This WUWT post from Willis Eschenbach misses a crucial point. He converts heat changes back to temperature changes (dT = dQ/mc), and writes:
Here’s the problem I have with this graph. It claims that we know the temperature of the top two kilometres (1.2 miles) of the ocean in 1955-60 with an error of plus or minus one and a half hundredths of a degree C.... So I don’t know where they got their error numbers … but I’m going on record to say that they have greatly underestimated the errors in their calculations.The basic point is that the statistical uncertainty of an average can be much less than that of any temperature measurement.
If you measure the temperatures T1 and T2 of two different objects, each to an uncertainty of ΔT, what is the uncertainty ΔA in their average A? The typical way this is done is explained in most freshman physics labs, such as this. So the average temperature of the two objects will be (T1 + T2)/2, and the uncertainty in the average will be
ΔA = ΔT/sqrt(2)
which is less than ΔT. For N measurements the denominator becomes sqrt(N), so the uncertainty is much less. This might seem counterintuitive at first, but it's akin to the statistics of coin-flipping -- over the long haul, the expected average is 50% heads, with a variance (standard deviation) that goes like 1/sqrt(number of flips).
This is essentially what Levitus et al do, and it's completely legitimate. Experimental scientists take uncertainties religiously, and it is often a major part of the analysis, even more so than simply getting a result.
I don't know yet what the uncertainty of an ARGO buoy sensor is, but (to this point) I suspect it's significantly less than 1°C. That comment asks:
There is an amusing example in which they say if you measure the length of an object to the nearest millimetre often enough, you ought to be able to resolve individual atoms. Since atoms are 10^-8 mm you need about 10^16 measurements. What do you think? Is it possible in principle?But this confuses two completely different concepts -- an individual measurement, and averaging. A measurement of a length is a completely classical measurement, with no notion of "atoms" or discreteness. So there's nothing wrong with a huge number of measurements resulting in an uncertainty less than an atomic length in a statistical sense. (Casinos, of course, rely on this to make their money.) But that says nothing about any particular measurement, only about the average of the measurements. So you're not "resolving atoms," which would necessarily happen in a particular measurement.
Just because the average height of U.S. men is 5 ft 9 in doesn't mean all U.S. men have a height of all U.S. men is 5 ft 9 in -- only the "average man," which is an abstract thing, not a thing that exists in the same sense that any of the men exist. (Viz. the average is a mathematical object. Men aren't.)