Dear Authors,
thank you very much for your careful replies to the reviews. I enjoyed reading them and I’m sure the reviewers did so, too.
I agree with many of your responses and concentrate here only on the one remaining critical aspect: the relation of your study to the real world. I’m very happy that Reviewer 1 has raised this (comment on P10140L24). It made me looking at this study in a different manner.
To begin with, I was wondering, why you discuss using your model with real world data in the methods and not the discussion section. I suggest making this a part of the discussion (action 1).
In general I agree and have not at all any problem with this work being a theoretical study. But inspired by your discussion with reviewer 1 I feel a bit confused about the objectives. There you write “This study seeks to develop a reliable inversion framework for determining the Q10 and Zp of different sites given continuous soil measurements.” (10140/21). This is clearly related to application with real world data. Consequently, when reading the manuscript the first time, I assumed that the main result from this study for practitioners was, to learn with which additional measurements they could constrain the process’s temperature sensitivity estimates better than with surface fluxes only. However, if this model is far from being applicable to real cases (correct me if this is exaggerated), the study is not of good help. If not with inversion, how can practitioners then use their additional soil CO2 concentration data to constrain their empirical temperature sensitivity estimates? Or more precisely: how can they otherwise reliably estimate Zp?
If I’m correct, the practical relevance of the study is much weaker (unless you don’t know Zp, your Q10 values are biased and this study tells you why, but cannot help you to reduce the bias) and this needs to be clearly understandable expressed in the conclusions (action 2). For example you write that “Depending on the tolerable level of error for a given application, almost every tested combination resulted in reasonably accurate returned Q10 and Zp values.”(10154/6). This is correct and sounds good, but you need to make sure that everybody understands that this is only true for the appropriately constrained theoretical case – but most likely not at all for realistic field data! Investing in a CO2 concentration profile measurement will then most probably not pay back. This is an important conclusion, but unfortunately speculative as you didn’t test it. Consequently you need to conclude from the discussion on why your model will probably fail in real field cases, to make this a clear consequence from your error analysis (still action 2).
With this regard using random errors (P10147/06) is not sufficient. The treatment of errors is of course a valuable step towards modelling real world data, but in real world, measured field data tend to have systematic errors (bias in installation, wrong calibration). This, together with soil inhomogeneity at the sensor position is probably the reason, why the model inversion approach will finally fail in real world. Please include the systematic errors in your analysis in addition to the random errors (action 3).
Per Erik’s first remark is another argument that you only partly tackle in the discussion, why an inversion approach in the real world is likely to fail, simply because the Q10 value can vary layer specific in your analysis you take it as a global parameter(“Q10 is the temperature sensitivity of soil respiration” 10142/14). Please review the literature on changes of Q10 with aging of soil organic matter and even with the average temperature level (because it is not the right function) and include in the discussion, what this means for the prospects of deriving accurate Q10 values from in situ field measurements (action 4).
In addition to this discussion I have three other comments that I like you to consider in your revision:
1. Figure 1. In the text I immediately understood why there are time lags, but I was and I still am lost with the logic of the figure. Isn’t the temperature sensitive gas production missing (link between heat transfer and gas diffusion)? Can you explain what the arrows under ‘Time’ mean? To shorten this, please consider removing this figure if it has only illustrative character (action 5).
2. Please do not use colloquial language in the revised version. Avoid, e.g., ‘sits in ... as’ (action 6)
3. 10154/5 Conclusion: why “preliminary”? If the study is preliminary shouldn’t we wait until it is finished? Please consider revision. (action 6)
I assume that the manuscript will still considerably change. Therefore, we will need it’s final version to evaluate it.
Sincerely,
Andreas Ibrom

Dear Authors

Thank you for your careful explanations and revisions, including fixing the errors that we didn’t see in the first place. In general I find the manuscript now ready for publication.

Thank you for taking the time for investigating the origin for the apparent misunderstandings. You are right the term you use to represent the Zp parameter as text was, and is still, confusing. Both ‘depth of production’ and ‘e-fold depth of production’ (= depth of production times e??. It should rather be height at 1/e of total production, shouldn’t it?) are in my opinion still not exceptionally well suited. These terms imply other meanings than simply describing a parameter that scales a vertical distribution function (maybe you should call it scaling parameter Zp?). Anyway, if there is no better solution, I suggest simply defining Zp as you did, explaining it once and then using the symbol all the way through.

Although a plausible claim, as you demonstrate with the references to previous work, it is still hypothetical that the chosen vertical distribution function is actually representing the CO2 production in a real world soil correctly. In a real soil the specific vertical distributions of SOM content in general and litter content specifically and of soil water contents, soil textures and not to forget roots may compromise the match with exponential shape and the model inversion will probably compensate for the inconsistencies between reality and the shape function by biased parameter values. I’m happy that you emphasised this reasoning in the discussion and in the conclusions.

So my last wishes for changes are:
1. change ‘e-fold depth of production’ preferably as suggested above
2. To avoid miss-understandings: when speaking of parameters it is always a challenge to make clear whether one means the term (e.g. parameter Q10) or its value (i.e. the Q10 value). In your text you, e.g., write ‘different Q10s ‘ (e.g. track changes version line 180), or ‘to determine depth-specific Q10’(line 410). To make clear that you mean the values and not the parameter per se, rather use Q10 values. –i.e. specific Q10 values,
3. 430 remove certainly

Best wishes,
Andreas Ibrom

Thanks for all your efforts and good success and scientific impact of the work!
Kind regards,
Andreas Ibrom