Liu et al. presented a promising predictive framework that combined a process-based model (physical knowledge and pre-train dataset) and a machine learning model for agroecosystem N2O emission estimate. The modeling framework is robust and thoroughly validated. This work will be an important milestone towards a better understanding, monitoring, and predicting agroecosystem greenhouse gas emissions.

The paper is well organized and written. Below are some of my comments that may help elucidate the strength and limitations of the proposed KGML-ag framework.

1. Robustness of physical (prior) knowledge

ecosys model plays a central role in guiding the ML model in terms of structure and providing a pre-train dataset. It will be important to discuss the structure uncertainty in ecosys N2O module, including e.g., underlying theories, major processes, difference/similarity to the classic leaky pipe type model (Davidson et al., 2000), and so on.

Again ecosys provides pretrain dataset, which has its own uncertainty and biases. It’s worthwhile to at least show some ecosys model performance across various different conditions at agroecosystems. For example, does ecosys pick up the high-frequency signals (fluctuation) of CO2/N2O flux that are observed in the chambers data? If not, is that the reason why PGML-ag could not capture the high fluctuation of CO2/N2O emissions in the field?

2. It’s not obvious which variables are used as inputs or intermediate variables and how that relates to the feature importance ranking. It will be better to show each variable in Figure 1. For example, W will be temperature and precipitation. Furthermore, feature importance analysis highlight NH3, H2, N2, O2, CH4, ET, CO2 are important variables that drive N2O emission (~ L230). It’s not clear in the main text, how this feature importance ranking helps the design of PGML-ag. What can we get out of this feature importance analysis?
3. There is a lack of discussion on uncertainty in PGML-ag, which is fundamentally important for predictive modeling. Also, what about chamber measurements uncertainty?

L254 based on the structure of process representation in ecosys

Reference:

Davidson, E. A., Keller, M., Erickson, H. E., Verchot, L. V., & Veldkamp, E. (2000). Testing a conceptual model of soil emissions of nitrous and nitric oxides: using two functions based on soil nitrogen availability and soil water content, the hole-in-the-pipe model characterizes a large fraction of the observed variation of nitric oxide and nitrous oxide emissions from soils. Bioscience, 50(8), 667-680.

General comments

This manuscript presents a new method for estimating N2O flux from cropland. The inputs to the method are known fertilization rate, weather forcings, soil and crop properties. The method also requires initial concentrations of nitrate ions, ammonium ions, and water in the soil, and optionally CO2 flux. The method employs gated recurrent networks organized in a hierarchical structure to mirror the time-dependence and causality present in the process.A process-based model provides pre-training data, and fine-tuning is done using observations from mesocosm experiments. The trained neural network models outperform the process-based model and many basic machine learning approaches.

The methodology employed is both novel and sound. The use of GRUs in hierarchical structures is well-justified and appropriate to the problem. The models have been well-validated, and various alternate choices for model architecture have been explored. I believe this work represent a substantive advance in modelling science. Below I list specific comments which I hope will serve to improve the manuscript.

Specific comments

• The use of the term "initials" confuses me. Upon first reading I thought it referred to the acronyms for various intermediate variables. I think it actually refers to the initial values of a sequence. Is this usage standard? If not, I recommend a different phrase such as "initial values" in place of the word "initials." Alternatively, clarify the meaning of the term in the manuscript.
• Another possible explanation for why KGML-ag2 better predicts IMVs but does not predict N2O as well is that KGML-ag1 may learn to use the IMVs as a kind of extra hidden layer, encoding information relevant to N2O predictions in them.
• Why not include KGML-ag2 in Figure 4? I can see simplifying the comparison by choosing only the best-performing model.
• Many standard deep learning models were included for comparison, but an LSTM was not among them. I would expect the LSTM to perform similarly to the GRU. I don't think it is crucial that an LSTM be included in this comparison. However, if the GRU outperforms an LSTM, it could provide further justification for choosing to use a GRU instead of an LSTM. Again, I could understand simplifying the comparison by including only one recurrent neural network.
• You tested two input combinations, IMVcb1 and IMVcb2, but it is not clear how that test informed the model development.
• The reason for evaluating slope and curvature in addition to N2O value could be stated more clearly.
• I recommend that the paragraph starting at line 194 be rewritten for clarity. First, data augmentation is a class of methods, not a single method. Second, Meyer et al. use copula-based models in particular to augment datasets. Do you use copula-based methods? The way this reference is cited suggests that you follow their approach. Third, do you randomly sample observed data, or synthetically generated data, or both? Do you randomly sample only the data which are hourly, e.g., air temperature, net radiation, N2O, CO2, and VWC? How is the daily value calculated from the sampled data? I did not find the answers to these questions to be clear from the text.
• How well does the model perform out-of-sample? Out-of-sample performance is mentioned in the introduction, but the discussion does not address it.

Technical corrections

• At line 239, Sec. 4.4 does not exist.
• At line 240, I believe this should refer to Fig. 1c and 1d, not 1b and 1c.
• Tables 1 and 2 have identical captions but different contents.
• Sections 4.1 and 4.2 are both entitled "Interpretability of KGML-ag."

    The authors are proposing the development of a new approach KGML-ag  to machine learning in estimating N2O emissions from fertilized agricultural fields. This approach involves using data generated from a process model and a mesocosm experiment to tune the relationships and their parameters among input and intermediate variables by which N2O emissions are thought to be governed.  The advantages of this approach over process models are simplified input data requirements, more rapid model execution, and possibly more accurate simulation of N2O fluxes measured in experiments for which the model is tuned. 

The ability of this approach to simulate N2O emission events under controlled laboratory conditions is impressive. It should be noted that the N2O emissions in Fig. 2 and the soil NO3 contents in Fig. 3 are much larger than those commonly encountered in field conditions. However the relationships and their parameters upon which this approach is based are not disclosed to the reader, and so remain a ‘black box’. For example, in section 4.1 the processes governing the time course of N2O emissions following a urea application are described, but the method by which these processes were represented in KGML is not. 

As for all black box approaches to modelling, it is vitally important that KGML be subjected to tests with truly independent datasets, i.e. datasets that are completely separate, and preferably very different, from those used in model calibration. Impressive results can always be achieved by calibrating enough parameters, but are these parameters robust? The extent to which such testing of KGML was conducted in this paper is not clear. At the very least, for this paper to be publishable, calibration and validation of KGML must be clearly distinguished, and clear evidence of independent testing must be provided. Further description of the key relationships and their parameters that govern N2O emissions in the model should also be provided so as to improve confidence in its robustness. 

In the Discussion, the authors rightfully address some of the factors that may limit the robustness of KGML. These limitations will likely become more apparent when the authors conduct tests of KGML under field conditions. Addressing these factors, as described by the authors, appears to require that KGML more closely resemble process-based models, and may reduce the computational advantages claimed for the KGML approach.