The authors found a positive correlation between soil properties that are related to soil aeration and the soil organic carbon content. Since soil organic matter plays an important role in soil structure formation and hence on soil physical properties like soil hydraulic conductivity, bulk density, gas diffusivity and permeability, this relation is not unexpected neither really novel. Many studies have already made the link between soil physical properties and soil organic matter. What is however novel is that the authors invert the causality of the relation. Their hypothesis is that an increase in soil aeration in arable soils leads to an increase in soil organic matter, rather than that an increase in soil organic matter leads to a better soil aeration. This inversion is interesting and opposite to other causal relations between soil aeration status and soil organic matter content that go in the other direction and that suggest an accumulation of soil organic carbon when organic matter turn-over is hindered by a lack of oxygen. The authors’ argument is that with increasing aeration, not only the respiration of organic matter is enhanced but also the input of fresh organic matter via an increased root development. When growth increases more than respiration, then there will be more accumulation and the equilibrium soil organic matter content will shift to higher levels. The crux is that growth should increase more at higher O2 levels than respiration does. Or opposite, the oxygen levels at which growth starts to decline are higher than the oxygen levels at which respiration starts to decline. The authors included references to studies that show that root growth is already limited at higher oxygen concentrations. It would be important to put that against limiting values that are reported for soil respiration.

The question is therefore whether better aeration corresponds with higher root development. Unfortunately, no root mass data are available. But, data on carbon inputs have been included and indicate that there is not a large variability in carbon inputs in the different fields. This suggests that larger soil organic matter contents must be due to higher input from roots. A question I have is whether yield data could be included. Higher root biomasses could be related to higher aboveground biomass and a positive relation between biomass production (or yield) and soil organic carbon could support the hypothesis. However, the question still remains whether this positive correlation (if it exists) is due to the effect of soil organic matter on soil aeration. Root growth and biomass could also be affected by other effects of soil organic matter like the release of plant nutrients or a reduction of drought stress by a better water holding capacity of soils with a higher soil organic carbon content. Or, higher nutrient concentrations can be related to a higher clay content, which is also related to a higher soil organic carbon content. Or, higher soil aeration could correspond with more drought stress and lower soil organic degradation. But, this hypothesis would go along with a decrease in plant growth and root carbon input with higher soil aeration. Including alternative hypothesis in the discussion than the main one that is brought forward is therefore important. The issue of several alternative hypotheses goes along with multicollinearity of different parameters that could be responsible for the observed variability of the soil organic carbon content in the different soils. I did not find a clear statement in the authors’ responses on how to deal with this issue. Maybe a principal component analyses could be helpful to identify correlated properties. A principal component regression (which by definition does not suffer from multicollinearity) could be useful to identify which (correlated) parameter groups explain the variation in soil organic matter.

Furthermore, soil aeration status like soil water status are defined by state variables like oxygen concentration, water content and water potential which vary considerably over time due to the dynamic meteorological boundary conditions and the dynamic respiration. How these state variables change over time and depth in response to external drivers depends on the soil properties. In their study, the authors focus on the soil properties, which influence of course the state variables. But it is important to keep in mind that microbial turnover processes and root groth depend on the state variables (temperature, soil water potential, soil water content, and oxygen concentration) and only indirectly on the physical soil properties.

Thank you for your detailed relpy to the reviewers comments. I think that you adequately responded to their comments. But, I still have a question about the causality between the relation between aeration and soil organic matter. Can you conclude that in increase in soil aeration is the cause of an increased soil organic matter (because of higher root input)? Or can the causility be in the other direction: an increased soil organic matter content (which generates better conditions foir root growth but because of other reasons than increasing soil aeration) leads to a butter soil aeration? Could you give a short discussion about this?

Dear authors, I am glad to communicate that the current version of the manuscript after all revisions made is now accepted for publication in SOIL.

Thanks for consider SOIL to publish your interesting research results.

Sincerely

Jorge