The manuscript is based on ASIM observation (BLUEs over cloud top) and make the parameter (CTH, CAPE, TP, CLWC, CSWC) fitting algorithm for BLUE occurrence rate using ECMWF ERA5 data. Then, authors used ASIM BLUEs occurrence rate to validate the adopted parameterization. Finally, they predict results with EMAC models and conclude that 17-28% large than present day model. The in-cloud corona schemes can help to understand the contribution of greenhouse gas and oxidant species from BLUEs.

I thoroughly enjoyed reviewing this manuscript and only have some minor requests for revision.

ASIM only recorded BLUEs at nighttime. Hence, the corona parameterizations with CAPE, TP, CLWC and CSWC were only validated at nighttime. In general, thunderstorm activity is expected to be more intense in the afternoon than nighttime since updraft are weaker without heating by sunlight. Are there any assumptions for BLUEs occurrence rate for nighttime or daytime?

The flash occurrence rate are several times larger than BLUEs. Is any significant difference between flash and BLUEs occurrence rate?

Do you explain more about the contribution of greenhouse gas and oxidant species for BLUEs?  Authors are encouraged to claim more important effects on the future weather system.

It is unclear that how the RCP6.0(Representative Concentration Pathway 6.0) affect the BLUEs occurrence rate? What is the important implication of climate changes for BLUEs rates?

Solar activity and aerosol from human activity may be related with climate change. In your modeling results, do you consider other external factors, e.g., solar radiation or aerosols and their relation to climate change. Bedsides, volcanic eruption or human activity will be the unexpected factors in your models.

Review of “Parameterizations for global thundercloud corona discharge distributions” by S. Soler et al.

The manuscript by Soler et al. presents for the first time a series of parameterizations of thundercloud corona discharges, which have been extensively reported by the Atmosphere Space Interaction Monitor (ASIM) onboard the international space station in recent years. At a rate of about one tenth of that of lightning flashes, corona discharges greatly contribute to the electrical activity within thunderclouds and were predicted to have a non-negligible impact on the atmospheric chemistry. They may therefore be an additional and yet unknown source of several chemical compounds besides the upper tropospheric dominant lightning NOx source. The parameterizations are applied to reanalysis data and to a chemistry-climate model, allowing extension of the study to climate scenarios. I believe the manuscript is a novel and relevant contribution to the Journal, although I have some remarks and suggestions that I would like the authors to consider before publication. I apologize for the delayed publication of my comments.

My main concern is on the quality of the parameterizations, which are based on yearly and globally averaged data. Adopting yearly averaged data implies that we move away from the physical processes, which are linked to hourly or sub-hourly activity of the storms with a large temporal variability in a certain region (or grid point), towards the dependence on the geographical variability of average occurrences, which is then largely affected by large scale circulation and specific local conditions. I understand this is due to having only instantaneous observations at different spatial location, but the difference between temporal and geographical variability should be dealt with. The parameterization is in fact then applied to hourly data. The concern arises from the comparison to the observations, which seems not very satisfactory to me when looking at Fig. 2 (ERA5), Fig. 3 or Fig. 4 (model). At a first glance, the distributions found are very similar to climatologies of precipitation or lightning. The differences with the observations over the oceans and lightning chimneys are very large, roughly an order of magnitude. The parameterizations lead to almost homogenous peak values over the oceans and land in ERA5, missing the major lightning chimneys that are instead very clear in the observations. In the climate simulations, major peak values are shifted from the continents to the Pacific Ocean (160 E). I also miss a quantitative comparison of the spatial distributions. The quantitative agreement is purely based on global mean rates: the simulated rates are very good, but due to underlying large discrepancies in different regions. It seems that additional constrains over the ocean are needed, which in turn may lead to higher values over land. I think the highlighted discrepancies should be properly addressed.

A further concern I have is on the climate scenarios. They are interesting but I feel treated as a secondary product with no full support. As a result of this approach, they are also relegated to the supplementary only. I think either the authors are convinced by their results, and they should gain full presentation. Or they are not, and they should not be included. I think the projections are interesting and relevant, so they should find a proper description with at least one figure in the main paper. On the other hand, the changes that are presented are shown to be largely dependent on the land-ocean contrast, with large positive changes expected over the continents, and negative over the oceans. Since the adopted parameterizations fail to correctly simulate these contrasts, this will greatly affect future estimates. The projected changes may be different (much larger?) than what currently reported in the manuscript.

DETAILS

L39-45: this is hard to follow, please break sentence/rephrase

L43: what is “6 – 3.5” standing for? If I read correctly, I would reverse that. Also, 45/6 and 45/3.5 does not give 7-12 times.

L47-48: I am not sure whether the results by Jenkins et al. 2021, and Brune et al. 2021, can be directly attributed to corona discharges. Could you elaborate better on this?

L50-59: this is a crucial point in your work but is not well introduced. It seems these meteorological parameters were used either because previously adopted or because they work pretty well. I would expect some minimal consideration on the physics behind. Also, it is not clear to the reader how this will be different from a lightning parameterization.

L58: please rephrase “seem to work pretty well”

L60: here and elsewhere. Several sentences are very long and complex. Could the authors revise the manuscript breaking/shortening such sentences?

L65: I understand the preliminary goal is to prove the adopted parameterizations work well. Please mention that the parametrizations are first tested on reanalysis data.

L68: please note that 2091-2095 is not a climate relevant time interval. One should consider a 20 or 30-year long period if dealing with climate change. 

L73: I find this unusual. If the authors explore the parameterizations in climate models under different climate scenarios, why relegating them to the supplementary only? If these are main results they should be in the main paper. If they are not, I would drop them.

L78-79: the sentence “ERA5 updates the previous ERA-Interim reanalysis (Dee et al., 2011) which were stopped being produced after 31 August 2019.” is out of date. ERA5 has already been adopted by thousands of studies.

L86: this is unclear to me. Year data are produced and adopted for all parameters but (L91) the parameterizations are tested on hourly data. Could you clarify?

L99-100: Soler et al. 2022 is cited twice

L102: “candidates, this distribution is described” something wrong in the sentence here

L116: could you please specify what lightning parameterization is adopted in EMAC and whether the approach followed in this study is similar to Gordillo-Vázquez et al., 2019 by some of the same authors?

L119-L120: are all these parameters obtained by subgrid parameterizations? Is this affecting your parameterization as compared e.g. to ERA5?

L131: please mention that the ERA-Interim starting field has no impact on the simulation (since you are then adopting ERA5 for the parameters).

L138-143: I understand the limited period of the observations, which are of course due to the novel space experiment. It is on the contrary unclear to me why the authors have chosen such a limited period of time for the model simulation. I would expect some 20 years (or at least 10 years) to obtain enough variability under a climate scenario. Also, could the authors specify whether the EMAC model is run together with ECHAM, or whether the climate run was already available and the EMAC model is run starting from its results? This would clarify how a scenario run can be performed with only a 1 year spin-off.

L151-158: isn’t CAPE simply showing the possibility of convection, rather than its actual occurrence? In fact, as you mention later, this is not working on the ocean. And moving to meridional distribution the correlation becomes fairly poor. It is not clear how often a high CAPE will be linked to lightning or BLUEs (see Husbjerg). Why not adopting the muCAPE?

L160: this is the first time slow and fast BLUE discharges are mentioned. Since this is a not well-known process, it would be of help for the reader knowing what slow and fast mean.

L162: this is the first time that values for coronas are compared to values for lightning. I feel more relevance should be given since the beginning of the section (and of the paper) to this comparison. How different do we expect the two distributions to be? How different are the driving processes/parameters?              

L165-166: as anticipated in the comments to the introduction, I feel there is too little explanation for adopting parameters that describe the liquid and frozen water content. This is the basis of the parameterization; I think the reader would much appreciate some better explanation. 

L166: I do not understand why the authors cited He et al. Could you please clarify? Is it to support the use of CLWC and CSWC? But here the authors are not accounting for electrification processes. In fact, looking at the results over the ocean, this is possibly a source of the shortages that are shown. When are CLWC/CSWC transformed into charges? Can the authors impose here a correction to the discrepancies found particularly over the oceans?   

L187: “predictand.”?

L195-205: the coefficients for the parametrizations are obtained fitting yearly global mean values. This leads to very large simplifications, which are then revealed by the spatial distributions in the following of the paper. Would the results be different if fitting directly convective precipitation or lightning? I.e., is the parametrization sensitive enough to corona discharges, or simply to lightning activity (or even convective precipitation)? If this is the case, what is the added value as compared to a lightning parametrization? This is not clear to me and I would very much appreciate seeing this discussed. This approach implies that only the average yearly conditions of a certain region are considered, rather than the full temporal variability within that region. Why not fitting the local (spatio-temporal) conditions and then average the results?

L210: I think the manuscript should make the different use of hourly, monthly and yearly data clearer. If I understand correctly, here the parameterizations are applied to ERA5 hourly data and then averaged over the time interval. This was not completely clear to me since the parameterizations are derived from annual mean data.

L213: “the proposed BLUE parameterizations work fine and are consistent with observations by ASIM”. I think this is overstated. Looking at Figure 2, I can see the parameterization leads to roughly 1 order of magnitude differences over the main lightning chimneys (too little) and over the ocean (too much). Not a word is currently spent on the discrepancies over the oceans.     

The authors should compare the observations and parameterized occurrence density quantitatively (difference, ratio, R^2, RMSE, etc). Also, adopting two different style of contour/bin mapping does not help, and I invite the authors to adopt a consistent approach to ease the comparison. One way could be downgrading the spatial resolution (e.g. 5x5 or even 10x10) and showing both observations and results with the same mapping style. I understand some interesting features at the edge of the active regions would be smeared out, but the comparison would be more robust. The same concern applies to the results from the climate model in Figure 3. Here the deficiencies over the ocean are even larger, with values in the western Pacific exceeding those over Africa. Once the comparison is improved, I feel these shortages should be tackled somehow, imposing further constrains over the oceans. Right now, the very good agreement on global rates depend on a counterbalance between large discrepancies.

L257-258: the authors should better describe this: is it ASIM shut-off over the SSA or not? How are the observations affected by the SSA?

L271: Why relegating climate projections to the supplementary. If these are robust, I think they deserve to have at least one figure in the text. On the other hand, since the agreement over the ocean is poor, also the estimates in projections will be affected. In particular, most of the negative changes are shown to occur over the ocean. Have the authors obtained their changes (e.g., 28% or 24%... depending on the type of parameterization) by a global average of the changes? Or as a change in average global rates in the past and in the future? I think the latter case would be more robust, since regions with little contribution will continue to have little contribution even if increasing by a large amount. The discrepancies over the ocean will greatly affect these estimates since projections show large negative differences over the ocean only. One may therefore expect a much larger positive change on a global average than currently estimated in the manuscript.