Thank you for your responsive comments to the reviewers. Please revise the manuscript as indicated, and I'll look forward to reading the revised version.

Thank you for your response to the reviewers - please proceed with revising the manuscript in accordance with your suggested changes and their recommendations.

Dear authors,

Firstly, my apologies for the confusion with the multiple replies you received from me. Your updates to the manuscript were so rapid that I actually thought the computer system was broken and that I'd somehow failed to submit my recommendation! I hope this didn't cause too much confusion at your end.

Secondly, I took this opportunity to give your manuscript a thorough review myself. In doing so, I've made many minor suggestions on the attached PDF. Most are essentially about language and wording. Some are basically technical corrections. Some are probably idle comments that occurred to me as I was reading that don't merit a reply! And a few ask for a little more interpretation of your results, and offer my perspective on what I think the most novel parts of the study are (overall I think you have over-emphasized the "novelty" of Fourier analysis, and perhaps under-emphasized the clever way you have "closed" the regression problem between sites - which strikes me as the more novel part of the study).

If you would please take one more round of these minor corrections on board, we'll truly be ready to publish! I hope that you'll find my suggestions are improvements, rather than irksome matters to attend to - mostly they are geared towards formalizing language around the Fourier methods, improving comprehension for a reader, and asking for a little more interpretation.

Best wishes,

Sally Thompson