Dear authors
Thanks for submitting a revised version of your manuscript addressing reviewer's comments. In general I think most issues were well addressed in the revised version. However, there are a couple of issues I identified that need attention before final acceptance.
- It is very important that you also present the model structure of the reference model you are comparing with, which seems to be a modified version of Century. From some of your comments and the entries in Table 2, it seems that you are using a version of Century with only 3 parameters, but the version of Century described in Parton et al. (1998) has more parameters that represent transfers among pools. To avoid confusion and misunderstandings, it'd be better if you also provide the equations for the version of Century you are using. This way, the reader can directly compare differences in model structure.
- Please be consistent with your notation of boldface on page 14 for the terms presented in equation (9).
- On line 292 you mention an important issue with correlation of errors that may occur in overparameterized models, but you don't show any results on this. Please add a table with correlations among parameter errors or posterior distribution values. In my own research I found serious identifiability problems for more than 4 parameters when using data only on respiration rates from incubations (see Sierra et al. 2015, SBB 90, 197–203).
- Figures 2 and 3. Cumulated is not a commonly used word in English and it doesn’t appear in some dictionaries (at least not in my New Oxford dictionary). Probably better to use cumulative. Also, can you reduce the length of the y-axis labels?
- Lines 484-485. How do you know your model doesn't show oscillations? The nonlinear structure of your model suggest to me that oscillations are possible, but this depends a lot on parameter values. To make any conclusive statement about oscillations you would have to do an eigenvalue analysis such as that in Wang et al. (2014, Biogeosciences 11, 1817). I suggest you don't make any conclusive statement about this unless you show a full eigenvalue analysis.

Dear Dr. Guenet
Thanks for submitting a revised version of your manuscript. Unfortunately, your last version suggest a problem with the posterior values of your optimization. Your new Table 5 is odd and extremely unlikely for any Bayesian parameter estimation method. Can you please clarify the zeros in your correlation matrix in Table 5? Please upload a new version of this table with the correct values and an explanation in the main text for the reason of these very small correlations.

Also, you didn’t include in the revised version the equations of the Century model as you used it. There are many versions of Century out there, the paper you cite doesn’t really have the equations, and we don’t know what actually got implemented in Orchidee. For this reason, I also would like you to add the equations in a revised submission.
Regards,
Carlos A. Sierra

Dear authors,
Thank you very much for submitting a revised version of your manuscript. The addition of the new equations and the significant figures in the correlation table help a lot with the clarity of the paper and to explain your results. To me, it is now clear that the transfer coefficients f_ij were not optimized and the values in Parton et al. (1998) were used as default. This partly explains the poor performance of the original Century model.
Regards,
Carlos A. Sierra