The author presents a useful “toy model” data assimilation environment for flux estimation, complementing a long history of such toy models in the dynamical literature. The model description is appropriate and the presented case studies are interesting, and I recommend publication after the following comments are addressed. My comments are from my perspective as a practitioner of emissions flux inversions (i.e., an enthusiastic potential user of EnviFlux), and are primarily about the extent to which the full range of problems arising in my work could be investigated with this tool.

What is the computational performance of EnviFlux, in terms that are meaningful for a typical practitioner? For example, what would it take to infer daily fluxes at roughly 2x2.5 degree resolution for a year? How many cores? How much wall time, memory, etc?

Clarify the spatial domain(s) supported by EnviFlux (e.g., does it have to be global).  Regional simulations with boundary conditions imposed by a global flux inversion are a very important case in, for example, methane, and introduce huge questions in error quantification (e.g., to what extent do we alias boundary condition error onto in-domain emissions estimates); it would be enormously useful to investigate this with a low-cost tool like EnviFlux.

What are the spatial and temporal resolutions of the case studies presented, and what are the range of possible resolutions?

How are wind fields specified? Could users prescribe assimilated wind fields?

The semi-Lagrangian approach makes simulating chemistry tricky, making this tool (at least at global resolutions) most useful for long-lived species. However, for problems like methane and N2O, it is necessary to account for 3D atmospheric sink terms due to tropospheric OH and stratospheric loss processes respectively. I would be very interested in exploring the sensitivity of inversion approaches to characterizing this sort of loss field. Could EnviFlux be adapted to such problems?

Section 3.2: observational error correlation has proven to be a big problem in my own satellite-based data assimilation. Shared surface characteristics (e.g. mountains) make for systematic errors that are irreducible due to averaging. How hard would it be to specify more complex observational error distributions with off-diagonal terms?

Section 3.3: How easy would it be to trade out this background matrix for other approaches that might better approximate the varied operational systems used by potential EnviFlux users?

Lines 411-414: This is a very interesting discrepancy. In my very rough experience, satellite data is more “reliable” because of the representation error of surface sites, and because satellite data is generally less sensitive dilution in a mischaracterized PBL (the convective transport explanation of Basu et al. is also plausible). Or at least, this is the way I have thought about it without rigorously investigating the issue. To what extent could these sorts of errors in convection/PBLH be studied with EnviFlux?

In this study, the author has developed a simple flux inversion analysis tool, named as EnviFlux, for estimating surface fluxes of atmospheric constituents. It is no doubt that this kind of tool is useful, because a flux inversion tool that is used practically for inverse analysis is computationally expensive. It is sometimes difficult to use a practically used system for several sensitivity studies, though those sensitivity experiments are needed to evaluate reliability of inversion results. I have found this simple “toy model” scientifically sound, however I cannot recommend this manuscript for publication because of two major reasons described below.

1. No information of computational efficiency or useful facility as a tool

Given the information described in this manuscript, this model seems not to have any advantage other than simplicity compared to other existing models (e.g., lacking turbulent and cloud convection processes, not assuring tracer masses). However, the most important things, how simple and easy to use as a tool this model is, are not well described. How fast this model can run should be explicitly discussed compared with existing models. I do not think just using the semi-Lagrangian scheme cannot make the model faster than others as this technique is often used in existing models. In addition, not implementing turbulent or cumulus convection scheme may make the model fast, but it does not provide novelty of the study, because other models can do the same thing by just turning off those processes.

2. Too simple experimental design

Usually, during development of this kind of inversion analysis model, one should perform ideal experiments to see whether the model appropriately works or not. In that sense, the experiments the author showed in this manuscript are not novel. Furthermore, scaling vertical wind speeds, the author applied to see the effects of model errors, is too simplistic and the results may not provide scientifically useful information. If the atmosphere is considered as hydrostatic (this assumption is usually valid), horizontal wind velocities should accordingly be corrected when vertical velocity is changed. Just changing vertical velocities would deteriorate the consistency with the continuity equation and induce considerable errors in mass conservation. It means that unexpected sources or sinks would occur in the atmosphere, which is not suitable for simulations of long-lived species such as CH4. In addition, the author did not consider atmospheric sink of CH4 due to oxidation with OH, which is one of the most important features of atmospheric CH4.

Minor comments:

L25-26: CO2, CH4, N2O; because they appear first, they should be fully spelled-out.

L34: That is true also for 4D-Var here.

L42: That is true also for CO here.

L76: Please specify what χ is here (e.g., mass concentration, mole fraction, mixing ratio).

L77: Please elaborate how to derive wind velocities and diffusion coefficients. Are they taken from reanalysis data?

L78: “u = (u v w)” should be a transpose of a vector, i.e. “u = (u v w)^T”

L82: “ppb” should be explained as “parts per billion”. In addition, this is not usually used as the unit of mixing ratio, but as that of dry air mole fraction.

L86: What does “τ_ρ” mean?

L110: “For the experiments shown in this paper, no explicit diffusion is applied”  This is a critical flaw of the experiments, which makes the results unsound.

L117: “EnviFlux does not include (sub-grid) turbulent or convective transport process”  I think that if a model does not include these processes, it cannot appropriately simulate any atmospheric constituent transport. This flaw critically affects its inversion results.

L165: Does “total column amount (TCA)” mean vertically integrated amount? Usually, satellite products provide column averaged amount.

L169: “The TCA observations are found from a discretization of …” The author should note that satellite data are made with averaging kernels, which should also be incorporated in the model.

Table 1: Please elaborate the experimental settings of Table 1 in detail in the main text. Please explain the validity of experimental length of 100 days and source time-step of 30 days (while temporal correlation scale is 3 months, I’m wondering if these settings are reasonable).  “nx = 33, ny=65” looks strange to me, because the number of longitudes is usually larger than that of latitude.  Furthermore, how long the assimilation window was set should be clarified. Please explain the validity of the number of 4D-Var iterations (=25). Is it enough to converge the parameters?

L256-257: “Here, each is taken as a point location in the horizontal…” Is the satellite orbit assumed here derived from GOSAT? Are data gaps due to clouds (typically existing in the tropics) considered?  

L443: “a simplified tool”  From my point of view, the model looks unmatured rather than simple. If the author claims this simplicity is advantageous, that should be elaborated.

L446: “cheaply without the need for high performance computing” To claim this, the author should describe what kind of machine was used and specify wall-clock time for each experiment. Furthermore, the author should also demonstrate those computational utilities by comparing with other existing models.