The ENSO forcing without the annual impulse can be used as the basis for the North Atlantic Oscillation (NAO) forcing. As in the prior comment, the 9-year repeat can be discerned by eye.
The big distinction is that (like the QBO), the NAO model requires a semi-annual impulse modulation rather than the annual impulse of ENSO. This together with the differing LTE modulation allows a good fit for essentially the same lunar forcing. In other words, very few DOFs required and even with over-fitting on a short training interval (shown in yellow below) the model still matches the data outside that interval
I would suggest that future research should be focused on cross-validating the various climate indices using a common lunar forcing.
Climate scientist James Hansen sent out another one of his regular mailing list briefings recently
According to Hansen, 40 years ago one parameterization of a global climate model took "a few years" to complete before the results were published.
Yet, there is now this finding reported by the mainstream news : [Climate Models Are Running Red Hot, and Scientists Don’t Know Why](https://www.bloomberg.com/news/features/2020-02-03/climate-models-are-running-red-hot-and-scientists-don-t-know-why). As the title says, the scientists interviewed can't explain why they are running hot, even though they should be able to systematically run sensitivity tests to isolate the root cause. This is how NASA's chief climate scientist explains the difficulty:
My take is that 40 years on, the complexity of the model appears to be increasing at such a great rate that they can't take advantage of the orders-of-magnitude improvement in computational power to isolate the causative factors.
It seems that they may need to take a step back and simplify their models -- unless they are content in following the lead of neural network models which seem to work in spite of understanding why https://cs.nyu.edu/~fergus/papers/zeilerECCV2014.pdf