The study by Yao et al. tested and evaluated a suite of machine-learning algorithms in filling the data gaps of eddy-covariance CO2 fluxes at a sagebrush site. They claimed that artificial neural networks and random forest algorithms perform better than the k-nearest neighbors and support vector machine algorithms. Last, they proposed a two-layer framework based on random forest algorithms and suggested providing a more reliable and robust alternative when filling extremely long data gaps.

The research topic is essential and attracts much attention in the science community. The manuscript is generally well-structured and written. I think the manuscript can be considered for publication in Atmospheric and Chemistry and Physics, after addressing a few general and specific comments.

[1] There have been studies, including several cited in the current manuscript, that tested and explored the applications of machine-learning algorithms in filling the data gaps of eddy covariance measurements. I suggest the authors summarize the previous studies’ findings and highlight this study’s uniqueness or innovative aspect (e.g., dryland ecosystem or the proposed two-layer approach). Below are two recent relevant studies:

Mahabbati, A., J. Beringer, M. Leopold, I. McHugh, J. Cleverly, P. Isaac, and A. Izady (2021), A comparison of gap-filling algorithms for eddy covariance fluxes and their drivers, Geosci. Instrum. Method. Data Syst., 10(1), 123-140, doi:10.5194/gi-10-123-2021.

Irvin, J., et al. (2021), Gap-filling eddy covariance methane fluxes: Comparison of machine learning model predictions and uncertainties at FLUXNET-CH4 wetlands, Agric For Meteorol, 308-309, 108528, doi: 10.1016/j.agrformet.2021.108528.

[2] Presentation of technical details: Certain parts of technical information are not clearly explained or only presented later in the Result and Discussion sections. I suggest reorganizing the texts and moving technical parts forward to the Materials and Methods section when feasible. It will also improve the readability by adding an overview subsection in the M&M, summarizing the study design and entire workflow.    

Specific Comments:

[3] Line 38: Since MDS is specifically called out, the original paper (Reichstein 2005) should be cited here.

[4] Line 42: MDS also may be the most widely applied method for gap-filling eddy covariance data and has been used extensively in FLUXNET data (e.g., Pastorello et al. 2020).

Pastorello, G., et al. (2020), The FLUXNET2015 dataset and the ONEFlux processing pipeline for eddy covariance data, Scientific Data, 7(1), 225, doi: 10.1038/s41597-020-0534-3.

[5] Line 50-52: The sensitivity of dryland ecosystems to water availability is essential and maybe less addressed in previous gap-filling studies. This could be a unique contribution of this study. Yet, it is unclear to me whether and how this current study addresses this knowledge gap. Soil moisture or groundwater table seem not used as input variables. I’d suggest the authors considering exploring additional input variables for water availability.

[6] Line 78-79: Certain variables (e.g., soil) may be spatially varied among the stations. Consider briefly explaining whether or how the spatial bias is corrected.

[7] Line 96-97: I think 10-fold cross-validation already implies resampling and grouping data for model training and validation. It doesn’t need to state “repeated ten times”. Would you please clarify it?

[8] Section 2.5: It may also be informative to explore the relative importance of input variables. For example, random forest allows the calculation of the relative importance of input variables, and such a feature has been utilized in previous studies to help interpret the results (e.g., Irvin et al. 2021). Other metrics have also been proposed to explain the variable importance, e.g., Knox et al. 2016; Kim et al. 2020.

Knox, S. H., J. H. Matthes, C. Sturtevant, P. Y. Oikawa, J. Verfaillie, and D. Baldocchi (2016), Biophysical controls on interannual variability in ecosystem-scale CO2 and CH4 exchange in a California rice paddy, Journal of Geophysical Research: Biogeosciences, 121, 978-1001, doi: 10.1002/2015JG003247.

Kim, Y., M. S. Johnson, S. H. Knox, T. A. Black, H. J. Dalmagro, M. Kang, J. Kim, and D. Baldocchi (2020), Gap-filling approaches for eddy covariance methane fluxes: A comparison of three machine learning algorithms and a traditional method with principal component analysis, Global change Biol, doi:10.1111/gcb.14845.

[9] Line 135-141: Some technical details need to be explained here. (1) For “10% of the total data length”, does it mean that an additional 10% of gaps (i.e., the total number of missing points) are created, or does it mean that artificial gaps are applied to 10% of the data records (i.e., some data points already missing)? I think it’s likely the latter case since it’s impossible to locate two months without any missing point. Would you please clarify it? (2) I assume the performance evaluation is done based on comparing score-0 observed data and estimated values. Following the previous comment, what are the actual number of data points that are used for each comparison? Would unequal sample sizes affect the performance evaluation or statistic metrics used?

[10] Line 141-143: Some of these metrics seem redundant. Several previous studies used Taylor diagrams, which may be considered, but I don’t insist on it.

[11] Line 157-163: As commented earlier, there may be spatial variability among the stations. Additional uncertainties may be introduced to flux gap-filling through these filled meteorological drivers. I suggest considering at least discuss the potential uncertainties.

[12] Figure 2: Please add units to the y-axis.

[13] Section 3.3: I think it’s more accurate to call these estimated (or empirical) probability density functions since they are estimated based on data. I’d suggest being more specific about how they are calculated (in M&M). For example, the kernel density function may be the most commonly used. Also, there are more robust statistic tests for comparing density functions, e.g., Z-test.  

[14] Section 3.4: I suggest briefly explaining and justifying the use of random measurement errors as a reference, e.g., Why? How to interpret it? In my opinion, gap-filling uncertainties are more like systematic errors, unlike random errors resulting from measurements or turbulence’s stochastic nature. I’m not sure it’s suitable to compare these two types of errors directly.    

[15] Figure 5 and relevant texts: I think it needs a reference (e.g., pure observation or best-case prediction) for the performance evaluation here. I don’t understand how the performance is evaluated here. Line 271-272 and analyses in Figure 6 seem to be a better option.

[16] Line 291-293: I suggest providing a brief justification or discussion of the proposed approach.   

Review report of “Technical note: Uncertainties in eddy covariance CO2 fluxes in a semi-arid sagebrush ecosystem caused by gap-filling approaches” by  Jingyu Yao, Zhongming Gao, Jianping Huang, Heping Liu, and Guoyin Wang

General Comments:

This study reports the result of applying different gap-filling approaches to access the change of NEE over the dry land ecosystems in the western US. Several types of artificial gaps were designed and put into the model to test the capability of using the various gap-filling approach. The authors noted that the performance among these available gap-filling approaches was silimiar, but all of these appraoches fail to fill large gaps over a period longer than two months. Among all selected gap-filling models, the ANN and RF approaches show a better model performance than others approaches, and the RF is relatively cheap in the cost of computational resources.  The authors suggested that using RF to fill the gaps is the most efficient way to fill small gaps, such as the gap between hours and several days.  In order to deal with the issue of data gaps over two months, the authors develop the strategy by adapting the information from the gap-filled dataset at a daily time scale. Again, the RF gap-filling approach was applied as defined as the second layer of the RF approach to avoid the issue of bias estimation (see Figure 2).

I aggreed with the point of view for dealing with the EC gaps suggested by the authors, and the strategy of using a two-layer RF approach is robust as the results shown in this study.  I think the idea proposed by the authors is good, but there is no need to stick to the RF approach. The same idea can also be applied to other gap-filling approaches to avoid bias estimation from long-term data gaps. As reported by the authors, the RF gap-filling approach shows a relatively good and stable result for filling short-term data gaps. Readers may be interested in understanding the importance of the potential variables used in the RF model. How does the RF model deal with the problems of collinearity among these variables?   I suggested the authors report this part of the information to reads in order to support the conclusion made by the autors. Besides, the structure of this manuscript is a bit confusing. Therefore, the idea of using two layer model can move to the section of methodology. The issue of bias estimation from long-term data gaps should also be emphasized in the introduction section.  Base on the evaluation mentioned above, I support the publication of this manuscript as a technical note in ACP.

Technical Comments:

L19:  …with this framework, the model performance is improved significantly, especially for the nighttime data.  

Shall we separate the dataset into daytime and nighttime because the mechanism of producing the CO2 ere quite different both for daytime and nighttime?

L50:  The motivation of this gap-filling practice was driven by the fact that dryland ecosystems are very sensitive to water availability,….

A short review of the global coverage of the dryland ecosystem is suggested.  Readers may have an overall view of the importance of the dryland ecosystem under the current pace of global warming. Is the ecosystem going to be enlarged or reduced?

L66: …197mm, …

How about the precipitation during the wet years and dry years?

L74: These data were sampled at a rate of 1 Hz…..

The frequency of 1Hz is too low for applying the eddy covariance approach to determine the surface exchange for the grassland ecosystem. Therefore, a 10Hz sampling rate is usually applied to determining the eddy flux for the surface exchange. I hope this is simply due to a typo. However, if the 1Hz is the actual system acquisition rate, I recommend conducting a spectrum analysis to be examined the contribution of high frequency to the total eddy flux by a theoretical correction.

L90: … a  score of 2 ….

I have no idea about the score. How to define the score in processing the  EC data?

L104: … we use two hidden layers with 12 and 10 nodes in the first and second hidden layers…

Why 10 and 12 layers. Any literature to support these values?

L111: Here, the optimized k value is 9…

Again, how to determine this value?

L265: …. RFs denotes the proposed two-layer RF based gap-filling framework, and MDS is the marginal distribution sampling algorithm….

The abbreviation of RF makes readers confused. Therefore, I suggested using  RF-2L to represent the two-layer random forest approach.

L287:  Section: A two-layer RF based gap-filling framework for extremely long gaps

I was confused about the two-layer RF approach while reading the manuscript for the first time. Did you mean that combining the approaches from two layers is for ANN + RF,  but there is no information on how to combine these two approaches? Therefore, I suggested moving this section to methodology.  

L309-L310: The RF algorithm outperforms the other 310 algorithms in terms of the overall performance.

I would like to see the importance of the potential variables that were applied in this study. How to deal with this issue of the collinearity problem?