An indirect estimate of the predictability of the monthly mean atmosphere

It is sometimes claimed that the near-constant anomalies in external conditions produce an atmosphere signal that could be useful for long-range weather prediction.
But, if anomalous external forcing were so important for the time-mean atmosphere,
how can we understand why the time-mean atmosphere is so highly variable while the controlling factors are nearly constant ?
Apparently, there is a great deal of internal random forcing, probably associated with large-scale transient eldies:
the noise.
The signal to noise ratio is estimated in this
paper by comparing the month-to-month persistence in the monthly mean circulation in models with and without eddies.
As a "model" that includes eddies we take the real atmosphere.
The model without eddies is the one described by Opsteegh and Van den Dool (1980). This model is forced with constant forcing and a highly persistent atmosphere emerges.
A comparison of the high level of persistence in the model (no eddies) and the much lower level of persistence in the real atmosphere yields a signal to noise ratio of 10 to 15% representing a large part of the northern hemisphere.
Our estimate is consistent with the one by Madden (1976).
The accuracy of the present signal to noise ratio estimate  depends on the quality of the eddy-free model. It is certainly a validation of this model in that it reproduces the annual variation in persistence derived from observations in the real atmosphere.