Thank you for the response to reviewer comments. Please proceed with a revised manuscript.

Please make sure that the substance of your posted responses are reflected in the text of the revised manuscript (not just contained in the review responses), as this will help clarify for readers the issues raised by the reviewers and comments.

Please also submit, with the revised manuscript, a point by point response to the comments specifically noting manuscript changes.

I would like to add two additional requests. One apparent simplification is that noise is assumed to be Gaussian. Climate model signals (and observed climate data) has considerable spectral structure (ENSO, PDO, AMOC, etc.). Presumably in these models this is simplified into some modled split between noise and signal. Could a more realistic noise representation impact the results?

It would also be helpful if you could comment if the assumption for the magnitude of the noise (sigma) plays a role in the final results since this appears to be a fixed assumption "generally use the value σ = 0.05".