Minnesota again--yes, Montevideo and Milan yet again. I aligned the daily temperature differences for these two towns for 105 years of data. Then I averaged each day--Jan 1 had its average temperature from 1894-2008, Jan 2 had a separate average, etc ad nauseum. The average daily temperature difference between Montevideo and Milan Minnesota is shown in the first picture.
One can immediately see that Montevideo has been warmer than Milan during most of the years and was more warm during the winter than during the summer. This implies either a cooling at Milan or a heating in Montevideo each winter since 1894.
There is no way to tell which is the case.
Now lets add a 30 day running average of the average daily temperature difference for each day. This means we take 15 days before and 15 days after and average them. and we do that for each day of the year. That gives the red curve below.
Now, most people will say that we can use the average daily temperature over this long a period of time to remove the bias for each day and get the temperature back to what it should be. But that won't work. Let's subtract the 1894-2008 bias for each individual day from the data for 2 periods of time, the 2000-2008 time period and the 1968-1975 time period. The temperature differences for these two time periods are shown below.
You can see that Montevideo is warmer than Milan from 2000-2008 but colder from 1968-1975. That presents a problem if we want to use the average to correct the daily temperature differences for these two time periods.
First using the raw data for the correction factor (meaning each day's 1894-2008 average temperature is used as the correction factor) we find that we don't make the two towns read the same temperature.
All we have done with this is make 2000-2008 more negative and 1968-1975 less positive. But we have not made the two periods of time give us what we expect they should have--the same temperature.
If we use the 30 day running average as the correction the same thing happens.
The only way to correct this and make these two towns give up nearly the same temperature is to have a temporally variant correction, and that is not very useful because it would be doing nothing more than making the record be what we think it ought to be. And that is what the current system does with its addition of heat to the modern record as it is corrected at GISS. If it is scientifically invalid for them to make the temperature record be what they think it should be (a warming record) it would be equally wrong for my side to make the temperature record say what I think it should say. If one can't correct the temperature record with solid methodologies, the only logical conclusion is that the record can't be corrected. It is uncorrectable.