There's a history to this topic I won't go into right now. Suffice to say, I've been pointing this out for a couple years now. BEST has a stronger seasonal cycle in its data than any other major temperature set I've seen.
A coherent signal in data means the data indicates a source of correlation within the data. This will necessarily impact the correlation structures within the data. This means this seasonal signal will affect the correlation structures within the data. Given kriging, which BEST uses, relies heavily upon correlation structures, this is a problem.
There are a number of related issues, but I just wanted to get this "out there" to start.