Time to get technical.
First, surf over to Willis Eschenbach’s gorgeous piece of statistical detective work of how GHCN “homogenized” temperature data for Darwin, Australia. Pay particular attention to his Figures 7 & 8. Take your time reading his piece: it is essential.
There is vast confusion on data homogenization procedures. This article attempts to make these subjects clearer. I pay particular attention to the goals of homogenizations, its pitfalls, and most especially, the resulting uncertainties. The uncertainty we have in our eventual estimates of temperature is grossly underestimated. I will come to the, by now, non-shocking conclusion that too many people are too certain about too many things.
My experience has been that anything over 800 words doesn’t get read. There’s a lot of meat here, and it can’t all be squeezed into one 800-word sausage skin. So I have linked the sausage into a multi-day post with the hope that more people will get through it.
After reading Eschenbach, you now understand that, at a surrounding location—and usually not a point—there exists, through time, temperature data from different sources. At a loosely determined geographical spot over time, the data instrumentation might have changed, the locations of instruments could be different, there could be more than one source of data, or there could be other changes. The main point is that there are lots of pieces of data that some desire to stitch together to make one whole.
I mean that seriously. Why stitch the data together when it is perfectly useful if it is kept separate? By stitching, you introduce error, and if you aren’t careful to carry that error forward, the end result will be that you are far too certain of yourself. And that condition—unwarranted certainty—is where we find ourselves today.
Let’s first fix an exact location on Earth. Suppose this to be the precise center of Darwin, Australia: we’d note the specific latitude and longitude to be sure we are at just one spot. Also suppose we want to know the daily average temperature for that spot (calculated by averaging the 24 hourly values), which we use to calculate the average yearly temperature (the mean of those 365.25 daily values), which we want to track through time. All set?
Scenario 1: fixed spot, urban growth
The most difficult scenario first: our thermometer is located at our precise spot and never moves, nor does it change characteristics (always the same, say, mercury bulb), and it always works (its measurement error is trivial and ignorable). But the spot itself changes because of urban growth. Whereas once the thermometer was in an open field, later a pub opens adjacent to it, and then comes a parking lot, and then a whole city around the pub.
In this case, we would have an unbroken series of temperature measurements that would probably—probably!—show an increase starting at the time the pub construction began. Should we “correct” or “homogenize” that series to account for the possible urban heat island effect?
At least, not if our goal was to determine the real average temperature at our spot. Our thermometer works fine, so the temperatures it measures are the temperatures that are experienced. Our series is the actual, genuine, God-love-you temperature at that spot. There is, therefore, nothing to correct. When you walk outside the pub to relieve yourself, you might be bathed in warmer air because you are in a city than if you were in an open field, but you aren’t in an open field, you are where you are and you must experience the actual temperature of where you live. Do I make myself clear? Good. Memorize this.
Scenario 2: fixed spot, longing for the fields
But what if our goal was to estimate what the temperature would have been if no city existed; that is, if we want to guess the temperature as if our thermometer was still in an open field? Strange goal, but one shared by many. They want to know the influence of humans on the temperature of the long-lost field—while simultaneously ignoring the influence of humans based on the new city. That is, they want to know how humans living anywhere but the spot’s city might have influenced the temperature of the long-lost field.
It’s not that this new goal is not quantifiable—it is; we can always compute probabilities for counterfactuals like this—but it’s meaning is more nuanced and difficult to grasp than our old goal. It would not do for us to forget these nuances.
One way to guess would be to go to the nearest field to our spot and measure the temperature there, while also measuring it at our spot. We could use our nearby field as a direct substitute for our spot. That is, we just relabel the nearby field as our spot. Is this cheating? Yes, unless you attach the uncertainty of this switcheroo to the newly labeled temperature. Because the nearby field is not our spot, there will be some error in using it as a replacement: that error should always accompany the resulting temperature data.
Or we could use the nearby field’s data as input to a statistical model. That model also takes as input our spot’s readings. To be clear: the nearby field and the spot’s readings are fed into a correction model that spits out an unverifiable, counterfactual guess of what the temperature would be if there were no city in our spot.
Counterfactuals, a definition of what error and uncertainty means, an intermission on globally averaged temperature calculations, and Scenario 3: different spots, fixed flora and fauna.