Responses to comments of Referee 1:

We would like to thank the referee for the useful comments and his/her interest for our study. We will include all the specific comments mentioned by the referee, clarify the vocabulary, and correct figures directly in the manuscript.

Comments 1:

Table.2: It is great that the code provides the details of how each PE formulation is calculated. However, it would be good to add a little more detail to Table 2 as some of these methods do not have a unique formulation. For example, which Morton estimate of ET is being used? Is the Penman-Monteith reference crop (FAO56) or a different version of Penman-Monteith? Which version of Penman is being used? The formula for each method would make this clearer and or an indication of whether the formulation is open water, potential evaporation or reference crop. In addition, Hamon should include sunshine hours as a variable

Section 2.2: The seven formulations in Table 2 include estimates of potential evaporation (unlimited water availability) over land or water, reference crop (well-watered short grass) and open water evaporation. Therefore, these formulations are not expected to produce results of a similar magnitude – it would be good to indicate which formulations estimate the different types of evaporation and which produce higher to lower values (I would expect open water evaporation > potential evaporation > reference crop). While I agree that all of these seven formulations can be used to represent future atmospheric demand for climate change impact assessments, it is important to be clear about what they actually estimate and how these differences may influence the later uncertainty estimates.

Figure.2a: Much of the difference in PE between the seven formulations is likely due to them representing different evaporation variables. As mentioned previously re the seven formulations in Table 2 they include potential evaporation (unlimited water availability) from a surface, reference crop (well-watered short grass) and open water evaporation. Furthermore, most of them are estimates of evaporation from a point, whereas Morton is likely to be an estimate for a large area, which we would expect to be lower than a point estimate. If these seven formulations are kept in the analysis, then it is important to be clear that the variability is not just different formulations of a single type of evaporation metric (potential evaporation), but variability between different evaporation concepts.

Answer to Comments 1:

The referee would like more details on the potential evaporation formulations we used. We agree that not all the formulations used were developed for the same purpose; however, we would like to emphasize that they are regularly used in a similar way in hydrological modelling. Therefore, we will add some clarifications regarding the type of formulation and the related environment.

Regarding the Hamon formulation, we chose the equation with theoretical sunshine hours, since observed sunshine hours are not directly produced by climate models. Furthermore, other Hamon formulations using theoretical or observed sunshine durations exist. However, again, the sunshine duration variable is not available in climatic projections and we cannot use such formulation straightforwardly. Thus, it would have been necessary to use an empirical relationship to calculate the daily observed sunshine hours from solar radiation data. Oudin et al. (2005) and Almorox et al. (2015) have already used Hamon equation with theoretical sunshine hours and the later reference will be added in Table 2.

Comments 2:

Figure.5 bottom row – signal-to-noise ratio: The method used in this manuscript to calculate the signal-to-noise ratio is not clear, despite the reference to Hawkins & Sutton (2012). Table 1 does not list any pre-industrial control simulations, so it is unclear what has been used in this analysis to define the natural climatic variability against which the RCP scenarios would be compared to see if the signal-to-noise ratio is > 1. In addition, it is not clear which RCP scenario is being shown in Figure 5 (bottom row) or whether the signal-to-ratio is average across the three RCP scenarios considered. The different RCPs will have different signal-to-ratios as they have very different signals, yet only one map is shown for all RCPs. It would not make sense to combine different RCPs into a single signal-to-ratio metric as they have very different signals – they should be considered one RCP at a time. More details about how the signal-to-ratio is calculated is required to understand what is being shown here and why the results are the way they are. I see that later at line 211 it appears that the different RCPs have been combined in the signal-to-ratio metric, which is not informative

Section 4.2: The authors note that the uncertainty due the PE formulation in this study is lower than in other studies (Line 237). They suggest this may be due to other studies only considering a single RCP, which is a reasonable suggestion. I recommend only considering a single RCP at a time, rather than combining the RCPs into the one analysis as combining the RCPs will likely inflate the uncertainty in the GCM/RCM/RCP components of the analysis. However, another suggestion may be that the other studies may have bias corrected the GCM/RCM output prior to assessing the uncertainty contributions. Bias correcting the GCM/RCM projections would remove any bias between GCM/RCMs and place each GCM/RCM on a common baseline from which the difference in GCM/RCM/RCP signal would emerge. Whereas, in this study it is not clear that any bias correction of the GCM/RCM projections has occurred, so there will be increased variability in the GCM/RCM projections due this uncorrected bias.

Answer to Comments 2:

One of the most important comments refers to the experimental approach used to conduct the uncertainty analysis. The referee suggests analysing the uncertainty on potential evaporation considering a single RCP at a time, rather than combining the three RCPs. We have considered all three RCPs all together for the QUALYPSO analysis in the study, as we consider them as the primary source of uncertainty when considering the impact of climate change, following (Evin et al., 2019), among others. However, we agree that considering only one scenario could be interesting to compare our results with other studies only considering a single RCP. Separating RCPs would certainly result in different time of emergence and signal-to-noise ratio outputs.

Performing such a test could be useful especially for the long-term projections, where the weight of the RCP factor is higher than at the short term. To conduct these experiments, it would be necessary to select GCM/RCM couples available for each scenario our data of climate projections to have same GCM/RCM couples for each RCP considering in the uncertainty analysis with QUALYPSO. However, only six GCM/RCM couples are common to the three scenarios, so it will drastically reduce the number of GCMs and RCMs accounted for in the uncertainty estimation.

To follow the reviewer’s recommendations, we will analyse the new partition of the total variance for each factor (GCM/RCM/PE formulations) through conducting one uncertainty analysis on a single RCP, namely RCP 8.5. Using only this RCP to compute the uncertainty will provide new insights on the signal/noise ratio and its interpretation. RCP 8.5 has the strongest change signal of the three RCPs, and all the GCM/RCM couples used are available for this scenario. This will help us to clarify the contribution of PE formulation to the total uncertainty.

We will add more details on the method used to calculate the uncertainty and the signal-to-noise ratio to improve justifications and the understanding of the method (also suggested by the second referee). The reference period defined in the article, namely 1976-2005, is used in the signal/noise analysis as the reference; we do not consider a pre-industrial period. Finally, we will make clearer that our data are not bias corrected, and the consequences on our conclusions will be discussed to improve the comprehensiveness of the results and the discussion part. Sources of uncertainty also exist in bias correction methods for the climate variables, and the interdependence of the climate variables must be preserved to calculate potential evaporation, which is not always warranted by statistical bias correction methods. The bias correction methods could be an interesting source of uncertainty to explore in further studies, but this point is beyond the scope of this study.

References

Almorox, J., Quej, V.H., Martí, P., 2015. Global performance ranking of temperature-based approaches for evapotranspiration estimation considering Köppen climate classes. J. Hydrol. 528, 514–522. https://doi.org/10.1016/j.jhydrol.2015.06.057

Evin, G., Hingray, B., Blanchet, J., Eckert, N., Morin, S., Verfaillie, D., 2019. Partitioning Uncertainty Components of an Incomplete Ensemble of Climate Projections Using Data Augmentation. J. Clim. 32, 18.

Oudin, L., Hervieu, F., Michel, C., Perrin, C., Andréassian, V., Anctil, F., Loumagne, C., 2005. Which potential evapotranspiration input for a lumped rainfall–runoff model? J. Hydrol. 303, 290–306. https://doi.org/10.1016/j.jhydrol.2004.08.026

 Responses to comments of Referee 2:

We would like to thank the referee for the useful comments and his/her interest for our study. We will include all the specific comments mentioned by the referee, clarify the vocabulary, and correct figures directly in the manuscript.

My specific comments are:

* Inacuracies, need revision:



** line 17

This is debatable, but to me "climate change" is more of a "consequence" than a "cause".

Thank you for this comment, we will modify to “climate change results in”.

** line 20-24

This part I would avoid in the introduction, since it leads the reader to think that the study will cover actual evaporation, which is not the case. But it could be material to place in the discussion, where potential consequences of this study on AET could be discussed.

We agree with the referee, moving the consequences of PE on AET from the introduction to the discussion part will enhance clarity to the manuscript.

** line 32

I don't get this sentence. What do you mean by "through calibration"? What do you mean by model sensitivity here? Sensitivity of model output or of PE? And sensitivity towards what?

Here we refer to the fact that PE generally feeds an impact model (for instance hydrological models), and the calibration step of the impact model compensates to a certain extent potential bias from PE.  We will rephrase as reviewer 1 also asked clarifications on this point.

** line 36

You cannot say "a more comprehensive way" because you are not aiming at the same things. Above you write about validity of assumptions, whereas here you write about uncertainty of modelling results.

We propose the following reformulation: “Here, we propose to assess the contribution of PE formulations to the overall uncertainty of projections by testing several formulations under several climate projections.”

** line 64

Why do you say that all PE formulations are questionable over mountainous areas?

Because physical processes involved for these areas are different from the rest of the study area. Indeed, part of the snow cover disappears by sublimation without melting. The tested PE formulations do not represent this process. We agree on the misunderstanding, so we propose to detail the difficulties of PE estimation under cold and mountainous regions in the revised version of the manuscript.

** line 75

Revise this sentence. I don't like it. Write something that you partitioned the total uncertainty on projected PE among...

We propose a new sentence: “Second, the total uncertainty on projected PE will be partitioned and quantified among all uncertainty sources (RCPs, GCMs, RCMs, and PE formulations)”

** line 84

For all RCP and GCMs/RCMs combinations (3*6*9) you get only 1 realization of the climate variables? This is a limitation of the study since you will not be able to reproduce uncertainty coming from internal climate variability (stochasticity). Indeed later in the text you write that you took a running mean on climate variables in order to reduce fluctuations. Not including internal climate variability and the running mean choice, both need better explanation/rational behind it.

We fully agree that using only a single realization for each combination is a limitation for the total uncertainty quantification, and hinders the quantification of an additional uncertainty source (namely internal climate variability). The main problem here is the access to several realizations of climate projections for the different GCMs / RCMs used in the study. However, as we focused on anomalies over long time slices, we assume that the natural climate variability may have a limited impact. We will add a sentence in the manuscript to improve explanations.

** line 121

See my comment above.



** line 124

Overall I find the methods section a bit difficult to follow. I think it would highly benefit from some schematics where the procedure is drawn out. Also, later in the text you would refer multiple times to "modelling steps/chain", and those steps were never explicitly defined in the text.

We agree that it could be difficult to understand the modeling chain used for the climate impact study, especially if the reader is not familiar with this type of study. We propose the following diagram to improve the understanding of the method. We will refer to this scheme in the new version of the manuscript.

** line 144

What exactly do you mean by "trend slopes"? I think you should be more specific.

In this case we mean “growth rate”, we will change this in the manuscript.

** line 150

"covariance" instead of "interdependence"

Thank you for this recommendation, we will modify the manuscript accordingly.

** line 157

"uncertainty contributors" instead of "factors"

Thank you for this recommendation, we will modify the manuscript accordingly.

** line 159

this modelling chain needs to be defined, see comment above

In order to clarify the manuscript, we propose to define the modelling chain at the beginning of the method section (line 82). We will add the following sentence, which completes the information given by the new scheme added in the same sub-section. “The modelling chain is a pathway from different RCPs to an impact model (here PE formulations), with a succession of models, whose simulations outputs feed the next model. The figure 1 represents the modelling chain used for this study with each modelling step, namely RCPs, GCMs, RCMs and PE formulations.”

** figure 2 caption

Instead of "absolute anomalies" I would use "expected increase"

Thank you for this recommendation, we will modify the manuscript accordingly.

** line 169

But why does it increase for RCPs? This could be the consequence of the total uncertainty being lower for locations in the south and RCPs uncertainty being equal throughout France, leading to higher relative contribution of uncertainty of RCPs.

We agree with the referee. This comment will be clarified by adding a panel on figure 4 with the total uncertainty, as suggested by the referee below. Besides, we will analyze the uncertainty contribution for one RCP (namely RCP 8.5) in order to address this issue that was also highlighted by referee # 1.

** figure 4

A further panel with total uncertainty would be good.

We agree (see previous comment).



** line 179

This belongs to the results



** line 180 to 185

This should be placed in the methods section

We agree with this comment and we will move these explanations in the method section (2.3), and provide more details.

** figure 5

Since 1 is the threshold here modify the lower row in order that it has 2 different colormaps, e.g. reddish for values above 1 and greyish for values below 1.

Thank you for this recommendation, we will modify the Figure accordingly.

Insert the equation of the signal-to-noise ratio in the figure caption.

Agreed, we will modify the figure caption.



** line 189

This belongs to the results

We agree, this sub-section will be moved to the Results section, to remain consistent with the previous change.



** line 216

I would not use the word "globally" here

We agree, we will remove the term “globally”. The sentence will become “Moreover, the uncertainty spread also increases with time, which adds up to the total uncertainty, despite the fact that the relative contribution of this factor to the total uncertainty decreases with time”

** figure 6

What are the distributions exactly? To my understanding looking at one boxplot in one panel gives information on the variability in delta PE given that one modeling step is chosen and "fixed"(specified by the color) and all the other modeling steps (all but the colored specified one) vary across their PE output range. Is this correct?

Yes, the referee’s interpretation is correct. We will add details in the Figure caption to avoid misunderstandings.

This figure needs time ticks to show the 3 periods distinction. Then you get it at first glance.

Thanks for this comment; we will add markers for the 3 periods to improve the readability of the figure for the reader.

** line 241

I don't think this is true.



To me, this is more the consequence of the higher variability (and therefore uncertainty), which is introduced when more RCP scenarios are considered. The relative contribution of PE formulations to total uncertainty is thereby reduced, but PE formulation would not vary more among one RCP.

The referee's interpretation, as well as the one from referee #1, is completely plausible. Therefore, we will present the results for a single RCP to quantify the impact of multi-RCPs analysis on our results (see answer to referee #1). We wanted to explain that by focusing on a single emission scenario, the relative contribution of the PE formulas to the overall uncertainty is mathematically larger. However, indeed in terms of absolute uncertainty it is the same. We propose deleting the following sentence from the manuscript: “…due to the higher future air temperature”.

** line 254

Which usage?

We agree that the term “usage” can be confusing. We propose the following reformulation by changing “usage” with “practice”.

** line 262

This is only valid for the give dataset. It would be interesting to see whether the same conclusion can be drawn if the dataset would contain also stochasticity of climate variables (multiple realizations of climate variables for the same RCP-GCM-RGM modelling chain)

We agree with the referee’s comment; however, we did not have access to multiple runs for each RCP-GCM-RCM. This lack is common to many climate impact studies. It could be an improvement for future works about the uncertainty quantification in climate impact studies but this is beyond the scope of this study.

** line 265

Personally, I would have appreciated some qualitative statements on how future PET uncertainty might transfer to AET uncertainty, since finally AET is the variable we care about, PET being only a "modelling"-byproduct.

We agree with this suggestion, and we propose to add a discussion section dedicated to this issue. The discussion section will address two related issues:

1. The spatial heterogeneity of the consequences of PE uncertainty on AE that may be limited over “water limited” regions, such as Mediterranean regions but more important over “energy limited” regions, at higher latitudes.
2. The sensitivity of the impact model to PE inputs variability, which was already addressed in the introduction but following the referee suggestion, this will be moved (and detailed/clarified) in the discussion section.

** line 267

Since AET is never mentioned in results or discussion I don't think mentioning it in conclusions is justified. I would delete the whole sentence.

As suggested previously by the referee, we will address this issue in a new discussion section.

* Recomendations related to style



** line 12

Delete "Finally"

Thank you for this suggestion, we will modify the manuscript.

** line 17

I would replace "modifications" with "changes"

Thank you for this suggestion, we will modify the manuscript.

** line 28

empirical temperature methods

Thank you for this suggestion, we will modify the manuscript.

** line 29

delete "some", replace "relatively to" with "other than"

Thank you for this suggestion, we will modify the manuscript.

** line 30

delete "and possible feedbacks"

Thank you for this suggestion, we will modify the manuscript.

** line 35

.. but assuming that models may represent past and future climates equally well is difficult to verify

Thank you for this suggestion, we will modify the manuscript.

** line 49

how future streamflow anomalies can be dependent on the choice of PE formulation

We mentioned the fact that for an energy-limited environment, the increase in PE leads to a decrease in runoff, if the changes in precipitation do not offset the increase in PE. But, if the increase is small, the changes in precipitation can offset the increase in PE, and lead to an increase in runoff.

** line 51

uncertainty of

Thank you for this suggestion, we will modify the manuscript.

** line 62

results appear to be..

Thank you for this suggestion, we will modify the manuscript.

** line 71

since outputs become inputs for PE I suggest choosing another word

Thank you for this suggestion, we will modify the manuscript.

** line 95

Be more specific here and mention the variables Rn and Ta.

Thank you for this recommendation, we will mention Rn and Ta variables.

** line 98

equilibrium temperature, which better represents the..

Thank you for this recommendation, we will change the sentence.

** line 99

what radiations? Solar radiation?

Yes, “radiation” will be replaced by “solar radiation”.

** line 103

since feedbacks between climate variables exist

Thank you for this recommendation.

** line 113

respective variance contributions

Thank you for this recommendation.

** line 144/146

on the selected forcing variables

Thank you for this recommendation.

** line 145

probably being

Thank you for this recommendation.

** line 150

this suggests "covariance" instead of interdependence.

I would stick to the term "covariance" throughout the text when you write relationships between climate variables.

Thank you for this suggestion, we will change “independence” for “covariance”.

I would stick to the term "covariance" throughout the text when you write relationships between climate variables.

We agree with the referee.

** line 192

I would not use the word significant since it induces the reader to think about statistical significance, but here you mean only higher vs lower, correct?

Yes. We will changed the expression “more significant” for “higher”.



** line 233

future trends

Thank you for this recommendation.

** line 253

relative insensitivity ..

.. study, compared to other sources ..

Thank you for this recommendation.

** line 260



are near the average

Thank you for this recommendation.