I have pounded the accuracy of the measurement issue hard in this blog. My main assumption is that, barring elevational changes, two closely spaced thermometers should give a quite similar temperatures. Indeed they should be quasi-duplicate measurements which is why this is such a valuable way to look at the data. The temperature difference should be almost zero or bounce around zero.
But, as readers of this blog know, such is not the case. The temperature differences are huge, sometimes exceeding 10 degrees for the average temperature difference. And this, in turn, raises the question of how accurately can we measure the temperature. The claim is made that the world has warmed by 1.1 deg F. To make that statement we must, in turn, have a capability of measuring the temperature to an accuracy of less than 1.1 deg F.
Now since two nearby measurements can be taken as duplicate measurements on the same day we can use that information to determine the measurement error. The standard deviation of the temperature differences represents the measurement error. In other words, from the standard deviation, you know that the true temperature has a 68% chance of being within 1 standard deviation of the thermometer reading. If the standard deviation is 2 and your read the thermometer as 73, you know that 68% of the time the true temperature is between 71 and 75 degrees. That is how it works.
Now below are pictures of the standard deviation of the temperature for each day of the year for the temperature difference between Chippewa Lakes, OH and Wooster, OH. A perfect measurement system would have the line at zero. You can see that it isn't at zero. And it varies throughout the year. One has more accuracy in the summer than in the winters.
At these two towns, separated by 1/12000ths of the earth's circumference, we can only measure the temperature to an accuracy of +/- 3 degrees.
It is no better when one looks at other closely spaced towns. Carlinville, IL and Hillsboro, IL, separated by 20 miles, show that this spot can only measure the temperature to within +/- 2.5 degrees.
Global warming is said to have warmed the earth by 1.1 deg F, which is 1/2 or 1/3 of the error in the measurement. When your measurements are that erroneous, you can't say the world has warmed from this data.
And the worst yet is between Mondevideo and Milan MN. The standard deviation for the entire data set shows that we can't measure the same temperature closer than +/- 4.4 deg F