Review of ‘Quantification of lightning-produced NOx over the Pyrenees and the Ebro Valley by using different TROPOMI-NO2 and cloud research products’ by Perez-Invernion et al.

This paper attempts to estimate the lightning production efficiency of NOx over the Pyrenees and northeastern Spain in Spring 2018 from 3 sources of information: lightning flash counts, TROPOMI satellite above-cloud NO2 column observations, and modelled NOx:NO2 ratios in the upper troposphere. Each of these have considerable uncertainties associated with them. The strength of the work is that the authors address these uncertainties carefully in their approach. Strong about this paper is the use of two different lightning flash networks, two standalone TROPOMI NO2 products, and different approaches to correct for the tropospheric background NO2 not caused by lightning. This is interesting in its own right, as there are considerable uncertainties associated with counting lightning flashes, with the satellite retrieval process, and with our knowledge about tropospheric background NO2. It is also interesting because applying this mini-ensemble provides a robustness check on the quantitative LNOx production, which is at the lower end of previously reported estimates.

The paper has some serious shortcomings which need to be addressed before publication in AMT can be considered in my opinion:

• A weak point of the paper is the reliance on just one CARIBIC flight (22 June 2005) over the Pyrenees-Ebro area. I understand that there may not have been many flights available, but the representativeness of this alternative method to estimate the NO2 background is debatable. A model (e.g. EMAC) analysis of NOx and NOy in the upper troposphere 22 June 2005 compared to April-May 2018 would be helpful to assess this concern.
• Another major concern is the usage of the concept of the “LNOx air mass factor”. In the DOAS-community the AMF is strictly defined as the ratio between the slant and vertical column, and since TROPOMI detects NO2, the use of a lightning NO2 AMF, followed by a model-driven NOx:NO2 correction factor, would be the appropriate way to present this aspect of the approach. It is thus misleading here to use a LNOx AMF since TROPOMI measures NO2, and not NOx. The authors should present the AMF aspect of their approach more clearly, specifically in Figure 5 – the simulations are now input to the center-stage box ‘LNOx PE’, but in fact the simulations both influence the NO2 AMF (the upper box) and the subsequent NOx-to-NO2 conversion. Also in Eq. (3) the application of an ‘AMF_LNOx’ is misleading and should be replaced by division by an AMF_LNO2, followed by a correction factor that accounts for the NOx-to-NO2 ratio. To clearly present how the model is required for their ultimate quantification is important given (a) future reproducibility of their results, and (b) the need to prevent leading readers into believing that NOx could somehow be detected from TROPOMI.
• Figures 6 and 7 actually give little evidence that “areas of high lightning activity coincide with areas with high SCD-NO2”. This undermines an important claim of the paper, i.e. that enhanced TROPOMI NO2 can be traced back to previous lightning flashes. The authors should provide more evidence that there is a relationship between flashes and enhanced NO2, e.g. via scatter plots suggesting a spatial correlation for lightning circumstances, and the absence of enhancements on cloudy days without recent lightning activity. The same unfortunately holds for Figures 8 and 9, while the relationship between lightning and enhanced NO2 is more evident of the low-wind day shown in Fig. 10 and 11.

Specific comments

Figure 1 is not particularly helpful. One way to provide more useful context is to overplot the mean NO2 columns on the map. That way the reader can appreciate the difficulty of distinguishing the lightning NO2 signal from the nearby anthropogenic hotspots such as Toulouse, Bordeaux, and Barcelona.

L34: ‘estima’ --> estimate

L84: Williams et al. (2017) describes the TM5-MP version which is actually used in the NO2 retrieval. I believe this is a more appropriate reference than the Myriokefalitakis-reference.

Williams, J. E., Boersma, K. F., Le Sager, P., and Verstraeten, W. W.: The high-resolution version of TM5-MP for optimized satellite retrievals: description and validation, Geosci. Model Dev., 10, 721-750, doi:10.5194/gmd-10-721-2017, 2017.

L85: where can ‘version 2.1_test’ be found? Please provide a reference. Are v2.1_test data also available for April and May 2018?

L108-109: it is unclear here if the authors have imposed temporal coincidence of lightning flashes with the observation of TROPOMI cloud fractions > 0.95 and OCP < threshold. Or has a time window been taken, such as lightning flashes within a few hours of TROPOMI overpass and TROPOMI fulfilling the above cloud criteria? Please clarify.

P6, Figure 3: I think the authors should show here the detection efficiency for April-May 2018 rather than March 2018 – December 2018. After all, the paper is about the lightning NO2 production in April-May 2018.

L177: it is unclear how the authors have formulated the SCD here. Which slant column do they mean? The total slant column, which also contains contributions from the stratosphere, or the tropospheric slant column?

L180: what is meant with the “absorption of the atmosphere”? I guess this is about the ratio of the slant to vertical (NO2) optical thickness, but it should be clarified.

P9, Figure 4: what was the pressure of the OCP on this day? Please indicate this in the caption. Also indicate the corresponding AMF LNO2 values.

P10, Eq. (1): I suggest to include the TROPOMI measurand, i.e. the NO2 column, here. This is now missing from the equation, which may give the impression that TROPOMI somehow provides a tropospheric NOx column, which is not the case.

L274: the authors state that the free tropospheric NO2 “may be overestimated” in TM5-MP, but I see no supporting evidence for this. Do the authors have any reason to suspect this, or could the TM5-MP NO2 background also be underestimated?

L323 and Tables 1 and 2: the “lower values” of V_tropNOx for the DLR vs. KNMI product are unclear to me. Has the V_tropbck been subtracted to arrive at V_tropNOx?

L359: “background NOx …activity” is printed in italics.  Not clear why. Same on line 371 and 393-394.

P18, Table 3: perhaps useful to also include the overall uncertainty estimate in the table.

The authors have analysed several convective systems around the Pyrenees in order to estimate the production of lightning NOx based on TROPOMI NO2 observations.

The Pyrenees are chosen as they are particularly suited for this kind of analysis. While I disagree here (see below), the paper contributes to the scientific question how much NOx is produced by lightning, and it matches the scope of AMT.

The study is generally well written, but there are some inconsistencies and probable bugs in the presented data.

The authors thus have to cautiously check the presented data, correct the existing bugs, and update the LNOx estimates (and, if needed, discussion and conclusion) accordingly.

In addition, they should consider the additional comments listed below. 

# General comments

1. Study region

As indicated in the title and at several places in the manuscript (e.g. line 70), the Pyrenees are meant to be the focus of this study. In the manuscript, the line of argument is that over the Pyrenees (a) lightning frequency is high, and (b) NOx background is low, and therefore the Pyrenees are an ideal region for this kind of study.

In the presented figures, however, most flashes are observed South or North of the Pyrenees, where also significant boundary layer pollution is present, in particular over large cities like Barcelona, Zaragoza, or Toulouse. This weekens the argumentation considerably, and I am not convinced that the study region is a good choice for studying LNOx from satellite, as the uncertainty of background NOx and the possible uplift of boundary layer pollution severely affect the overall uncertainties.

2. Background 

As most events are not observed over the Pyrenees, the NOx background might be considerably larger in general. The potential uplift of boundary pollution might bias the observed NO2 over the lightnin pixels.

In addition, also the non-flashing pixels over deep convection might be affected by the advection of LNOx. 

The inclusion of two different NO2 products is quite illustrative. For instance, the differences in the estimated stratospheric column between the products are far larger than the given uncertainty of the tropospheric background. Please comment on this.

3. "Lost" NOx

As far as I understood, the study only focusses on cloudy pixels. So in case of LNOx produced within a convective system that disappeared by the time of the TROPOMI overpass, the LNOx would be overlooked in the described procedure, while the respective flashes are included. Consequently, PE is biased low. This seems to actually happen on 29 April.

I propose to skip 29 April, as there are only few TROPOMI observations available, and the extension of the study area to large parts of France is also confusing.

In addition, this effect has to be included in the discussion and the overall uncertainty estimate.

Effects 2 and 3 go in different directions, are hard to quantify, and will increase the overall PE uncertainty.

# Inconsistencies and possible bugs

- Please be consistent with respect to units. Column densities are given in petamolec per cm2 in the text, but in molec per m2 in the figures which makes direct comparisons difficult.

- Please check tables 1 and 2:

  - Mean Vstrat is quite large (> 8e15 molec/cm2 for DLR), while the maps in Fig. 6ff shows values < 4e15 molec/cm2.

  - The 30th percentile of Vtropbck is listed as 9.5e15 molec/cm2 for DLR. This would be a quite considerable tropospheric pollution. Please check.  

- Please check Figs. 10 and 11. The number of flashes displayed in the figures is considerably different, while the numbers listed in Tables 1 and 2 are almost the same for 28 May. Please also check for the other days. 

# Minor comments

Line 8: Over the Pyrenees, the NO2 background is low indeed. But for the investigated events over the Ebro valley, this is not the case, see e.g. http://www.tropomi.eu/data-products/nitrogen-dioxide

Lines 31-34: "Nadir-viewing satellite instruments ... estimate the column densities of NO2 over thunderstorms" - I think this is too fuzzy. The satellite instruments measure spectra. This allows quite accurate quantification of NO2 slant column densities. The conversion into vertical column densities is the main challenge, involving further input data (like cloud fraction and surface albedo, so this might be denoted as an "estimate". But usually, the retrieval focusses on cloud free conditions. Focussing on thunderstorm clouds instead is a quite different and challenging setup which should be pointed out here.

Lines 45-46: I propose to flip the order: "The horizontal resolution at nadir is 3.6 km × 7.2 km before 6 August 2019, while it is 3.6 km × 5.6 km thereafter."

Figure 1: I propose to show a map of tropospheric NO2 instead in order to assess the "clean background" issue.

Line 70: "8 deep convective systems in the Pyrenees": The number of actual flashes over the Pyrenees is quite low. The presented events reveal highest lightning activity South and North of the Pyrenees, with several anthropogenic sources present (e.g. Barcelona, Toulouse).

Section 2.3: I think it is quite bold to estimate "the" tropospheric background NOx column (!) from one day of aircraft measurements (in-situ measurements at 12 km!). The authors should discuss the limitations and uncertainties of this approach in more detail and compare with model results.

Eq. 1: Please specify which quantities are dependent on space (TROPOMI pixel) and which quantities are just scalar (means, percentiles). For this you might use Copernicus style where vectors and matrices are shown in bold type. Please also explain how the total PE is calculated (spatial mean or summation over which area/pixels?).

Eq. 3: Stratospheric VCD and AMF are provided for each TROPOMI pixel. So the stratospheric correction can be performed for each pixel as well. I see no reason to calculate the average here.

Lines 227-231: Several events are outside the Pyrenees, with considerably higher background NOx. In addition, in case of deep convection, tropospheric pollution might be uplifted and transported over considerable distances. So the local tropospheric background estimate over the clean Pyrenees can at best be considered as a lower limit. 

Line 251: Please explain why the DLR product is missing.

Line 509: Please list the existing and the new methods here.

- Figs. 6ff: Maps of stratospheric AMF and VCD are not that informative. Listing these values in tables 1&2 would be sufficient, but the numbers listed there need to be checked.

Instead, I would like to see maps of AMF_LNOx here. 

- Fig. 12 needs some further explanations:

  - how was the median calculated? 

  - what is the meaning of color?