The authors present a new method for estimating NOx emissions and effective lifetimes from large cities. They combined observations for calm as well as two opposite wind directions to shorten the period of data needing for estimation. The method is sound, and the paper is well written. I would recommend minor revisions before publication.

General comment

1. Additional details for the fitting procedure would be helpful for readers to follow up. For instance, Line 113, “E(x) has the same unit as L(x) (amount per length unit) and corresponds to the line density that would be observed if no wind transport would occur. “ Does it indicate that E(x)=L(x) when w=0? Does this condition be used for the fit? If not, in Line 120, “the distribution of emission densities E(x), lifetime τ and backgrounds b are fitted simultaneously.” It looks like too many parameters, each item in E(x), are required to be fit here. How it could be achieved?
2. Seasonal analysis. The big improvement of the method is to shorten the required data period from annual to seasonal. A seasonal analysis of derived emissions will help to clarify this improvement.
3. Section 5.3.1. I’m wondering how much the bias of TROPOMI NO2 over urban areas contribute to the lower NOx emissions?

Specific comment

1. Line 74. Too many full stops here?

The original ERA5 data is 0.3 degree, but the intermediate meteorological dataset is 1 degree. I suppose additional errors have been introduced by this interpolation. A case study using both the original and interpolated datasets for a few cities would be useful to quantify the level of uncertainties.

1. Figure 2. The period used for averaging is missing in the caption.
2. Line 133. How many fitted lifetimes are not plausible? A ratio of the failed values is helpful for readers to understand the results.
3. Figure 5. The period used for comparison is missing in the caption.
4. Section 5.3.1. It is surprised to see the large power plants are missing from TROPOMI NO2 maps. Could you confirm the locations of power plants by Google map to support the guess that emissions are shift?

This paper by Beirle and Wagner presents a new method for estimating NOx emissions and lifetimes for 100 large cities from TROPOMI observations. The estimate is based on the downwind plume evolution for different wind directions separately. A simultaneous fit of downwind patterns for opposing wind directions makes the estimate more robust than previous studies using a single fit.

Results are compared to EDGAR. Seasonal NOx emissions and lifetimes are provided. The assumption of point-source like cities, the background dependency on wind direction, and the benefits of the described method are discussed.

The paper is well-written, falls into the scope of AMT and is scientifically relevant. Therefore, I recommend publication in AMT after addressing the following comments.

General comments:

Line 91: You wrote: “As the NO₂ photolysis rate is driven by the SZA, which shows a seasonality with minimum and maximum close to the solstices, seasons are defined accordingly as winter (NDJ), spring (FMA), summer (MJJ) and autumn (ASO) in this study.” This definition of seasons is not in line with the meteorological and more common definition of seasons as winter (DJF), spring (MAM), summer (JJA), and autumn (SON) and might cause confusion when comparing the presented results with other studies. It may lead to wrong seasonality in the presented emissions and lifetimes. I understand that adapting the seasons to the meteorological and more common definition is probably a lot of work and not easily possible. Therefore, I would recommend pointing out your definition of seasons at important points. This would hopefully avoid confusion and inconsistency in future comparisons for readers not reading the manuscript in detail.

It is possible to do your analysis on a seasonal basis, even if for many cities only one or two seasons are possible to analyze. But is it also necessary to do the analysis on a seasonal basis, as wind directions and speed have a seasonal dependence, or would your “Selection and averaging of fit results”, that is described in Sect. 3.6, consider this? Please comment on this.

If you are not separating the data set into seasons, you wouldn’t need to work on such long-term temporal averages (Line 231).

Specific comments:

Abstract: Add that your study is based on satellite data, maybe even more specifically, 3.5 years of TROPOMI NO2 data.

Line 65: There is a newer, consistently reprocessed data product than the used v2.3.1. Can you comment on how the latest reprocessed data product v2.4 may influence your results?

Line 66: How are the good viewing conditions determined? Have you tested for larger SZA? You mentioned that this may influence the lifetime estimates.

Line 69: Are ozone concentrations from ERA5 as well or only the temperature data?

Line 76: You wrote ERA5 wind data were interpolated on a regular horizontal grid with a resolution of 1° and stored in intervals of 6 hours. This means the closest interval to the TROPOMI overpass is chosen? Can it still represent the wind conditions around the TROPOMI overpass? ERA5 data are available in intervals of one hour. Is horizontal variability a problem when interpolating the original 0.25° resolution of ERA5 to 1° resolution? This is significantly larger than TROPOMI pixel sizes. The study would probably benefit from using finer temporal and spatial grids.

Fig. 2/3: Please add the used data period. Are these figures based on data from May 2018 to November 2021 or a specific season?

Some wind directions show distinct outflow patterns (Riyadh: North-West-wards and South-East-wards), some do not (Riyadh: East-wards) or are not very pronounced. Can you comment on this? How is the data availability? Is there a way to provide information on data availability for the different wind sectors?

Line 100: You wrote you consider distances of +/-50km in all directions. I agree that this is enough in the across-wind direction, but is it enough in the outflow direction? For Riyadh, plumes cover more than 50 km in the outflow direction.

Line 104: You wrote “the mean line density is calculated for calm, forward and backward wind direction”. Maybe replace with: calculated for calm wind conditions and forward and backward direction for windy conditions. Or replace direction in condition. Are windy conditions considered as >= 2? I think this was not specified yet, maybe obvious, but it is better to add it when introducing the criterion for calm conditions.

Fig. 4: “The line densities for calm (blue), forward (green) and backward (purple) wind directions” See comment above “calm” is not a wind direction.

Line 115 & Fig 4: You wrote: “E(x) represents the spatial density of emissions. It is considered to be the same for all 3 wind conditions.” Is this the case, I see that it is sometimes very similar to one of the wind conditions. Which E(x) is plotted in Fig. 4, the result from the simultaneous fit?

Line 122: You wrote: “observed line densities within 150 km of the city center”. This is not in line with the statement in line 100 that you consider distances of +/-50km in all directions, please clarify. The resulting emission estimates are determined within 100 x 100 km², but line densities are fitted within 150 km of the city center?

Line 132: You wrote: “Fit results for a wind axis are considered only if at least 2 directions have sufficient data”. This is not clear to me. One wind axis, e.g., North-South, only has three wind conditions: calm, forward, and backward. Do you mean the wind conditions, or is it something else?

Line 138: You wrote “weighted by the number of contributing directions for each axis”. If the weighting considers calm, forward, and backward wind conditions, I would prefer to replace “directions” maybe with “wind conditions”. The same is true for the word direction in lines 140 & 141

Fig. 5: Please provide error bars for the TROPOMI based emission estimates.

Line 153: You mentioned that for most cities, valid emission estimates could only be derived for 1 or 2 seasons. How do you think this influences this comparison? For most cities, emission estimates are only derived for summer and autumn, but EDGAR considers data from all seasons.

D o the estimated emissions show seasonality for cities for which estimates are available for all seasons?

See your discussion in Line 200. If higher emissions are expected for winter months, TROPOMI based estimates are low biased because most of them do not consider winter months, and EDGAR does. In your comparison, most cities are close to the 1:1 line.

Line 214: Which seasons are considered for Jeddah, Vishakhapatnam, and Copenhagen? Could this explain the overestimation of EDGAR compared to the TROPOMI based emissions? I think it is not given that ERGAR is wrong (too high) here.

Line 219: Add mean lifetime with standard deviation.

Technical corrections:

Line 51: I think m/s should be in exponential notation, please check throughout the manuscript

Line 68: Change Ozone to ozone

Line 83: Add a reference/link and add that you use NOx data

Line 86: Change ERA-5 to ERA5 to be consistent

Line 94: Change Winter into winter.

Line 105/6: Change calm to calm wind conditions

Line 110: Delete “the patterns”

Equation 1: multiplication should be a dot and not x.

Line 146: Add NOx

Data availability: You could add links to used data like EDGAR, ERA5 wind data, ozone data, and the World Cities Database.