the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Aug 2026
Isotope-enabled modeling of fast streamflow dynamics in a steep Alpine catchment
Abstract. Alpine headwater catchments often produce streamflow peaks anywhere from minutes to hours after a rainfall event, quickly mobilizing previously stored subsurface water. Understanding and describing this response to rainfall events and its variations via modeling remains challenging, despite the growing availability of data, including tracer data such as stable isotopes of water, to inform internal flow partitioning.
Here, we present a novel flux partitioning routine integrated into an existing hydrological model based on the Geomorphological Instantaneous Unit Hydrograph and multiple subsurface reservoirs. The model structure is based on a detailed perceptual model derived from available field data, and it simulates streamflow magnitude and streamwater isotopic ratios at high temporal resolution (10-minute intervals) in a snow-dominated headwater catchment in the western Swiss Alps (Vallon de Nant) over two consecutive summers. By jointly calibrating the model with both streamflow quantity and streamwater isotopic ratios, we obtain a reliable representation of catchment-scale partitioning of streamflow between groundwater, snowmelt, and direct runoff. The simulations showed that despite the catchment’s high level of flashiness, with peak streamflow occurring within an hour of peak rainfall, most streamflow originates from subsurface flow pathways with limited contributions from direct runoff. Even during short periods of intense convective rainfall events, peak flows mostly comprise water released by subsurface storage, which are mobilized by rainfall.
Our results show that incorporating stable water isotopes into a relatively simple catchment-scale model can refine model structure, reduce parameter uncertainty, and improve process attribution of short-timescale streamflow generation dynamics. We discuss the advantages and limitations of the proposed isotope-enabled modeling approach and its potential extension to other catchments and year-round modeling.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-4249', Anonymous Referee #1, 12 Oct 2026
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AC1: 'Reply on RC1', Harsh Beria, 24 Oct 2026
Reviewer 1
We would like to thank Reviewer #1 for a careful assessment of our manuscript and constructive feedback. We will address the raised concerns in the revised manuscript.
In the following responses the reviewer’s comments are in bold, followed by our responses in plain style. Section, line, and figure references to the main and supplementary text refer to the submitted manuscript (EGUsphere discussion opened on August 17, 2026) unless indicated otherwise.
This manuscript combines discharge and stable water isotope observations with hydrological modelling to investigate rapid streamflow responses in a steep Alpine catchment. The authors collected a valuable dataset over two summer periods and integrated these observations into an isotope-enabled model to explore the contributions of different flow components. The results highlight the substantial contribution of groundwater to summer streamflow and demonstrate the potential of isotope observations to constrain modelled flow partitioning. The research questions and approach are well suited to the HESS readership, and the study offers a useful contribution to understanding streamflow generation in Alpine catchments.
However, I have several concerns about the prescribed isotope signatures, the calibration procedure, and the robustness of the inferred flow contributions. These issues affect how confidently the model results can support the process interpretations.
Response: Thank you for a positive critique of our work. Our responses to the individual suggestions are below.
General comments
(1) The model assigns the mean winter snowpack isotope signature to snowmelt during the summer simulation period. The authors acknowledge that snowmelt can differ isotopically from the snowpack, but the justification for assuming a small effect during July–September is not sufficiently clear. The timing of the analysis alone does not establish that the winter mean represents the residual snowmelt entering the stream.
Could the authors explain whether any observations or citations support this assumption for the study catchment? If direct observations are unavailable, I suggest testing plausible alternative snowmelt isotope signatures and evaluating their effects on the estimated snowmelt and groundwater contributions.
Response: Previous snow isotope synthesis work has shown that the mean isotopic ratio of snowmelt is similar to the mean isotopic ratio of the snowpack (Beria et al., 2018). However, recent studies from Finnish Lapland, representing a very different climatic setting from the Swiss Alps, have shown that late-season snowmelt can become isotopically enriched due to isotopic fractionation associated with melt-refreezing cycles (Ditlevsen et al., 2025; Noor et al., 2023b, a). The extent to which such enrichment occurs in the Swiss Alps (if any) remains unclear. Direct late-season snowmelt isotopic measurements were not collected during our study period.
To assess the potential biases introduced by this assumption, in the revised manuscript, we will conduct a sensitivity analysis in which the prescribed snowmelt isotopic ratio is progressively enriched over a plausible range of values, and its effects on the partitioning between different fluxes will be assessed, thereby evaluating the robustness of our conclusions.
In addition, snowmelt discharge is represented using a storage-discharge relationship. What evidence, beyond the discharge and isotope data used to constrain the model, supports the simulated timing and magnitude of summer melt? Please distinguish the evidence for residual snowmelt occurrence from the evidence supporting its estimated contribution.
The residual snowmelt component was motivated by the depleted streamwater isotopic ratio in early July and the diel fluctuations in streamflow seen during July 2017 (Figure 4). However, we agree with the reviewer that a storage-discharge model for snowmelt is over simplified. To address this limitation, we will replace the storage-discharge formulation of snowmelt with a temperature-based degree-day model in the revised manuscript.
(2) direct runoff and soil drainage are assigned the same summer-average rainfall isotope signature. It is unclear why this is appropriate for soil drainage, which could include water stored before the rainfall event and mixing within the soil. Please explain the physical basis for this assumption and provide supporting observations or references.
Response: We agree that soil drainage may contain pre-event water, and assigning it the rainfall isotopic signature is a simplifying assumption. In the original manuscript, direct runoff and soil discharge were represented separately in Figure 5 but combined into a single component called “direct flow” in Figures 8 and 9. This assumption was partly motivated by the relatively shallow soil storage represented in the model (posterior Smax,soil ≈ 0.2-0.3 m; Figure S3, S4). Additionally, previous tracer studies in Swiss alpine and pre-alpine catchments have shown that shallow soil interflow in young moraines can be dominated by recently infiltrated rainfall, particularly where preferential flow pathways facilitate rapid drainage (Leuteritz et al., 2025; Maier and van Meerveld, 2021; Weiler et al., 1999). Nevertheless, we acknowledge that mixing with pre-event soil water is not explicitly represented in our model. We will clarify this assumption, report the inferred soil storage capacity, and consistently represent the combined “direct flow” component in Figure 5 of the revised manuscript.
(3) The use of a constant rainfall isotope signature within each summer also needs further justification, particularly because the study focuses on rapid responses to individual rainfall events. How much variability is present in the available precipitation isotope observations, and how might neglecting this variability affect the inferred component contributions?
Response: In the revised manuscript, we will quantify the effect of variability in available biweekly rainfall isotope measurements on flow partitioning by using temporally-varying rainfall isotopic signatures instead of a single summer-average value. The two approaches will subsequently be compared to assess how neglecting the variability of rainfall isotope signature affects the inferred component contributions.
(4) I noticed that Section 7 already acknowledges limitations associated with spring representativeness and endmember variability. However, these limitations should also be connected to the reliability of the reported flow fractions. A focused sensitivity analysis would help establish whether the main conclusions remain consistent under plausible alternative isotope assignments.
Response: In the revised manuscript, we will conduct two sensitivity analyses:
- Assigning progressively enriched isotopic signatures to snowmelt end-member relative to the winter snowpack mean, and
- Introducing temporally-varying rainfall isotopic ratios based on available biweekly rainfall samples.
We will compare the resulting flow partitioning with our original estimates to evaluate the robustness of our main conclusions. We will further discuss the uncertainties associated with the representativeness of spring-derived isotopic end-members.
(5) I found Section 4.3 difficult to follow. Please distinguish clearly between the observed variables used for calibration, the four likelihood components, and the performance metrics used to evaluate the simulations. My understanding is that calibration uses discharge and streamwater δ¹⁸O, each separated into low-flow and high-flow conditions. These are therefore four likelihood components derived from two observed variables.
Response: This understanding is correct. We will revise Section 4.3 to clearly distinguish between the observed variables, likelihood components, and performance metrics.
The sequence of calibration and evaluation should also be clearer. Initial states are first estimated using both summers and then fixed before the reciprocal single-year calibrations. Consequently, observations from the evaluation year have already contributed to estimating its initial conditions. This does not invalidate the comparison, but it limits its independence. Please state this explicitly in Section 4.3 and distinguish evaluation conditional on fitted initial states from a fully independent validation.
Response: The initial storages were estimated using observations from both summers and subsequently held fixed during model calibration. Consequently, observations from the validation period contributed to the estimation of initial conditions, limiting the independence of the split-sample validation strategy. We will acknowledge this in Section 4.3.
(6) Please clarify which parameter sets were used to produce Section 5.3 and Figures 8 and 9. Figure 8 displays multiple simulations, whereas Figure 9 presents single percentages. How many parameter sets contribute to each figure? Do the percentages represent a selected simulation, an ensemble mean, or another summary?
Response: We agree that the calculation of ensemble statistics was not sufficiently described. In the revised manuscript, we will specify the parameters used for ensemble averaging in Section 4.3.
(7) The uncertainty in the component contributions is central to interpreting these results. I suggest reporting intervals for the seasonal flow fractions and explaining how they were calculated. Please also distinguish uncertainty arising from sampled model parameters from uncertainty associated with the prescribed isotope signatures and model structure.
Response: We will add the uncertainty bands in figures 8 and 9, describe how these intervals are calculated from the posterior parameter ensembles in Section 4.3, and acknowledge the uncertainty sources. The proposed sensitivity analyses will help assess the influence of end-member assumptions, but we regard a formal decomposition of uncertainty into individual sources as beyond the scope of this study.
(8) The narrower range of contributions obtained with isotope calibration is useful evidence that the additional observations constrain the model. However, a narrower range under fixed assumptions does not necessarily demonstrate that the resulting partitioning is more accurate. This distinction should be reflected in both the results and discussion.
Response: We will acknowledge this in Section 7 (Limitations) in the revised manuscript.
Specific comments
(1) In Section 3, please distinguish field observations from the hypotheses used to construct the perceptual model. This would help readers follow how the observations motivate the proposed flow components.
Response: In the revised manuscript, we will clarify which hypotheses are supported by our observations and which ones are supported by existing literature.
(2) In Figure 4, please explain the black points and connecting line in the isotope panels as streamwater observations in the caption.
Response: We will revise Figure 4 caption to clarify that the black points represent individual streamwater δ¹⁸O observations, with the connecting lines included as a visual guide between successive observations.
(3) In Section 4.1, which model elements were developed for this study and which were adopted or adapted from previous formulations? Also please explain which processes are spatially distributed and which are lumped, including the role of the 25 subcatchments.
Response: All individual model components were developed specifically for this study, based on the perceptual model of Vallon de Nant. We will revise Section 4.1 to better clarify which processes are spatially-distributed versus lumped.
(4) In Section 4.3, can authors describe how the low-flow and high-flow periods were selected and provide enough information for this classification to be reproduced?
Response: High-flow periods were identified visually as periods following a rain event during which a high-frequency streamflow response was visible. The beginning of a high-flow period is set as the last time step before the streamflow rises in response to rainfall. The end of a high-flow period corresponds to the first timestep where no high frequency streamflow variability is observed. A figure showing the high- and low-flow periods delineation used in the study will be added in supplementary material.
(5) Figures 8 and 9, The model contains five flow components, but these figures show four and three component categories.
Response: In the original manuscript, we combined direct runoff and soil discharge into one flux called “direct flow”, which is also spatially distributed (Figures 8, 9). However, figure 5 showed direct runoff and soil discharge separately causing this confusion, which will be rectified by combining direct runoff and soil discharge into “direct flow” in the revised manuscript.
(6) Figure 9, each percentage is calculated from total component volume divided by total streamflow volume, or from the mean of instantaneous fractions? These calculations can produce different results.
Response: The percentages in Figure 9 are calculated as the cumulative discharge volume of each flow component divided by the total simulated streamflow volume over the modeling period, rather than as the mean of instantaneous flow fractions. We will clarify this in the revised manuscript.
(7) In Section 5.3, the word “confirming” links simulated snowmelt to the observed daily discharge fluctuations. These fluctuations already helped motivate the snowmelt component in the perceptual model, so their use as independent confirmation should be qualified.
Response: We agree that the observed diel streamflow fluctuations partly motivated the inclusion of residual snowmelt in the perceptual model and therefore cannot serve as independent confirmation of the simulated snowmelt contribution. We will revise the wording in Section 5.3 to avoid implying independent validation.
Reference:
Beria, H., Larsen, J. R., Ceperley, N. C., Michelon, A., Vennemann, T., and Schaefli, B.: Understanding snow hydrological processes through the lens of stable water isotopes, Wiley Interdisciplinary Reviews: Water, 5, e1311, https://doi.org/10.1002/wat2.1311, 2018.
Ditlevsen, C., Marttila, H., and Ala-aho, P.: Stable Water Isotope Signal of Snow Meltwater: Testing Three Different Measurement Setups in Boreal-Subarctic Conditions, Hydrol. Process., 39, e70277, https://doi.org/10.1002/hyp.70277, 2025.
Leuteritz, A., Gauthier, V. A., and van Meerveld, I.: Spatial and Temporal Variability in Event Water in Near-Surface Flow Pathways in a Humid Steep Headwater Catchment, Hydrol. Process., 39, e70186, https://doi.org/10.1002/hyp.70186, 2025.
Maier, F. and van Meerveld, I.: Long-Term Changes in Runoff Generation Mechanisms for Two Proglacial Areas in the Swiss Alps I: Overland Flow, Water Resour. Res., 57, e2021WR030221, https://doi.org/10.1029/2021WR030221, 2021.
Noor, K., Marttila, H., Welker, J. M., Mustonen, K. R., Kløve, B., and Ala-aho, P.: Snow sampling strategy can bias estimation of meltwater fractions in isotope hydrograph separation, J. Hydrol. (Amst)., 627, 130429, https://doi.org/10.1016/J.JHYDROL.2023.130429, 2023a.
Noor, K., Marttila, H., Klöve, B., Welker, J. M., and Ala-aho, P.: The Spatiotemporal Variability of Snowpack and Snowmelt Water 18O and 2H Isotopes in a Subarctic Catchment, Water Resour. Res., 59, e2022WR033101, https://doi.org/10.1029/2022WR033101, 2023b.
Weiler, M., Scherrer, S., Naef, F., and Burlando, P.: Hydrograph separation of runoff components based on measuring hydraulic state variables, tracer experiments, and weighting methods, IAHS PUBLICATION, 249–256, 1999.
Citation: https://doi.org/10.5194/egusphere-2026-4249-AC1
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AC1: 'Reply on RC1', Harsh Beria, 24 Oct 2026
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RC2: 'Comment on egusphere-2026-4249', Anonymous Referee #2, 14 Oct 2026
In the manuscript “Isotope-enabled modeling of fast streamflow dynamics in a steep Alpine catchment” by Beria et al., the authors aim to disentangle conceptual sources of stream flow and the temporal evolution thereof using a detailed data set of stable isotopes together with a simple rainfall-runoff model conceptual model. The overall topic is of interest and fits well into the scope of HESS. The manuscript follows a logical set-up and is well-written.
I particularly appreciate the authors’ effort in producing such a detailed data set in such a challenging environment. That is quite an achievement in itself. I similarly want to applaud the authors for the very well thought-through and instructive perceptual description of the hydrological functioning of the study catchment in section 3. Such in-depth process-contextualization is unfortunately more and more forgotten in a research environment that is increasingly relying on the automated exploitation of large data sets, leveraging the power machine learning.
To balance this enthusiastic assessment, I also would like to flag a few concerns that the authors may want to look into. More specifically, I was quite surprised by the model they use. No pun intended, but the authors sort of “re-invent the wheel” with their model. That is in principle ok. However, several choices along the modelling process lead to the situation that the resulting “wheel” has somewhat of a hexagonal shape. These rough edges make the model experiment a somewhat bumpy ride. Although some of the over-simplifications and limitations of the model are acknowledged in section 7, it remains unclear why the model was designed in such a way instead of making use of model architectures and parametrization schemes provided by many other existing tracer-aided models, that have similar or even lower number of parameters. Some examples include Birkel et al. (2010, 2020, etc), Benettin et al. (2015), Wang et al. (2023) and many, many more.
The most critical concerns are:
(1) The model does not account for evaporation in a way that goes beyond a constant, calibrated(?) and bulk initial abstraction. What this initial abstraction actually represents does not even seem clear for the authors (see l.525: “ […] evapotranspiration […] most likely included in the initial abstraction […]”).
Even in such high-elevation settings, evaporation is typically ~30% of annual precipitation and to a large part confined to the modelled summer months. As evaporation is controlled by the subtle interactions of energy and water supply, it does not sound reasonable to set it to a constant value, in particular as it will also affect the isotopic signature of the water volume that is in storage at any time.
(2) The model has a similarly over-simplified representation of snow dynamics. Although, I do understand that a detailed energy-balance-based snow module is beyond the scope of this analysis and most snow melt has already occurred before model periods start in July, I do not understand why the authors do not use a very simple degree-day model to represent snow melt. As far as I understand, the model now assumes that snowmelt occurs from a water storage Ssnow, that in fact is assumed to be completely liquid and independent of temperature. Despite the thermal momentum of the snowpack, some temperature dependence should nevertheless be assumed. In addition, I found it surprising that *all* the snowmelt bypasses the subsurface and directly feeds the stream. While I can understand the reasoning for some of the snowmelt, I strongly disagree that none of it reaches the subsurface. Further, it seems as if no elevation discretization for snow melt has been attempted. This may lead to additional uncertainties due to the temporally differential snow melt input (and snow storage) at different elevations.
(3) The distinction between Qd and Qsoil is rather vague and will only add unnecessary complexity to the model, actually having very little discriminatory power because for both the rainfall isotope composition is assumed. The fact that both represent very fast responding processes, I doubt that the available data allow for a clear and unambiguous distinction between the two.Other comments:
p.2l.40: it may be worth to be a bit more precise here. “Streamflow-only” calibration is not the actual problem. It has been shown in many studies that using signatures of streamflow, such as flow duration curves, autocorrelation functions, baseflow index and in particular runoff coefficients are powerful additional model calibration objectives. The runoff coefficient in particular allows to approximate closure of the energy balance as it forces the model towards reproducing evaporation fluxes that are consistent with observations, i.e. E/P = 1 – Q/P + dS/dt.
Would be good to emphasize that the real problem is the frequent one-dimensional calibration to exclusively *time series* of stream flow using, not even distinguishing high- and low flows and not making use of signatures.p.2,l.46: would be good to add the more recent work of Tong et al. (2021) here.
p.2,l.49: “water transport” is quite awkward. I know what you mean, but try please try to rephrase
p.2,l.50: “hydrological celerity” reads also a bit awkward. Please rephrase
p.2,l.51f: this is not logical. Should be the other way round. Stream flow does not propagate through the system. Instead, rainfall signals propagate through the system to generate stream flow. Please rephrase.
p.4,l.119: what is a “typical European alpine climate”? The hydro-climatic characteristics vary substantially between the Eastern and Western as well as between the Northern and Southern Alps. Even between individual adjacent valleys, the climate characteristics can considerably differ. Please rephrase.
p.4,Fig.1: the symbols in the figure are not very well visible. Please adjust the color scheme. As in any good map, please add scale and north arrow
p.5,l.141: please be more precise here. Am I right to assume that these are volume-weighted bulk samples? Please add.
p.5,l.149: how was the snow sampled? Was a core over the entire depth taken? Or just one part of the snowpack? Please specify.
p.5,l.153: also here: are these bulk samples over that period? Volume-weighted? Or grab samples at each interval?
p.5,l.153: also here, grab or bulk samples? If the different samples (rain, snow, spring) are different type of samples, how was this accounted for in the model?
p.6,l.185f: I know what you mean, but it would be nevertheless nice for the reader if you described how this is visible and add some summary numbers here.
p.6,l.191: replace “lower” with “less”
p.8,Fig.4: please add (daily) rainfall and snowmelt volumes to the figures
p.8,l.216: ok, but please provide an estimate of the areal fraction of the catchment covered by a glacier
p.8,l.223-230: nice! But please add some specific summary numbers
p.9,l.253: how is a rain event defined?
p.9,l.255: “storage potential” is confusing here, as it may be interpreted as the maximum theoretical storage, which is in your notation Smax,soil. Please rephrase.p.10,l.266f: how are vH and vS determined? Are they calibration parameters?
p.11,section 4.2: please mention somewhere in the section that your model set-up implicitly assumes complete mixing in each storage component.
p.13, section 5: please add somewhere (1) a complete table or figure, showing all model parameters, and their prior as well as posterior distributions. Right now, it is completely unclear how many and which parameters the model has; and (2) a table or figure given a complete overview of the model performance metrics.
p.14,l.377: this is of course quite subject, but I would be careful calling a NSE = -0.07 “reasonably well”. Please rephrase.
p.16,Fig.8: this figure is nice, but difficult to read. Please adjust the colour schemes so that colours can actually be distinguished. In addition, consider showing the uncertainty intervals as semi-transparent shaded areas instead of showing all individual lines.
p.16,l.409: No. Only the snowmelt in the *modelled period* is a small contribution. Given that 40% of annual precipitation is falling as snow (as mention earlier in the manuscript), overall spring/summer snow melt *must* be higher, but it largely occurs before the model period. Thus, please rephrase.
p.18,l.437: of course, as there is almost no snow left in the modelling period…
References:
Benettin, P., Bailey, S. W., Campbell, J. L., Green, M. B., Rinaldo, A., Likens, G. E., ... & Botter, G. (2015). Linking water age and solute dynamics in streamflow at the Hubbard Brook Experimental Forest, NH, USA. Water Resources Research, 51(11), 9256-9272.
Birkel, C., Tetzlaff, D., Dunn, S. M., & Soulsby, C. (2010). Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate, upland catchments. Hydrological Processes: An International Journal, 24(3), 260-275.
Birkel, C., Duvert, C., Correa, A., Munksgaard, N. C., Maher, D. T., & Hutley, L. B. (2020). Tracer‐aided modeling in the low‐relief, wet‐dry tropics suggests water ages and DOC export are driven by seasonal wetlands and deep groundwater. Water Resources Research, 56(4), e2019WR026175.
Tong, R., Parajka, J., Salentinig, A., Pfeil, I., Komma, J., Széles, B., ... & Blöschl, G. (2021). The value of ASCAT soil moisture and MODIS snow cover data for calibrating a conceptual hydrologic model. Hydrology and Earth System Sciences, 25(3), 1389-1410.
Wang, S., Hrachowitz, M., Schoups, G., & Stumpp, C. (2023). Stable water isotopes and tritium tracers tell the same tale: no evidence for underestimation of catchment transit times inferred by stable isotopes in StorAge Selection (SAS)-function models. Hydrology and Earth System Sciences, 27(16), 3083-3114.Citation: https://doi.org/10.5194/egusphere-2026-4249-RC2 -
AC2: 'Reply on RC2', Harsh Beria, 24 Oct 2026
Reviewer 2
We would like to thank Reviewer #2 for a careful assessment of our manuscript and constructive feedback. We will address the raised concerns in the revised manuscript.
In the following responses the reviewer’s comments are in bold, followed by our responses in plain style. Section, line, and figure references to the main and supplementary text refer to the submitted manuscript (EGUsphere discussion opened on August 17, 2026) unless indicated otherwise.
In the manuscript “Isotope-enabled modeling of fast streamflow dynamics in a steep Alpine catchment” by Beria et al., the authors aim to disentangle conceptual sources of stream flow and the temporal evolution thereof using a detailed data set of stable isotopes together with a simple rainfall-runoff model conceptual model. The overall topic is of interest and fits well into the scope of HESS. The manuscript follows a logical set-up and is well-written.
I particularly appreciate the authors’ effort in producing such a detailed data set in such a challenging environment. That is quite an achievement in itself. I similarly want to applaud the authors for the very well thought-through and instructive perceptual description of the hydrological functioning of the study catchment in section 3. Such in-depth process-contextualization is unfortunately more and more forgotten in a research environment that is increasingly relying on the automated exploitation of large data sets, leveraging the power machine learning.
To balance this enthusiastic assessment, I also would like to flag a few concerns that the authors may want to look into. More specifically, I was quite surprised by the model they use. No pun intended, but the authors sort of “re-invent the wheel” with their model. That is in principle ok. However, several choices along the modelling process lead to the situation that the resulting “wheel” has somewhat of a hexagonal shape. These rough edges make the model experiment a somewhat bumpy ride. Although some of the over-simplifications and limitations of the model are acknowledged in section 7, it remains unclear why the model was designed in such a way instead of making use of model architectures and parametrization schemes provided by many other existing tracer-aided models, that have similar or even lower number of parameters. Some examples include Birkel et al. (2010, 2020, etc), Benettin et al. (2015), Wang et al. (2023) and many, many more.
Response: Thank you for a positive assessment of our observation-based perceptual model approach. Our objective was to develop a model tailored to the dominant hydrological processes identified in Vallon de Nant (Section 3). One key specificity of this catchment is its strong flashiness which forced us to design a hydrological model able to run at high temporal resolution (10 min) Although the model structure was developed specifically for this study, its individual process formulations build on established hydrological modeling approaches.
For example, direct runoff and soil drainage are routed using a spatially-distributed width-function formulation of the geomorphological unit hydrograph, which leverages catchment’s geomorphological properties while requiring only two routing parameters: hillslope and channel velocities (Rinaldo et al., 1995; Rinaldo and Rodriguez-Iturbe, 1996). To the best of our knowledge, the application of this approach to isotope-enabled modeling does not exist in hydrological modeling literature. The two subsurface reservoirs were motivated by observed differences in spring temperature dynamics and represent fast and slow groundwater pathways through nonlinear and linear storage-discharge relationships, respectively. This conceptualization is similar to the widely-used bucket-type model structure that represents runoff generation through multiple storage compartments (Seibert and Bergström, 2022). The residual snowmelt component was represented using a simplified linear storage-discharge relationship, which we will replace with a temperature-based degree-day implementation in the revised manuscript.
In the revised manuscript, we will further clarify the rationale behind the choice of model formulations used in this study, with a focus on the requirement for high temporal resolution.
The most critical concerns are:
(1) The model does not account for evaporation in a way that goes beyond a constant, calibrated(?) and bulk initial abstraction. What this initial abstraction actually represents does not even seem clear for the authors (see l.525: “ […] evapotranspiration […] most likely included in the initial abstraction […]”).
Even in such high-elevation settings, evaporation is typically ~30% of annual precipitation and to a large part confined to the modelled summer months. As evaporation is controlled by the subtle interactions of energy and water supply, it does not sound reasonable to set it to a constant value, in particular as it will also affect the isotopic signature of the water volume that is in storage at any time.
Response: Evaporation is indeed highly simplified in our model. The initial abstraction parameter represents rainfall losses before runoff generation, reflecting evaporation effects from intercepted rainfall and soil evaporation. A clear justification for this interpretation is that the modeled and observed runoff coefficients were similar during both summer periods: (obs: 0.705; model: 0.697) in 2017, and (obs: 0.932, model: 0.922) in 2018.
This approach was considered acceptable given our primary objective of understanding and modeling short-timescale streamflow generation processes during summer rainfall events, rather than achieving annual or seasonal water balance (Section 7, L525-531). In addition, this approach does not impact the isotopic signatures of the two subsurface components, which are directly informed from observations (L305-307).
We will report the observed and simulated runoff coefficients in the revised manuscript, and further discuss which processes are aggregated in the initial abstraction parameter.
(2) The model has a similarly over-simplified representation of snow dynamics. Although, I do understand that a detailed energy-balance-based snow module is beyond the scope of this analysis and most snow melt has already occurred before model periods start in July, I do not understand why the authors do not use a very simple degree-day model to represent snow melt. As far as I understand, the model now assumes that snowmelt occurs from a water storage Ssnow, that in fact is assumed to be completely liquid and independent of temperature. Despite the thermal momentum of the snowpack, some temperature dependence should nevertheless be assumed. In addition, I found it surprising that *all* the snowmelt bypasses the subsurface and directly feeds the stream. While I can understand the reasoning for some of the snowmelt, I strongly disagree that none of it reaches the subsurface. Further, it seems as if no elevation discretization for snow melt has been attempted. This may lead to additional uncertainties due to the temporally differential snow melt input (and snow storage) at different elevations.
Response: We agree with the reviewer that the current storage-discharge formulation for residual snowmelt is oversimplified and will replace it with a temperature-based degree-day model in the revised manuscript.
The residual snowmelt component was introduced primarily to reproduce the depleted streamwater isotopic signatures observed in early July. We acknowledge that some snowmelt during this period may recharge subsurface storages rather than directly contributing to streamflow. However, our simulations focus on July-September period, when most seasonal snowmelt has already occurred. In this period, due to the unique topography of the catchment, remaining snow is confined to the precipices above cliff faces or the minimal surface of the relict glacier. The corresponding melt enters the stream network, bypassing the soil, either via the talus at the base of cliff faces or via the glacier outlet. This will be made clearer in the revised version.
The effects of earlier snowmelt recharge are implicitly reflected in the initial subsurface storages and the observed spring isotopic signatures are used to constrain groundwater contributions. Hence, although it is very likely that some snowmelt water reaches the subsurface during the summer period as pointed out by the reviewer, we would like to emphasize that the impact of this water on the isotopic signature of the subsurface is already informed by observations.
In the absence of spatially-distributed snow depth and snow water equivalent observations, we consider a spatially-lumped representation of residual snowmelt more parsimonious than introducing an additional elevation-dependent parameter that cannot be independently constrained.
(3) The distinction between Qd and Qsoil is rather vague and will only add unnecessary complexity to the model, actually having very little discriminatory power because for both the rainfall isotope composition is assumed. The fact that both represent very fast responding processes, I doubt that the available data allow for a clear and unambiguous distinction between the two.
Response: We agree that it is implicitly difficult to separate Qd and Qsoil with available observations. However, the two components represent different hydrological responses: Qd represents instantaneous overland flow generated during rainfall events, whereas Qsoil represents slightly-delayed drainage from shallow soil storage. The inferred maximum soil storage capacity (posterior Smax,soil ≈ 0.2-0.3 m; Figures S3, S4) is physically plausible, although direct observations are unavailable to independently validate it.
In the original manuscript, these components were shown separately in Figure 5 but combined into a single component in Figures 8 and 9. We will group both processes under “direct flow” in Figure 5 of the revised manuscript, while retaining their separate hydrological formulations.
Other comments:
p.2l.40: it may be worth to be a bit more precise here. “Streamflow-only” calibration is not the actual problem. It has been shown in many studies that using signatures of streamflow, such as flow duration curves, autocorrelation functions, baseflow index and in particular runoff coefficients are powerful additional model calibration objectives. The runoff coefficient in particular allows to approximate closure of the energy balance as it forces the model towards reproducing evaporation fluxes that are consistent with observations, i.e. E/P = 1 – Q/P + dS/dt.
Would be good to emphasize that the real problem is the frequent one-dimensional calibration to exclusively *time series* of stream flow using, not even distinguishing high- and low flows and not making use of signatures.
Response: We respectfully disagree: the use of many signatures computed from the observed streamflow helps extracting information from that timeseries, but it does not add information. For example, the autcorrelation function is simply a frequency-domain representation of the time series. So, using a type of data to inform parameter calibration remains the most critical problem. But we agree that calibration on signatures computed from that time series can have some value. In the revised manuscript, we will acknowledge the distinction between calibration with a streamflow timeseries and constraining a hydrological model with streamflow signatures. We will also report runoff coefficients for our model simulations, even if it is important to underline that forcing a hydrological model to close the water balance is an important source of error since it will try to compensate for precipitation biases, e.g. by increasing or decreasing ET.
p.2,l.46: would be good to add the more recent work of Tong et al. (2021) here.
Response: We will cite Tong et al. (2021) in this section.
p.2,l.49: “water transport” is quite awkward. I know what you mean, but try please try to rephrase
Response: We will rephrase the text as “Such additional observations can constrain simulated storages and fluxes, but do not necessarily resolve the distinction between water flow transport and rainfall-streamflow response”.
p.2,l.50: “hydrological celerity” reads also a bit awkward. Please rephrase
Response: We will rephrase as “This distinction is commonly framed in terms of velocity and celerity”.
p.2,l.51f: this is not logical. Should be the other way round. Stream flow does not propagate through the system. Instead, rainfall signals propagate through the system to generate stream flow. Please rephrase.
Response: Thanks for catching this, we will rectify this in the revised manuscript.
p.4,l.119: what is a “typical European alpine climate”? The hydro-climatic characteristics vary substantially between the Eastern and Western as well as between the Northern and Southern Alps. Even between individual adjacent valleys, the climate characteristics can considerably differ. Please rephrase.
Response: We will rephrase.
p.4,Fig.1: the symbols in the figure are not very well visible. Please adjust the color scheme. As in any good map, please add scale and north arrow
Response: We will revise Figure 1 to improve symbol visibility and add scale and North bar.
p.5,l.141: please be more precise here. Am I right to assume that these are volume-weighted bulk samples? Please add.
Response: We will improve the wording in the revised manuscript.
p.5,l.149: how was the snow sampled? Was a core over the entire depth taken? Or just one part of the snowpack? Please specify.
Response: Snowpack was sampled with multiple approaches to capture the spatial and vertical variability in snow isotopes. Snow samples were collected either across the entire snowpack depth, from individual snow layers, or occasionally only from surface snow. Whenever feasible, sampling was conducted along short transects to capture its spatial variability. The resulting isotope ratios were averaged to obtain a representative snowpack isotopic signature. We will mention the sampling procedure in the revised manuscript.
p.5,l.153: also here: are these bulk samples over that period? Volume-weighted? Or grab samples at each interval?
Response: Streamwater samples were collected at discrete times using an automatic sampler or as manual grab samples. These are instantaneous samples rather than time-integrated or volume-weighted composites. We will clarify this in the revised manuscript.
p.5,l.153: also here, grab or bulk samples? If the different samples (rain, snow, spring) are different type of samples, how was this accounted for in the model?
Response: Rainfall was collected as biweekly volume-integrated samples, whereas snowpack, spring, and streamwater samples were collected at discrete sampling times. In the model, constant rainfall and snowpack isotopic ratios were assigned as the year-specific mean values, while spring isotope measurements were temporally distinct.
In the revised manuscript, we will assess the sensitivity of the inferred flow partitioning to variations in rainfall and snowmelt isotopic end-members.
p.6,l.185f: I know what you mean, but it would be nevertheless nice for the reader if you described how this is visible and add some summary numbers here.
Response: We will describe this better in the revised manuscript.
p.6,l.191: replace “lower” with “less”
Response: We will replace “lower” with “less” here.
p.8,Fig.4: please add (daily) rainfall and snowmelt volumes to the figures
Response: We will add catchment-averaged rainfall in this figure. As snowmelt fluxes were not measured, these cannot be added.
p.8,l.216: ok, but please provide an estimate of the areal fraction of the catchment covered by a glacier
Response: Glacier area (4.4% of catchment) is mentioned in L112. We will also mention this here.
p.8,l.223-230: nice! But please add some specific summary numbers
Response: Rainfall-event characteristic and streamflow responses were already reported in a previous study (Michelon et al., 2021), which we will cite. We will also revise the text to better highlight the key patterns from Figure 4, making the interpretation more directly connected to the observations.
p.9,l.253: how is a rain event defined?
Response: Rain events are defined as in Michelon et al., 2021: "Using areal rainfall time series, the rainfall events are identified as periods with rainfall higher than 1 mm separated by at least 90 min with rainfall smaller than 1 mm".
p.9,l.255: “storage potential” is confusing here, as it may be interpreted as the maximum theoretical storage, which is in your notation Smax,soil. Please rephrase.
Response: Thanks for catching this, we will change the wording to “soil storage”.
p.10,l.266f: how are vH and vS determined? Are they calibration parameters?
Response: Yes, these are calibrated.
p.11,section 4.2: please mention somewhere in the section that your model set-up implicitly assumes complete mixing in each storage component.
Response: To avoid making assumptions about mixing in subsurface storages, we directly assigned Qfast and Qslow isotopes from field observations (L305-306; L541-543).
p.13, section 5: please add somewhere (1) a complete table or figure, showing all model parameters, and their prior as well as posterior distributions. Right now, it is completely unclear how many and which parameters the model has; and (2) a table or figure given a complete overview of the model performance metrics.
Response: The posterior parameters are shown in Supplementary figures S3 and S4. We will better link the supplementary figures with the main text.
p.14,l.377: this is of course quite subject, but I would be careful calling a NSE = -0.07 “reasonably well”. Please rephrase.
Response: We agree that a negative NSE indicates poor simulation diagnostics. Our intention was to highlight that the posterior simulation envelope encompassed most observed streamwater isotopic values, and its temporal dynamics. We will revise the wording to clarify this in the revised manuscript.
p.16,Fig.8: this figure is nice, but difficult to read. Please adjust the colour schemes so that colours can actually be distinguished. In addition, consider showing the uncertainty intervals as semi-transparent shaded areas instead of showing all individual lines.
Response: We will improve this figure in the revised manuscript.
p.16,l.409: No. Only the snowmelt in the *modelled period* is a small contribution. Given that 40% of annual precipitation is falling as snow (as mention earlier in the manuscript), overall spring/summer snow melt *must* be higher, but it largely occurs before the model period. Thus, please rephrase.
Response: We will further improve the framing in the revised manuscript.
p.18,l.437: of course, as there is almost no snow left in the modelling period…
Response: Yes, we agree.
References:
Benettin, P., Bailey, S. W., Campbell, J. L., Green, M. B., Rinaldo, A., Likens, G. E., ... & Botter, G. (2015). Linking water age and solute dynamics in streamflow at the Hubbard Brook Experimental Forest, NH, USA. Water Resources Research, 51(11), 9256-9272.
Birkel, C., Tetzlaff, D., Dunn, S. M., & Soulsby, C. (2010). Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate, upland catchments. Hydrological Processes: An International Journal, 24(3), 260-275.
Birkel, C., Duvert, C., Correa, A., Munksgaard, N. C., Maher, D. T., & Hutley, L. B. (2020). Tracer‐aided modeling in the low‐relief, wet‐dry tropics suggests water ages and DOC export are driven by seasonal wetlands and deep groundwater. Water Resources Research, 56(4), e2019WR026175.
Michelon, A., Benoit, L., Beria, H., Ceperley, N., and Schaefli, B. (2021): Benefits from high-density rain gauge observations for hydrological response analysis in a small alpine catchment, Hydrol. Earth Syst. Sci., 25, 2301–2325.
Tong, R., Parajka, J., Salentinig, A., Pfeil, I., Komma, J., Széles, B., ... & Blöschl, G. (2021). The value of ASCAT soil moisture and MODIS snow cover data for calibrating a conceptual hydrologic model. Hydrology and Earth System Sciences, 25(3), 1389-1410.
Wang, S., Hrachowitz, M., Schoups, G., & Stumpp, C. (2023). Stable water isotopes and tritium tracers tell the same tale: no evidence for underestimation of catchment transit times inferred by stable isotopes in StorAge Selection (SAS)-function models. Hydrology and Earth System Sciences, 27(16), 3083-3114.
Citation: https://doi.org/10.5194/egusphere-2026-4249-AC2
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AC2: 'Reply on RC2', Harsh Beria, 24 Oct 2026
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This manuscript combines discharge and stable water isotope observations with hydrological modelling to investigate rapid streamflow responses in a steep Alpine catchment. The authors collected a valuable dataset over two summer periods and integrated these observations into an isotope-enabled model to explore the contributions of different flow components. The results highlight the substantial contribution of groundwater to summer streamflow and demonstrate the potential of isotope observations to constrain modelled flow partitioning. The research questions and approach are well suited to the HESS readership, and the study offers a useful contribution to understanding streamflow generation in Alpine catchments.
However, I have several concerns about the prescribed isotope signatures, the calibration procedure, and the robustness of the inferred flow contributions. These issues affect how confidently the model results can support the process interpretations.
General comments
(1) The model assigns the mean winter snowpack isotope signature to snowmelt during the summer simulation period. The authors acknowledge that snowmelt can differ isotopically from the snowpack, but the justification for assuming a small effect during July–September is not sufficiently clear. The timing of the analysis alone does not establish that the winter mean represents the residual snowmelt entering the stream.
Could the authors explain whether any observations or citations support this assumption for the study catchment? If direct observations are unavailable, I suggest testing plausible alternative snowmelt isotope signatures and evaluating their effects on the estimated snowmelt and groundwater contributions.
In addition, snowmelt discharge is represented using a storage-discharge relationship. What evidence, beyond the discharge and isotope data used to constrain the model, supports the simulated timing and magnitude of summer melt? Please distinguish the evidence for residual snowmelt occurrence from the evidence supporting its estimated contribution.
(2) direct runoff and soil drainage are assigned the same summer-average rainfall isotope signature. It is unclear why this is appropriate for soil drainage, which could include water stored before the rainfall event and mixing within the soil. Please explain the physical basis for this assumption and provide supporting observations or references.
(3) The use of a constant rainfall isotope signature within each summer also needs further justification, particularly because the study focuses on rapid responses to individual rainfall events. How much variability is present in the available precipitation isotope observations, and how might neglecting this variability affect the inferred component contributions?
(4) I noticed that Section 7 already acknowledges limitations associated with spring representativeness and endmember variability. However, these limitations should also be connected to the reliability of the reported flow fractions. A focused sensitivity analysis would help establish whether the main conclusions remain consistent under plausible alternative isotope assignments.
(5) I found Section 4.3 difficult to follow. Please distinguish clearly between the observed variables used for calibration, the four likelihood components, and the performance metrics used to evaluate the simulations. My understanding is that calibration uses discharge and streamwater δ¹⁸O, each separated into low-flow and high-flow conditions. These are therefore four likelihood components derived from two observed variables.
The sequence of calibration and evaluation should also be clearer. Initial states are first estimated using both summers and then fixed before the reciprocal single-year calibrations. Consequently, observations from the evaluation year have already contributed to estimating its initial conditions. This does not invalidate the comparison, but it limits its independence. Please state this explicitly in Section 4.3 and distinguish evaluation conditional on fitted initial states from a fully independent validation.
(6) Please clarify which parameter sets were used to produce Section 5.3 and Figures 8 and 9. Figure 8 displays multiple simulations, whereas Figure 9 presents single percentages. How many parameter sets contribute to each figure? Do the percentages represent a selected simulation, an ensemble mean, or another summary?
(7) The uncertainty in the component contributions is central to interpreting these results. I suggest reporting intervals for the seasonal flow fractions and explaining how they were calculated. Please also distinguish uncertainty arising from sampled model parameters from uncertainty associated with the prescribed isotope signatures and model structure.
(8) The narrower range of contributions obtained with isotope calibration is useful evidence that the additional observations constrain the model. However, a narrower range under fixed assumptions does not necessarily demonstrate that the resulting partitioning is more accurate. This distinction should be reflected in both the results and discussion.
Specific comments
(1) In Section 3, please distinguish field observations from the hypotheses used to construct the perceptual model. This would help readers follow how the observations motivate the proposed flow components.
(2) In Figure 4, please explain the black points and connecting line in the isotope panels as streamwater observations in the caption.
(3) In Section 4.1, which model elements were developed for this study and which were adopted or adapted from previous formulations? Also please explain which processes are spatially distributed and which are lumped, including the role of the 25 subcatchments.
(4) In Section 4.3, can authors describe how the low-flow and high-flow periods were selected and provide enough information for this classification to be reproduced?
(5) Figures 8 and 9, The model contains five flow components, but these figures show four and three component categories.
(6) Figure 9, each percentage is calculated from total component volume divided by total streamflow volume, or from the mean of instantaneous fractions? These calculations can produce different results.
(7) In Section 5.3, the word “confirming” links simulated snowmelt to the observed daily discharge fluctuations. These fluctuations already helped motivate the snowmelt component in the perceptual model, so their use as independent confirmation should be qualified.