first and foremost, we heartily apologize for the delay in responding to your very helpful report. the reason is that we had a file system failure at stanford, and we lost the data we had used to make our plots. most of it was archived, but it turned out we hadn't quite recorded enough detail to reproduce our previous processing exactly. the conclusions are unchanged, though. this is discussed in more length in the relevant response below. >Reviewer #1 (edited): The paper entitled "Global-Mode Analysis of Full-Disk Data from the Michelson >Doppler Imager and Helioseismic and Magnetic Imager" by Larson and Schou >presents new and interesting results that warrants its publication in Solar >Physics. > This being said, while the authors show that some systematic errors are no > longer present when using full-disk MDI data, there is no indication as to > what in the data processing of the 'Structure' MDI observation is causing > these systematics. It is not clear that these systematics are caused > by using only a fraction of the solar disk, and not by an inadequacy in the > mode fitting of taking into account the effect on the time series coefficient > of both the Gaussian convolution and the apodization. we agree with the referee that the origin of the error is likely somewhere in the analysis codes as there is no indication that the gaussian binning and subsampling is incorrectly implemented onboard. we infer from our results that the models for the vw_V analyses are indeed worse than those for the full-disk, and we have rephrased the text to state this more clearly (see below). > The work presented would benefit from a more substantial analysis of the root of > the vw_V fitting problem, since the bulk of the MDI observations are in vw_V > mode. Also, the authors choose to not compare their determinations of mode > parameters to those derived others (GONG, etc...). we note that the present paper, as indicated by the title, is about the full disk data, which does not have the systematic error. The older paper (LS, now LS15) was about the vw_V data and the systematic errors were noted there. we agree that that it would be useful to know the root cause, but we were not able to determine that in LS15 despite substantial efforts and unfortunately the additional analysis presented here did not allow us to identify the cause. and in all likelihood our time would be spent better writing a new and less restricted code. as for comparing with GONG data this could potentially be done, though we note that there are no 72 day or 360 day results available for GONG. further, if MDI cannot be made to agree even with itself, comparison with GONG hardly seems pressing. analyzing GONG time series with our code would be possible but quite time consuming as it would require addressing a number of additional effects, especially the ones from varying atmospheric conditions. not to mention the technical challenges. we are not sure which other contemporaneous instruments "etc..." refers to? AIA? This is an interesting idea, but would almost certainly imply having to deal with even more instrumental effects. perhaps most importantly, addressing these points would represent a significant expansion in the scope of an already long paper and will have to be deferred to a future paper. > I would also recommend that the authors consider using more subsection headings. we are not opposed to this, but are at a loss to guess where they might be desired. if the referee feels strongly about this, we invite them to make a specific suggestion. > p.2 l.4: with a 4096 × 4096 CCD -> with a 4096 × 4096 pixels CCD done. > p.2 l.5: "resolution of about 0.5 arscec per pixel," avoid about 2x done. > p.2 l.5-6: HMI is in geosynchronous, ... MDI ... > replace HMI/MDI by SDO/SOHO done. > p.2 l.16: I would recommend using 'LS15' in lieu of 'LS' sure, done. >p.2 l.16: "Before an attempt can be made to extend this analysis to HMI data, > it is fitting to compare it to the analysis of the MDI full-disk data." > > what is 'it' in 'to compare it to' - rephrase. ok. we changed to this: "Before an attempt is made to extend this medium-l analysis to HMI data, it is fitting to apply it to the MDI full-disk data and compare the results." > p.2 l.28: 'dynamics' -> 'Dynamics', like 'Medium-l Program' further, although > 'Medium-l Program' ought to be 'Structure Program', no? Or use full-disk and > medium-l thorough. we have already used "Medium-l Program" in our previous work and prefer not to needlessly confuse readers by using a new term. properly speaking, the structure program includes stuff besides helioseismology. however, "Dynamics Program" is the proper counterpart in our usage and we have changed these two sentences. > p.2 l.31: the paragraph staring with "One might say that" is not clear. Please explain first the vw_V data cropping, then the resulting choices > of apodization. changed: now defer apodization details and mention only cropping in the intro. > p.2 l.42: "This also allows us to investigate" -> " This also allows us to > further investigate" done. > p.2 l.50 "and the resulting inversions." -> "and the resulting solar rotation > rate inversions." changed: added "for solar rotation". > p.2 l.50: "these results" not clear what this refers to. changed to "our findings". > p.3 l.7: "known as the dynamics runs." this was already defined (see comment > above.) it is now defined here for the first time. > p.4 table 1: add references to "the timeseries used by various other > researchers." and make it clear whether you analyzed these as well or not > (confusing.) reworded to "... shows timeseries we created for use in various other investigations" and added "processing was carried out through the mode fitting". also added two sentences to the table caption. > p.5 l.29: "is also repeated using asymmetric mode profiles in addition." > In addition to what? (rephrase.) added "to the normally used symmetric profiles". > p.5 l31-32: "Hence, the only geometrical correction applied here is for the > inclination error." > > Inclination of what? Please be explicit. we added "mentioned in the previous paragraph". > p.5 l.43-44: "We have fit these data only as 72-day long timeseries and only > using symmetric profiles." > > Why? we assume the referee means that we could have also analyzed the vw_V proxy as 360d timeseries and using asymmetric profiles. true, but it would not add anything to the results presented here, as the effect of both length of timeseries and asymmetry are already addressed using the full-disk results, which we show do not suffer from the same systematics as the vw_V datasets. > p.6 l.2-3: "Due to its orbit and potential problems with calibration, the HMI data contain > a strong daily oscillation." > > What is oscillating? (the RV I believe, please be explicit) changed "data" -> "spherical harmonic timeseries". also removed the word "potential". > p.6 l.31-32: "Apparently the regular full-disk analysis was less susceptible > to this than all the other ones." > > What is "this"? inserted "low duty cycle". > p.7 l.4-7: "We then take a weighted average in time over whatever dynamics > runs had each mode successfully fit." > > It is not clear what is precisely computed and how it is weighted. Are > the quantities shown in Fig. 2 the mean relative changes for all 15 runs? If > you compute a delta/sigma, why would there be an additional weight? > > Also, is there any point in showing if these differences are consistent with > time? added phrases "For each mode parameter" and "in both analyses". we also noticed that we had omitted one detail about the errors, which we have now inserted. to answer your questions, yes. for figure 2, the parameters and their errors have been separately averaged (weightedly). the delta/sigma will be different for each mode, but they must all be averaged together with identical weights. and yes, the results look similar for all the dynamics runs. when they do not we explicitly draw attention to it, as in figure 4. > p.7 l.14: "In Figure 2 we show the result for six mode parameters." > > Are those for the six or 36 a-coefficients? (six mode params, six a-coefs, > this gets confusing). added a sentence to preceding paragraph and in this one list the mode parameters explicitly. > p.8 l.43: Sentence starting with "In this case, we formed" is not clear > enough. inserted "all three of". > p.9 Fig. 4: consider adding as error bars rms(mean) and a dotted line at y=0. we are very glad you made this suggestion. while considering it we discovered that we had used the modes common to all three of fd_ap90, fd_ap83, and vw_ap83 when making the plot, whereas we should have taken modes common only to the last two. we say this only to explain why the values plotted have shifted slightly, in case you noticed :) thanks! however, we don't think it's appropriate to add error bars to this plot, because it is already the significance plotted. it would be like putting error bars on error bars :) we did add the dotted line though. > p.10 l.29: "In order to see how the different analyses affect our inference > ..." > > Why are you inverting the mean of 15 sets? Could any of these results be > dominated by some subsets? A large set of these 15 runs are 72 day long (the > canonical length for fitting a data set) or longer, very few are much > shorter. because we are attempting to measure the mean of the changing rotation, as opposed to measuring a quantity constant in time. and this is the reason we have weighted the mean as described, so shorter runs contribute less. > p.10 l.43: "Using the vw_V apodization results in both systematic errors, which > are then removed by using more data from the input images, although the data > added is expected to contain only a small fraction of the helioseismic > signal." > > Isn't it obvious that the problem is not adding or removing 'data', but some > misfit between the analysis (the fitted model) and the data processing, and > most likely with the adequacy of the leakage matrix? yes, that is obvious, but now we say so explicitly. > The vw_V processing, or even the fd_ap83 processing, leads to larger > leaks. If somehow the leaks are not accounted for as one may think they are, > wouldn't this explain that? Hence my recommendation of an inquisitive analysis > of the root of the vw_V fitting problem. Is the fitted model for fd_ap90 > doing a better job modeling the data than the vw_ap83 and/or fd_ap83? yes, that would explain it. see discussion at the beginning of this response. > p.11 l.36: why not fit asymmetric profiles to the vw_V? see above. > p.11 l.46-50: "However, in the region where the modes are observed to have > strong asymmetry, one must accept that using asymmetric profiles more > accurately characterizes them. Hence, the parameters resulting from both > types of fitting have become standard data products." > > It is not clear that this make sense. If "using asymmetric profiles more > accurately characterizes [modes]", one should no longer use symmetric > fitting, no? that is only true for modes that actually have asymmetric profiles. furthermore, we think many people find mode parameters fit using symmetric profiles better than none at all, which is the case for many modes. most importantly, the symmetric fitting is retained for consistency with other results. and lastly, there is no universally accepted way of modeling the mode asymmetry. > p.12 Fig.7: the triple solid line (to indicate error bars) for fd_ap90 is > confusing at first. Consider drawing error bars (like every 10th point). The > vw_ap90 solution is barely visible, consider adding colors. the triple solid line is what we used in our previous paper; we prefer not to change it. and the fact that the vw_ap90 solution is the same (within errors) as the fd_ap90 is the whole point; it doesn't need to be more visible. > p.11-12 and Fig.9 : "The difference in coverage for the 72-day fits is shown in Figure 9, > where diamonds indicate a mode that failed at least once using symmetric > profiles, and dots indicate a mode that failed at least once using > asymmetric profiles." > > Couldn't this be better quantified than just for n>1; 6 years of HMI data, or > 30 sets, why only mark when n>1? firstly, we should have put the contents of the caption in the text, and have now done so. in response to your query, we have simply shown the most conservative measure of the difference in mode coverage. to quantify it further would be possible, but it would make the figure much harder to read. > p.12 l.45: "Clearly, the asymmetric profiles have a large effect on the > frequencies" > > -> Clearly, fitting asymmetric profiles has a large effect on the > resulting frequencies done. > Consider showing the mode asymmetry (and mode width) as a function of > frequency, it will probably make it clear where its effect is most > significant, although it is the combination of the asymmetry and the mode > width that result in a mode frequency shift. we created these plots and considered including them, but we don't think it elucidates much. bear in mind that it's the standard error that determines the significance, and that varies with frequency as well. > p.12-13 Fig.10: again, is this picture constant with time/epoch? we wouldn't say constant, but essentially yes. > p.15 Fig.11 caption: "The sense of subtraction is 360 day minus 72 day." > -> The sense of subtraction is 360-day long fits minus 72-day long fits. done. > p.18 l.12: "for the first 72 days of HMI." > This is the only set with coeval observations, hence you may want to point > that out in the beginning of that section, not here. Something like: > > Both MDI and HMI were operating during the 2010 dynamics run, that was 67 > days long. Hence, we have the opportunity to compare the mode parameters > resulting from each dataset, but only for the first 67, in full disk mode, > or 72 days of HMI (in vw_V mode). > > Also, make it clear in the Figs 15 & 16 captions that these differences are > for one fitted set only. that is already clear. further, we remind the referee that HMI overlapped with MDI by almost a full year in vw_V mode. > p.18 l.15: "since these parameters should not depend on the height of > formation." of? I.e.: > > .. the height of formation of the respective absorption lines used for the > observations. sure, done. > p.20 Section 5.1: This is not limited to MDI vw_V processing only, this can be > better presented/explained. Can Figs 19 & 21 and 20 & 22 be combined? it is at this point that our confession must be made. this is how far we had gotten in our response at the time of the file system failure: "we didn't say it was limited to mdi vw_V. however, since we are talking about f-modes, the gong fitting provides nothing. since we are talking about 6 month periods, the mdi full-disk doesn't help either. whether or not this oscillation is seen in hmi data is one of the findings of this paper." we're not sure if it was your intention, but you seemed to be pointing out that we hadn't checked the hmi full disk results to see if they showed the 6 month oscillation, and we agreed that we certainly should have. it was only when we set out to do so that we realized what information had been irretrievably lost. in particular, we had not recorded how we had sampled the magnetic field for the averaging we did. now we have added a footnote providing these details exactly. in any case, the changes you see in figures 20 and 22, and the corresponding correlation values, are mostly the result of different sampling and outlier rejection. note that figures 19 and 21 have just barely changed at all. we checked a couple different samplings and found they made similar changes to the figures, but still left our conclusions unchanged. in any case, we have made extensive changes to the text of this section, too many to list here. please try to read it with fresh eyes :) as for combining figures, we prefer them as they are in order to compare the two instruments. there is no reason to assume they will see the same signal. > "entire mission" -> "entire MDI mission" done. > "In Figure 19 we show the fractional change in f-mode frequency for the > entire mission using the updated mode parameters. The values shown have been > averaged over a range in from 251 to 300 and the Doppler correction has been > applied." > > what do you mean by "updated mode parameters"? and "Doppler correction has been > applied." > > Consider writing > > "In Figure 19 we show the mean fractional change in f-mode frequency, > averaged over a range in degree from 251 to 300." etc... change "updated" -> "most recent" and "the Doppler correction has been applied" -> "corrected for Doppler shift". > p.21. Fig.18 caption: both in the caption and the text, make it explicit that > these are MDI Dynamics observations, and the mean for 15 runs. it is only for 2010 dynamics, and we have tried to make this more clear. > p.22-23: "To illustrate the issue, " what issue? changed "issue" -> "relative magnitude of the odd leaks". > p.23 l.38: "For the sake of brevity," you mean clarity? You also do not really > explain what the sensitivity to the target mode is. no, we mean brevity. added a parenthetical "$\Delta \ell = \Delta m = 0". > p.24 Fig.24 caption: why not be explicit: "high |B_not|" -> B_not = -6.35\deg added a parenthetical "= 6.35\deg" to this figure and figure 25 as well. > p.25: "The result is shown in Figure 28. The shape of these ratios is roughly > the same as the differences shown in Figure 2, where we plotted only the > significance." > > The same shape is not clear (what panel of Fig. 2?) nor is the statement "where we plotted only the significance." > > Overall, Section 6 could use some more work. added "the second and third panels of" and changed to "which were plotted in units of significance". > p.28 Fig 30: left two panels, contours at high latitudes are not 'erased' > where the inverted rate is now shown. that is intentional, and we have expanded the figure captions to make this clear.