The authors would like to thank Referee#1 for his/her positive feedback on the quality of the paper.

The question about the value of using a hybrid model is indeed a legitimate one. We provided the first elements of an answer in the previous paper (Mimeau et al, 2024) in which we described in detail the J2000-RF hybrid flow intermittence model and its implementation in 3 basins. Here is an extract from the introduction to this paper explaining the reasons for developing such a model: « Studies have already looked at modelling intermittent rivers with a physical hydrological model (Jaeger et al., 2014; Tzoraki et al., 2016; Llanos-Paez et al., 2023). One major difficulty in modelling flow intermittence is that hydrological models have difficulties in simulating zero flows (Shanafield et al., 2021). First there is a numerical challenge: the flow routing scheme implemented in the models to propagate the streamflow across the river networks cannot represent sudden transitions from wet to dry. Second, the origins of intermittence are multiple (disconnection between the river and the water table, drying up following a long period without precipitation, infiltration from the riverbed into a fault or a karstic subsoil, drying up following anthropic withdrawals, etc.) (Datry et al., 2016) and sometimes very local. Representing all these processes in the models is thus complex and requires a large amount of data. A more common approach to modelling intermittent rivers is the use of artificial neural networks (ANNs) (Daliakopoulos and Tsanis, 2016; Beaufort et al., 2019) and random forest (RF) (González-Ferreras and Barquín, 2017; Beaufort et al., 2019; Belemtougri, 2022; Jaeger et al., 2023) models. These models are easier to implement, do not require a priori knowledge of the origins of drying, and show good performances in predicting the spatial distribution of flow regimes (perennial or intermittent) in the river networks. »

Physically-based models such as ParFlow, HGS and MIKESHE explicitly represent the groundwater-river connection and are used to model river networks with intermittent or ephemeral regimes. However, these models are to be used in specific contexts. Gutierrez-Jurado et al. (2021) list 11 studies using fully integrated surface–subsurface hydrologic models (including ParFlow, HGS, tRIBS) to simulate runoff and streamflow processes in non-perennial systems in semi-arid regions or Mediterranean climate regions. The authors state that « the required level of information to adequately parameterise boundary value problems has restricted the use of fully integrated surface–subsurface hydrologic models (ISSHMs) in non-perennial river catchments to mostly small-scale hillslope or headwater catchments (0.001–0.9 km²) ». In these regions, flow intermittence can be a very local phenomenon and generally occurs on small streams at the head of a basin. Taking account of the groundwater-river connection in modelling these systems therefore requires a very fine spatial discretisation and very precise topographical data, which prevents the use of this type of model for larger catchment areas. In another context, Herzog et al. (2021) were able to use ParFlow to model the hydrology of ephemeral rivers in a large (14,000 km²) West African basin at a 1 × 1-km² resolution, because in this region flow intermittence occurs at a much larger spatial scale (streamflow is mainly controlled by perched aquifers discharging into inland valleys during the rainy season).

The 6 European basins in our study are characterised by local flow intermittence, which generally occurs in small headwater streams. The representation of intermittence in these basins, covering between 150 and 300 km², would therefore be very complicated for the reasons given by Gutierrez-Jurado et al. (2021). In addition, each of the 6 studied catchments has its own particular characteristics, with processes that are difficult to represent with ISSHMs. For example, in the Albarine catchment (France), intermittence in the upstream part of the catchment is caused by infiltration of the river into a karstic soil. We know that this karstic soil leads to exchanges of groundwater with adjacent basins, but the current knowledge of this karstic system is insufficient for it to be represented in a physical model (lack of data to represent the karst with its underground flow paths and directions). Another example is the Genal catchment (Spain), which is characterised by intermittent water flow caused by both a semi-arid climate and water abstraction for irrigation. It is quite possible to represent water abstraction in a hydrological model (surface and groundwater abstraction modules are implemented in J2000), however, in the case of the Genal basin, data on the volumes of water abstracted are not available and it is therefore impossible to represent these abstractions explicitly in the models.

Finally, another limitation is the computational power. Gutierrez-Jurado et al. (2021) indicate that the 11 studies listed which sought to simulate intermittence in small semi-arid basins using SIHM models were able to carry out simulations over periods ranging from a few hours to almost 1 year. Herzog et al. (2021) indicate that a 2-year hydrological simulation with the ParFlow model in their basin can be carried out in 5 hours of calculations. Our study focuses on the evolution of intermittence over the long term. To do this, we carried out 15 simulations for the 6 catchment areas studied, from 1985 to 2100 (3 greenhouse gas emission scenarios x 5 climate models), i. e. more than 10k model-year. These long-term simulations, that crucially take into account both the uncertainty related to the emissions scenarios and the uncertainty of the climate models, would not have been possible with an ISSHM.

The association of the J2000 process-oriented hydrological model with a random forest model therefore makes it possible to take account of flow intermittence in different climatic, geological and anthropogenic contexts and in medium-sized basins over the long term, which would be very difficult to achieve with an ISSHM.

We hope that these elements have answered your questions and we look forward to reading your detailed comments on our study.

Louise Mimeau, on behalf the co-authors.

References :

Herzog, A., Hector, B., Cohard, J. M., Vouillamoz, J. M., Lawson, F. M. A., Peugeot, C., and de Graaf, I.: A parametric sensitivity analysis for prioritizing regolith knowledge needs for modeling water transfers in the West African critical zone, Vadose Zone Journal, 20(6), e20163, https://doi.org/10.1002/vzj2.20163, 2021.

Gutierrez-Jurado, K. Y., Partington, D., and Shanafield, M.: Taking theory to the field: streamflow generation mechanisms in an intermittent Mediterranean catchment, Hydrol. Earth Syst. Sci., 25, 4299–4317, https://doi.org/10.5194/hess-25-4299-2021, 2021.

Mimeau, L., Künne, A., Branger, F., Kralisch, S., Devers, A., and Vidal, J.-P.: Flow intermittence prediction using a hybrid hydrological modelling approach: influence of observed intermittence data on the training of a random forest model, Hydrol. Earth Syst. Sci., 28, 851–871, https://doi.org/10.5194/hess-28-851-2024, 2024.

The authors would like to thank Referee#2 for his/her thoughtful feedback and constructive comments. We appreciate the opportunity to clarify and expand upon aspects of our methodology, model validation, site selection, network geometry, and accuracy assessment. Below, we address each of Referee#2's comments in detail:

1. "Data Scarcity and Model Validation: As mentioned in section 4.1, the scarcity of data presents challenges in validating the accuracy of the model. While the authors propose potential approaches, a clearer description of the methods and the data used is necessary. For instance, how many gauging stations, the duration of the observations, and how they are utilized for validation is not clear. Since the model operates at the reach scale, Table 1 should include the number of reaches for each study catchment or other relevant quantitative parameters. Are the parameters used for POD and FAR based on the number of reaches or temporal averages?”

We understand the importance of comprehending the methods as well as the data used for calibration and validation. In our prior publications (Mimeau et al., Künne et al. 2022) we presented a detailed methodology to develop a hybrid model using a process-based hydrological model and random forest as well as the calibration and validation procedure. In addition, we moved further information on the pilot river basins to the supplementary material of this paper in order to make it better readable. The location of gauging stations used for calibration and validation can be found in Figure S3 of the Supplement. Information on the flow observations can be found in Table S1, including the type of data used (e.g. crowdsourced, field campaign, expertise etc.), the time frame, number of observations, number of reaches and length of river network.

In the revised manuscript, we will complete Table 1 with information regarding the total length of river and the number of reaches in the DRNs.

The model is trained and evaluated based on all observations of the state of the flow (flowing or dry) collected in the DRNs. Observations are here considered as independent events and characterised by their date and location in a reach. POD and FAR are therefore not based on the total number of reaches or on a specific time period, but rather on the number of observations and their spatial dispersion in the network and their temporal dispersion in the year (see Table S1). Our prior publication (Mimeau et al., 2024) describes in more detail the method for training the RF model and computing the POD and FAR efficiency criteria. Mimeau et al., 2024 also present a sensitivity analysis of the POD and FAR criteria to the size of the training sample and the type of observed data (characterized by their quantity of observation and their spatio-temporal distribution).

2. “Justification for Site Selection: The rationale behind selecting the six study catchments is unclear. The introduction suggests an intention to explore outcomes under varying climatic conditions across Europe; however, the results and discussions seems do not adequately address the characteristics of these climatic regions or the influence of hydrological processes (e.g., dominant rainfall or snow dynamics). If the focus is more on the responses of different tributaries within a single catchment, the significance of the chosen regions becomes ambiguous.”

Our study catchments were chosen to represent diverse climatic and hydrological regimes across Europe, as described in the introduction. This selection enables us to examine the model's applicability under a variety of environmental conditions, from temperate to semi-arid regions. However, we are aware that our study is still far from being comprehensive in capturing Europe’s biogeographic regions. Besides, as part of a larger consortium, our team collaborates closely with others in this project. We described this collaborative approach in our introduction, underscoring that the selection was not made in isolation but as a collective decision and is also incorporated in a larger logistic framework.  

In the manuscript, the analysis and discussion of the results covers both the analysis of the processes in each of the 6 river networks and the inter-comparison of the study sites.  For example, section 3.1 ‘Climate and hydrological projections’ shows the differences in climate projections between the different climatic regions of our 6 study sites, with a north-south gradient in precipitation trends and simulated flows. In addition, Figures 1, 5a, 8b and 9a clearly show the differences in intermittence between the different climatic regions: the DRNs in southern Europe with dry climates (Genal, Butiznica) are very intermittent, whereas the DRN in northern Europe (Lepsämänjoki) is relatively little intermittent. Figure 6 also shows a general tendency for the percentage of intermittent river network to increase more in the southern sites than in the north. However, our results also show that local processes, such as geological characteristics and water abstractions, have a significant influence on intermittence. This suggests that the climatic region alone is insufficient to fully explain intermittence at the scale of local river networks. We acknowledge that these findings may not always be explicitly stated in the manuscript. Therefore, additional elements will be incorporated into the results and discussion sections of the revised manuscript to better emphasize the intercomparison of the study sites.

3. “Geometry of River Networks: The seasonal dynamics of river networks could be significantly influenced by their geometry (e.g., Horton’s law, Roy et al., 2020). I recommend that the authors include some relevant geometric parameters for the regions studied and conduct a corresponding analysis or at least a discussion.”

Thank you for the insightful suggestion and reference. Our spatially distributed modeling approach already accounts for network geometry and connectivity through parameters like reach length and slope, derived from static data sources such as Digital Elevation Models (DEMs). These parameters, alongside factors such as drainage area, land use, soil, and geology, have been previously analyzed in related publications (Mimeau et al., 2024; Künne et al., 2022).

While our model does not explicitly incorporate topological metrics like Horton’s Laws or advanced cluster analyses as discussed in Roy et al. (2022), the hybrid modeling technique we employ—combining the physically based JAMS-J2000 model with a Random Forest machine learning component—provides a robust framework for capturing seasonal flow behaviors. The machine learning element, in particular, helps identify hidden patterns in flow data that may not be directly captured by physical parameters alone.

Regarding the potential influence of network geometry and connectivity on intermittence and seasonality, we acknowledge its importance but note that the limited number of our six case studies does not allow us to comprehensively assess such effects. Furthermore, the hydrological model already accounts for several predominant factors, such as climate and geology, which also have a strong influence on flow behavior. Additionally, specific geological characteristics, such as those in the downstream Albarine, are integrated into the model via intermittence data and the hybrid approach.

We will, however, expand upon this topic in more detail within the revised manuscript's discussion section.

4.  “Model Accuracy Assessment: The assessment of model accuracy presented in Figure 3 appears to rely on cross-validation of the average proportion of dry reaches over time. If my understanding is correct, the persuasive power of this validation remains relatively weak. It may be beneficial to present the uncertainty in model simulations (not just the uncertainty associated with climate change projections). Additionally, while the authors note in lines 166-167 that two catchments exhibit lower model efficiency due to data scarcity, the paper does not specify the available sample sizes for each catchment. Furthermore, could the differences in model efficiency be attributed to variations in river network structure? I encourage the authors to address this point.”

The assessment in Figure 3 provides a summary of model performance over time, using cross-validation to evaluate accuracy in predicting drying and flowing events across reaches. However, we acknowledge that cross-validation alone may not fully capture the modelling uncertainties. In the previous study (Mimeau et al., 2024), we utilized additional approaches to achieve model performance, including sensitivity analysis on sample sizes and data types, which helped us better understand uncertainty in model simulations. Specifically, two configurations were tested -one with a full dataset (configuration 0) and another with a reduced dataset (75 % of training data, configuration 1) to evaluate prediction variability across the reaches and seasons​ as published in Mimeau et al. (2024).

The observed data availability across different catchments indeed varied, which influenced model robustness. For instance, in the Genal catchment, where a significant portion of the river network experiences prolonged drying, the model was more sensitive to data limitations. Although we did not specify all sample sizes in the main text, the supplementary material and cited prior publications provide a detailed breakdown of data coverage across catchments addressing this data heterogeneity explicitly​.

To answer the questions about the available sample size for each catchment as well as if the differences in model efficiency could be related to variations in river network structure: The sample sizes can be found in Table S1 in the supplementary material of this paper. Regarding the influence of variations in river network structure, it is true that this has an impact on the modelling, since the river networks were delineated from digital elevation models (DEMs), which had different resolutions (10 m to 30 m), depending on the available data for each country. We did mention this in the discussion part under section 4.4 (line 451-457): “The resolution of the DEMs used to delineate the spatial reach entities influences the accuracy of reach length and connectivity calculations, which evidently has an impact on the indicators. Thus, the overall river length with a certain flow condition (LengthD/LengthF ), Table 2) is determined by the DEM used, which varies from 10 m to 30 m resolution. In addition, smaller streams and tributaries may not be well-represented in the data, which can result in underestimations of flow intermittence in smaller streams. The calculation of the indicator (PatchC, Table 2) also relies on accurate representations of network connectivity. DEM resolution also determines reach connections, which should be taken into account when using this indicator to assess e.g. habitat fragmentation.”

We hope this helps to answer your questions and clarifies our approach with all its uncertainties. Thank you again for your valuable comments.

Sincerely,

Annika Künne, Louise Mimeau and Jean-Philippe Vidal on behalf of the co-authors

References:

Künne, A., Mimeau, L., Branger, F., and Kralisch, S.: Report on catchment-scale spatially distributed models for the 6 European focal DRNs, Tech. rep., Horizon 2020 project DRYvER, Securing biodiversity, functional integrity and ecosystem services in DRYing riVER networks, 2022. https://www.dryver.eu/results/reports-and-documents

Mimeau L, Künne A, Branger F, Kralisch S, Devers A, Vidal J-P (2024) Flow intermittence prediction using a hybrid hydrological modelling approach: influence of observed intermittence data on the training of a random forest model. Hydrology and Earth System Sciences. https://doi.org/10.5194/hess-28-851-2024

Roy, J., Tejedor, A., & Singh, A. (2022). Dynamic Clusters to Infer Topologic Controls on Environmental Transport of River Networks. Geophysical Research Letters, 49, 1–11. https://doi.org/10.1029/2021GL096957