Please submit a revised manuscript. In particular, referee #1 had some salient concerns to address to ensure your main result was robust, and should be carefully considered in your revisions.

The authors have addressed the reviewer's concerns adequately, and so I am happy to accept the paper for publication after the authors consider the reviewer's final comments a bit more.

I believe the issue with respect to the inertial oscillations is they are hard to see in figures 8 and 9 (in 9, their effect is clear for Sep-Oct, but less so for other months, although the discussion in the text does clarify this reasonably well). I think perhaps these figures aren't the best way to show the magnitude of the inertial oscillations, so the author's might consider how to improve this. As the reviewer states, the resolution in figure 8 is not high enough to really resolve the peak, but perhaps it would not be so apparent in the IWSR anyway? It would also be good to consider whether the significance in the trends in beta and c could be calculated. If so, that would support the author's conclusions about the spatio-temporal variability in these. These should be relatively straightforward to address.