The authors present an implementation of a so-called physical parallelization (PP) for variational flux inversions: from a previously described PP aimed at carbon dioxide (CO2), they add developments to take into account the chemical reactivity of methane (CH4).
General comments
As already stated in the review of the first version of the paper, the developments described in this paper are particularly relevant since long-term methane inversions are now run by several teams and the issue of the trends in methane emissions by various types of sources is still under study. The revisions made after the first review have lead to a clearer introduction and description of the work. Technically, the notations are now clearer in the mathematical description. The writing has been improved but I think, although I am not an native English speaker, that some small mistakes remain.
The introduction to the paper is now clear and focuses on the main relevant points so that the reader understands why this implementation of PP is interesting for methane inversions at the global scale.
In Section 2 Physical parallelization for methane inversions, it is now clear which parts are the general or Chevallier (2013) developments and which are specific to this work and therefore, to methane.
In Section 3 PP Performance test, only the prior uncertainties are now used, which makes the message simpler.
Section 4 Discussion contains elements which have been asked for by the reviewers of the first version and makes clear the potential of the PP.
Specific comments
Section 1 Introduction
- p.2 l.36: "Inversions have been performed on multidecadal scales to assess the information content of long records of methane mole fractions." This sentence is a bit strange to me because running an inversion means that it is assumed that the assimilated data does actually contain information on the fluxes (and other variables). It would be good to be able to assess the information content prior to running inversions, which is sometimes approximated by using sensitivity studies.
Section 2 Physical parallelization for methane inversions
- p.3 l.81: the choice of x^a for the prior is not very good because in the notations used for analytical inversions, ^a denotes the posterior. Usually, the prior state vector is noted x^b.
- p.4 l.108: "the emission differences between the prior and the iteration in the period preceding the block": it is not very clear what is preceding what: is it the same iteration but for the preceding period of time? the same period of time but the previous iteration? the previous iteration in the preceding period of time?
- p.4 l.114 Eq. 5: the [ and ] do not seem to be necessary, they give the idea that f is a function of x - x^a.
- p.4 l.123-124: "implementing an atmospheric sink operator S": here, either give more details on what is in this operator or put a reference to the section which contains the information.
- p.4 l.122: Fig. 1 is not totally clear and consistent with the text here. The colours red and green in Fig. 1 are not explained in its legend so that a first idea of the reader is that what is in red comes from Chevallier (2013) and what is in green is linked to this work. But the last sentence of the legend states that it is the blue boxes which indicate which part comes from which work. Nevertheless, the "corrections calculation" is from Chevallier (2013) according to Fig. 1 but from this work Please make the text and figure very clear on which parts come from whose work.
- p.5 l.131: "Sl,k accounts for the impact of atmospheric sinks": the reader still does not know at this point what is in S and the link to Sl,k. A paragraph dedicated to the sink, which is the main feature of the PP elaborated here is required at some point.
- p.5 l.143 Eq 8: the notations are not clear to me in this equation. The adjoint of S is denoted by *, which indicates that it is not assumed to be linear. But the adjoint of h is indicated by T, which indicates that it is linear. This is not totally consistent with H begin the CTM operator, with an adjoint denoted by * in Eq. 3 and p.5 l.138 above. Could you provide more details on the derivation of the equations and make the notations totally consistent?
- p.6 l.161 seq.: the summary of the practical steps of the PP is a good idea but there is nothing about the sink. Please add the necessary steps since it is the main feature of the PP described here.
Section 3 PP Performance test
- p.7 l.215: the title of the subsection is "Emission estimation errors" but the first two paragraphs are about the match in the concentration space. Maybe it would be clearer to make a subsection dedicated to the concentrations separated from the subsection on the emissions.
- p.8 l.228: "For both inversions, a good model fit to the observations" Shouldn't "a good fit" be defined, if possible with reference to R?
- p.8 l.237: "should be in good agreement" Same remark as above: how is a "good" agreement defined?
- p.8 l.237-238: "from the inversions integrated over the globe and over TRANSCOM regions". According to the description of B (p.7 l.195 seq.), the inversions are performed at the pixel's resolution. It is a bit strange therefore to assess the performances of the PP using (very) large regions. I guess a lot of inversions can be in "good" agreement over the whole globe since the constraint on the mean total emissions of methane is strong (as stated l.240-241 "The global methane emissions are in general well constrained by the NOAA observations in a serial inversion"). The same applies for large regions such as TRANSCOM's: for example, an inversion with homogeneous emissions inside a region and an inversion with a dipole of negative/positive increments can give the same total over a large region. I understand that it is not simple to compare two inversions at the grid cell's resolution but showing maps would seem to me to be more relevant than the average global total.
- p.8 l.241-242: "the additional error introduced by the PP method does not seem to have a significant impact on the global emissions': please define "significant".
- p.8 l.244: "is well within the prior emission uncertainty". I don't understand the argument here. The difference between the two inversions should be such that they are inside each other's (posterior) uncertainty; the prior uncertainty is what the inversion aims at reducing so it does not seem to be a good measure for a "small" difference.
- p.8 l.249: "estimates for the TRANSCOM regions deviate within < 5 % from the serial emissions": how can you convince the reader that 5% is a small difference?
- p.9 l.260: "the PP inversion can effectively reproduce results of the serial inversion" but only at a coarser resolution than the actual control vector, according to what is shown previously. This sentence is too optimistic as such.
- p.9 l.265-266: "a forward or adjoint TM5 CTM run of one year took about 15 minutes": it is a bit strange that the adjoint and forward codes take the same time to run - usually, the adjoint takes more time as it requires to recompute (or at least read) parts of the forward in sub-time-steps.
- p.9 l.270 seq.: the times for each step are indicated but nothing is said on the sink (see also comments on Section 2). Please add the information, even if it is only to state that it takes a very small computing time.
Section 4 Discussion
- p.10 l.307-309: "the need for a serial sequence of inversions to provide a time series of initial mole fractions imposes a limitation to the model resolution that can be used." This sentence is not very clear to me. Do you mean that the model's resolution must not be too fine so that the serial sequence of inversions does not take too long?
- p.10 l.310: "the wall time performance of the CAMS reanalysis inversions will improve in future". Taking into account the estimated gains in computing time given in Section 3, is it possible to give an order of magnitude of this expected improvement?
- p.11 l.323: "optimizing emissions from large TRANSCOM regions". I understood from the description of the B matrix that the emissions were optimized at the resolution of the model's pixel (see also my comments on p.8 l.237-238). Here, it looks like the control vector contains the TRANSCOM regions. Please clarify.
- p.11 l.334-336: "Furthermore, the performance gained by performing the inversions at higher resolution because of the improved computational performance will likely outweigh the accuracy loss due to the assumptions made in the PP method." This does not seem so likely to me. Do you have any references or examples of such a positive case?
- p.11-12 l.348-349: "These studies assume a quasi-linearity for the inversion as changes to the methane mole fractions are expected to remain small compared to the mean." This is not a definition of (quasi-)linearity. Please elaborate.
Section 5 Conclusions
- p.12 l.355: "An atmospheric inversion with a very large state vector is needed" This is not exactly true: many inversions are run with large regions and are able to use the available information on the tendencies, the North-South gradient, etc.
Figure 5
What is the link between the "2-sigma uncertainties of the prior emissions" and the description of B (p.7 l.195 seq.) i.e. 50% per grid cell per month plus the covariances (spatial and temporal correlations)?
Technical corrections
- in the introduction (and maybe other places also): "CTM's" (saxon genitive, I guess) must be changed to "CTMs" (plural of CTM)
- p.2 l.63: "emissions adjustments" -> emission adjustments?
- p.4 l.122: "scaler" -> scalar?
- p.4 l.124: "we use a CTM block sensitivity vector $h_k$ distribute global emission changes more precisely" -> we use a CTM block sensitivity vector $h_k$ TO distribute THE global emission changes more precisely?
- p.7 l.200: "The emissions in 2008 applied to every year in the inversion period" -> The emissions of
the year 2008 are used for every year of the prior?
- p.7 l.208: ". sufficient for our test inversion (Section 3)" -> does this part of sentence goes with the previous one? If so, change "." to ",". Also, why is there a reference to Section 3 inside Section 3? Please check.
- p.7 l.224: "as good as" -> as well as? |
