related disasters in the U.S. and around the world.

Not that scientists and advocates haven’t helped. They have countered much of the propaganda from fossil fuel interests and ideologues, as well as informed the public of the essential nature of the problem. But its urgency, and the severity of the danger, hasn’t really gotten through to the mass of people.

Now that people are becoming more aware, they’re hungry for a deeper understanding of what the issues are. We can help. But to do it effectively, we need to take a new approach to telling the story of science. We’re not just targeting the geeks, or the hardcore interested who might watch a series like Cosmos, we’re now doing science communication for everybody, including the farmer or factory worker who doesn’t give a rat’s ass about the spotted tree owl, but knows that this is some important stuff. Hurricanes and heat waves and wildfires and droughts and floods — some important stuff.

To help the truly new get some background which doesn’t overwhelm or bore them, but which won’t oversimplify so much as to neuter the message, is a challenge. Some of the things we need to do, may include:

  • #1: use a better description of what climate is.
  • #2: communicate the tremendous importance of changing the odds of extreme events (related to #1 above).
  • #3: devise the best (most eye-catching and informative) graphics to convey these messages.

    As for #1, I’m quite fond of my own description. Climate is the odds. Weather is the roll of the dice.


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  • 14 responses to “What Is Climate? Really?

    1. Susan Anderson

      I always liked Heidi Cullen’s “Climate is weather over space and time.”

      I usually put a bit more, sometimes mentioning trends, “weather over space (whole globe and its atmosphere) and time (several decades)”

    2. David B. Benson

      And climate change is a die with more spots.

    3. Climate is the man, not the dog.

      Which is a reference to a [Youtube ?] video made by Neil D. G Tyson where he is walking a dog on the beach and he [Neil] is walking more or less in a straight line whilst the dog, restrained by a long leash is wandering left and right led by his nose [ or her nose].
      damned if i can find the video, but maybe someone else can.


    4. Tyson and the dog.

    5. “The graph is also visually stimulating (in my opinion) and makes good use of color (quite eye-catching I think). I have no idea how the color-blind might be hampered by it.”

      I think it works well with most forms of anomalous color vision. There’s a nice online test page here, where you can upload a graphic and see what it looks like under various color vision scenarios:

      https://www.color-blindness.com/coblis-color-blindness-simulator/

      Your graphic works pretty well for all of them. Obviously it looks different, but the distinction between the two histograms is pretty clear.

      Thanks for mentioning this issue, BTW.

      • I’m red/green colour blind, and often enough (to comment) find some graphs tricky to see. For instance:

        http://www.woodfortrees.org/plot/gistemp/from:1900/mean:12/plot/hadcrut4gl/from:1900/mean:12/offset:0.4

        I’d need reassuring that the red line is below.

        I see the histogram fine. But this graph:

        https://tamino.files.wordpress.com/2018/12/reg4_smooth.jpg?w=500&h=333

        Can’t tell New England from Mid-Atlantic South on the plot – can just make out the colour difference in the legend.

        I was chatting in a climate forum some time back and a commenter spent an hour posting up the same graphs in different colours, curious to know what I could and couldn’t see. It was one of the most generous online encounters I’ve experienced. There were quite a few versions that were impossible for me to differentiate.

        It might be worth investigating what colours trouble the least people, for making graphs. Colour-blindness of various types are very common and little mentioned (because what can you do?).

        Thanks for the link, J. You can see what I see if you click on Deuteranomaly.

      • There are color schemes for use with certain types of color blindness which my colleagues and I have used for lecture materials when we’ve had color blind students.

        • For spaghetti plots and the like, quite often normally-functioning color vision isn’t enough, either–between teeny-tiny reference patches on the legends and the perceptual shifts arising from close juxtapositions of various colors in the plots themselves, often enough I’ve just had to give up trying to figure it out.

          And why wft–which I love to use in so many respects!–picked the worst possible pairing for the #1 and #2 chart colors from a color-blindness perspective, I don’t know. Well, except that people tend not to think about this–as mentioned above.

    6. Weather is the sample, climate is the population.

    7. Weather is day to day variation, locally, in temperature, pressure, rainfall, cloud cover, wind direction and speed, etc. Climate is average weather over a large region, or the entire globe, for thirty years or more.

    8. “Climate is the odds and weather is the roll of the dice.” I agree 100% and that has to be the best description of the difference that I’ve come across.

      There are many implications for a warming global climate that have to do with the dynamics of atmospheric and ocean circulation patterns and how they interact with each other and with all the emerging feedback loops that they trigger throughout the whole system. (Ice and permafrost melt from dramatic warming in the Arctic is probably the most glaring example.) So, the change in the odds have to include not only changes in the odds of expected events and their extremes, but also a change in the odds of unexpected events, the so-called “black swans”, that will most certainly pop up as time goes on and the changes accelerate. Those are the things that keep most climate scientists awake at night and fearing for an uncertain future!

      Thanks for all your efforts in trying to wake people up, Tamino!

    9. It is a common if sad misunderstanding of statistical densities that the mean is considered king, and this manifests itself in many ways, even among technical folk. For one thing, assuming the mean and variance for the density exist, things like Chebyshev’s inequality seem to assure that the mean is all you need. Moreover, some confuse the variance of the estimate of the mean with the variance of the population from which the observations giving the mean are drawn. And, most persistently, there is thing about unbiasedness in estimates which sticks around, even if some biased estimators have lower mean squared error and lower variance.

      Besides, Chebyshev assumes the student knows nothing else about the density in question. Surely, if it’s known that the density is strictly positive and heavy tailed, as is Equilibrium Climate Sensitivity, for example, being content with planning from the mean is foolish, no matter what Chebyshev says.

    10. I tend to think of it as climate being the parameters of a random number generator and weather the output. I’ve found that some people get the wrong idea from the traditional definition of climate being statistics of weather, with it kind of suggesting that climate results from weather, rather than the other way around, and therefore that climate is not really predictable. Whereas in reality it is: you don’t need any weather data to predict that average temperatures at the South Pole will be colder than at the Equator. Also, climates could exist without weather, or what we think of as weather anyway.

      In the random number generator framing the statistics of weather are then seen to be really a reflection, or projection, of climate rather than being climate itself. I think other people have talked about drawing a distinction between “the climate system” and “climate”, with the former being essentially random number parameters and “climate” retaining its traditional definition as the statistics of weather.

      Although, after writing this I’ve realised that all these definitions really only define the relationship between weather and climate, and says nothing about what weather and climate actually are. What’s included in climate? Basically we have temperature and precipitation, I guess wind, then maybe you have things like sunlight/cloud cover, air pollution, uv levels, but what is it about these things which means they should be collected under the same climate banner? What makes them the same and other things not climate? Ultimately it seems to be things which affect the living conditions of us as humans, and our various biological and technological appendages, relating to the thermodynamics and dynamics of an ocean-atmosphere system driven by a (or some) heat source(s).