Dear Reviewer,

Thank you very much for your valuable comments and suggestions on our manuscript. We appreciate the time and effort you have dedicated to reviewing our work. We have carefully considered each point raised and have revised the manuscript accordingly. A detailed response to each comment is provided below.

• In Section 1, [...] it would be helpful to clarify the specific advantages of using GAMCR over ERRA. [...]

We thank Reviewer 1 for this comment. An exhaustive discussion of the differences between the models is presented in the discussion, but we will clarify already at the end of the introduction that ``Differently from ERRA, GAMCR aims to estimate the hydrologic response to each individual precipitation events using combinations of spline basis functions, with coefficients determined through machine learning techniques. This approach, though requiring to fit Generalized Additive Models, allows for greater flexibility since additional information (e.g., temperature, dam operations, or site-specific characteristics) can be incorporated into the model."

•  In Section 2.3 – Model training: [...] it is not clear what specific data period or proportion of data

We thank the reviewer for the comment. For real data, we used 13 years of data (2005-2017) to train the models. We used data from the years 2018 and 2019 to test the model. We will clarify this detail about the training/test split for the real data in Section 3.2. Section 2.3, instead, describes the general training methodology, which is not specific to either synthetic or real data.

• In Section 2.3 – Model training: It would be helpful to provide the final hyperparameter λ1 and λ2 values used in the model training process. The default values of λ1=10^-3 and λ2=1 are mentioned in Section 3.3.

We will specify in Section 2.3 that the default values λ1=10^-3 and λ2=1 were used.

• In Section 2.3 – Model training: the model validation is only introduced later in Section 4.

We will introduce a subsection ``Model validation strategy'' already within the methods section (Section 3), to clarify our strategy from the beginning. This will allow us to simplify Section 4 to focus entirely on the results. Thank you for this comment. 

• In Section 2.4, you could provide the link to the GAMCR model software and online tutorial mentioned in the text would be helpful.

This will be certainly done in the revised manuscript, thanks.

• In Section 3.1 - Synthetic data: You note that the simulation ‘closely mirrors actual measurements’ and provide a four-month example from 2010 to support this. However, to strengthen this claim, it would be helpful to include quantitative model performance statistics (e.g., R2, NSE, PBias, RMSE) for Case A. Ideally, this should cover the full 40-year period and also highlight in a figure the performance for a wet year (e.g., 2014) and a dry year (e.g., 2003) [...]

We will include the RMSE statistic (which is 0.20 mm h^-1 ) in the supplement but prefer to omit it from the main manuscript, as it might mislead readers into thinking the synthetic data generator is designed to best reproduce observed data. Its purpose is instead to create hydrologically realistic series with fully known responses, not to best replicate the specific data at the Chiasso, Ponte di Polenta station. We will clarify this in the manuscript and in the supplement.

• In Section 3.1 - Synthetic data: Have you considered also generating a synthetic streamflow time series using CombiPrecip (2005 to 2019) as the precipitation input to train the model? This would allow for a more direct comparison and could potentially improve consistency in training and evaluating model performance.

As for the previous response, we will better stress in the revised manuscript that the purpose of the data generator is just to create realistic synthetic data featuring nonlinear and nonstationary hydrologic responses. Using a different precipitation input would not result in increased consistency between training and evaluating model performance. The different input series would result in slightly different model parameters, but the synthetic data on which the GAMCR model is tested would still be ``perfect'' (in the sense that it is not subject to measurement errors) because it is produced by a model.

• In Section 3.2 – Real-world data: it would help if you clarified why selecting a medium-sized catchment was a criterion.

We thank the reviewer for the insightful request and we will discuss in more detail why we chose the selected basins and how we can define them as midsize catchments. We selected basins between 34–185 km², which are considered small to medium-sized. In the Swiss context, they are well-suited for hydrological analysis, as their scale reduces the need for complex distributed models while still capturing key processes. The chosen sites also represent diverse hydrological regimes, elevations, and soil depths. This will be clarified and detailed in Section 3.2.

• In Section 3.2 - Real-world data: Could you: i) Tabulate key hydrological statistics for each watershed   ii) Provide a Flow Duration Curve (FDC) for each watershed.

We will add a Table 2 in section 3.2 with key hydrological statistics; we will also provide the FDCs for each watershed for the snow-free period in a new figure.

•  In Section 3.2 – Real-world data: Since CombiPrecip also includes a quality index for assessing data reliability, have you considered excluding data before 2010 to enhance the robustness of your analysis?
  
  

We were aware of the modifications to the Swiss radar network implemented between 2005 and 2016, which significantly improved the data quality of the CombiPrecip product. We included data starting from 2005, as initial experiments indicated that the model's performance was not substantially impacted by the lower data quality prior to 2015. This decision also reflects a more realistic scenario in which flux data is available over at least a decade.

• In Section 3.3 – Implementation details: Should this threshold be consistent with the previously stated Jth = 0.05 mm/h?

It is normal that the thresholds differ: the 0.05 mm/h threshold was used for training stability and efficiency, while the 0.5 mm/h threshold was chosen for analysis, focusing on more hydrologically relevant events. We will clarify this point in the revision.

• In Section 4 – Results: Be consistent when referring to the three cases. in Figure 5, the labels are inconsistent

We thank the reviewer for raising this point. We will change the order of the panels in Figure 6 to make sure figures a, b and c match the cases A, B and C considered.

• In Section 4 - Results: Could you elaborate on why GAMCR struggles with peak lag prediction? Additionally, what are the implications of this limitation for applying GAMCR in cross-site hydrological comparisons at a global scale.
  
  In section 5: For clarity, could you be more specific about what changes to the basis function structure you are proposing? Providing a brief explanation would help readers understand how this adjustment could improve peak timing estimation.

We believe that predicting the peak lag is particularly challenging from a statistical perspective. This is because changes in the peak lag can result in only minor differences in the induced discharge, making the estimation problem very difficult. The main implication is that the peak lag estimated by GAMCR should not be used for cross-site hydrological comparisons, as we already stated in the discussion (lines 318--319, ``GAMCR should currently not be used to estimate the timing of the hydrologic response").

In such an ill-conditioned scenario, the first lever to improve peak lag estimation is increasing the size of the training dataset. However, model architecture also plays a significant role. GAMCR, for instance, relies on a set of positive, unimodal basis functions that are denser at shorter lags. The choice and design of these basis functions directly affect the accuracy of peak lag estimation.

It would therefore be valuable to investigate the optimal knot placement for B-splines in the context of peak lag estimation. Reducing the number of knots may limit the model's expressiveness, while having too many basis functions can cause identifiability issues—different combinations of basis functions might result in similar discharge responses, further complicating peak lag estimation.

For this reason, we believe that instead of predefining the basis functions, it would be an interesting research direction to learn them directly from data. This would allow the model to adapt the number and shape of basis functions to better match the characteristics of the watershed under study. The challenge, however, lies in imposing appropriate constraints on the learned basis functions: a well-designed inductive bias is essential to mitigate the ill-posed nature of recovering the latent transfer function from streamflow time series. We leave this investigation for future work.

These points will be included in Section 5 of the revised manuscript.

• In Section 4.2: For clarity and consistency, it would be helpful to use consistent terminology throughout the paper, either "calibration" or "training".
  
  In Section 5: Be consistent with the terminology you used, calibration period in Figure 7, not the term in-sample data. 

We thank the reviewer for pointing out this lack of consistency in the terminology. In the revised manuscript, we will stick to the terminology "training" and "test periods" to enhance clarity.

•  Section 4.2: Are the out-of-sample predictions 1 year sufficient to test the GAMCR model performance?

The test period spans two years: 2018 and 2019. With hourly data, we believe that this gives a reasonable dataset to evaluate the model performance. In section 3.2 of the revised manuscript, we will clarify the training/test split considered.

• Section 4.2: Referring to Figure 7, are there any issues with the quality of the observations at high flows at Chiasso for the Breggia (2349), i.e. the stage discharge relationship? Have you investigated the confidence in the stream flow records at this river gauge?

We do not see any particular issues with the quality of the high-flow observations at Chiasso (Breggia, 2349). The discharge data used in this study were official data provided by the Federal Office for the Environment (FOEN), which applies standardized procedures for flow measurement and quality control at all official gauging stations in Switzerland. As such, we rely on these validated records, and no indications of systematic uncertainty or bias at high flows were reported for this station.

• In Section 4.2: The NSE for the out-of-sample prediction for the Chiasso dataset is 0.19, which indicates poor model performance. Can you clarify why the model shows such a poor NSE and a weak fit to the observed streamflow time series, despite the apparent agreement between the synthetic and observed training data? Additionally, do you think the predictions for Chiasso would improve if you used the CombiPrecip product as the rainfall input, rather than Lugano rainfall data used here?

For all real-world data experiments, we rely on the CombiPrecip product as the rainfall input. The Lugano rainfall was used only to create the synthetic datasets. 

To clarify, in Section 4.2 we focus exclusively on real datasets; synthetic data is not considered. Figure 7 presents the streamflow estimates obtained with GAMCR for the six study sites. It is important to note that GAMCR was not specifically designed to achieve state-of-the-art performance in streamflow prediction. A model optimized for this task would need to be carefully designed and trained to handle rare events such as extreme rainfall or very high streamflow. Nevertheless, we included Figure 7 to demonstrate that GAMCR is capable of streamflow prediction, even though it is not tailored for it. The NSE coefficient is known to be sensitive to high-flow values, and a few large errors—typically occurring under high-streamflow conditions as illustrated in Figure 7, and possibly affected by poor rainfall estimates—can markedly reduce NSE values, even when the model performs well in most other cases.

• Technical Corrections

We thank the reviewer for these helpful corrections, which we are happy to implement in the revised manuscript.

• I consider this study interesting and scientifically valid. However, it needs improvements before it can be published. Below are the corrections needed for the publication of this article, and I would like to be able to review this article again after the requested corrections have been made.

We thank Reviewer 2 for their evaluation of our manuscript and for providing useful and constructive feedback. We agree with the comments and will incorporate the suggested revisions (see detailed responses below). Since the reviewer has already given clear guidance and the required changes are rather minor, we do not see the necessity of another round of review. The manuscript has already been under public discussion for five months, and we believe there is no reason to further delay its publication.

• Major revision
  
  The main limitation of this study is that it considers the developed method to be of global application (in any watershed worldwide), but only calibrated and validated it in small and small/medium watersheds with climatic and physiographic characteristics existing in Switzerland. Therefore, I recommend two solutions to this problem: all mentions of the method's worldwide application should be replaced by mentions of its application restricted to the types and conditions of calibrated/validated watersheds. Or (better), the developed method should be calibrated and validated in basins with different climatic and physiographic characteristics worldwide. An example of a data source for large-sized tropical basins is the Ore-Hybam (but other sources should also be used).

We thank the reviewer for this constructive feedback. A recurring concern was the limited geographic and climatic diversity of the study sites, since all basins are located in Switzerland. We acknowledge that we may have been unclear about this point and would like to emphasize that it was not our intention to claim that GAMCR has already been validated across global climatic conditions. Our deliberate focus on Swiss basins ensured the use of high-quality, high temporal resolution, well-documented data from sites free of strong anthropogenic disturbances (e.g., dams, major abstractions), allowing us to conduct a robust first evaluation of the method. We have now computed the Flow Duration Curves (FDCs) of streamflow for all six basins (new figure that will be added to the manuscript) and shown the runoff coefficient values, obtained with ERRA, to comment on Figure 9. These analyses will complement the existing ones and reinforce that, even within Switzerland, the selected watersheds span a gradient of hydrological regimes and flow behaviors, ranging from rainfall-dominated systems with frequent low flows to nival- and nivo-pluvial-influenced catchments capable of sustaining higher discharges. This supports our claim that the method was tested across distinct runoff regimes and hydrologic responses, even though all sites belong to the same national context. 

We don't see reasons why the method should not work in different climatic regions, as long as a streamflow response to precipitation is recorded in the data, but we agree that this claim would need to be tested. Therefore, we will carefully revise the manuscript to restrict statements about worldwide applicability. Our results are now explicitly framed as valid for basins with climatic and physiographic characteristics similar to those studied here. Broader testing in other climatic regions is indeed an important avenue for future research, but it is beyond the scope of this initial study.

• Minor revision
  
  
  
  
• Line 7. Describe the abbreviation ‘GAMCR’ at its first mention in the abstract.

We thank the reviewer for having noticed it. We will clarify the abbreviation GAMCR in the abstract.

• Lines 17-18. Insert a source (citation) for the sentence: ‘The hydrologic response (or runoff response) is usually defined as the change in streamflow induced by a given input of precipitation.’

We will add the following sources supporting this statement: 

    [1] Ponce, V. M. 1995. Hydrologic and environmental impact of small and medium-size basins. San Diego State University. Available from: https://pon.sdsu.edu/protected29/cive445_ponce_chapter05a_lecture.html

    [2] Kirchner, J. W., P. Benettin, and I. van Meerveld. 2023. Instructive surprises in the hydrological functioning of landscapes. Annu. Rev. Earth Planet. Sci. 51:277–299. doi:10.1146/annurev-earth-071822-100356.

    [3] Kirchner, J. W. (2022). Impulse Response Functions for Nonlinear, Nonstationary, and Heterogeneous Systems, Estimated by Deconvolution and Demixing of Noisy Time Series. Sensors, 22(9), 3291. https://doi.org/10.3390/s22093291

• Lines 99-101. Explain (rewrite) this sentence further. It suggests that it varies smoothly between basins with different climatic and physiographic characteristics.

Thank you for identifying this unclear statement. GAMCR is trained and applied within a specific catchment. What we meant in that sentence is that the hydrologic response is expected to vary over time, and we assume that such variations are not abrupt/discontinuous. We will rephrase the sentence as: "The feature vector encodes the catchment’s current state, reflecting that its response tends to follow predictable patterns; for example, minor variations in precipitation three months prior are expected to produce moderate changes in response."

• Line 102. The correct word is ‘third’, not ‘second’.

We thank the reviewer for noting this oversight.

• Lines 163-164. Insert a source (citation) for the sentence: ‘In the case of the hydrologic response, the evaluation step is particularly important because the real-world impulse response functions cannot be measured directly...’.

We plan to update the manuscript with the following: "In the case of the hydrologic response, the evaluation step is particularly important because impulse response functions in real basins cannot be measured directly and the model is trained on streamflow data only [3,4,5]."

    [3] Kirchner, J. W. (2022). Impulse Response Functions for Nonlinear, Nonstationary, and Heterogeneous Systems, Estimated by Deconvolution and Demixing of Noisy Time Series. Sensors, 22(9), 3291. https://doi.org/10.3390/s22093291

    

    [4] Gupta, H.V., Wagener, T. and Liu, Y. (2008), Reconciling theory with observations: elements of a diagnostic approach to model evaluation. Hydrol. Process., 22: 3802-3813. https://doi.org/10.1002/hyp.6989

    [5] McDonnell, J. J., and K. Beven (2014), Debates—The future of hydrological sciences: A (common) path forward? A call to action aimed at understanding velocities, celerities, and residence time distributions of the headwater hydrograph, Water Resour. Res., 50, 5342–5350, doi:10.1002/2013WR015141.

• Line 198. I don't agree that basins measuring 34 to 195 km² are considered medium-sized. They are all small to small/medium in size. Please, correct this! Moreover, this is one of the many reasons to calibrate and validate the method in other basin types.

We thank the reviewer for this important comment. We agree that, based solely on drainage area, the studied basins are better classified as small to small/medium. At the same time, we note that there is no universally accepted, size-based classification for catchments. In hydrology, many definitions consider process-based characteristics rather than area alone when describing catchment size. For instance, [1] defines a midsize catchment based on hydrological behavior, including features such as rainfall intensity varying within a storm, spatially uniform precipitation, runoff dominated by overland and channel flow, and negligible channel storage due to steep slopes. We would claim that the selected basins meet these hydrologic criteria. We will revised the manuscript to clearly distinguish the area-based classification (small to small/medium) from the process-based hydrologic definition, to avoid ambiguity while providing proper justification for our methodological choices.

    [1] Ponce, V. M. 1995. Hydrologic and environmental impact of small and medium-size basins. San Diego State University. \par Available from: https://pon.sdsu.edu/protected29/cive445_ponce_chapter05a_lecture.html

• Lines 203-206. Even when analyzing out of the snowy months, the basins' antecedent conditions are influenced by snow. This is another reason to calibrate and validate the method in other types of watersheds.

We thank the reviewer for this observation, and we acknowledge that antecedent conditions in the studied basins can be influenced by residual snow, even outside the main snowy months. In this study, we carefully selected events and basins to minimize snow-related effects, ensuring a robust evaluation of the GAMCR method under the targeted conditions. While this choice limits the generality of the results, it was necessary to avoid confounding factors such as snowmelt that could bias model assessment. Extending calibration and validation to basins with different snow or climatic regimes is an important avenue for future work but lies beyond the scope of the present study.

• Line 321. The basins are not climatically diverse as you mention. They are similar considering Switzerland's climate conditions in relation to the planet's climate diversity. Please correct this! Moreover, this is another reason to calibrate and validate the method in other parts (continents) of the world.

We acknowledge that, in a global context, the selected Swiss basins are not {\it climatically} diverse. However, within Switzerland, the basins were chosen to cover a range of hydrological regimes, including Jura-nivopluvial, transition nival, pluvial, southern nivo-pluvial, and southern pluvio-nival. This diversity allowed us to test the GAMCR method across different runoff behaviors and seasonal patterns resulting in a broad range of responses. Indeed, Figure 7 shows that the same rainfall intensities result in hydrologic responses that are ten times larger at Euthal compared to Salmsach.

We believe that our site selection does not diminish the value of the results, as the methodology and framework developed with these basins are applicable to other regions, provided that careful data evaluation is conducted. Testing in other climates and continents is an important avenue for future work, but it lies beyond the scope of this initial study.