I’m no statistician but if I take (e.g.) three measurements of three different objects (sea, air, warm beer), does it make sense to look for a standard deviation? What exactly does the standard deviation mean if the things being measured are different? Is it a meaningful value?
Just to clarify, we aren’t talking about the standard deviation of the ensemble of measurements (in this case sea, air, and warm beer). We are talking about the standard deviation of the average of those three measurements, taken as a random variable. That is, if I performed the measurement of those three items 1000 times and reported the averages of each set of three, those 1000 averages will have some standard deviation. That standard deviation will be about 57% (1 divided by the square root of 3) as big as the standard deviation of the 1000 warm beer measurements, or air measurements, or sea measurements (assuming all three quantities, as disparate as they are, were measured with the same accuracy). Of course one may well ask why we are interested in the average of an air temperature, a sea temperature, and a warm beer temperature. And to that I have no answer. But assuming someone was interested in that average, they would also be interested in how the variability of the three components of the average related to the variability of the average.
In the case of averaging many Argo float readings, even though they are in different parts of the ocean and are expected to register markedly different temperatures, their average is exactly what we do want for the purposes of assessing total heat content of the world’s oceans. And therefore it is important to know that the variability of the average is much less than the variability of any one Argo float reading.
I will admit, though, that one thing worries me about applying that statistical principle in this case. Each individual measurement is modeled as a random variable with a mean equal to the exact temperature. What if there is a systematic error? For example, suppose all Argo float measuring systems were built with the same design error of 0.1 degrees? In that case each individual measurement would be biased
in the same direction. So the average of all those measurements would also be biased to the same degree. There would be no square root of N advantage. I hope the makers of that system verified that there is no systematic error.
If his claim that the heat is not in the oceans cannot be substantiated even though that is what the data appear to indicate, it is surely true that the claim that the extra heat is in the oceans is even less viable. Despite which, this is the more common claim.
I would not argue that. I only dispute the claim that says the extra energy is definitely not in the oceans.