General Remarks:

The authors studied the contribution of lightning nitrogen oxides (LNOx) to global nitrate aerosols and the impact of global nitrate aerosols on tropospheric composition, aerosol optical depth (AOD), and atmospheric radiation fields. They found that lightning leads to an increase in atmospheric nitrate and sulfate aerosols, with the most significant increase in coarse-mode nitrate, up to 12%. The inclusion of nitrate aerosols reduced tropospheric ozone and increased methane lifetime, both by about 4-5%. The reduction in atmospheric oxidants caused by the inclusion of nitrates is one of the reasons. They also reported that nitrate aerosols increase AOD and contribute -0.4 W m-2 to the net downward radiation flux at the top of the atmosphere. This is an interesting and valuable study. I recommend it for publication in ACP after the authors make the following minor revisions.

Major comments:

The main concern of this study is how confident one can be about the reported contribution of nitrate to the atmospheric chemical and radiative fields. The HNO3 absorption rate is a key factor that directly affects nitrate formation and its subsequent contribution. The rates reported in this study range from 0.193 (fast rate, used in this study) to 0.001 (slow rate). The uptake rates vary by more than a factor of one thousand, so further discussion of the uncertainties in the nitrate effect is necessary, at least qualitatively. For example, the authors may need to conduct a literature review summarizing HNO3 uptake rates on various aerosol types measured in the fields and in the laboratories. They can further provide qualitative uncertainty estimates by combining the measured uptake rates with nitrate formation from various aerosol components.

The main scientific goal of this study is to investigate nitrate-related atmospheric effects, so the description of the chemical mechanism of nitrate formation needs to be strengthened. What features of the formation of fine-mode NH4NO3 component make it a quasi-instantaneous thermodynamic equilibrium scheme? How does this approach differ from the "commonly used instantaneous thermodynamic equilibrium nitrate scheme"? What are the advantages of using a quasi-instantaneous thermodynamic equilibrium scheme in this study? The authors should make it clear in the abstract that their results likely represent an upper limit on nitrate effects, as they used a fast uptake rate for the condensation of HNO3 to produce NH4NO3. The authors should also elaborate on how the model treats coarse-mode nitrate formation. Does the model use first-order condensation of HNO3 on dust and sea salt? If so, what are the corresponding uptake rates?

It is strongly recommended that the authors add tables summarizing their findings on changes in atmospheric composition, AOD, and radiation fields due to lightning and the presence of nitrates. These results in the current framework are scattered throughout the tests and are difficult for the readers to follow. At the same time, the authors should also summarize the emissions from various nitrogen emission types in a table to help readers understand the relative importance of lightning and other emissions to the atmospheric chemistry and radiation fields. It would also be helpful for the authors to report the atmospheric oxidant fields and their changes from the designed experiments in tabular form, as changes in the oxidant field are one of the key reasons for the corresponding atmospheric composition changes.

Specific comments:

1. The conclusions in P1L19-25 are controversial. P1L19-23 showed that the inclusion of LNOx increases atmospheric nitrate and sulfate aerosols, and that the inclusion of nitrate aerosols leads to a reduction in tropospheric ozone loading. This effect of reduced tropospheric ozone appears to be in dispute with P1L24-25, which showed that with increased LNOx, global AOD and top-of-atmosphere net downward radiative flux increase through increased tropospheric ozone.
2. P3L7: What are these “conductive atmospheric conditions”?
3. P5L142: Can you give the mean global ocean flash rate based on Eq. (3) and the observations?
4. P6L158 and P6L166: Given Pno, ic = Pno, cg, how do you partition the flash rate (Fl or Fo) into Fic and Fcg?
5. P8L226: For which aerosol particles does the HNO3 uptake rate coefficient apply here?
6. P12L334: Please explain the significance level defined here? How was the significance level calculated?
7. Figure 8: The figure only shows the difference between the two simulations (Lu21 – no LNOx), instead of “Annual-mean tropospheric NH4, fine NO3, coarse NO3, and SO4 burdens from the Lu21 and no-LNOx simulations (both with nitrate) and the differences ….” in the figure caption.
8. P20L484: Why is “Conversely….” used here? It would be better to explain this sentence and the previous one in more detail.
9. P21L501: How much have tropospheric oxidants increased?
10. P23L519-521: “The coarse mode (soluble) particles (plot not shown) are the least in number and confined to very close to the surface due to their effective gravitational sedimentation, with more particles in the Southern Hemisphere than in the Northern Hemisphere (probably due to a larger oceanic surface in the NH so as to cause a large sea salt particle number concentration).” Please check the sentence. The oceanic surface in the NH is smaller than in the SH.
11. P25L507: How to obtain the uncertainty AOD here?
12. P28L620-622: It is suggested that the sentence be changed to "The negative changes in RnTOA in simulations with and without nitrate indicate a reduction in atmospheric radiation absorption, implying cooling conditions when nitrate is considered." Such a statement is more in line with the common sense of the aerosol cooling effect.
13. P30L642-643: What is the difference in tropospheric CDNC with and without nitrate included?
14. P31L656: What are these “globally averaged modelled atmospheric parameters”?
15. P31L660: Suggest further analysis of changes in the atmospheric oxidant field.
16. P31L666-667: Please elaborate on “the variation considered in LNOx”. What is the variation you are referring here?

Technique corrections:

P2L47: Delete “production” after oxidation.

P4L124: Change the sentence to be “this is followed by results and discussion in Section 4 and then conclusions in Section 5”.

P6L152: Change “parameterisation” to “parameterization”.

P7L193-199: To make the logic more reasonable, move the sentence "Radiative changes include direct aerosol radiative forcing …." before the sentence "The Predicted Cloud Cover and Predicted Condensate (PC2) schemes ….".

P8L213: What is the “10” in “the UKLA-model setup 10”?

P17L437-438: Change “particularly over South Asia with values as high as 3 mg[N] m-2 and over East Asia / China with values as high as 2 mg[N] m-2. Over central North America, values as high as 1.1 mg[N] m-2 are predicted” to “particularly the values as high as 3 mg[N] m-2 in South Asia, 2 mg[N] m-2 in East Asia/China, and 1.1 mg[N] m-2 in central North America.”

Summary

This manuscript uses the the UKCA chemistry-climate model (CCM) to evaluate the impact of lighting NO_x emissions on particulate nitrate chemistry (recently implemented in the UKCA model), and thereby, its influence on climate. 

Overall Comment

I see no overall flaws with the study as performed and reported. However, the manuscript as written oversells its originality and its accuracy. Many global atmospheric chemistry models — including those cited in the introduction — have had nitrate aerosol chemistry for decades, e.g., GEOS-Chem (Park et al., 2004), GISS (Bauer et al., 2007), GFDL (Paulot et al., 2016; and ref. therein). Therefore, any of the many publications that have used these models to look at the impact of lightning on atmospheric composition and climate have included the impact of nitrate particles. The main reason that it has not been highlighted in the manuscripts is because it was noticed be negligible compared to other impacts and/or the nitrate simulation was evaluated to have too poor a skill in reproducing observational constraints, precluding meaningful conclusions. The UKCA implementation of nitrate as reported in Jones et al. (2021) similarly shows very poor skill in reproducing surface nitrate observations over the United States and Europe. I would support this manuscript's publication if it is recast as a theoretical exercise assuming the chemistry is correct (the lightning chemistry-climate interactions via nitrate and cloud microphysics are very interesting!) or if a proper evaluation of the in situ nitrate and aerosol optical depths were included to provide confidence in the simulation.