Dear authors,
Thank you for the detailed responses to the referee comments. Both referees agree that the manuscript is potentially publishable in HESS, but request major revisions, due to lack of clarity and methodological questions. Upon re-reading the manuscript, I agree about the lack of clarity, and I am left with a lot of open questions about the methods and doubts about the insights provided by this manuscript. Therefore, I believe that the manuscript requires a thorough overhaul to improve clarity and potentially eliminate methodological flaws, as pointed out by the referees and in my own comments and questions below.
It would be very helpful if you could accompany the revised manuscript by a document where you explain the modifications in response to the points raised by the referees and myself. Thank you in advance.

GENERAL COMMENTS
In the manuscript, you analysed daily and monthly fluxes, stating that this is what the equations are mostly used for. But since you are citing Slatyer and McIlroy (1961), you may give some consideration to their statement on P.58: "However, use of average values in equations like 3.13, containing products of variable quantities, means neglecting the effects of short-term correlations between these quantities, which could sometimes lead to significant errors (cf. discussion of eddy flux versus mass flux, Section 9(f)). For this reason individual values of all quantities, including G wherever possible, should be entered into the equation as frequently as they can be obtained, and only the consequent
values of E should be averaged."
Since the eddy covariance data does contain hourly data, it would be worthwhile following their advice or at least explaining why you did not use it.

I do not understand why new parameters are chosen for the use with the CR. Actually, I struggled to understand the procedure, as explained in the detailed comments. Here is what I took away after re-reading multiple times: First you fit parameters to reproduce LE_ref as closely as possible for different filter settings (closeness of LE_ref and LE_p). Then you compare the resulting alpha values with LE_ref/LE_e and the estimated LE_PT with LE_ref (Fig. 3). The differences between methods are minimal here. Then, you use the PT-equation in combination with the CR, but re-calibrate the parameters. At some stage, I assume when you use the CR, you seem to have calibrated the parameters to either make alpha match LE_ref/LE_e as closely as possible, or to make LE_PT match LE_w as closely as possible or to make LE_PT match LE_ref as closely as possible (Tables 1 and 2). But I am really guessing here.

Since you are filtering for data points where LE_ref is very close to LE_p, it is not clear to me what is the use of the CR, as the CR is supposed to be relevant for estimating LE_ref when it is not close to LE_p. Secondly, since you are re-calibrating the parameters, what is the predictive power of the method? If the parameters need re-calibration before being used in the CR, this suggests to me that a well calibrated LE_PT is not useful in the CR and hence the CR as you used it, is not useful. I think it would be very helpful if you could describe at the beginning of the Methods section the overall approach (what is fit to achieve what) and what you expect to see.

In Tables 2 and 3, very different parameter values were needed to reproduce either alpha, or LE_w or LE. The text is not very clear about how this was done (see detailed comments), but also not what it means. I had the impression that the different methods did not matter too much when matching LE_PT to LE_ref, so why do they matter when using the CR? Your explanation in L362-365 is not very clear. Also, in the text, you describe the RMSE as the deviations between the simulated values and the reference, but in the figures and tables you provide it along with the parameters of the linear fit (slope and intercept), so I am not sure if the RMSE was not calculated based on the deviations between the simulated data and the regression line. For example, in Fig. 4 top left, the reported "RMS" is very close to that of the top right panel, which has a similar spread of data, but a much smaller regression slope and therefore probably greater deviations from the 1:1 line.

Referee 1 criticised that your manuscript ignores surface-atmosphere feedback when discussing the difference between wet surface and potential evaporation. Although most of your analysis focuses on wet surfaces, where both are very similar, as you state in your response, when you relate to the CR method, it would be important to explain the feedback between evaporation and atmospheric conditions, mainly temperature and humidity. The temperature feedback is also not mentioned in L188. In your response and in some of the text, you focus a lot on surface temperature, but I really do not see the point of re-introducing surface temperature into a framework formulated explicitly to eliminate the need for specifying surface temperature (Penman, 1948). In this respect, I have noticed a confusion about the meaning of Delta, as Penman did explicitly use the slope at air temperature, not at surface temperature. Since the eddy covariance data does not contain surface temperatures, it is actually not clear how you calculated Delta in this study.

Referee 1 also found Section 2.2 difficult to follow. Perhaps it would help to remove all the equations that are not actually used, and instead explain the concept a bit better (perhaps including a plot of the key CR formulation) and refer to the papers for the other equations.

Referee 2 is concerned about the effect of an inadequate wind function on your results and you mention additional analysis in your response. Could you include in the paper or SI the figure you mention in your response?


SPECIFIC COMMENTS

L120-: Please provide page numbers when referring to books as sources. Slatyer and McIlroy (1961) based their derivations on Penman (1948), where Delta (s in Eq. 3.19 in SM1961) is evaluated at air temperature, not at the wet surface temperature, as stated in L121, and then again in L144. I am aware that Yang and Roderick (2019) also used Ts, but it would be worth pointing out here that Penman (1948) did not.

L131: I have not found that PT (1972) actually referred to Eq. 4 at all. They introduce alpha ad-hoc in their Eq. 5, so, as intuitive as it sounds, your statement may be misleading.

L264-: I do not understand this paragraph. What is the "realistic range of values" for each parameter, and how many values were randomly chosen? What does L266 mean? How was LE_e calculated? How is T0 obtained from the data for calculating the slope "at the wet surface temperature" in Eqs. 8, 9 and 11?

L274-: Why were again new parameter values fitted for the use in the CR?

L283: This would be better off in the figure caption instead of the main text.

L356 and throughout: I find the use of the word "optimize" very confusing here. It seems that you are referring to the target variable you want to reproduce, as the "optimized" variable. Most readers would associate with "optimized" variable the variable that is being tuned. Why not write "parameter values that reproduce observed alpha" instead of "parameter values that optimize estimation of alpha"? And then you could refer to the variables that you actually tuned as either "tuned" or "calibrated".

L360-: If the parameters have to be re-calibrated depending on the context, this would suggest to me that they actually don't have a consistent meaning. Why was the CR not applied using the parameters obtained in the previous step?

L362-: This paragraph is hard to understand. What do you mean by "estimated correctly"? What is a "correct" value of alpha? What do you mean by "the LE_PT estimate LE_est may not adequately represent..."?

L372: This is the first time you mention the term "iso-enthalp". It would be good to explain what it means.

L384: The RMS errors are similar, but the slopes of the correlation are quite different. It is actually not clear whether RMSE refers to the fitted curve or to the 1:1 line. In the former case, RMSE does not say much about how well one variable reproduces the other.

Tables 1-2: Please describe RMSE, R, S, I, NSE. What do you mean by "Optimized variable"? Actually calibrated variable or the variable to be reproduced? What do you mean by LE_w and LE? I thought that LE_ref was observed LE filtered for wet conditions, so not sure what is the difference here. You also never mentioned the NSE in the methods, so this needs to be added.

Fig. 1: The black lines are not visible. The caption does not explain the difference between plots in each column. Where are the reference values stated?

Fig. 3: What does alpha_est and alpha_ref refer to? Please mention that S is slope, I is intercept.

Fig. 4.: Please label the sub-plots as a, b, c, and d. Please also specifiy whether the RMS (I would call it RMSE) refers to deviations from the regression line or from the 1:1 line. The regression lines should also be visible.

Dear authors,
Thanks again for the careful revision of the manuscript and detailed responses to referee comments. The referees are both supporting publication of your article now, subject to technical corrections. I would still like you to consider/address a few last points before publication, as listed below. Thanks again for your patience and commitment to high quality research.

Best regards,
Stan

L193: In your response about surface-atmosphere feedback, you mention humidity, but not temperature, as suggested by the referee. Could you add this to your consideration?

L261: Should be McMahon.

L262: The Penman equation is not based on any assumptions about adjustments of atmosheric temperature and humidity, please correct. Could you also mention that Slatyer and McIlroy (1961) advised against such averaging: Slatyer and McIlroy (1961, P. 3-38): "However, use of average values in equations like 3.13, containing products of variable quantities, means neglecting the effects of short-term correlations between these quantities, which could sometimes lead to significant errors".

L264-266: The reader would benefit a lot from a comparison between values obtained using hourly and monthly data. Here it sounds as if the results would be similar, but this is in contrast to the statement by Slatyer and McIlroy mentioned above.

L587: Please also create a release of the github repo and publish it on a suitable archiving platform (e.g. zenodo.org), to create a static version with its own DOI. See https://www.hydrology-and-earth-system-sciences.net/policies/data_policy.html

Dear authors,
Thanks a lot for the further clarifications and improvements to the manuscript, and for providing a static reference to the underlying data and scripts. Perhaps a last tiny suggestion for the readers' convenience, could you provide the direct link to the zenodo repo (https://doi.org/10.5281/zenodo.8172604) and if you don't mind, also a link to your original github repository, in case someone would like to fork it and/or collaborate with you on it?

Best regards,
Stan