|This paper describes LUMIA, a new modular regional inversion framework to estimate CO2 fluxes. The framework is demonstrated with pseudo and real CO2 observations used to estimate net ecosystem exchange over Europe, and the sensitivity of the results to various inversion settings. I believe that the paper is a worthwhile contribution. I think the balance between description of the framework, presentation of results and sensitivity studies is about right to highlight some important aspects of the framework. Some of the responses to Reviewer 1 would be worth including in the paper but as far as I can see are not currently there. Some of the inversion terminology and concepts should be explained more clearly for readers that are not already very familiar with them. Also, the paper needs some editing to improve the English (I have suggested some corrections below). I recommend publications after attention to the following comments:|
Response to Reviewer 1: Some of the discussion in the response to Reviewer 1 doesn't come through in the revised paper and would be valuable to add. For example, Comment 1 - add the paragraph that mentions the outgoing air mass, and the paragraph on the performance limitation. I think it is worth suggesting ways to improve the annual estimate (as already mentioned in the response to Reviewer 1, comment 2, on air exiting the domain, and putting a constraint on the annual budget). The authors say the poor annual flux estimates are a general issue with regional inversions, has the problem been discussed or solved elsewhere that could be referred to? Mention the cost of computing the footprints in the paper.
line 32: "For future climate simulations, the only available options is through "direct" (bottom-up) modelling ..." - this may be confusing to readers. Only option for what? The whole sentence could be improved to be more informative.
line 38 - 'inverse approaches provide robust estimates of total fluxes at large scales ...' - perhaps temper this with 'can provide'. The Gurney paper is a global study, this should be pointed this out. The example in this study shows that total fluxes are not always robustly estimated on large scales by inversions. 'On the contrary' is out of place here.
line 57-58 - why are there a lack of options for cross-validation? Perhaps also briefly explain what cross-validation is.
line 72-73 - explain foreground and background concentration
I think it would help readers relatively new to the area if a couple of sentences were added to explain how footprints come from and relate to the transport model, that we can take H(x) as equiv. to Hx, and how inversions can use either the footprints or the full transport model and adjoint. There are elements of this information scattered around, but something fairly early on to draw it all together, maybe around line 87, I believe would help. At line 146, H(x) equiv to Hx comes after both H(x) and Hx have been used separately without being clear how they relate, so this information should come earlier than line 146.
line 89 - 'In the simplest cases, the system can be solved for x analytically, but most often inversions use the Bayesian inference approach' - I believe that a simple case be solved analytically and also use the Bayesian approach? The sentence makes it sound like it can't.
line 96 - 'of each departure from each prior control variable xib and from each observation yj' - the each ... each ... each doesn't sound good. Can the sentence be improved?
line 129: The scripts folder is not mentioned above with the other folders, lumia and transport. Are there any other folders? Can all folders be mentioned together?
Fig 1 - the text is very small in the printed copy. Flux files, and Flux pre-processor - are these just for the prior fluxes? If so, could you add 'Prior'?
line 145-149 - number these steps, to match step numbers at line 162
Fig 2 - could add latitude and longitude numbers around the grid
line 162 - add lower case omega after 'vector' to emphasize what quantity is referred to here.
line 179 - 'the inversion adjusts an offset to the prior, high temporal resolution fluxes' - I would put that sentence before equation 6, as I think it is easier to understand in words first, then eqn 6.
line 193 - sometimes the word 'footprints' is used, other times 'response functions'. It is good to use both terms when the concept is first introduced, but then stick to one of the other.
line 212 - number the steps
line 211 - 'inversion-derived CO2 fluxes' - could add the word global again here to emphasize that they are from a global inversion
line 222 - is subtraction of foreground concentrations from total ones the same as running the model with only fluxes outside the regional domain?
line 231 - 'accounted for' - need to be more specific about how they are accounted for. Same at line 322.
line 232 - what is 'It'? The global inversion?
line 236 - this refers to the global inversion, right? Add 'global' after 'The'?
line 246 - 'for each observation site' - in the regional domain?
line 282 - 'very contained' - is there a better word to use here?
Table 1 - Could add to the caption that set 'A' is mainly high altitude sites, and set 'P' includes only low altitude sites.
line 365 - I don't understand 'absolute next monthly flux'
Table 3 is a good description of the cases, I would refer to it a bit earlier in the text, perhaps before the tests are listed (e.g. 'In the sensitivity tests (Table 3), we vary ...'). Table 3 caption refers to the letters R and B that are no longer relevant.
line 391 - 'In total, the absolute prior error slightly exceeds 3 PgC...' what quantity is this referring to, and what are the units?
line 394 - units PgC/month?
line 396 - 'this results in a strong degradation of the annual estimate' - presumably this happens because the prior was already a good estimate of the annual NEE. If the prior had been worse at the annual scale this may not have happened. Similarly at line 551.
line 397 - begin a new paragraph to move from discussing temporal to spatial.
Fig 5 caption - Mention at the start that this is for the OSSE. Be clear that the 'ensemble' is the set of sensitivity tests (also in Fig 6 and section 4.2 and elsewhere).
Section 4.2 repeats earlier text.
Fig 7 - blue and cyan are very similar in the middle plot. Is 'posterior bias' the right y-axis label for the right plot, why not 'distribution of residuals'? Making the blue line in the right plot a lighter blue would make it easier to distinguish from the black line.
line 579 - 'model calibration effort' - is that calibration of the transport model or terrestrial model? An OSSE could be done with one atmospheric transport model used to calculate the pseudo observations and a different one in the inversion.
line 586 - 'possible seasonal offset towards the month of October' - be more specific.
Have other regional European inversions also had trouble constraining the annual budget of CO2?
Check formatting in some refs - Peters et al, NOAA 2019, van der Laan.
line 767 - update Rayner et al (2018) reference to 2019, ACP
Line 2: add 'that' after 'accuracy'
line 27: forcings -> forcing
line 45: informations -> information
line 47: ran -> run
line 54: strains -> strain
line 57: of -> for. 'more boundary conditions', or just 'boundary conditions' (i.e. remove 'more')
line 60: models -> model
line 66: to -> with
line 76: against -> using
line 87: of -> for. Remove second 'of'
line 95 - weigh -> weight
line 100: estimates -> estimate
line 102: feature,is,is -> features,are,are
line 107: 'On the other hand' is out of place, perhaps 'Unfortunately' would be better
line 119: delete 'a'
line 130 'helps keeping' -> 'will help to keep'
line 131: 'easily constructing' -> 'the easy construction of'
line 210 in -> of, concentrations -> concentration
line 222 - to -> from
line 223 - assumptions -> assumption
line 223-226 - improve the sentence
line 226 - 'On the other hand' is out of place here
line 287 - 'it -> in
line 333 - processed-based -> process-based
line 335 - either remove 'the' before 'Farquhar', or add 'model' after '(1980)'
line 336 - account -> accounts
line 351 - regarding -> compared to
line 374 - add 'the' after 'as'
line 459 - remove 'the'
line 461 - performances -> performance
line 473 - coherent -> consistent
line 479 - inversions -> inversion
line 494 - 'the double of the average' -> double the average'
line 521 - something wrong with the sentence here - remove first 'is'?
Fig 10, middle panel - right y-axis labels are cut off at the top
line 551 - these -> the
line 564 - identifying -> identify
line 591 - from -> with?
line 597 - against -> for?
line 620 - remove the second 'be'
line 626 - enablesd
line 631 - performances -> performance