Stevenson et al. explained the extraordinarily high methane growth rate in 2020 with anomalously low methane sink (less OH) in response to reduced anthropogenic NO_x emissions due to COVID-19 lockdown.  They referred to previous modeling results to quantify the sensitivity (CH₄ mixing to NO_x emissions) and argued that the observed additional methane growth can be almost fully explained by reduced NO_x emissions. While their hypothesis is an interesting and potentially important one,  it still lacks concrete and convincing proof of the hypothesis as usually found in a research paper.

Specific comments are as follows. 

First, the authors did not assess the impact of other species whose emissions may also have reduced together with NO_x during COVID-19, for example, CO and NMVOC. Reduced emissions of these species have an opposite effect to that of NOx, that is, to increase OH and reduce CH₄ lifetime.  According to Fig 3 of Lamboll et al. (2021), emissions of CO and NMVOC were also substantially reduced though with slightly smaller fractions compared to NO_x. Fry et al. (2012) showed with their model that the net effect on OH is close to 0 with compensating effects from a combined 20% reduction of NOx, CO, and NMVOC. So, the author's argument can be much stronger if they can estimate the net chemical effect of the COVID-19 emission perturbation.

Second, the calculation of the authors relies on the sensitivity of CH₄ mixing to NO_x emissions, taken from previous studies. Most of the studies cited are from the 2000s. The "baseline" emissions of NO_x as well as other chemicals may have changed a lot from the early 2000s to 2020. I wonder if the sensitivity of global OH and CH₄ to NO_x emissions will also change, and if so change by how much, with the "baseline" emissions. This chemical system is known to be nonlinear. 

Third, independent observation evidence on reduced global OH, if there is, can be really powerful. The 5 ppb additional increase in methane mixing ratio translates roughly to a 3% decrease in global OH concentration if they were attributed entirely to reduced NO_x emissions. This magnitude of decrease in global OH can have detectable signals on burden or distribution on many species besides CH₄ , such as CH₃CCl₃. If these analyses are consistent with the author's hypothesis of NO_x chemical feedback, it can really increase the confidence, though it may be a lot of work.

The manuscript discusses the impact of NOx emission reduction on the atmospheric CH4 growth rate associated with COVID-19 lockdowns around the world. They show that the changes in NOx are the key factor that drive the CH4 changes. The research topic is important for understanding the role of anthropogenic emissions on atmospheric oxidability and the CH4 budget. However, I cannot agree that the simple calculation presented in this study can support the conclusion.

1. My main concern is that the authors directly apply the sensitivity of CH4 to NOx emission changes estimated by previous studies for broad regions using different models for different periods. Since the OH chemistry is higher nonlinear, such estimation can lead to a large bias. For example, if we use the sensitivity of OH to NOx emission changes in the N. Hemisphere (-0.39) and the 16.72Tg NOx emission changes to estimate CH4 changes, we get 6.5Tg CH4 changes in the N. Hemisphere, much smaller than the 8.5Tg when considering sensitivity in 4 different regions. The sensitivity given by Wild et al. (2011) and Derwent et al. (2011) are estimated by perturbing the emission for the whole year, but the lock-down time-period are different in each country. For example, the emission reductions in China (East Asia) mainly occur during February, and gradually back to normal from April (Fig.6 in Miyazaki et al. (2021)). In winter the sensitivity of CH4 to OH may be much lower than in other seasons (low OH production and CH4+OH reaction rate). Thus apply the sensitivity estimated for the whole year may lead to overestimation of CH4 changes. In addition, most of the sensitivities in table 1 are estimated based on simulation for 2000 or earlier. Changes in global emissions from 2000 may influence the sensitivity of OH to precursor gases.

I agree that the reduction in NOx can contribute to the rising CH4 during 2020, but I don’t think the 4.9ppb increase in the CH4 mixing ratio estimated in this study is reliable considering the nonlinearity in OH chemistry. Besides, emissions of other chemical species such as CO also changed during the lockdown period. So, the conclusion that “the NOx changes can account for all or most of the observed methane changes” cannot be supported by the simple calculation present in the manuscript. The changes in emissions are already available (Lamboll et al. 2021). I recommend the authors quantify the sensitivity of OH to emission reductions by conducting model simulations for 2020.

2. Most of the sensitivity of CH4 to NOx emissions changes listed in Table1 is not the original data that we can find from the references. I think the authors should clarify how they convert the data from the references to which is listed in table 1 in the supplementary.

The paper by Stevenson et al. uses model-derived sensitivities of methane to nitrogen oxides (NOx) emissions changes and estimates of NOx emissions reductions resulting from COVID-19 lockdowns to estimate the impact of changes in NOx emissions on atmospheric methane growth rates. Their hypothesis is that reductions in NOx emissions during COVID lockdowns are the main driver for the increase in atmospheric methane growth rate seen in 2020 compared with 2019.

General comments

This short paper is well written, well organised, and comes to an interesting conclusion about the role of NOx emissions on the atmospheric methane growth rate in 2020 compared with 2019. Using pre-existing model output of methane sensitivities and estimates of NOx emission changes, they find that the dramatic reductions in NOx emissions brought about by the COVID-19 national lockdowns can explain a large component of the surge in methane growth rate seen since early 2020.

While the findings are definitely interesting and make use of pre-existing model studies, for a research paper in Atmos. Chem. Phys., the analysis is not substantial enough. For example, the paper makes use of methane-to-NOx sensitivities based on very broad regions in the case of surface emissions (N. America, Europe, S. and E. Asia, Southern Hemisphere) and a global sensitivity scaling factor in the case of aircraft emissions, despite the spatial heterogeneity in sensitivity, as the authors themselves noted. In particular, the southern hemisphere is treated as a single region, despite the potential for increased sensitivity in low-NOx regions. More regional-scale sensitivities could be available through Phase 2 of the Hemispheric Transport of Air Pollution initiative, but the authors did not explore their applicability to support their hypothesis.

The second major consideration is that the potential impact of changes in commensurate emissions of carbon monoxide and/or volatile organic compounds during national lockdowns on the atmospheric methane growth rate was not quantified. Although NOx is clearly a contributing factor, it is not the sole influence and these other potential contributors to changes in methane growth rate were not assessed.

Finally, the authors cite the paper of Lamboli et al. who estimate the emissions reductions due to COVID lockdowns and outline a protocol for global climate and Earth System Model simulations. First results on the climate response from these model simulations have been published and interactive chemistry was included in a number of models. Therefore, there is data available that could address the spatial heterogeneity of the methane sensitivities and the role of other emission changes that would add substantially to this analysis.

Given these concerns, I would not recommend publication in its current form.