Peer review of: Intradecadal variations in length of day and their correspondence with geomagnetic jerks (2020)

RR2

REVIEWERS' COMMENTS:
Reviewer #1 (Remarks to the Author):
  In my initial review, I gave 2 major points I believed should be addressed, namely,
 1. A failure to discuss the uncertainty of jerk timings
 2. A failure to adequately demonstrate
 a. how the decadal variation of LOD series was derived
 b. that TMWT cannot resolve periods as close as 6yr and 8.5yr
 From the revised manuscript and supplement, I can now see that both these points have been
 expanded upon.
 On my first point, I think the reader is now given enough background to see that there are various
 views expressed in the literature and the authors here support one of these.
 On my second point, I think the manuscript coupled with the supplement provides the information
 required.
 I see that the concerns of the other referees have been responded to, while I don’t see any obvious
 error in the response (and am generally happy to see synthetic tests to back up the authors
 arguments) it would perhaps be better for the other referees to affirm to this.
 There are a handful of references such as “see supplement” that should refer explicitly to where in the
 supplement a reader should look, especially since this supplement has grown somewhat.
 From my point of view the content of the manuscript is now acceptable to publish, though the sections
 of text that have been added could use a copy edit as the grammar is awkward in several places.
 Reviewer #2 (Remarks to the Author):
 Please find my report on on the revised manuscript entitled « Intradecadal variations in length-of-day
 and their correspondence with geomagnetic jerks » by P. Duan and C. Huang, and submitted to
 Nature Communications.
 The authors have performed important efforts to test the robustness of their results. This point should
 be acknowledged. They have also significantly changed their discussion of the geophysical implications.
 Provided they take into account my comments below, I consider the manuscript is now acceptable for
 publication with minor revisions.
 In particular I have to important remarks, detailed below : the authors
 - should modify their discussion of the inner core oscillations, which cannot be considered without
 motions in the fluid outer core ;
 - should avoid mentioning that jerks imply LOD changes, since they may well result from the same
 cause (concommittance is not causality !)
 see attached document for detailed comments.
 
Reports on the revised manuscript entitled « Intradecadal variations in length-of-day and their correspondence with geomagnetic jerks » by P. Duan and C. Huang, and submitted to Nature Communications.
The authors have performed important efforts to test the robustness of their results. This point should be acknowledged. They have also significantly changed their discussion of the geophysical implications. Provided they take into account my comments below, I consider the manuscript is now acceptable for publication with minor revisions. In particular I have to important remarks, detailed below : the authors
- should modify their discussion of the inner core oscillations, which cannot be considered without motions in the fluid outer core ;
- should avoid mentioning that jerks imply LOD changes, since they may well result from the same cause (concommittance is not causality !)
list of comments :
- l 17 : « indicates that the geomagnetic jerks may excite the 8.6-year signal amplitude ». I do not agree on this, they may as well have a similar origin (see Aubert & Finlay, 2019)
- l 160-161 : « Recently, the idea that the geomagnetic jerks originating from the Earth interiors has been widely accepted »... this idea is accepted since the 1980’s !!
- l 162 : rather than refer to Ref. 30 (Bloxham et al, 2002), I would refer to more complete time- dependent core flow inversions (e.g. Jackson et al 1991 ; Jackson et al 1997)
- l 164 : « Therefore, the jerk events may excite the LOD variations on the intradecadal scales... » I do not agree, they may result from a same source !! (see Aubert & Finlay, 2019)
- l 207 : « From the intradecadal variations in LOD and their time-varying characteristics, one can infer the geomagnetic field strength inside the Earth’s core » why refer to Ref. 18 there ?
- On the same page : If I follow the scenario by the authors, torsional waves may only correspond to the 6 yr signal, the 8.6 yr signal, being related to another physical phenomenon (trapped waves in a stratified layer or QG-Alfven waves as in the study of Aubert & Finlay (2019). Depending on the physics chosen, the link to the magnetic field within the core will differ. This should be clearly stated somewhere.
- l 23 and below (+ rebuttal on pages 32-33) : I agree with the derivation and the 0.2 deg/yr for the inner core... if no angular momentum is carried by the fluid outer core. However, the issue here is that it corresponds to a ~4.6 km/yr rms zonal velocity at the inner core equator, which is about 10 times what is inferred from geomagnetic field changes !! this is one reason for accounting for the fluid core even in the case of a MICG. Another reason is the EM torque between the inner core and the fluid outer core, which will couple the two. For these reasons, one cannot explain LOD changes with angular momentum only in the inner core... (it is not possible to ignore the outer core in this ballance).
- l 231 : « is likely due »... is possibly due
- l 237-238 : « If it is this case, then it will be not appropriate to use the observed 6-year period to estimate the cylindrical radial component of the magnetic field »... unless if 6-yr were to correspond to a harmonic of the 8.6 yr signal, which would still be possible given the uneven relation between eigen frequencies of the torsional modes, in the likely case where the torsional Alfven wave velocity is not constant throughout the outer core (see Gillet et al, 2017).
- on page 10 : another possibility is QG-Alfven waves as supported by Aubert & Fourier 2019... but why would their signature be necessarily periodic ?

- l 272-273 : « ... that geomagnetic jerks are probably responsible for the increasing of the amplitude » : see above points for l 17 and 164.
- « ... these jerks can induce the acceleration of the azimuthal flow motions »... can be associated with the acceleration of the azimuthal flow motions
- « ... which makes the amplitude of the 8.6yr signal continuously increasing » at some point it should decrease. Why do the authors want to see there a causality and not just a concommittance ?
- l 291 : « while this work further provides a directly observed evidence to show this oscillatory behavior »... SA pulses (e.g. Finlay et al, 2016) seem to occur every 3 yr or so, making jerks periodicity ~6 yr. This differs from the 8.6 yr periodicity argued for by the authors. How would the authors reconcile this ?

Reviewer #3 (Remarks to the Author): Referee: Richard Holme
  The authors have certainly done a very substantial amount of work. I worry that much of the work
 doesn't answer the question - they do demonstrate from the synthetics that they are able to recover
 their proposed double harmonic signal, with exponential growth and decay. What they do not
 demonstrate is that this signal would could not be explained in another way (as for example a trend
 and one harmonic signal).
 The authors argue strongly that their approach is more complete because they consider both the time
 and frequency domain. However, considering the frequency domain is not an automatic solution to
 problems. In the end, all they can do is fit data with some weighting applied - a fourier method does
 this ias much as a parameterised method, it is just hidden by formalism. If I have one major worry
 with the work, is that the authors believe more refined mathematical methods will give "truth" - I
 doubt this strongly.
 However, as I see that the other reviewers were more friendly, I cannot argue against the paper. I
 make one request, probably in the supplemental information - the authors provide in one place the
 detailed parameterisation of their fit (frequencies and exponential rates). This will allow testing of their
 model against future data (some of this is already available) and also past data from occultation
 information. This can then be tested against a single wave fit (which anyway breaks down sometime
 back in time in the 1950s) to allow, in a couple of years, an objective test as to whether their model
 has any long term predictive properties.