Dear authors, please find my comments on your manuscript in the attachment.

General comments

In this work, “Unveiling the Impact of Potential Evapotranspiration Method Selection on Trends in Hydrological Cycle Components Across Europe,” the authors assess 12 potential evapotranspiration (PET) formulations across the European continent using regional hydrological modelling to quantify their impact on PET trends and their implications for the main hydrological cycle components: actual evapotranspiration (AET), total water storage (TWS), and runoff (Q). They conclude that the PET model selection conditions the simulated trends and influences the analyzed hydrological component. The paper reads well; I enjoyed it while reading it. Moreover, I think the study is relevant for the catchment hydrological community; the impact of PET formulations has usually been overcome in calibration frameworks, and assessing its actual impact at a continental scale is a valuable result. However, I have some concerns, especially regarding the methodological approach. On the one hand, I missed information about the model framework, for instance, what baseline calibration you used and how the main analyzed hydrological cycle components are linked to the model. This is key to understanding the impact of your analysis. On the other hand, the authors talked about trends, but no proper statistical trend analysis has been performed. 

Specific comments

Introduction

• In paragraph one (lines 24-33), it would be nice to briefly mention that other concepts like reference evapotranspiration are widely used when computing AET.  
• In paragraph two (lines 24-33), I would also include some sentences explaining why there have been more than 50 models for computing PET. Are they physically based formulations? Are they empirical and therefore linked to where they were initially formulated?
• In the third paragraph (lines 41-47). Since your study assesses the impact of PET selection in other water cycle components, I would include more context and references about the connection between different components.

Methods and data

• Could you elaborate a bit about the quality of your data? Later in the discussion, you mentioned that their uncertainties were important to your results.
• How were the criteria used for choosing the 533 catchments? You mentioned that you try to cover all European climates, but is that the only reason? Why is there no catchment in Italy or Greece? Why are there these big differences between catchment sizes?
• Why do the authors select these 12 specific PET models? Please add in Appendix A1 reference to each one of the chosen formulations.
• The authors mention that “the basins were not calibrated for each PET method to access their response in hydrological cycle components.” I understand that this is a hypothesis of your study, but in any case, I assume they must be a baseline calibration. How does the model perform in this baseline calibration? Which PET is considered in this baseline calibration? Which parameter set was used in this reference calibration? Which the target variable that the model was calibrated for? I think that, in general, a deeper description of the model might help the reader to understand the implications of selecting one or other PET. Especially how the parameterization of PET-AET-soil water balance interaction is solved.
• Regarding the trend analysis, to my knowledge, Sen’s slope method is a non-parametric test to compute the magnitude and direction of linear change on a time series, as the authors state in lines 146-150. To be able to talk about a trend, it needs to be significant. To assess that, other statistical tests should be performed. The Mann-Kendall test and its variations are the most commonly used for these purposes. For instance, one paper you cited, Anabalón and Sharma, 2017, used a test of the Kendall family (Seasonal Kendall trend test) to determine the trends and the Sen’s slope test to determine their magnitudes. If only Sen's slope is computed, the authors might talk about the evolution of the slope but not about trends.

Results

• As I stated before, the authors should not talk about trends but rather the evolution of the slope. So, sections 3.1, 3.2, and 3.3 might be rewritten in this sense or carried out the trend analysis and talk about trends.
• Besides talking about trends, I think it would be nice for the reader to have some information about the actual values, at least for PET. I would include 12 maps, one per PET model selected with actual PET values. It would help the reader to spot differences.

Discussion

• There are topics I would highlight in the discussion that it did not. For instance, are the different sizes of the catchments conditioning your results? Another issue I would appreciate including is a discussion about why specific models produce different results when they are within the same category. That is, why are there differences between temperature models? Is it linked to their specific formulation?

Summary and conclusions

• Conclusion 7 is obvious. I would remove it.

Technical corrections

• Please homogenize “combination type” vs. “combinational type.”
• Figure 1b: it is unclear what each dot represents. I assume they are catchments, but it seems to me less than 533.
• Line 141: “For the each” should be “for each.”
• In Figures 2 and 3, I recommend using the same range on the y-axis for each variable to see the differences. In addition, I would add the number of catchments in each category, that is, 189, 330, and 34 for energy-limited, mixed, and water-limited, respectively.
• Figure 6, not all categories sum 553. Please revise. In addition, I think the bar representation with different numbers of catchments and models in each is not intuitive. Maybe the same structure but in a table format for the upper part, in which models are rows, would be more intuitive.
• Please check the name of the PET model throughout the manuscript; there are some inconsistencies.

Overall evaluation

The authors presented a study on the impact of 12 PET formulations on the trend of a set of components of the hydrological cycle in 553 catchments across Europe. They used a large-scale rainfall-runoff model to simulate actual evapotranspiration (AET), total water storage (TWS) and runoff (Q) multiple times by varying the PET forcing according to the 12 selected methods. Then, they analysed the annual and seasonal trend of PET, AET, TWS and Q obtained thought the different PET methods. They concluded that the choice of PET formulation influences the components of the hydrological cycle.

The work has a strong potential and the issue is of great interest in the field of catchment hydrology. In addition, this experiment could help fill a gap in the literature, which currently lacks a clear understanding of the effects of different PET formulations on rainfall-runoff modelling. However, I have few major concerns, especially about the methodological approach, which I think should be addressed in order to enhance the reliability of the results, facilitate and improve their interpretation, and meet the standards required for publication in HESS.

Most of my concerns were already highlighted in detail by the other two referees. Therefore, I would focus exclusively on the most critical issues, which need significant improvements.

General comments

[1] Modelling framework and model accuracy

A more detailed description of the modelling framework is certainly needed in order to better understand the experiment and its results. Please provide information about model spatial and temporal resolution, model calibration (or previously calibrated model settings) including objective function(s), calibration/validation period, input data used, etc. If a default parameterisation is used, as stated in the very last part of the manuscript, I believe the authors should elaborate about it and its impact on the outcomes of the analysis (i.e. can it be reliable?).

In general, I suggest providing a brief overview about model performances against observed streamflow (which I suppose were used somehow for model parameterisation and/or to evaluate the default parameterisation) across the study catchments. I am aware that's definitely not the focus of the study but, since the entire analysis is based on a set of model outputs (streamflow included), I believe it is important to verify (and show) model accuracy in order to consolidate the interpretation of the results and draw solid conclusions. In fact, even if on one hand good model accuracy in reproducing streamflow does not guarantee a faithful reproduction of other hydrological components, on the other hand I would tend not to rely on the state variables of a poorly performing model. Maybe you can mention about model performance in the text and report the details in the Supplement.

Finally, I agree with referee Franziska Clerc-Schwarzenbach that, if a method for potential evapotranspiration was involved in the model parameterisation, authors should provide details about it and comment about the potential effect it could have on the outcomes of the experiment.

[2] Trend analysis

First of all, I am sorry to say that the trend analysis is lacking. In particular, authors computed and took into account exclusively the non-parametric Sen’s slope test, which estimates the magnitude of the trend of a time series but does not ensure its statistical significance. To affirm that a signal has a trend, it must be statistically significant. Therefore, I ask to the authors to complete the trend analysis by associating a significance test (e.g. Mann-Kendall) to each trend magnitude (Sen’s slope) and, consequently, change all the results and their interpretation accordingly.

In addition, I suggest excluding (maybe adopting a threshold) very week positive/negative trends when computing DCI, which may include a lot of noise and mask some aspects of your results.

[3] Results and discussion

I personally find some parts of the results section very hard to follow. In particular, please consider reviewing the text on seasonal trends (Section 3.2) and on combination of hydrological cycle components (Section 3.4).

In addition, when commenting DCI outcomes in Figure 4 and 5, authors refer to Northern/central/Southern Europe to develop the description. It would be useful to be more specific, because sometimes the text is misleading. For instance, at line 256 you state “…Q shows a strong decreasing trend for all PET methods in most central European catchments” but if I look at figure 5, central-Eastern DCI for Q are mostly negative. Is eastern Europe not included in “central”? If so, comment also about Eastern Europe. Again, Great Britain is considered Northern or central Europe?

Figure 6 is not intuitive and difficult to interpret (and must be revised since some of the PET methods don’t sum 553?). I strongly agree with the suggestions of Franziska Clerc-Schwarzenbach and Anonmymous referee #2. Also, the figure format and meaning should be explained in detail in the text before commenting it. Moreover, I suggest adding maps of the catchments coloured accordingly to the obtained combinations (or at least some of them), in order to be able to locate basins in space.

The trends of AET, TWS and Q are strongly influenced not only by the PET method but also by PRE trends. Even if it is obvious, I would report PRE trends (and their significance) in the results (and not only in the Supplement) and use it to justify the trend direction of the other components.

Finally, the discussion about the obtained combinations of hydrological cycle components is poor. I believe it should be extended.

Additional minor comments

[1] Figure 1b: I would specify in the text (not only in the caption) that the example refers to the catchments with bolder black contours in panel a. In addition, I would avoid interpolating the points: please use just dots of different colour.

[2] line 95: Please give some information about time coverage of the datasets, which I guess can justify your following choice regarding the simulation period.

[3] lines 103-104: I perfectly understand this choice, since ERA5-Land precipitation and temperature are known to be often not accurate, leading to a degradation of model performances. However, since one may wonder why not all variables from ERA5-Land are used, I would refer to recent studies highlighting such issues (e.g Clerc-Schwarzenbach et al. 2024, Tarek et al. 2020)

References

Clerc-Schwarzenbach, F., Selleri, G., Neri, M., Toth, E., van Meerveld, I., and Seibert, J.: Large-sample hydrology – a few camels or a whole caravan?, Hydrol. Earth Syst. Sci., 28, 4219–4237, https://doi.org/10.5194/hess-28-4219-2024, 2024.

Tarek, M., Brissette, F. P., and Arsenault, R.: Evaluation of the ERA5 reanalysis as a potential reference dataset for hydrological modelling over North America, Hydrol. Earth Syst. Sci., 24, 2527–2544, https://doi.org/10.5194/hess-24-2527-2020, 2020.