Many thanks for your valuable input on our manuscript. Your comments provided mach insights into the computation and implication of our study. These comments and suggestions helped us clarify our own concerns and improve our manuscript.

The key feedback has been categorized into four main comments as the general comments were not numbered. Each major comment has been discussed in detail and the manuscript has been revised in response to all comments and suggestions. Almost all suggestions have been accepted. Responses are provided directly below the comments or suggestions. The revised portions have been highlighted in red in the revised manuscript. The responses are as follows: RMC (reviewer's major comments), RSC (reviewer's specific comments), and AR (author's response).

General comments:

RMC 1: The authors state that ‘For 30-min and annual forest ecosystem carbon flux measurements, ignoring Fs would underestimate the NEE (Zhang et al., 2010)’. This idea is then repeated by Li et al., 2020, and the authors based on a very complex and uncommon computation support this idea. I am sceptical about these findings. To my knowledge, the storage flux has a relevant impact on daily NEE course, but no or negligible impact on cumulative NEE. I believe the authors have made a mistake in the computation, or possibly it is a result of a wrong gap-filling procedure.

AR: Theoretically, the impact of storage flux on the annual cumulative NEE can be neglected, but the storage flux has a relevant impact on half-hourly NEE course. For example, a significant CO₂ emission in the forest ecosystem is usually observed in the early mornings as the accumulation of CO₂ overnight released instantly. This “flush” has been repeatedly reported in field (Novick et al., 2014). Neglect of CO₂ storage could indicate that the ecosystem is a CO₂ source, leading to mistaken estimation of half-hourly NEE. In addition, our findings showed that the contribution of storage flux to half-hourly NEE observations is significant even under the condition of strong turbulence. In practice, it is necessary to fill the gaps in half-hourly NEE time series when calculate the annual cumulative NEE. Since gap filling relies on the half-hourly NEE data, the mistaken estimation of half-hourly NEE may propagate to the cumulative NEE.

The mentioned statement in the introduction section aims to highlight the significance of half-hourly CO₂ storage. Our study did not perform any gap filling for CO₂ concentration, storage flux, and NEE observations, and all the analysis was based on observation data. Instead, Zhang et al., 2010 and Li et al., 2020 did gap-filling procedure in their works. To express clearly, we rewrite these sentences (see Lines 70-74 and Lines 107-108, respectively) as “For 30-min ecosystem carbon flux measurements, ignoring F_s would underestimate the NEE (Zhang et al., 2010). The F_s value typically ranges from −2 to −5 μmol m⁻² s⁻¹ in the early morning, and the F_s is about 1–3 μmol m⁻² s⁻¹ after sunset for temperate forests. The effect of the F_s on the NEE of forest ecosystems decreases with the increase of timescale (Li et al., 2020).” and “A proper measuring system with improving the horizontal representativeness can reduce the bias of F_s to 2–10% (Nicolini et al., 2018).”

RMC 2: Although my opinion is possibly biased by my involvement in the ICOS network, I cannot understand why the authors did not consider the instrumental setup and the computational procedure we developed and applied in Europe. At least in theory, the use of spatially distributed air intakes in the control volume would overcome the problems arising from the presence of single gusts of CO2-rich air.

AR: We have studied the guidelines of ICOS Ecosystem Instructions that provide a technical solution to minimize the problems of inadequate spatial sampling of gas concentration from a single intake at one height. We have used AP200 Atmospheric Systems (Campbell Scientific Inc., UT, USA) for CO₂ and H₂O profiles. In this system, air is mixed at each level inside a mixing bottle, which reduces the error due to the fluctuations from a single gust. Modification of AP200 to follow ICOS protocol is not an easy engineering task, without manufacturer’s help, beyond our ability. Additionally, we had to follow the conventions of using AP200 series in ChinaFlux network, in which the manufacturer’s guides are used in the installation for long-term measurements. The computation procedure embedded into the AP200 code, which has been adopted for raw data collections.

We have realized that we need to reconcile the AP200 configurations and algorithms with the ICOS setting and computation procedure in our future applications of AP200 or other Atmospheric Profile Systems if any.

To statement comprehensively, we have discussed ICOS and spatial sampling in discussion. We have added the sentence in discussion section as follow (see Lines 622-624): “By increasing the number of gas concentration sampling points near the ground, the horizontal representativeness can be enhanced, thereby reducing the bias in the estimation of F_s (Nicolini et al., 2018).”

RMC 3: Within ICOS, the computational period is defined between the concentration measurements done around the beginning and the end of the half-hour, while the authors consider a large interval, in my view possibly not compliant with the Reynolds decomposition.

AR: We agree with the reviewer on this point. Actually, the computational period for estimating storage flux is the same as averaging period of turbulent flux, which is half-hour in this study. However, using a single gas analyzer to measure CO₂ density at multiple levels, the synchronous observation of a CO₂ profile is practically impossible. Sampling at one level takes about 15 s (with 10 s for the flushing of the manifold and 5 s for logging the average), leading to a measurement cycle of 2 min for 8 levels in total. In addition, discrete time averaging is usually needed to remove the noise in the time series of CO₂ records. With this consideration, during routine operation at our site we compute the storage flux term using the CO₂ values within a 2-min window (the shortest possible) around the beginning and ending of each half-hour interval. This approach is fully compliant to the principle of Reynolds decomposition.

In this study, we did expand the averaging windows to 4, 8, …, 28 min, respectively. The purpose was to demonstrate how enlarged windows around the beginning and ending of each half-hour interval for CO₂ averaging would affect the accuracy in storage flux estimates. We have rewritten these sentences into (see Lines 194-204 in the revised MS): “When measuring the F_s by sampling CO₂ at several levels using a single analyzer, the synchronous observations of CO₂ profile are impractical. Consequently, discrete temporal sampling and time averaging become necessary. To ensure the temporal alignment of F_s with F_c, the average [CO₂] measurements within the control volume at the beginning and end (τ) of an averaging period (30 min) are calculated by averaging over a time window (τ min) as follows:

where τ = 4, 8, …, 28 min. Theoretically, the time window should be kept as short as possible in comparison to the turbulence flux averaging period to comply with the principle of Reynolds decomposition. We use large windows here for CO₂ averaging in an attempt to demonstrate the effects of different window sizes on the accuracy of storage flux estimates.”

RMC 4: I would also like to see what the effect of the CO2 storage flux is when combined with the turbulent component, if it improves the correlation with environmental drivers, like PPFD, or if it deteriorates it.

AR: We appreciate your thoughtful comment. The analysis provided indeed underscores the significance of F_s. As you suggested, we examined the correlation between NEE observations and PPFD as well as air temperature. The figures reveal that the combination of Fs and Fc exhibits a superior fit with PPFD compared to F_c alone, while it demonstrates a comparatively less favorable fit with air temperature (Ta) than F_c alone. In response to this observation, we have incorporated two supplementary figures to visually depict the corrected correlation with these environmental drivers when CO₂ storage is taken into account. These figures are uploaded as supplementary material (Figure S1 and S2).

Special comments:

RSC 1: Line (L) 30. A_max is an acronym largely used to represent maximum assimilation capacity through photosynthesis. I find it confusing to use the same acronym for another meaning.

AR: We have modified A_max as A_m. Correspondingly, we also modified P_max to P_m.

RSC 2: L86: ‘…cold air moves from the ground to the valley forest canopy’. In principle, cold air tends to move downward since it is heavier, so it does not reach the canopy. This process is the basis of Katabatic flows and advection. Please explain.

AR: Thank you for pointing this mistake. We modified this sentence as “…cold air moves from the valley forest canopy to the ground”.

RSC 3: L93: ‘In practice, the Fs represents the integration of the time derivative of the vertically determined column-averaged [CO₂].’ I believe that this ‘practical’ and traditional assumption is wrong and undermines the possibility of correctly measuring the storage flux since a profiling system is not representative of the whole control volume. The authors cite several times the paper by Nicolini et al. but they do not take advantage of that study.

AR: Thanks for your comments. In practical, the NEE observations were obtained through the jointly measurements of F_s and F_c. Under the conditions of well-developed turbulence or well-mixed air, these “practical” and traditional assumptions are correct. This implies that an accurate estimation of F_s can be obtained using a single gas analyzer in a relatively economical manner. When these conditions are not met, as you said, these assumptions do not hold. We rewrite these sentence as (see Lines 96-101 in the revised MS) “The estimation of Fs at numerous sites frequently employs a vertical profile system. This is based on the assumption that the F_s represents the integration of the time derivative of the vertically determined column-averaged [CO₂]. However, the column-averaged [CO₂] cannot well represent the average [CO₂] of the control volume due to insufficient sampling when the air mixing is inadequate.”

RSC 4: L126: ‘lack of clear guidelines’. Being part of ICOS, I disagree with this statement. We wrote a protocol, a paper and the instructions are publicly available, https://fileshare.icos-cp.eu/s/LzAZfgkc4znRtz6

AR: Thanks for your suggestions. We acknowledge that this ICOS Ecosystem Instructions provide good guidelines for estimating storage flux. This sentence was modified as (see Lines 131-133 in the revised MS) “Furthermore, resource constraints in the measurement system leads to the gap that the systematic bias and random error in F_s estimate are irreconcilable.”

RSC 5: L185. I did not check all the equations reported, but to my knowledge, the CO2 molar mass is around 44 g mol-1, and not 12.011 g mol -1. This is the mass of the carbon only.

AR: Thank you for pointing this mistake. We thoroughly checked all the equations. The eq.5 was accepted in CIPM (Picard et al., 2008), where Mc is the carbon molar mass (12.011 g mol^-1). We corrected this mistake in the revised MS.

RSC 6: L242. ‘The average Fs was calculated in a certain time window (15 d)…’. Why do the authors make such a computation? Probably the result of a significant value of Fs in the long term comes from this averaging. Did the authors perform a gap-filling, quality test or other? And how did they fill the gaps, if any? These are delicate passages in which a wrong computational window or filling procedure can have an impact.

AR: The goal of this computation is to estimate the uncertainty of the storage flux, rather than estimating the F_s values. We rewrite the steps of this computations and add five formulas in the revised MS (see Lines 254-262 in the revised MS). As mentioned above (RMC 1), we did not perform any gap filling. Indeed, we only removed extreme outliers (the standard is 4σ) in CO₂ concentration, storage flux, and turbulence flux time series.

Rewrite: To determine the uncertainty of F_s, expressed as , this study compared the observations at moment i to the average of several observations during a similar period and with similar meteorological conditions. The specific computations were as follows:

where  was the moment interval (i−0.5 h, i+0.5 h) within a certain time window (15 d); I was indicator function; the set Λ represented consisted of elements that meet similar meteorological conditions, including the u_*, air temperature (Ta), and sensible heat flux (H); σ_u*, σ_Ta, and σ_H  are the standard deviation of the u_*, Ta, and H, respectively;  was the threshold of Euclidean distance; and  was the random error of F_s.

RSC 7: I find Figure 12 very interesting, well done. I must be sincere, I cannot understand what the authors try to explain in line 485 and the following.

AR: The goal of line 485 and the following was to evaluate the difference in F_s estimates between the dynamic-time-window and the fixed-time-window method. For the practical application, we also assessed the role of our efforts in estimating F_s on the observations of NEE. Although it is very difficult to completely eliminate the uncertainties in NEE observations, the analytical results of the MS indicate that our efforts reveal statistically significant meaning.

RSC 8: I believe that Tables 4 and 5 contain too many values to be informative, better placing them as supporting material or making a synthesis.

AR: Thank you for your suggestion. Tables 4 and 5 have been removed. We placed them as supporting material.

RSC 9: L542: ‘Complex terrains introduce multiple factors that influence [CO2] fluctuations, including gravity-induced waves, drainage, and advection. These contribute to uncertainties in estimating Fs.’. I am not fully convinced. Advection is a separate term from storage, and storage cannot account for advection. It is a different term.

AR: Thanks so much for reviewer to provide this theoretical insight. The uncertainties in estimating F_s depends on the vertical configuration of the profiling system and the number of sampling levels (Yang et al., 2007). The optimal vertical configuration should be subject to the structures of air flow, which predominantly governs the [CO₂] fluctuations. Therefore, the systematic bias and random error in F_s estimate with a single profile system are irreconcilable. Acknowledging this point, we rewrite these sentences (see Lines 551-544 in the revised MS) as “Complex terrains introduce complex changes in air flow structures, including gravity-induced waves, drainage, and nonlinear waves induced by single gusts, leading to dramatic [CO₂] fluctuations. These dynamics contribute to uncertainties in estimating F_s.”

RSC 10: L574 and following. Again, the uncertainty in the storage term depends a lot on the set-up used, together with the biological activity of the ecosystem and the height of the control volume. It does not make much sense to discuss typical uncertainty.

AR: We agree with your understanding of the uncertainty in the storage term. We delete L574 and following. Indeed, the typical uncertainty as F_s approached zero might be site specific.

RSC 11: L597: In Montagnani et al., 2018 it was not discussed the AP200.

AR: Thank you for pointing this mistake. We had modified the reference as (Cescatti et al., 2016) in the revised MS. We have rewritten this sentence into (see Lines 592-594 in the revised MS) “The buffer volumes are fully mixed during gas extraction and performs a weighted average of [CO₂] instantaneous measurements to minimize the sampling error for each level’s [CO₂] measurement (Cescatti et al., 2016).”

Reference

Cescatti, A., Marcolla, B., Goded, I. and Gruening, C., 2016. Optimal use of buffer volumes for the measurement of atmospheric gas concentration in multi-point systems. Atmospheric Measurement Techniques, 9(9): 4665-4672.

Nicolini, G. et al., 2018. Impact of CO2 storage flux sampling uncertainty on net ecosystem exchange measured by eddy covariance. Agricultural and Forest Meteorology, 248: 228-239.

Novick, K., Brantley, S., Miniat, C.F., Walker, J. and Vose, J.M., 2014. Inferring the contribution of advection to total ecosystem scalar fluxes over a tall forest in complex terrain. Agricultural and Forest Meteorology, 185: 1-13.

Picard, A., Davis, R.S., Gläser, M. and Fujii, K., 2008. Revised formula for the density of moist air (CIPM-2007). Metrologia, 45(2): 149-155.

Yang, B. et al., 2007. Biases of CO2 storage in eddy flux measurements in a forest pertinent to vertical configurations of a profile system and CO2 density averaging. Journal of Geophysical Research, 112(D20).

We would like to extend our sincere gratitude for the valuable feedback and recommendations provided by the anonymous referee. The feedback has enabled us to identify areas where additional clarification and depth were needed. We have carefully considered the referee’s comments and have made the necessary revisions to address the concerns raised. The revised portions have been highlighted in red in the revised manuscript. Below, we have provided a detailed response to each of the referee’s points (RMC: reviewer’s major comments; RSC: reviewer’s specific comments; AR: author’s response):

General comments:

RMC 1: I think the title of the work is very striking, but it seems to me that the discussion about the complexity of the terrain went to the background, the discussion about this issue should be broader.

AR: Thanks for the comment. In the discussion section, we have broadened the discussion to incorporate a comprehensive analysis of CO₂ concentration variability and the methods employed for flux measurement within complex terrain.

Proposed revision:

Compared to flat and uniform underlying surface, complex terrain and heterogeneous canopies modify the trajectory, speed distribution and direction of the airflow. Increased wind speeds and shifting wind directions also increase turbulent activity above the canopy, facilitating the mixing and dispersion of CO₂. (Lines 529-532 in the Section 4.1)

The terrain complexity and the diversity within the canopy significantly affect the airflow separation in the atmospheric boundary layer. This results in weakened air circulation within the canopy and spatial variation in the patterns and extent of airflow separation (Grant et al., 2015). (Lines 579-582 in Section 4.1)

Fluxes are significantly higher in heterogeneous regions than in uniform regions. The energy transfer from the ground surface to large eddies occurs primarily in areas with pronounced heterogeneity, and this energy distribution is uneven across the region (Aubinet et al., 2012). Once large-scale eddies acquire energy, their cascading of energy to smaller-scale eddies is influenced by topographic features, leading to variations in these smaller-scale eddies along different flow streams (Chen et al., 2023). (Lines 639-644 in Section 4.2)

RMC 2: I think that the Appendix about the TCI needs at least a couple of references and more context (images), since it is a complex topic to understand and it is not clear if the authors propose the descriptor or it was previously established.

AR: Thanks for the comment. The terrain’s features and spatial element distribution were considered when developing the TCI. Additionally, the relationship between the local and the whole was taken into account. Quantifying terrain complexity is not the focus of this MS, therefore it will not be discussed in depth. We are currently working on a MS that aims to quantify terrain complexity.

We have created a conceptual diagram to illustrate the quantitative assessment of volume filling ratio (P_d) in details (Figure A3). This figure provides the estimations of the volume of terrain above the relatively lowest elevation of an area unit () and its largest vertically projected area (). Therefore, the quantitative estimation of P_d is methodically derived.

We have included corresponding references for roughness and the Shannon Wiener index. To provide a clearer introduction to the TCI descriptor, we have expanded the details in Appendix A.2.

Proposed revision:

Given , an increase in  correlates with a higher degree of terrain complexity. Notably, the  is defined as 1 when the terrain volume is 0 or when the terrain surface of the area unit was parallel to the horizontal plane and was smooth and homogeneous. (Lines 726-728)

The value of Z_d is in the range of [1, +∞). The larger Z_d, the more complex the terrain. (Lines 730-731)

A larger H indicates a more complex terrain. When the number of pixel aspect types in the area unit is kept constant, it’s essential to recognize that greater uniformity in the distribution of all pixel aspect in the area unit results in a larger H. Similarly, when the uniformity of the distribution of pixel aspects in the area unit is kept constant, a larger H is achieved with an increase in the observation of the number of pixel aspect types. (Lines 741-745)

RMC 3: A couple of figures in the paper (Figs. 10 and 11) need some quality touches, since it is not possible to clearly see the legend to distinguish the lines.

AR: Thanks so much for this suggestion. We have redrawn the Figures 10 and 11 in bitmap format.

Special comments:

RSC 1: L. 97: Personally, I think you should use numbers when referring to time averages along all the text. So replace two-min by 2-min

AR: Revised.

RSC 2: L. 158: The exact name of integrated system from Campbell Scientific you are using is the CPEC310. So for me it would be better read something like: "The CPEC310 integrated system from Campbell Scientific comprising an ..."

AR: Thanks for the suggestion. We have rewritten this sentence (Lines 163-165 in the Section 2.1) as “The CPEC310 integrated system from Campbell Scientific comprising an EC155 closed-path infrared gas analyzer (IRGA) and a CSAT3A sonic anemometer, was employed to monitor the three-dimensional wind speed and CO₂/H₂O concentrations (10 Hz)”.

RSC 3: L. 159: Remove "ray" word. IRGA = InfraRed Gas Analyzer

AR: Thanks for the suggestion. It has been removed in the revised MS.

RSC 4: L. 175: replace "Dolton's" by "Dalton's"

AR: Replaced “Dolton’s” by “Dalton’s” in the revised MS.

RSC 5: L. 185: the CO₂ molar mass is 44.01 grams per mole.

AR: Thank you for pointing this mistake. The eq.5 was accepted in CIPM (Picard et al., 2008), where M_c is the carbon molar mass (12.011 g mol^-1). We corrected this mistake in the revised MS.

RSC 6: L. 218: Mention explicitly the average time windows you employed.

AR: We have included specific details regarding the averaging time windows in Lines 231-232.

Proposed revision:

CO₂ storage fluxes were calculated for different [CO₂] averaging time windows (τ), ranging from 4 to 28 min in increments of 4 min.

RSC 7: L. 225: In Equation (9) explain what the "i" index refers to

AR: Thanks for the comment. We calculated the normalized root mean square error to evaluate the relative error between F_{s_τ} and F_{s_28} using Equation (9). In this equation, i indicates the i^th observation of F_{s_τ} or F_{s_28}. This information has been added in the revised MS (Line 240)

RSC 8: L. 242-244: Why did you use 15d window? What does "i was located" mean?

AR: We employ multiple observations under similar meteorological conditions over a 15-d window to substitute for repeated observations. The meteorological conditions include friction velocity, air temperature, and sensible heat flux. Considering that the estimation of the sensitivity of flux measurements to temperature mostly adopts a 15-d window (Reichstein et al., 2005), this study also uses a 15-d window to find flux observations under similar meteorological conditions. Actually, the key constraint are the similar environmental conditions and the corresponding half-hour flux measurements at the time of a day rather than the window size (e.x., 15-d window). Here, 'i' represents a specific half-hour period within a day.

To express clearly, we rewritten this sentence (Lines 254-256 in the Section 2.4) as “To determine the uncertainty of F_s, expressed as , in this case, we compared the observations at moment  i within a day to the average of several observations during a similar period and with similar meteorological conditions.”

RSC 9: L. 254: As mentioned previously: It seems not to be very comprehensible. More detail and references need to be added to the Appendix A.2.

AR: Please see our response to RMC 2.

RSC 10: L. 303-305: I am not sure if "amplitude" is the appropriate word, because you are referring to the "variation or magnitude" in the diurnal cycle. It might be confused with the amplitudes you got using EMD and spectral analysis.

AR: Thank you for your insightful comment. We appreciate your attention to this detail and ensure that the terminology is clear. When referring to the “variation or magnitude” in the diurnal cycle, our intention was to highlight the extent of change within this diurnal cycle. While “amplitude” is indeed commonly associated with the peak values in EMD and spectral analysis, in this specific context, it is used to describe the overall size or intensity of the short-term fluctuations of the CO₂ concentration.

To avoid any ambiguity, we have revised the terminology. Using terms like “extent of variation” in the diurnal cycle would be more appropriate and less likely to cause confusion with the amplitudes derived from EMD and spectral analysis.

RSC 11: L. 314: Caption in Fig. 5 replace "donate" by "indicate", or "represent"

AR: Replaced.

RSC 12: L. 355-357: I think it is very important to why the reduction in random error approaches to behavior of white noise.

AR: We appreciate your thoughtful comment. The random uncertainty of F_s () is positively correlated with the F_s magnitude (|F_s|). This implies that  increases as the |F_s| increases. The distribution of random error in F_s can be regarded as a mixed Gaussian distribution with non-constant variance. Increasing the [CO₂] averaging time window, results in a reduction of the random error in F_s and the correlation coefficient between  and |F_s|. When the correlation coefficient is smaller and closer to zero, it indicates that the variation in  is smaller. In this case, the random error in F_s is closer to white noise. To express clearly, we have rewritten the sentence (Lines 366-369 in the Section 3.2) to “These findings suggested that increasing the [CO₂] averaging time window results in a reduction of the random error in F_s and the correlation coefficient between  and |F_s|. This indicates a decrease in variability and a behavior similar to white noise.”

RSC 13: L. 408: It is necessary to explain what is shown in Figure 10. Explain clearly each one of the predictors (independent variables) you employed in the multiple linear regression. Why does mean ln(A_max) and ln(P_max)? You can explain this better in the caption of the figure.

AR: Thanks for the comment. The use of logarithmic transformation on [CO₂] fluctuations reduces data dispersion and helps to meet the assumption of homoscedasticity in regression analysis. We have revised the caption of the Figure 10 as follows: “Linear regression coefficients of the CO₂ storage flux (F_s) magnitude––driving factors relationships for the seven CO₂ concentration ([CO₂]) averaging time windows. The predictors of the multiple linear models are (a) the logarithm of maximum amplitude of [CO₂] fluctuations (ln(A_m)); (b) the logarithm of the corresponding period of maximum amplitude (ln(P_m)); (c) the terrain complexity index (TCI); (d) the friction velocity (u_*); and (e) the interaction term of TCI and u_*, respectively. (f) β₀ represents the intercept term.”

RSC 14: L. 419-422: Figures 10 and 11. Use the tags ((a), (b), (c), ...) from the plot to better describe the caption of the figure.

AR: We have rewritten the caption of Figures 10 and 11.

RSC 15: L. 428-442: This discussion is not easy to follow.

AR: Thanks for the comment. For greater clarity, we have added the following statements in the paragraph, respectively.

Proposed revision:

A multiple linear regression model was used to analyze the effect of [CO₂] fluctuations on the random uncertainty of F_s, , in complex terrains. This model considered the interaction effects of [CO₂] fluctuations and terrain complexity on , as shown in Fig. 11. (Lines 432-435)

The magnitude of these correlation coefficients decreased with the increasing [CO₂] averaging time windows. (Lines 438-440)

These observations suggested that the relationship between the random uncertainty in F_s and [CO₂] fluctuations was moderated by topographic complexity. Increasing the [CO₂] averaging time window reduced the effect of [CO₂] fluctuations on the random uncertainty in F_s. (449-452)

RSC 16: A.1 L. 689: Equation A.1. In the denominator is missing the "j" index

AR: Added the “j” index in Equation A.1.

RSC 17: A.2 L. A figure would be illustrative to understand what are P_d, S_v, etc.

AR: Thanks for the comment. We have added a figure (Figure A3) to explain the P_{d}, S_{u}, and S_{v}. This figure has been uploaded as supplementary material.

Reference

Aubinet, M., Vesala, T., and Papale, D.: Eddy Covariance: A Practical Guide to Measurement and Data Analysis, Springer Atmospheric Sciences, Springer, Dordrecht, XXII, 438 pp., 10.1007/978-94-007-2351-1, 2012.

Chen, J., Chen, X., Jia, W., Yu, Y., and Zhao, S.: Multi-sites observation of large-scale eddy in surface layer of Loess Plateau, Science China Earth Sciences, 66, 871–881, https://doi.org/10.1007/s11430-022-1035-4, 2023.

Grant, E. R., Ross, A. N., Gardiner, B. A., and Mobbs, S. D.: Field Observations of Canopy Flows over Complex Terrain, Boundary-Layer Meteorology, 156, 231-251, 10.1007/s10546-015-0015-y, 2015.

Picard, A., Davis, R. S., Gläser, M., and Fujii, K.: Revised formula for the density of moist air (CIPM-2007), Metrologia, 45, 149-155, 10.1088/0026-1394/45/2/004, 2008.

Reichstein, M., Falge, E., Baldocchi, D., Papale, D., Aubinet, M., Berbigier, P., Bernhofer, C., Buchmann, N., Gilmanov, T., Granier, A., Grunwald, T., Havrankova, K., Ilvesniemi, H., Janous, D., Knohl, A., Laurila, T., Lohila, A., Loustau, D., Matteucci, G., Meyers, T., Miglietta, F., Ourcival, J.-M., Pumpanen, J., Rambal, S., Rotenberg, E., Sanz, M., Tenhunen, J., Seufert, G., Vaccari, F., Vesala, T., Yakir, D., and Valentini, R.: On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm, Global Change Biology, 11, 1424-1439, 10.1111/j.1365-2486.2005.001002.x, 2005.