The research topic is very timely, the manuscript is well written, and the model simulates seem to be well done. Furthermore, the authors have really made a lot of simulations and obviously went to great lengths. However, many things need to be addressed before the paper can be accepted. The most important points are: (a) Discussing Lacroix et al. (2021), (b) adding many more references to support the text, (c) evaluating the model results with observations and show where the model is good or bad, (d) evaluating the global news present-day river fluxes to understand how realistic they are, (e) discussing the far too low NPP in the Arctic Ocean, and (f) testing if results are statistically significant. In this state, the main conclusion that rivers might be of importance in coastal region has no underlying prove and large parts of the manuscript are not possible to review. I would focus more on regional coastal areas and discuss and analyze these further, but this is up to you.

Major comments

• References are often missing. One of the most important references missing is probably Lacroix et al. (2021) who performed very similar simulations. Comparison to their results would be essential. Please revise the entire manuscript for the many missing references. Here some examples:
  • Lines 30/31: no references for this statement
  • Lines 33/34: no references for this statement
  • Lines 34/35: no references for this statement
  • Lines 37-48: Almost no references here!
  • Lines 49/50: No references
  • …

• Lines 49-54: A more detailed explanation is missing on how ESMs simulate rivers. Seferian et al. (2020) gives a good overview. There were already 5 ESMs in CMIP5 that simulated riverine C, N, and P (3 also simulated Fe) fluxes and there are now 8 in CMIP6. Some of them even simulate dynamically changing riverine fluxes.
• In the main manuscript, a large space is given to the Arctic Ocean. Please introduce the Arctic Ocean accordingly and explain in the Introduction already why it might matter if you want to keep it as one of the regional seas that you want to discuss (see Terhaar et al., 2019 & 2021 and citations within).
• The model is not evaluated. Only a reference to previous publications is mentioned (lines 111-113). However, to understand and discuss the changes in the future and the sensitivity to riverine fluxes a much more detailed model evaluation is needed. For example, NPP is far too low in the Arctic Ocean: for the 2^nd half of the 20^th century the simulated NPP is around 100 TgC/yr. However, the observation-based NPP in the last years of the 20^th century is slightly above 450 Tg C/yr (Arrigo and van Dijken, 2015). If the model is not capable of simulating NPP in a part of the ocean, why should we trust any of the projections done by that model? Having demonstrated that this is the case in the Arctic Ocean, I cannot trust the other numbers. Especially, given that the model-obs differences (Fig 3b) are so much larger than the differences between rivers and no rivers (Fig. 3c). Please make a thorough comparison and evaluate your results on the background of the model performance and tell the reader about the models’ strong points and weaknesses when it comes to ocean biogeochemistry.
• Four different scenarios for the future riverine fluxes are introduced in line 125. However, it is impossible to know which scenario is which. Please introduce the scenarios carefully so that the reader knows these scenarios are.
• Riverine data in general: How good is the data that you use? I would like to see a comparison to observations of larger important rivers such as the Amazon or the rivers in the Arctic that are observed by ArcticGRO (https://arcticgreatrivers.org/). Nutrient fluxes from Global News 2 in the Arctic can be off by 300% (Kaiser et al., 2017; Thibodeau et al., 2017; Terhaar et al., 2019). Without knowing the quality of the present-day riverine fluxes, it is not possible to evaluate the results.
• Some of the organic nutrients are remineralized directly due to the fixed stoichiometric ratio in the marine organic matter (line 140). Please tell the reader how much is remineralized directly and discuss later if that influences the results. The lability of terrestrial organic matter is an important factor for the impact of riverine nutrient fluxes on NPP and carbon fluxes on air-sea CO2 fluxes (Terhaar et al., 2021).
• Is there a particular reason why you use fluxes from 1970 for the FIX run? Later you compare the NPP results to observation-based NPP from after 2000. Wouldn’t it be better to use the 2000 fluxes for the FIX run?
• As mentioned above, nutrient fluxes often do not scale at all with runoff as concentrations can decrease strongly when discharge increases. Furthermore, apart from DOM and DIP the global news scenarios all give very different future scenarios compared to RUN. I think the simulation RUN hence really makes very little sense and I do not know what its value is. I would certainly not make such strong statements in the Discussion (line 321). I am happy to be convinced otherwise.
• It seems that large changes are always simulated in the Black Sea. However, results from ESMs in enclosed or semi-enclosed seas usually make no sense. Did you mask these seas, including the Mediterranean Sea? If not, how does masking these seas change your results?
• I am really struggling with the significance of the results. For example, in line 192, I would like to see the inter-annual variability as a measure of the standard deviation to see how much they are really different. Similar, is there an uncertainty estimate for the observation-based estimates in line 197? Overall, the differences in annual NPP and RMSE seem to be so small that I am not sure if it makes sense to use terms such as ‘better’ or ‘improve’. Can you find any statistical way to evaluate if the changes are significant? This comment should be addressed to other numbers throughout the manuscript. Please be also careful with the word ‘significant’ as used in line 238 if it has no statistical meaning.
• Please refrain from making strong claims about the Arctic. Indicating a ~76% increase in NPP is misleading giving how bad the model simulates the present-day NPP. Based on an observation-based NPP of 450 TgC/yr, a change of 70-80 TgC/yr is only an increase in 17%. Moreover, the very low present-day NPP suggests either strong light or strong nutrient limitation. If it is strong nutrient limitation, riverine fluxes would have an overly strong effect because all nutrients would be used immediately. So maybe even the 17% are still too high. This goes back to the point that the reader must know how good the model performs locally.

General comments

• Often ‘biogeochemistry is used as a synonym for PP and air-sea CO2 fluxes. But the word biogeochemistry also includes acidification, carbon and nutrient cycles, and other things. Please just say PP and air-sea CO2 fluxes. ( for example line 250).
• Please adhere to the best practice guide (https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/Handbook_2007/Guide_all_in_one.pdf) and use C_T and A_T instead of DIC and ALK.
• I find the name ‘reference run’ misleading. It is rather a control run. Reference should be the best case or something.
• Significant digits should always be the same. For example, in lines 204 and 205 you cite air-sea CO2 fluxes and use different number of digits.

Minor comments

• Lines 19/20: Can one speak of improve based on such small changes in the RMSE? Is it significant?
• Line 13: Suggest changing “not only regionally but also globally” to “regionally and globally”
• Line 18: Suggest changing “modelled” to “simulated”
• Line 22: Unclear what you mean by depending on the riverine configuration. There is no range in the numbers given in this sentence.
• Lines 23/24: the last part of the sentence should be rewritten
• Lines 22-25: A lot of words that do not tell much. Nutrients increase CO2 uptake, CT fluxes decreases it. But where does it increase it and where does it decrease it? Maybe shorten this or explain.
• Line 26: Can you be more quantitative?
• Line 31: Not sure if you can count runoff.
• Lines 31/32: transporting nutrients where? Suggest adding “into the ocean” after “transporting nutrients”.
• Line 34: What do you mean by “absolutely dominant” source? More than 50%? Please be clear.
• Line 34: Suggest adding “into the ocean” after “transport of carbon”.
• Line 34: Suggest writing air-sea CO₂ exchange instead of air-sea C exchange. It CO₂ and not C that is exchanged across the air-sea interface.
• Line 36: What is “it”?
• Line 36: Do you mean global ocean carbon cycle or really global carbon cycle?
• Line 36: Global and regional changes of what?
• Line 37: Suggest starting a new paragraph here
• Line 55: In the Arctic, Terhaar et al. (2019) started to assess future changes.
• Line 56: Please say which datasets you are referring to.
• Line 58: Why does more data make the impact study more ‘desirable’?
• Line 58: Please say why it is now feasible? One could argue that the CMIP6 horizontal resolution is still not good enough to resolve the global ocean.
• Line 68: Please already say here why you use RCP4.5.
• Line 84: Configured sounds strange here.
• Line 88: ‘d’ is missing in ‘based’.
• Lines 88-113: Does the ocean biogeochemical component also have a name? It is very confusing that you say it is based on HAMOCC and then you only describe HAMOCC. That makes it impossible to understand what has changed.
• Line 129: What is the motivation to use CT and AT data from Hartmann (2009)? What kind of data is that? Modeled, observed, extrapolated? What is the underlying data? Please explain what you use.
• Lines 129-133: Why do you use iron riverine fluxes from 1990? Is there nothing newer including observations since 1990? Does it make sense to weight iron river fluxes by runoff? Often nutrients do not scale at all with runoff (Holmes et al., 2012), so I would like to see some support for this assumption.
• Line 135: Is there a reason why you use 1000 km and 300 km here?
• Line 145: Any reason why not GLODAPv2 is used?
• Line 147: Is the additional spin-up of 200 years is sufficient to get into a new equilibrium.
• Line 153: In what sense is RCP4.5 the most representative scenario? Most likely? Based on what?
• Line 160: What means not considered? Deactivated?
• Lines 168-170: It is not entirely clear that you make 4 simulations. Can you be a little bit more explicit?
• Line 194: In the figure it does not look as if only 15% of the increase is in the coastal shelf seas. What do you mean by predominantly, can you be quantitative here?
• Line 214: Is this a result or a speculation. If you cannot prove it, I suggest to either add it to the Discussion and add literature that supports this point or delete it.
• Line 244-245: Does it really make sense to say slightly higher if the difference is that small?
• Line 272: Please be quantitative
• Line 279: Is not nitrogen the limiting nutrient in the Arctic Ocean (Tremblay et al., 2015)?
• Line 286: Why do you not add CMIP6 data?
• Why do you speculate in the Discussion in lines 290 to 293: You can show that with your model results.
• Figure 4c is almost impossible to read.
• Figure 5a: Could you highlight the +38 more? I was confused first.

References

Arrigo, K. R., & van Dijken, G. L. (2015). Continued increases in Arctic Ocean primary production. Progress in Oceanography, 136, 60-70.

Kaiser, K., Benner, R. & Amon, R. The fate of terrigenous dissolved organic carbon on the Eurasian shelves and export to the North Atlantic. J. Geophys. Res. 122, 4–22 (2017).

Lacroix, F., Ilyina, T., Mathis, M., Laruelle, G. G., & Regnier, P. (2021). Historical increases in land-derived nutrient inputs may alleviate effects of a changing physical climate on the oceanic carbon cycle. Global Change Biology, 27, 5491– 5513. https://doi.org/10.1111/gcb.15822

Holmes, R.M., McClelland, J.W., Peterson, B.J. et al. Seasonal and Annual Fluxes of Nutrients and Organic Matter from Large Rivers to the Arctic Ocean and Surrounding Seas. Estuaries and Coasts 35, 369–382 (2012). https://doi.org/10.1007/s12237-011-9386-6

Séférian, R., Berthet, S., Yool, A. et al. Tracking Improvement in Simulated Marine Biogeochemistry Between CMIP5 and CMIP6. Curr Clim Change Rep 6, 95–119 (2020). https://doi.org/10.1007/s40641-020-00160-0

Terhaar, J., Orr, J. C., Ethé, C., Regnier, P., & Bopp, L. (2019). Simulated Arctic Ocean response to doubling of riverine carbon and nutrient delivery. Global Biogeochemical Cycles, 33, 1048– 1070. https://doi.org/10.1029/2019GB006200

Terhaar, J., Lauerwald, R., Regnier, P. et al. Around one third of current Arctic Ocean primary production sustained by rivers and coastal erosion. Nat Commun 12, 169 (2021). https://doi.org/10.1038/s41467-020-20470-z

Thibodeau, B., Bauch, D. & Voss, M. Nitrogen dynamic in Eurasian coastal Arctic ecosystem: Insight from nitrogen isotope. Glob. Biogeochem. Cycles 31, 836–849 (2017).

Tremblay, J. E. et al. Global and regional drivers of nutrient supply, primary production and CO2 drawdown in the changing Arctic Ocean. Prog. Oceanogr. 139, 171–196 (2015).

Using a global ocean biogeochemical model, the authors assess the future impacts of changing riverine inputs while performing simulations with several scenarios of riverine inputs. In the paper, the authors show a slight reduction in root mean square error of primary production with respect to observations on the continental shelf and in parts of the ocean highly affected by rivers. They show that, overall, riverine nutrients may alleviate part of projected primary production decline. The topic is very relevant and potentially important for fully constraining the ocean carbon cycle. However, while the modelling work is very sound in its closed framework, I believe the author’s review of literature seems to be lacking, which leads to, at times, questionable assumptions and too high confidence in a model setting not necessarily adequate for investing impacts of riverine tracers and their fate in the ocean. I do think the study should be published, but the authors should discuss the following points and, in my opinion, clearly point out uncertainties related to their framework in the abstract.

General Comments

It is debatable that the model configuration used here is actually adequate for the research question addressed in this paper. The model is limited in terms of resolution (~1 degree), and this is a strong constraint for representing fine-scale circulation features that are thought to be of particular importance in the coastal ocean. This is a topic that many studies have discussed previously, and these should be considered. Secondly, the model doesn’t consider specific biogeochemical processes relevant to the coastal ocean. For instance, organic matter decomposition rates are shown to be much higher in the coastal sediment than in the open ocean (Ardnt et al., 2013), bed shear stress also re-suspend biogeochemical from the shelf seafloor. I think omitting both of these physical and biogeochemical limitations lead to the important underestimation of primary production on river-dominated continental shelves shown in this study, which seems to indicate the model is underrepresenting. This also affect exports of riverine biogeochemical compounds to the open ocean, and thus this has very important consequences for the main outcomes presented in this study. The authors do mention these limitations briefly in the limitations section, but this should be considered omni-present in attempts to interpretate the results, and at the least mentioned in the abstract.

A second, perhaps less central point, but still relevant to the study, is that the authors spin-up their model to present day fluxes, whereas these are actually more strongly perturbed over the historical time period (Beusen et al., 2016), than what is projected in terms of their future changes. Since time-scales of the ocean carbon cycle are notably long, this historical perturbation could have important legacy effects propagating into the future, potentially enhancing the primary production more than is estimated here. This should, in my opinion, also be discussed in the limitations section.

Specific Comments:

Abstract

L16 “With four riverine configurations: deactivated, fixed at a contemporary level, coupled to simulated freshwater runoff, and following four plausible future scenarios.” Are only the nutrients (and if yes which ones) changing, or also carbon and alkalinity? This should be stated here.

L17 “The inclusion of riverine nutrients and carbon…” Those numbers are valid for contemporary I guess?

L20 “Riverine nutrient inputs alleviate nutrient limitation,…“ Should be reformulated, since riverine nutrient inputs are unlikely alleviated nutrient limitation in general, but reduce (?) it in some regions (?).

Introduction

In general, there are very little citations in the introduction, and often the same ones are used repeatedly.  There are some recent modeling studies of implications of riverine inputs in the ocean that would be very relevant for this study. These should, in my opinion, be considered in the introduction:

Lacroix, F., Ilyina, T., Mathis, M., Laruelle, G. G., & Regnier, P. (2021). Historical increases in land-derived nutrient inputs may alleviate effects of a changing physical climate on the oceanic carbon cycle. Global Change Biology, 27, 5491– 5513. https://doi.org/10.1111/gcb.15822

Liu, X., Stock, C. A., Dunne, J. P., Lee, M., Shevliakova, E., Malyshev, S., & Milly, P. C. D. (2021). Simulated global coastal ecosystem responses to a half-century increase in river nitrogen loads. Geophysical Research Letters, 48, e2021GL094367. https://doi.org/10.1029/2021GL094367

I would furthermore suggest citing some regional-scale studies that investigate implications of riverine inputs on biogeochemistry of specific shelves, literature is abundant here. In addition, I would read and refer to the last 2-3 Global Carbon Budget studies for potential importance of riverine carbon fluxes for the ocean.

L25 “The large range of the riverine input across our four riverine 26 configurations does not transfer to a large uncertainty of the projected global PP and ocean C uptake…“ In terms of global PP, one could argue this could be due to the representation of continental shelf in the model, which leads to heavily underestimated continental shelf PP.

L35 “Although riverine carbon only plays a minor role in the global carbon cycle, …“  Recent Global Carbon Budget publications disagree with this (Friedlingstein et al., 2021). If the higher estimates of outgassing of riverine carbon are true (up to 0.8 Pg C yr^-1), they could potentially play a large role in explaining discrepancies between CO₂ estimates arising observation-based products and model-based results.

L44 Maybe add the more recent Beusen et al. (2016) estimates to this for the historical time period?

Methods

L118 “The riverine influx includes carbon, nitrogen and phosphorus, each in dissolved inorganic, dissolved organic, and particulate forms, as well as alkalinity (ALK), dissolved silicon and iron (Fe).“ Are there specific ocean variables for terrestrial dissolved and particulate organic matter? If not how does not model deal with organic P-N-C ratios that differ from those of the Redfield ratio? This is an important point to clarify because high C-to-nutrient ratios are thought to be largely responsible for ocean outgassing.

L140 “Any remaining riverine organic matter is then added to its inorganic pool” This is not really clear. Is excess organic carbon is added to the DIC pool? If not I think this might be the reason why river inputs cause a net sink in the model, and not source as is relatively well acknowledged (see e.g.,  Global Carbon Budget, 2021). Also keep in mind that organic carbon mineralization has a small effect on alkalinity (which I don’t think would have a huge impact here).

Also, maybe more important here: are you assuming the large particulate fluxes (particulate P and N) from NEWS2 are organic? Because from my understanding, these can be inorganic (for P bedrock erosion, occluded etc..), and this would not at all be bio-available in the coastal ocean.

L156 “REF: Reference run. Riverine nutrient and carbon supply is deactivated.“ Are there other sources of nutrients and carbon in the model? If riverine nutrients and carbon were the only inputs to the ocean model and their sediment loss is non-zero, I would expect all related variables to thrive to zero, which does not make a very interesting reference run. In the case there are other inputs, they should be given in numbers and explained.

L179-L185 In my opinion the authors don’t need to specifically defend themselves on this particular point, at least not to this extent. I would consider shortening or removing.

Results

L198 “Although the total PP in FIX is still considerably lower than the satellite-based estimates, the inclusion of riverine nutrients and carbon does slightly improve the distribution of PP especially on continental margins (Figure 3), according to our area-weighted root mean square error (RMSE) analysis. „

Figure 3 really shows that a large part of the underestimation of PP is originating from the continental shelf, in particular regions of riverine inputs. The improvement is minor compared to the actual bias. In my opinion, this actually shows that the model underestimates the impacts of rivers on PP, which does have a strong implication for the conclusions of this paper, and should be assessed somehow.

Figure 4: It’s a bit concerning to me that considering riverine inputs lead to a sink of carbon in the ocean. It is relatively well acknowledged that river inputs are thought to cause a source of carbon (e.g., Regnier et al., 2013; Resplandy et al., 2018). The reason for this is that carbon to nutrient ratio of the (bio-available) terrestrial inputs is larger than the Redfield ratio. I guess the fact that most particulate P and N is thrown in as dissolved inorganic species might be the explanation for this. How is the alkalinity to DIC ratio of riverine inputs constrained? Either way, either explain the reason for this or I would consider not discussing the CO2 flux for the “unperturbed” river simulation.

L305 “Our experiments show that riverine nutrient inputs have a dominant role over the organic matter inputs in FIX, enhancing CO2 uptake along continental margins via sustaining PP in both historical and future time periods.“ This is however purely a consequence of the ratio of (bio-available) nutrients to organic matter that is added to the ocean, which as mentioned, I don’t think is completely correct from a process-based perspective. In fact, I think most river-dominated shelves show C outgassing, see regional CO₂ fluxes from Chen and Borges (2009) or regional-based studies.  

L337 “…do not transfer to large uncertainties in future global marine biogeochemistry projections in NorESM.” Yes, but if you would have taken uncertainties related to the coastal ocean into account, through e.g. sensitivity analysis of sediment degradation, I wonder if the conclusions would be different here, I would assume so.

Minor edits

L22 “and thus lessen the projected future decline in PP by up to 0.6 PgC yr-1 22 (27.3%) globally depending on the riverine configuration.“ -> , globally,

L55 “Taking the advantage of the latest improvement of global” Remove “the”.

L171 “By comparing FIX versus REF…“ Add comma here.

L332 “. Therefore, it is worth exploring the merits of using GNS in future projections of marine biogeochemistry.” Not really sure what is meant here.

Arndt S., B.B. Jørgensen, D.E. LaRowe, J.J. Middelburg, R.D. Pancost, P. Regnier,Quantifying the degradation of organic matter in marine sediments: A review and synthesis,Earth-Science Reviews, Volume 123, 2013, Pages 53-86, ISSN 0012-8252, https://doi.org/10.1016/j.earscirev.2013.02.008.

Beusen, A. H. W., Bouwman, A. F., Van Beek, L. P. H., Mogollón, J. M., and Middelburg, J. J.: Global riverine N and P transport to ocean increased during the 20th century despite increased retention along the aquatic continuum, Biogeosciences, 13, 2441–2451, https://doi.org/10.5194/bg-13-2441-2016, 2016.

Chen C.-T. A., Borges A.V., Reconciling opposing views on carbon cycling in the coastal ocean: Continental shelves as sinks and near-shore ecosystems as sources of atmospheric CO2, Deep Sea Research Part II: Topical Studies in Oceanography, Volume 56, Issues 8–10, 2009, Pages 578-590, https://doi.org/10.1016/j.dsr2.2009.01.001.

Regnier, P., Friedlingstein, P., Ciais, P. et al. Anthropogenic perturbation of the carbon fluxes from land to ocean. Nature Geosci 6, 597–607 (2013). https://doi.org/10.1038/ngeo1830

Resplandy, L., Keeling, R.F., Rödenbeck, C. et al. Revision of global carbon fluxes based on a reassessment of oceanic and riverine carbon transport. Nature Geosci 11, 504–509 (2018). https://doi.org/10.1038/s41561-018-0151-3