Brekenfeld et al. propose a new method to analyze multi-elemental time series acquired at the outlet of two long-term experimental catchments using a high frequency in situ laboratory. This method is based on event-scale variability of concentration of solute pairs. They determine the “synchronous” behaviour of two given solutes, in that case major ions, based on their concentration relationship and state that this synchrony can define a two-end-member mixing: pre-event and event water. This methodology is divided in three steps: (1) classification based on concentration-concentration plot, (2) variation of the molar ratio at event scale and (3) the calculation of the inter-event synchrony of concentration variability. This technique is proposed as a complementary data analysis from other methodologies, such as EMMA and c-Q relationship.

This manuscript corresponds to the scope of HESS publications. However, in the form it is presented for the moment, it mainly introduces an innovative data treatment approach for interpreting solute transport at catchment scale. It does not really improve the solute transport knowledge at catchment scale for some reasons that will be discussed later on. For this reason, I suggest, instead of targeting a research article, to go for HESS technical note because this new contribution introduce a new development, which is relevant for scientific investigations within the journal scope. And this is an interesting approach, which could contribute to the revisit of the conservative tracer hypothesis. Moreover, the submitted draft still needs significant improvement before to be published.

General Comments

On the form, the structure and the clarity of the manuscript still needs improvements. Some parts are not located at the more judicious place (see detailed comments). The comparison between the two catchments should be more clearly separated. Indeed, the result part need a clearer structure to clarify the different solute behaviors between the two experimental catchments. Some results are provided without any introduction in the material and method part. The labelling of the figures could be harmonized and defined according to the used parameters: ions in this case.

All data used in a published article should be provided and/or being accessible, via online application or directly in the manuscript. This is not the case with this new contribution and I would insist to have access to all datasets used. If this information was provided and I did not find the link, I hope the authors would accept my apologies.

One of my main concerns is about the definition of an “end-member” and the capacity we have to determine its contribution at catchment scale by only using data observed in the stream. Indeed, according to the biogeochemical complexity and the hydrological connectivity, observations made in a stream should only be extrapolated to some “near-stream” locations, like the riparian zones. To my understanding, what novelty is provided in this study is a chemical identification of the common “old” versus “event” water that are used since long time in hydrological studies. Unifying catchment biogeochemical response to hydrological dynamics based on two end-member mixing seems to be very reductive and the defined “endmembers” may not be real ones from a given contribution of a catchment compartment but more a mixing of different water (with different chemical pattern and age) along a flowline that would exist in the system during specific hydrological conditions. In other world, is it really end-member that are observed or a specific stream hydrochemistry driven by interaction with existing near-stream end-members? Even if we could assume that the event water may most of the time present similar characteristics, what about the variability of processes that could contribute to the chemistry of the pre-event water? For this reason, I suggest providing in the introduction a clear definition of what is called an end-member and present current limitation to observe end-members in a stream from the remote part of a catchment. This would allow to suggest how this new methodology could improve such limitation.

The method is based on statistical threshold to justify the existence of some ion relationships and propose a paired chemical element classification in three groups: synchronous variation, invariant and complex variation. Then the observed synchrony is used to explain the processes that drive the mobility of the paired of synchronous elements to the outlet of the catchment. In my opinion, based this methodology only on statistics is a mistake because the main drivers of the hydrochemistry at event scale is the hydrological state of the catchment - meaning the status of the water storage when the rain start – and the season – meaning the activity of the vegetation and related living (micro)organisms. The statistical choice that is done here is not able to justify properly the link between observed relationship and determination of detailed and specific processes that could explain the given relationship. I think that the difficulty of this methodology relies in the selection criteria based on the number of events and not on the typology of events that would take into account hydro-climatological state of the catchment during the selected events. An event typology that relates to event characteristics and hydrological dynamics (connectivity, storage dynamics…) in the catchment would have been more appropriate to link the c-c relationship to catchment process functioning. For instance, this would inform about the potential connectivity between functional compartments inside the catchment and the potential water mixing happening close to the stream during contrasted seasons. With the long-term hydrological timeseries that may exist at these two experimental catchments, placing the selected events in a more general hydro-climatological context would be an important added-value to this study and to the community. I wonder if the authors could go deeper in this suggestion.

Specific/detailed comments

Introduction

Lines 69-73: this part should be included in the material and methods

Material, methods and site descriptions

Line 94: replace Ca²⁺ by “Ca” or “calcium”

Lines 105-110: Is alkalinity also measured in the in situ laboratory system? How did you check the ionic balance in the samples?

Lines 117-162: How did you define the two threshold values used to differentiate the three relation types?

Lines 163-165: I would agree for each individual site but how the different delays (distance from the sampling to the in situ laboratory and membrane saturation) could affect the comparison between the two sites?

Line 173: “Parts of the catchments” should be replaced by “near stream parts/contribution areas”

Line 180: in what context were those two examples taken? Are they comparable with the context of the studied catchments?

Lines 184-192: this paragraph is not clear to me because it would need more specific example of what processes are considered and what compartments/end-members are taken into account. The processes you are considering here are driven by biogeochemistry, water transit time and connectivity at the same time. What about the consideration of mixing water from different end-members in the pathway to the stream?

Line 196: Why looking only at the denomination ion?

Results

Lines 200-204: this part should be in the methodology in §2.4.1. It could be interesting to know the total number of events that were used for this selection to evaluate some kind of “success rate” for both in situ laboratory in the two different catchments.

Lines 211-213 are redundant and could be removed.

Lines 214-227: I do not really understand this analysis. Why and how the thresholds of % event is defined and how this impact the interpretation. Events that represent <5% should not be also of interest to explain different dynamics and link to processes functioning?

Line 215: from where is coming the value 56%

Line 219: Cl and Mg not presented in this part and should be replaced by Ca

Line 220: K not shown in the table

Line 256: molar ratio in the rain and the throughfall are not presented in the methodology part. This should be added. Were the rain and throughfall sampled accordingly to the stream sampling frequency? If not how can you be sure that you capture the real variability of chemistry in those input samples and that this one can be compared with the high-frequency variability you observed in the stream?

Line 264-265: this is not true for the Strengbach catchment.

Lines 272-278: should be part of the methodology

Line 284: I see in the figure C1 0.69-0.87 and 0.62-0.88 instead of the values indicated in the text.

Discussions

Line 305: I do not understand how you can prove the spatial homogeneity of water chemical signature at catchment scale if you only have observation in the stream. What you observe actually are processes that happen in the “near-stream” environment. You only should focus on those areas that stay closer to the stream network. You cannot infer about the complex reactivity and mixing that may happen inside the catchment and which are driven by the water saturation state and by the flowpaths connectivity in the catchment subsurface.

Lines 306-308: I find this process description quite weak in this paragraph and I suggest to remove this sentence because you try to relate the element ratio to the processes in the following parts.

Line 310: no information is provided in the methodology about the piezometer and soil solution.

Line 311: interpreting all the concentrated (old water) contribution with evapotranspiration needs more explanation. Is it a seasonal evolution of this relationship? Did you only observe this during the vegetative period (ok for the evapotranspiration) or did you also observe this in winter (another explanation should be found)?

Line 321: the Strengbach should be removed from this part dedicated to agricultural catchment. This would reduce the confusion that already exists in this discussion. The structure between the element ratios and the linked processes should be improved.

Line 340: how deep are this groundwater in the catchment?

Line 342: Can the contribution of the denitrification generalized during all seasons? what would be the seasonal effect on the contribution of the denitrification? Would you expect having the same contribution from this process in summer and winter?

Line 356: rain data are not used in this study: might be throughfall?

Line 387: the link between hydrochemistry and hydrology in this study is missing and would have been an important new contribution and strengthen the proposed methodology.

Lines 395-396: not clear

Lines 401-409: the technical uncertainty should be similar for all samples or you should explain how this could affect your methodology. Is it not more the choice of the statistical criteria that would impact the sensitivity of your classification?

Lines 416-417: you are providing references from a forested catchment to explain processes in the agricultural one, is it really relevant?

Line 424: any reference to strengthen this?

Lines 433-440: this should be developed and this is also why an event typology should have been used to more efficiently understand the dynamics and related processes observed with this new methodology.

Lines 442-458: You are proposing a very pertinent and novel approach but according to all the questions I highlighted your method present similar limitation than EMMA and PCA. For instance, you are not able to explain a detailed temporal contribution of the real different end-member at catchment scale and you mainly provide more precision to link the chemical composition of the “old” and “event” water to some related processes during flood events in the “near-stream” parts of the catchment.

Tables

Table 1: You should stay consistent and or showing all the pairs you studied or only the ones you discuss (why keeping NO3/Na?). Presenting all analyzed ratios would allow having a larger overview about expected variability from the full dataset.

Figures

Figure 2: the x and y axis should be replaced by the ions instead of having the full name of the element.

Figure 3: same remark as Figure 2

Figure 4: Why Mg/Ca ratio is not presented? The “pairwise difference” is not presented in the legend

Figure 5: same remark as figure 2. The synchrony is not clear in Fig. 5b. Should it not be 39 and 23 events (then dots) for the 2 catchments in both graphs?

Critical review of the paper’s discussion on solute synchronies and end-member mixing

• Introduction: The paper aims to determine the minimum number of end-members required to explain the variation of stream water solute concentrations during storm events based on the synchronous or asynchronous behaviour of different solute pairs. The authors propose a novel methodology that uses high-frequency solute synchronies to identify simple two-end-member mixing scenarios and more complex higher-order mixing scenarios. They apply this methodology to two French catchments with contrasting characteristics and analyse several major ion pairs on the event scale.
• Event-scale concentration-concentration pattern: The authors present the results of their methodology for each catchment and each solute pair, using concentration-concentration plots and histograms of the slope and intercept of the linear regression between the solute concentrations. They classify the events into three categories: (1) events that can be explained by a simple two-end-member mixing model; (2) events that require a higher-order end-member mixing model; and (3) events that show no clear pattern or relationship between the solute concentrations. They discuss the possible causes and implications of these categories, such as the influence of precipitation amount and intensity, the spatial variability of solute sources and flow paths, the occurrence of biogeochemical processes, and the uncertainty of the end-member composition.
• Strengths and weaknesses: The paper’s discussion on the solute synchronies and end-member mixing is comprehensive and informative, as it provides a detailed description and interpretation of the results for each catchment and each solute pair. The authors also acknowledge the limitations and uncertainties of their methodology and data and suggest ways to improve them in future studies. However, the paper’s discussion could be improved by comparing and contrasting the results with results obtained using EMMA.
• Conclusion: The paper’s discussion on solute synchronies and end-member mixing is a valuable contribution to the field of catchment hydrochemistry, as it introduces a new methodology that can help identify the minimum number of end-members and the hydro-biogeochemical processes that affect the stream water solute concentrations during storm events. However, the paper could benefit from a more extensive comparison with other studies that have addressed similar research questions in order to provide a broader perspective and context for the results and implications. A good example of current views on this topic is CHEMMA (Convex-Hull End-Member Mixing Analysis).

Minor revisions:

• Given that both PCA in EMMA and the proposed methodology operate under the same assumptions of conservation of mass and non-reactivity of solutes and both interpret variance in solute concentrations as evidence of hydrodynamic mixing, could the authors elaborate on the unique contributions of their proposed methodology? Specifically, while PCA in EMMA not only identifies end members but also provides information about the main solutes contributing to each end member through the loadings of the principal components, it is not immediately clear what additional insights the proposed methodology offers. Could the authors provide further justification for the introduction of this new method?
• In the figure 2 caption, it should just be mentioned that the colours of the data points correspond to different consecutive flood events.
• The intext reference in line 200 showed an error.
• I would suggest performing a PCA on the data in order to see if these interpretations discussed about solute behaviour makes sense in terms of the covariance of parameters.

Suggestions

• This technique is only relevant in specific cases of streamflow generation since it is based on the premise that there are only two end members, which is only true when the water sources are near the stream.
• The technique does not account for variance in the pre-event end member, which will most likely change as the system wets up and flowlines extend further away from the stream.
• Sensitivity of the classification:
  • Choice of Threshold: To address the arbitrariness of the threshold, the authors could conduct a sensitivity analysis. This would involve varying the threshold and observing how the classification results change. This could provide a more robust justification for the chosen threshold or suggest a different optimal value.
  • Non-linearity: To account for non-linearity, the authors could consider using non-linear regression models or machine learning techniques that can capture complex relationships in the data. This would allow them to classify solute variations without assuming linearity.
  • Overlap of Classification Types: To address the overlap of classification types, the authors could consider using a probabilistic classification scheme. Instead of assigning each solute to a single category, they could assign probabilities to each category, reflecting the degree of certainty in the classification. This would acknowledge the complexity of the system and the potential for solutes to exhibit characteristics of multiple categories.
  • Case of Ca²⁺/Mg²⁺: For cases like Ca²⁺ and Mg²⁺, where there is evidence of synchronous variation but the relative variation is low, the authors could consider creating a separate category or sub-category. This would allow them to acknowledge the synchronous variation without contradicting their classification criteria.
• Meybeck and Moatar (2012) proposed a method for segmenting c Q curves based on the stream's median flow (q50), resulting in nine distinct c Q modalities. This method can be used to subset the chemistry data to find solute pairs that exhibit this synchronous behaviour. I am primarily interested in how the linear regression line was fitted to the data. There seem to be inflection points in the data suggesting a switching of the dominance of one end member over another. I believe fitting only one regression line may not be the best way to go about it.
• “In addition, our methodology does not require the a priori assumption of conservative solutes, as it is required in the EMMA approach (Christophersen et al., 1990).” I do not completely agree with this statement. The interpretation of two end-members by looking at the co-variance of solutes very much relies on the fact that no chemical reaction takes place.
• Adding c Q graphs of the solutes discussed will help to link this work to current work revisiting this concept. It will also give the reader a better conceptual feel of what is going on (flushing or chemostatic behaviour, for instance).
• It would be interesting to see pH also added to the time series data.