This manuscript describes the development and application of a 4DVAR system to optimize SO2 emissions in China. An OSSE test shows improved consistency with the true emissions after optimizing emissions using this system. The framework has also been applied to estimate SO2 emissions during the COVID19 shutdown and shows a reduction of 18% compared to 2019. The topic fits the readership of ACP. I recommend publication after addressing the following comments:

L18, please specify the studied region in the abstract.

L64 – 77, I would expect literature reviews on the application of 4D-Var to SO2 emission estimates in this paragraph. There are several of such studies. How are these 4D-Var estimates compared with previous EnKF SO2 estimates and your results?

Eqn1, it was not clear to me whether H is an operator or a matrix from my first glance. I suggest using a different font for H.

Eqn3, the use of H delta(c) here implies that the operator is linear, but I doubt that for SO2. Could you discuss the impact of this assumption on the results?

L239, it is not clear to me what is the objective of these experiments just based on what is described here. Please clarify.

Fig 7 & 8, how are these emission changes compared with previous studies?

Fig 11, the observation is significantly smaller than the simulations, even after DA. Could you address this a bit more and discuss the implications of this? How is this compared to other studies?

Comments to “Four-dimensional Variational Assimilation for SO₂ Emission and its Application around the COVID-19 lockdown in the spring 2020 over China” by Hu et al.

A timely and accurate emission is important for atmospheric chemistry simulation and pollution control. It is challenging and difficult to estimate the emission by using the “top-down” approach of 4DVAR. To my knowledge this is the first time when the 4DVAR system is development for optimizing SO2 emission and applied to investigate SO2 emission changes during the COVID-19 lockdown. The results shows that there is a significant decrease of SO2 emission between 2019 and 2020 due to the COVID-19 lockdown. It is reasonable and helpful for the improvement of atmospheric chemistry forecast. I suggest publishing this paper after the following points are addressed.

1. In the introduction, I suggest the author add some descriptions of emission optimization with the EnKF method.
2. In Fig. 2, how does the author classify the assimilating stations and verifying station?
3. In Fig. 3, there is not a box of observation in the flow chart. In addition, the variable of output is only SO2 emission. It should be added the initial SO2 concentration, since both the SO₂ concentration and the emission are the state variables in this study.
4. Why the author firstly optimized the SO2 emission of 2019 from the emission of 2016. Did the author directly optimize the emission of 2020 from the emission of 2016?
5. The author did not show the increment field of SO₂ concentration. I suggest the author add it. The scatter point of SO₂ concentration between observation and assimilation also should be illustrated.
6. L166-168：The variables such as Lturb and Ldry in the description and Eq. (9)-(13) are inconsistent. Please clarify.
7. L172: should be  in Eq. (10).