Statiscal significance of 150 years of data over 4.5 billion years

The subject line is close to a recent search query that lead someone here, and echoes a comment that's not unusual in blog comment sections. The thing about it is, it's not a very strong question.

One part of the question's failure is that it isn't really a proper statistical question. Given limits of search strings, that's no surprise. But it does show up in comments (usually in the vein of assertion "150 years is too small a statistical sample of 4.5 billion years of climate.") where such limits don't apply.

The basis of any good question is to try to understand something. If what you are trying to understand is not statistical, then pursuing statistics is not going to help you. "What is your height?" is marginally statistical. If you measure the length of a short metal bar many times, which I did in freshman physics lab, you'll get slightly differing answers. So you may well answer statistically with your mean and a sample standard deviation. This is only marginally statistical, in that it is purely descriptive statistics and no hypothesis testing is involved.

Your question, however, could be non-statistical: Did it rain in my back yard last night? How much rain did my rain gauge capture? If so, you will be wasting your time if you chase after statistical tables. More at hand, someone raising statistics in a blog debate about a non-statistical question is wasting your time.

But suppose that what you're trying to understand truly does require statistical considerations beyond minor description. What would such a question look like? One could be "Given the population of voters in the USA, how many randomly selected voters would I need to ask a yes/no question in order to have a standard error in my sample of 3% or less as compared to asking the everybody?" or, for more climate-related flavor "How many satellite observations with a (known) standard error of measurement would I need to find an average sea surface temperature whose standard error would be less than 0.1 K?"

Required is a description of the 'population' -- all possible observations (the population of voters in the USA, satellite observations) -- of your 'sample' (ask some number, which we want to determine, of voters, or satellite observations -- and what statistic you are trying to estimate (% of voters who like your candidate, mean sea surface temperature).

So, back to the original question. Does it describe the population? No. 'data' certainly doesn't limit us to anything in particular. I'll guess that it is global mean temperature, of the earth (maybe it's Mars -- I've read interesting papers about Martian climatology), that is the point of interest. But we shouldn't have to guess, a good question is clear on what it is asking about. Does it describe a sampling method? Not really. 150 years, well, I'll guess that this means 'take the most recent 150 years'. Most importantly, however, does it describe what statistic one is trying to estimate? No. Again, I'll guess: that it is "Global mean temperature over the entire history of the earth."

Putting it all together, the statistical question more reasonably posed is something like "Does the last 150 years of global mean air temperatures provide a good estimate of the global mean air temperature through the history of the earth?" (better would be to define 'good', say 'standard error within 0.2 K')

That's the statistical side. But since we're not interested solely in statistical questions regarding climate, at least not most of us, we also have to ask, "Is this a physically meaningful question?" The person who did the search, I don't know what they have in mind. They could indeed have in mind a question for which the mean temperature of the planet throughout its history is exactly the right number to answer.

Usually, though, comments about the 150 years vs. 4.5 billion surface in debates about modern climate and modern climate change. I'll have to invite contributions on what relevance the planetary mean temperature from 4.5 billion years ago to ... oh, let's say 30 million years ago ... has to questions of current climate and climate change. Certainly one wants to know how climate has changed through all of time, and why. I'm one such person. But at hand is those who argue that the global mean over that entire period matters.

What's important regarding human responses to climate change is the climate on human time scales. The last 150 years handily covers me back through my great-grandparents. The next 150 years will cover my children, grandchildren, and possibly great-grandchildren. Even a 'mere' million years ago, much less 4.5 billion, there weren't any humans around to think about climate change at all. So the 4.5 billion years is, for 'what do we do now' questions, a spectacularly large red herring.

Human society infrastructure also dictates a much shorter term (than 4.5 billion years) concern. Almost every mile of paved road in the world is less than 150 years old. Almost every mile of railroad. Almost all port structures. Absolutely all air transport terminals are less than 150 years old. Absolutely all electrical distribution structure, all phone lines, and even more so all cell phone towers are less than 150 years old. Coal, oil, natural gas distribution networks, again, are almost entirely or entirely less than 150 years old. Many of the world's major cities are less than 150 years old (I'll count Chicago here, as the great fire in 1871 erased so much of the city).

The climate-related concern here is that all these things were constructed based on what climate was like around the time of their construction. That climate drove what the standards would be for, say, tolerance to flooding, tolerance to drought, high winds, high rain rates, high and low temperatures, and so on. If climate changes outside the range that the infrastructure was built for -- almost all of it globally being much less than 150 years old -- then there is a serious risk that the structure will fail when it encounters brand new climate conditions.

In this vein, then, comments about the 'we did fine in the medieval warm period' are a different flavor of red herring. Chicago, Sao Paulo, Melbourne, Johannesburg, ... didn't exist back then. They did not 'do fine' in the medieval warm period, they never encountered it. Even cities that did, such as London, Rome, Xi'an, did so with far smaller populations than today's. London, ca. 1100, had a population around 18,000, and is about 1000 times larger today (taking the metro area). Rome was about 20,000 around 1100 AD, vs. 200 times as large now. Xi'an was among the largest of cities in the world then, and may have been about 500,000 around 1100 AD. But almost 20 times that today. (mostly Wikipedia figures). While a Rome or London of 10-20,000 survived a medieval warm period ok, Rome and London of many millions have never see it before.

As usual, we can get far by asking two questions: "Is this question statistically meaningful?" "Is the question physically meaningful?" After looking at the former, regarding the original search string, and not infrequent comment, we see that it isn't a meaningful statistical question. After rephrasing it to something that is statistically good, we check to see whether it makes physical sense. Turns out, for the sort of thing I'm concerned about and others use it, that even the rephrased question isn't physically meaningful. Knowing that global mean temperature for the last 4.5 billion years was 20 C (I make up a number) as opposed to 15 C still doesn't tell us whether major modern cities, and their millions of residents, will be able to manage likely climate changes. Nor does it tell us what adaptations to take, much less how expensive it would be to make those adaptations. And it doesn't tell us what the costs, both dollars and lives, would be if there were no adaptation.