|The presentation of the manuscript improved compared to the previous version, but not enough. Some required additional analysis has not been done. With the better representation several issues became more clear that need to be tackled. The manuscript should only be published with more serious work on reacting on the review comments.|
The study reports changes across the entire soil profile. However, changes seem to be most important in the top 20cm and in the tree alleys (See strange legend in Fig 4 bottom with a change in magnitude for one level). When reading only about the aggregated results, it implied to me different conclusions than reading the full paper in detail. The authors did some small notes in reacting on review requests for these details but did very little adjustments in presenting the overall results. I suggest reporting and discussing results independently in a) tree-alleys, b) top 20cm in rows c) below 20cm d) aggregated space.
The study claims performing a Bayesian analysis because it applies prior information on model parameters. However, exact prior information is still not presented (e.g. diagonal values of P_b in eq. 34) let alone motivated sufficiently. Moreover prediction uncertainty is not presented and reasons for not doing that are very weak (see detailed comments). Uncertainties and full probability distributions are essential components of a Bayesian analysis. I again require to present and motivate the priors and to discuss predictive uncertainties. I still recommend using log-transformed parameters (and hence log-normal prior information) where prior parameter ranges span several orders of magnitude.
The presentation of the numerical solution is now sufficient to be understood. There is still works to do on notation (see detailed comments). Why did the authors not check that the resolution of the spatial grid is sufficient? Why should the spatial modeling grid be regular? In the used Soetart's ode.1d code there is no such constraint. With looking at the results, I again strongly recommend repeating the analysis with a finer vertical resolution at the top 30cm.
I can see the point in the current quantifying the priming effect with transferring the decomposition of the priming model to the agroforestry plot with a parameter fixed to conditions of the control (L 627ff). However, I do not agree in the interpretation. To me it is not an absence of priming but is the priming effect as it worked in the control. I still have difficulties in accepting the approach. For me it does not make sense to apply the priming-explicit model with parameter fixed to the control as a no-priming base scenario. Also the results of this run with stock increases of 60t/ha in 18 years are not reasonable (Fig. 6). I am still curious on the comparison of the current quantification to the (to my opinion more straightforward and without much work obtainable) model comparisons I suggested in the previous review involving comparison of priming-explicit vs. no-priming model variants. Therefore, I cannot follow the numbers in abstract of priming effects reducing potential SOC storage by 75 to 90%. (In addition one should differentiate between tree rows/alleys and different depth)
Table 5 caption: “the prior values that minimized J(x)”. Why is the prior information different for different model variants? I hope that you did not try/optimize for different prior information means. Prior information is defined as an information that is independent of the observations and the calibration. Please add an additional column with mean and standard deviation of the prior parameter pdf.
Fig. 4. I is still interesting to compare depth profiles across control, tree row, and alley. I agree that the closeness of the values makes a combined plot hard to read. But it is even harder to compare across facets. Please, make an attempt to display at least the data or one variant of the prediction in one plot.
Fig 5. First I though the [10,11] entry in legend of the bottom subplot was an error of omitting the decimal point, but the change of magnitude and the non-continuous scale are deliberate. Please, make this really obvious and discuss.
Eq 12 (and other eq.): Notations (here d for \partial) dFoc/dt and dFoc_t,z,d/dt are ambiguous. Eq. 14 for dFoc/dt involves terms specific to t,z,d. I suggest renaming all dFoc/dt to dFoc_t,z,d/dt and renaming all previous dFoc_t,z,d/dt to dec_Foc_t,z,d as it only describes decomposition/mineralization. Similar for HSOC.
L 649: Suggest modifying “importance of of priming” to “importance of additional priming due to tree row vegetation and trees”
L 654: I do not agree with “correspond to the absence of priming due to trees”. To my opinion it corresponds to “same magnitude of the priming effect as in the control”. See may general comments on my difficulties with the current priming effect quantification.
L 567: Please write more specifically what is “the associated uncertainty”. In the previous sentence the known is “These parameters”. The 93 soil samples estimate the uncertainty of observed C stocks. How did you use the uncertainty of the observed stocks in the optimization?
L 605: Manzoni et al 2012 is not a good citation for BIC. Please go back to the original literature cited therein.
Eq. 21: I still do not understand the reasons for using an unusual variant of BIC when you defined your Likelihood by the first term in eq. 21. In effect the current BIC variant uses some different Likelihood that ignores observation uncertainty used in matrix R in eq. 21. It might be an adequate Likelihood for the Manzoni 2012 studied system, but I cannot see how it applies to your case. It would have been very easy to report the requested standard BIC formulation alongside your variant.
L 836: Why do the correlations hinder you to compute prediction uncertainty? They are important to consider in Bayesian analysis. The straightforward way would be an MCMC run on eq. 21 to obtain a proper sample from posterior parameter distribution. Perhaps more easy: From the curvature at the optimum you already got and report correlations of a first approximation of a multivariate normal of the parameters posterior distribution. You can draw samples from this distribution and do (say ~1000) forward model runs to compute 95% confidence interval on predictions.
L 902ff: I suggest moving the part on differences in soil temperature and soil moisture and the sensitivity study to the part where you describe what you have not done “simplifying assumptions”. Instead of strongly concluding that OC inputs drive SOC storage I recommend formulating more weakly that in this study OC inputs are sufficient to explain the differences in stocks. (You did not compare to explicitly modelling the differences in temperature and moisture with the agroforestry)
L 996: Its a result section. “results were not significantly different” ? Hence, ...