Dear Author,

It seems that the uploaded manuscript addresses only the editorial comment about code availability.
Please respond to all the reviewers comments:
RC1: 'Comment on gmd-2021-134', Anonymous Referee #1, 15 Oct 2021 reply
RC2: 'Comment on gmd-2021-134', Anonymous Referee #2, 21 Oct 2021 reply
in order to proceed.

Best regards,

The editors

The modified manuscript will be sent to the referees for evaluation of the changes and further review.

Dear Authors,


Please address the points raised by the reviwers:







#1
The authors have addressed my comments to my satisfaction. I cannot see any remaining substantial issues beyond the requirement for a thorough check of the english. There are many minor grammatical errors that do not affect the overall readability, but will need to be addressed. I would be happy to proofread the entire article again after the authors have addressed the remaining comments from reviewer 2.


#2
The revised manuscript

A Regional multi-Air Pollutant Assimilation System (RAPAS v1.0)1
for emission estimates: system development and application

by Shuzhuang Feng et al.

has been re-evaluated. While a part of recommended modifications have been provided by the authors, there are still substantial questions, which either are not directly addressed (probably misunderstood) or insufficiently dispelled.

In summary (for more detail see items below) the presentation quality of the proposed two-step emission inversion method does not demonstrate sufficient mathematical rigour or convincing evidence of a favourable performance, which could be taken as a substantial contribution to scientific progress within the scope of GMD. Therefore the scientific approach and applied methods cannot be confirmed as valid.

The paper cannot be recommended to be published in its present form. As for the application results resting on case study simulations, a submission to a less algorithm or model design oriented journal as GMD may be considered.


Evaluation of responses:

Point 1: Literature survey is still substantially incomplete. The authors might wish to consider the following selection, which mostly share key objectives of their study.

o Bocquet, M.: Parameter-field estimation for atmospheric dispersion: application to the Chernobyl accident using 4D-Var, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 138, 664–681, doi:10.1002/qj.961, 2012.

o Bocquet, M. and Sakov, P.: Joint state and parameter estimation with an iterative ensemble Kalman smoother, NONLINEAR PROCESSES IN GEOPHYSICS, 20, 803–818, doi:10.5194/npg-20-803-2013, 2013.

o Elbern, H., A. Strunk, H. Schmidt, and O. Talagrand, Emission rate and chemical state estimation by 4-dimensional variational inversion, ACP, 3749-3769, 2007.

o Meirink, J. F., Bergamaschi, P., and Krol,M. C.: Four-dimensional variational data assimilation for inverse modelling of atmospheric methane emissions: method and comparison with synthesis inversion, ATMOSPHERIC CHEMISTRY AND PHYSICS, 8, 6341–6353, 2008.

o Muller, J. F. and Stavrakou, T.: Inversion 10 of CO and NOx emissions using the adjoint of the IMAGES model, Atmos. Chem. Phys., 5, 1157–1186, 2005.

o Navon, I. M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn. Atmos. Oceans, 27, 55–79, 1997.

o Yumimoto, K., Uno, I., Sugimoto, N., Shimizu, A., Liu, Z., and Winker, D. M.: Adjoint inversion modeling of Asian dust emission using lidar observations, ATMOSPHERIC CHEMISTRY AND PHYSICS, 8, 2869–2884, 2008.



Point 3 a.: The authors were encouraged to provide mathematical facts on their two-step mixed method approach, or resort to a consistent
method with verified BLUE property (Best Linear Unbiased Estimate). Yet, the two-sstep method, despite its single steps is not shown to have
this property. There is no further evidence provided than ad hoc description based on a single cas study, without sound comparison on the
same weather case with other methods, not to mention any basic explanation. Rather, the authors offer no further supporting matter than
multiple "we believe phrases"

"Although the biases in the high levels were not evaluated, with only ground
observations, we believe that the performance of the EnKF method in the high levels is
similar. .... Therefore, we believe that in this comparison, a combinatorial
assimilation approach used in the "one-step" scheme is an acceptable approach ..."

"... we believe that the “two-step” scheme has better performance
than the “one-step” scheme in emission inversions"

The latter claim of superiority is therefore not at all justified to be adopted as a step forward in aerosol inversion modelling.


Point 4. The authors' response remains unclear. They have added
" H reflects the
combined information of emissions, the physics and chemistry processes in simulations
and the transformation of different species from model space to observation space..." in phase space denoted X for the vector of concentrations. So H acts on X. The problem is not in understanding H. The confusion is whether it only applies to concentrations X, or also on emissions, whereit remains from the first version:
"delta X_b represents the randomly perturbed samples that are added to the prior emissions"

So here it is emissions, not concentrations.

The authors should clarify the scope of X (and delta X), whether it comprises concentrations only (for 3D-var this is obvious), or emissions only, or both concentrations and emissions (feasible in EnKF). The explanation of H is clearly not required.



Point 6: Authors' approach:
"... O3 observations are not assimilated to improve NOx and
VOC emissions using cross species information due to the strong nonlinear effects
within the O3‐NOx‐VOC relationship,..."

Degradation of performance upon assimilation of additional data (here O3) is a typical indication of system inconsistency, which in this case is presumably the model resolution. NOx emissions are often point sources ( industrial, domenstic) or line sources (traffic). In any case, sources are small compared to the model resolution and the assimilation degrades the simulation. The authors make reference to other studies. Yet in assimilation and ensuing forecasts the proof of concept can be demonstrated, but is not done. Therefore the emission inversion cannot be improved!

Therefore I uphold my my recommendation to increase the resolution.

After Reviewer #1, on the three serious points raised, he was unable to see any convincing reasoning beyond the previous argument.
The points raised are as follows:

1. Comparison of the one-step method with the two-step method
2. Notational confusion between concentration and emission
3. Omission of the O3 observation and the NOx-VOC-O3 balance

Please refer to the Reviewer’s report for a detailed explanation of the objections.

Dear Authors,

Thank you for addressing the scientific remarks provided by the reviewers. Please see attached pdf where you can find a few formal changes (typos, grammar, etc.) necessary before publication.

Best regards,

The editors

Dear Authors,

Almost all corrections were incorporated. A couple of typos in the abstract are changed in the tracked changes but not on the revised manuscript. See the attached pdf.

Best regards,

The editors