The authors are providing a description of how the original local fractions method has been extended making it suitable for application to pollutants influenced by non-linear processes. While the technique is quite complicated and requires some brain crunching to grasp its approach,  the authors have done a good job at taking the reader by the hand through two illustrative examples, allowing easier understanding of the methodology.

The paper thereby can be considered as a good reference for a novel methodology, which provides opportunities to advance in the science of emission change sensitivities. The paper is well written and structured.

General comments:

- Since it seems the method is developed to be applied for source attribution applications

(as illustrated in the applications mentioned in the conclusions some more attention

should be paid to the applicability of the method for such applications. Explain a bit

further how this method could be used to investigate potential impacts of 15% emission

reductions, which is a common emissions reduction used for policy studies. The reader

is now referred to an EMEP report for the comparison with brute force at 15% emission

reduction, but it would be good to include the conclusions of that work in this paper

aswell focusing on potential differences and possible implication for the interpretation

of LF results.

In several places in the text it is mentioned that because of the small perturbations linear

assumptions can be made, what does this mean for application to investigate the impact

of potential policy measures.

Also the LF results are presented as contributions, i.e. transforming the sensitivity to a

very small emission change to a 100% contribution, please explain what is the validity

and limitations of this, for example are the contributions adding up to the total

concentration? This is related to the interpretation of the results for policy makers.

- Throughout the paper maker sure to consistently use the word generalized in

combination with local fractions wherever appropriate to distinguish between the

original local fractions method and the newly developed generalized version.

Specific comments:

- Introduction: explain why it is fundamental to relate the air pollution to emission sources

(i.e. for policy), add some background on how this is normally done (current practice

broader than BF) and how LF comes in.

- Introduction page 1, mention also the need for tracking source sectors besides source

regions.

- Introduction line 25-26, mention interaction between sources

- Introduction line 28 – chemical species , make it clear that this concerns non-inert

chemical species

- Sections 1 and 2, as mentioned in the general comments put the method in the context

of other methods, what is the range of applicability, explain additivity limitations or

limitations with respect to the range of emission changes for which the method can be applied. What happens if there is a limited chemical regime and an emission change

does not have any impact? This question relates mainly to applicability for single source

sectors or pollutants.

- Page 3 line 66, what do you mean with second order effects, which ones? Again here you

focus on small perturbations but how would you apply this method when the policy

maker is interested in impact of large emission changes?

- Page 3 – lines 70-73, What is the difference with the linear adjoint model? What is new to

this generalized LF, why not use the existing linear adjoint model?

- Page 3 – line 76, can it also be a source sector?

- Page 5 equation 8, explain a bit further, especially the minus sign

- Page 5 line 145, ‘however the range of validity is now limited’, please explain what that

means in practice.

- Page 6 line 147, ‘this may not be the case anymore’, what does that mean for the

applicability of the method?

- Page 6 line 154, general equations: what do you mean with general? do you mean the

equations for the entire method, not only chemistry? Do you show the SIA chemical

transformations as example for other chemistry?

- Page 6 line 175, ‘those are’ I guess you are referring to aij with the word those? Or to the

environment, ......? So do you mean that for example the change in NO3 because of a

change in SO4 is assumed constant?

- Page 7 lines 197-199, this is a difficult part, for me hard to follow, explain the small c

versus capital C

- Page 7 lines 190-199, it made it easier for me to follow when I filled in example species,

maybe an extra sentence can be added giving the example of delta SO4 as a result of

delta NO3.....

- Page 8 line 227-228 I do not understand this sentence

- Page 9 line 233 – what are those sets? You mentioned before 3 sets for SIA, but what

would be the others, can you give some additional examples?

- Page 9 line 244 how are the fluxes dependent on the five nearest cells?

- Lines 246-247: these are nearly a duplicate of lines 244-245

- Lines 248-250, isn’t a change in the advection rate also physical?

- Line 276 ‘improve’ you have already put in italics, but isn’t it more stable results?

- Line 281-283 how small/large do you expect this impact to be and in which situations

can it be expected?

- Line 292-293 again is expected impact small/large and in which situations can it be

larger?

- Line 318-319 this is not the case for all tagging models, also in those methods they

make use ‘smart’ computationally more efficient methods, such as calculating the loss

and production rates for the total tracer concentration and then multiplying a followed by

a (sparse) matrix multiplication to get the chemical conversions for each tag.

- Table 1 caption is fairly complicated to understand change title to relative run times

generalized LF and speed up in comparison to BF. And move the sentence ‘the reference

time....’to the end  by the time required using the LF method (...) where the reference

time is taken .....

- Table 1 total time  LF total time and add unit here (reference time) to clarify

- Lines 341-342 is this for generalized LF? Which spatial resolution

- Lines 343-344 I think the detailed numbers could be omitted, to me it would be enough

to state that in practice the LF run is 10 times faster than corresponding BF simulation,

which then agrees with table 1.

- Section 3.4 add a short introduction what this is about, are you looking for options to

simplify and obtain a speedup? Maybe change the title to optimization through

approximating chemically active species. Implemented and possible simplifications

seem to be mixed in this section, make this more clear. Are you trying to say that the

method can be sped up if you would look at S, N, .. atoms instead of species such as

NO2, NH3, .....?

- Lines 383-388 which emissions are used?

- Lines 394-397 the paper would benefit from including the conclusions of the 15%

emission reduction investigations since these are relevant to understand the

applicability (range) of the method

- Line 430-432 and 437-438 do you mainly see them over sea? Did you check other days,

while July seems an appropriate period for ozone chemistry, maybe for SIA another time

period should be preferred. And are the differences so small they would not impact in a

policy application?

- Line 438, what do you mean by these are also present in BF simulations

- Lines 468-477 here you make the connection to practical source attribution

applications, I believe it is important already earlier in the document to identify the

needs for this, how the assumptions and simplifications made will impact this and how

to deal with larger emission reductions.

Technical corrections

- Page 3 line 83 and 85, page 5 line 118 (also in other places in the report), please add the

units of e.g. Ci, E, vi....

- Line 248 add an s after emission --> emissions

- Line 262 same fluxes --> same base fluxes

- Line 280 ‘a change of emissions will change’ --> may change

- Line 287-288 move the word however : the impact of this limitation is however.....

- Line 297 a test may --> a test is

- Line 299 procedure may --> procedure is; iterations used may --> iterations used depends

- Lines 301, 312, 317, 327, 379, LF approach --> generalized LF approach

- Line 356 this represent --> this would represent

- Line 363 emission --> emissions

“Generalized Local Fractions – a method for the calculation of sensitivities to emissions from multiple sources for chemically active species, illustrated using the EMEP MSC-W model (rv5.5)”

by Peter Wind and Willem van Caspel, submitted to Geoscientific Model Development (GMD).

Summary and Overall Evaluation

This manuscript presents an important and methodologically sound extension of the Local Fractions (LF) approach to account for chemical transformations in chemically active pollutants, enabling efficient estimation of source sensitivities in a single simulation. The generalized LF method is implemented in the EMEP MSC-W model and validated against the brute force (BF) method. This is a highly relevant contribution to the field of atmospheric chemistry and chemical transport modelling, particularly in the context of source-receptor relationships and emission control policy support.

The paper is well-written, technically solid, and clearly illustrates the method, its implementation, and validation. The generalization of LF to chemically active species represents a significant advancement with substantial computational benefits. I recommend that the paper be accepted with minor revisions.

Major Comments

The core methodology is presented in detail and with rigor. However, the paper could benefit from including a flowchart or schematic summarizing how the generalized LF sensitivities are calculated in comparison to the BF sensitivities.

The validation section is appropriate but could be strengthened. The comparison is limited to a 24-hour period and a single country (Germany). While this suffices for proof-of-concept, readers might benefit from including or summarizing more from the referenced EMEP Status Reports (e.g., provide direct comparisons of longer-term simulations or bias metrics).

The handling of discrepancies arising from chemical regime discontinuities is important. The authors mention filtering but do not show filtered vs. unfiltered results. Including one such illustration would be helpful.

The citation of other relevant literature in the paper is done in a very narrow way. The authors tend to cite large amounts of their own work and work of their colleagues, and what seems like a bare minimum of other work from the broader literature. As a result of this, the paper lacks context about how the work fits in with other related studies. The narrow citation strategy will also limit the discoverability of this new work through tools like citation databases. The authors should make an effort to discuss their work in relation to previous literature on adjoint / tangent linear modelling, other source attribution techniques such as tagging, and policy-relevant source/receptor modelling.

Minor Comments and Suggestions

Line 59: how large is “large enough”?

Equation 1: explain why there is no subscript i on the LHS. Shouldn’t the local fractions be defined per chemical species?

Line 85: shouldn’t the emissions E_k also have subscript i?

Equation 3: the absence of the subscript i here implies that the reduction factor applies equally to all species emitted by sector k. Is this correct, and if so, is this a limitation of the method?

Equation 4: Define “S” here.

Section 2.3.1: Are there any examples of this non-linear deposition in a real CTM simulation?

Section 2.4.1: Does the choice of a small delta limit the size of the perturbations (difference from the base case) that can be calculated using Local Fractions?

Line 233: how are these 60 perturbations chosen?

Line 396: This strikes me as a cop-out. The whole point of the Local Fractions method is to approximate the sensitivities of non-linear systems, so some discussion of the differences between the results obtained from Local Fractions and the results of 15% perturbations is definitely appropriate in this paper.