Intelligent scientists in legitimate professions understand that when working with large data sets, error distributions tend to be quite random – and the best way to deal with them is to assume that they average out to zero.
This understanding also provides a way to find if the error distribution is skewed, as would occur if there has been selective dropout of rural stations or if the data has been deliberately tampered with.
The approaches of using anomalies, gridding and infilling mask systematic changes to the data, and must be avoided when doing this sort of analysis.
If the data set is legitimate, then random dropout of monthly data or movement of stations will have very little effect. Some stations will get warmer, some will get cooler. Trying to “correct” for this opens the door to confirmation bias – or worse.
The fact that there are systematic adjustments cooling the past and warming the present seen in nearly every state and city, throws up a huge red flag that the adjustments are not legitimate. Why would anyone want to hide this information by using anomalies, gridding and infilling – which would be unnecessary in a legitimate data set anyway?