But there is nothing wrong with the infilling method.
I think USHCN should use anomalies, and I suspect they in effect do, and just convert back. So for them USHCN just estimates a value from neighbouring stations, and proceeds. USHCN does it by ensuring that every month has an entry for each of its 1218 stations, which ideally never change. That can be done, but needs care (unlike here). The background is that USHCN tries to do something that no-one else does - to give an average (for the US) in absolute ☏ (absolute=not an anomaly). When he found that there were quite a lot, 'zombie' stations became the enemy. Anthony got invested in disputing SG's claims, only moderately exaggerated, about the number of USCHN stations that actually reported each month. Initially Anthony Watts wrote with Zeke some good posts on some flaws in SG's methods. Judith Curry gives a summary, with links. For some reason Steven Goddard has gone viral, and has been on some right wing media. There's been a lot of grumbling lately about USHCN.