General comments

The presented manuscript describes an important bias in the estimation of gross nitrification rates in catchment soils based on Δ¹⁷O in stream water nitrate. The authors were able to demonstrate that Δ¹⁷O of soil nitrate should be also taken into account, first because it is not equal to what is measured in stream water, second because it can vary with soil depth. This can be considered as an important methodological contribution to the improvement of the method for future applications. The authors applied a quite simple model of nitrate movement and transformation across soil layers to show that nitrate Δ¹⁷O decreasing with soil depth (as usually observed) gives lower, more realistic estimations of gross nitrification rates than just relying on Δ¹⁷O in stream water nitrate. Their simulation is based on a case where nitrate fluxes decrease with soil depth, which is the case if net nitrification is negative (nitrate consumption larger than gross nitrification). It would be very interesting to see what happens in the case of a positive net nitrification. This could be done with just one more simulation.

In many soils, preferential water flow can be observed. In such cases, there is not a single, homogeneous nitrate pool per soil layer but nitrate that is more or less mobile along the flow paths and nitrate that is more bound within the soil matrix. The first is more prone to leaching and perhaps uptake, the second to denitrification. Simulating this would be a difficult task, probably out of the scope of the present article. Nevertheless, it would be useful if the authors would discuss this point and especially if they could make recommendations on how to sample nitrate from the soil for Δ¹⁷O determination: zero-tension lysimetry, tension lysimetry, centrifugation, extraction? I'm not sure if clear answers can be given with the present knowledge of soil nitrate transformations, but at least the question would deserve to be raised.

For a reviewer using English only as a third language, it seems that the wording of this contribution could be improved. There are especially quite many long sentences. I'll try to give some hints in the following details.

Details

L. 3: the word "eluted" is rather used for the what is done on purpose in the lab. In this case, for the process observed in the nature, a better choice would probably be "leached".

Line 6: instead "nitrate metabolized", it would be better to write "nitrate that is consumed", first because as soon as it is consumed, it is no longer nitrate, and second because "metabolized" is rather used to indicate that it is incorporated into organic matter, which is not the case for the denitrification.

L. 24: on the same idea: "consumption" instead of "metabolic".

L. 27: "is negligible" is too general, better add "often".

L. 28: "by order of magnitude": do you mean "one" order?

L. 21-29: very long sentence.

L. 31: it would be useful to explain shortly that the Δ anomaly is based on the δ of both ¹⁷O and ¹⁸O and that it is purposely defined so as to make it independent of mass-dependent fractionation.

L. 31: in my opinion, "conservative" would be better than "conserved" (because it tends to be conserved but it is not always perfectly conserved).

L. 33: it seems strange to write "REmineralized" when it may be mineralized for the first time after centuries of N staying in the soil in the organic matter.

L. 34-38, 53-57: long sentences.

L. 76: in this equation, some processes are denoted as subscript of NO₃^- (like deposition) while others are denoted for themselves (like GNR). GNR and GDR are usually expressed as a nitrogen rather than as a nitrate flux. As it is written, the equation lets it open. It would be better to explicitly express all rates either as N or as NO₃^-.

L. 74-80, 85-90: it is not clear why the word "each" is always used for the catchments (not only here, in general in the text).

L. 112-113: repeated usage of the word "limited".

L. 116: which one of the Δ¹⁷O is this? Or is it the difference?

L. 127-128: fine roots would be much more relevant than the total root biomass (with coarse roots obviously overrepresented close to the stem and thus close to the surface).

L. 146-148: it may be useful to explain this as a gradual uptake (consumption) of nitrate as water moves down the profile.

L. 152-160: these assumptions are obviously simplifications compared to real measurements, but they make sense for the demonstration. It would be interesting to test also the assumption of nitrate fluxes increasing with depth because of a positive net nitrification.

L. 175-179: long sentence.

L. 220: as written, it is like anonymous reviewers would be named, which does not make sense.

Fig. 1, fig. 2: the soil does not float above water and therefore "soil layers" and "water layer" should rather be marked "unsaturated soil layers" and either "water-saturated soil layer" or "seepage water" (as these two are considered to exhibit the same flux).

This study provides a critical analysis of existing methods for estimating the Gross Nitrification Rate (GNR) and Gross Denitrification Rate (GDR) using Δ¹⁷O signatures. The critique offered regarding the independent calculation of nitrate production (nitrification) and consumption processes (denitrification and assimilation) in previous studies is well-founded, considering these processes often occur concurrently within the same temporal frame. The initial assessment of the methodologies by the authors appears to be methodologically sound. Nevertheless, a detailed examination reveals areas that warrant further consideration as discussed below.

Major comment 1: Equation 4 and another reverse possibility

The authors assume in Equation (4),

 Δ17O(NO3)uptake = Δ17O(NO3)denitrification = Δ17O(NO3)stream.

However, this assumption is not necessarily correct. It requires the assumption that nitrates deposited from the atmosphere are first diluted by nitrification (increasing nitrate amount with decreasing D17O) and then (i.e., “afterward”), reduced in nitrate amount without changing D17O by uptake and/or denitrification. Another reverse possibility could be that atmospheric nitrates are reduced in quantity through uptake and/or denitrification without changing D17O, and then nitrates are added through nitrification (by decreasing D17O). In this assumption, one could hypothesize:

D17O_uptake = D17O_denitrification = D17O_atm   (A1),

and calculate GNR as follows:

GNR = NO3_st × (D17O_atm – D17O_st) / D17O_st   (A2).

To compare using Equation (4) versus Equations A1 and A2, let's assume a system where 100 nitrates (assuming D17O is 24‰) are initially deposited. In this case, when suppose the stream water nitrate is also 100 but with D17O decreased to 3‰. Using the same assumption as the authors (using Eq. 4 and 6), GNR is calculated as 700 using Equation (6) in the manuscript (GNR = 100 x (24-3)/3 = 700). However, assuming A1 and A2, GNR can be calculated as 87.5 (GNR = 100 x (24-3)/24 = 87.5), which is an extremely lower result compared to another case. Yet, in both outcomes, the final stream water remains the same at 100 in nitrate amount and 3‰ in D17O of nitrate from the same starting point (100 of nitrate with D17O = 24‰).

In reality, production and consumption occur simultaneously. Therefore, both cases may overestimate or underestimate GNR to an extreme. It is necessary to find a converging point by differentiation, and it can be understood that this is the “heterogeneous” method assumed by the authors in the manuscript with 10 soil layers. In the above-mentioned case, a GNR of ~208 will be the case when considering production and consumption occur simultaneously, as far as I calculated briefly (dividing layers > 1000). Thus, authors should consider this case considering equations A1 and A2, in addition to the case considered in this study.

Major comment 2: A similar problem can be happened to other N cycling rate calculation

Additionally, the authors have limited their verification of GNR calculation overestimation in their manuscript (underestimation in the case of A1 and A2 in this review report) to the soil profile. However, if pointing out such overestimation in GNR calculation methods, it would be better to also consider similar considerations for N cycling rates (e.g., GNR) calculated for lake systems, as advanced by the authors' group. Hasn't there been an overestimation for similar reasons in studies using nitrogen cycling rates in Lake systems, as shown in Tsunogai et al. (2011 and 2018) and other previous research? In lake and/or river studies, might they have calculated rates assuming that nitrates are added by nitrification (increasing the amount and decreasing D17O), and then the amount reduces by uptake and denitrification without changing D17O “only once” within each observation period unit (monthly or quarterly)? Wouldn’t both assumptions based on Equation 4 and those similar to A1 and A2 be equally valid?

Assuming simultaneous production and consumption as in lake mass balance calculations, converging to a single value might provide a more reliable N cycle rate. It should also be pointed out that the authors' group's previous N cycling research may have been overestimated. Especially, since Tsunogai et al. (2018) concluded that the nitrogen cycle rate was faster compared to 15N tracer experiments, which makes their study significant, it is important to consider the possibility of overestimation. Overall, this manuscript should consider and comment also on the case of their application for other systems like lake/river.

Based on the above two major comments, here are some suggestions for the cases considered in this study:

1. Consider that the case of Equation (4) may not always be correct. Consider also the case assuming Equations A1 and A2 provided in this review report.
2. Instead of comments using other group’s case as an example, verify the calculation process and resulting GNR in the more general system.
3. Not only soil profile cases, but also consider possible changes for the other systems led by their research group (e.g., Tsunogai et al. 2011 Biogeos; Tsunogai et al. 2018 L&O).

I also note that the current manuscript seems to criticize other groups' research, which may be due to language issues, so I want to avoid pointing out each by each in this review report. However, it might be worthwhile for the authors to reflect similar self-criticism on their group's previous nitrogen cycle research.

In conclusion, the manuscript provides a valuable perspective on the calculation of GNR based on Δ17O, highlighting areas for further refinement. By addressing the outlined considerations, this study has the potential to offer a more comprehensive and balanced analysis that could significantly contribute to the field. To be honest, the current manuscript feels like an incomplete consideration that criticizes others' research one-sidedly. I also note that a similar modification of the calculation way for GNR based on D17O, considering both the production and consumption of nitrate simultaneously, has been already considered/published in another paper (Hattori et al. 2023).

After a thorough review, it is with careful consideration that I suggest this manuscript may not be ready for publication in its present form. 

Minor specific comments

Title: It is better to replace “error” with “bias”?

L149: Why 10 layers? If you consider fewer or more layers, do you expect any changes?

Reference:

• Hattori, S., Z. Li, N. Yoshida, and N. Takeuchi (2023), Isotopic Evidence for Microbial Nitrogen Cycling in a Glacier Interior of High-Mountain Asia, Environmental Science & Technology, 57(40), 15026-15036, doi:10.1021/acs.est.3c04757.
• Tsunogai, U., S. Daita, D. D. Komatsu, F. Nakagawa, and A. Tanaka (2011), Quantifying nitrate dynamics in an oligotrophic lake using D17O, Biogeosciences, 8(3), 687-702, doi:10.5194/bg-8-687-2011.
• Tsunogai, U., T. Miyauchi, T. Ohyama, D. D. Komatsu, M. Ito, and F. Nakagawa (2018), Quantifying nitrate dynamics in a mesotrophic lake using triple oxygen isotopes as tracers, Limnology and Oceanography, 63(S1), S458-S476, doi:https://doi.org/10.1002/lno.10775.