1. The manuscript describes an interesting phenomenon -- but doesn't explore plausible explanations. One may expect that the water temperature in the Class A pan is influenced by sediment at the bottom of the pan, and by having waterplants that limit water circulation. The temperature at the water surface will influence evaporation. Even measurements of surface water temperature for a relatively short period could help quantify such effects. One expects the temperature differential to be highest under full-sun conditions and lowest with an overcast sky. So plotting the temperature differential to environmental conditions could give some indication of the mechanism involved.

2. The statistical toolbox used is rich -- but one wonders how replicable results might be under conditions beyond those of the experiment if there is no mechanistic understanding of the process. The 'machine learning' methods are deemed successful in 'fitting', but results are not presented in a way that allows others to use them in new settings.

Minor:

sipctatum ==> spicatum

Anonymous Referee 

Received and published: 07 December 2021

 “Estimation Standard And Seeded Pan Evaporation Using Modelling Approach” by Brigitta Simon-Gáspár et al.

General comments

The paper concerns a topic consistent with the research domain of the Special issue:

Experiments in Hydrology and Hydraulics in the HESS journal.

The authors used FAO-56 Penman-Monteith equation (FAO56-PM), multiple stepwise regression (MLR) and Kohonen self-organizing map (K-SOM) techniques to estimate daily pan evaporation (Ep) in three treatments. And in an six-season experiment. The 10 modelling approach included six measured meteorological variables were compared and evaluated. The results showed that the MLR method provided close compliance with the observed pan evaporation values, but the K-SOM method gave better estimates than the other methods.

I really appreciate the huge work made by the authors. However, I have some questions about the innovation of the research method and the purpose of this study. First, the ,methods of FAO-56 Penman-Monteith equation (FAO56-PM) (Allen et al., 1998), Kohonen self-organizing map (K-SOM) techniques (Kohonen, 1982) and multiple stepwise regression (MLR) are classic, but also relatively old methods. Predecessors have done a lot of research and published a lot of relevant papers on the comparison of these methods. If only a few traditional, classical methods are compared and discussed, I think that there is not enough innovation in terms of methodology to be published in HESS, and there are already many ready-made papers on comparative studies of evaporation calculation methods. In addition, the authors said that “there is little information in the literature on how submersed macrophytes affect the evaporation of a lake” in Introduction (Lines 64). Is this statement supported by the literature? (Wang, J.H. 1994. Effects of aquatic plants on water surface temperature and evaporation. Arid Land Geography, 17(2), 3. doi: CNKI:SUN:GHDL.0.1994-02-009).

The second main aim of this paper was to estimate daily Ep using FAO-56 Penman-Monteith (FAO56-PM), Kohonen self-70 organization map (K-SOM) and multiple stepwise linear regression (MLR) methods. Since this purpose is only the comparison and evaluation of several traditional methods, and I personally still feel that the innovation is not sufficient for HESS.

Specific Comments

1. English language needs to be modified. I found several unclear sentences that make it difficult to understand the analysis and results carried out.
2. The description at the beginning of the Abstract is too simple and empty, two to three sentences should be used to focus on the shortcomings of the current study and the innovation of this study.
3. Some of the references in the Introduction are too old. It is suggested that the author update some relevant studies recently published.
4. The font resolution in Figure 1 is too low to see the relevant text clearly. I suggest the author to redraw it.
5. The numeric font in equation 2 is suggested to be Times New Roman, and the rest of the formula is the same.
6. In Materials and methods, it would be better to give specific steps about the experimental design of this study, the current presentation is relatively sketchy.
7. The Results and Discussion session. I found some good results from this study, but unfortunately the authors' description of these results is too brief (Both in Figures and Tables)and suggest a more specific analysis and evaluation of the results. And the discussion was not in-depth enough and was only a brief description of the Results. It is recommended to fully evaluate and discuss the results obtained by several different methods used in this study in terms of the mechanism of influence.
8. The content of the conclusion should not be a simple retelling of the results and discussion, but also a more in-depth explanation of the scientific significance and potential application value of the study, rather than the kind of formulaic statement in the last paragraph of the conclusion.
9. I am not quite sure if the current hess format requires line numbers to be marked every five lines, which causes some reading difficulties, if not required by the journal format, it is recommended that authors mark all line numbers.

This paper discusses a way of modeling pan evaporation using 3 methods: the Penman-Monteith equation, multiple step-wise regression, and the Kohonen self-organising map.  The novel element to this work appears to be the fact that the pan evaporation was measured with 3 class A pans but two contained sediment and one contained submerged macrophytes on top of sediment. To me, this is the part that sets the paper apart and is important, because the authors are trying to create more realistic conditions for the observational experiment before using the data for a modelling study. 

I liked the part of the discussion lines 248-250 where the authors discuss the low winds in this study and in earlier studies.  I think that the fact that they honestly state a kind of negative result is helpful and proper.

1. I was disappointed that the methods were not discussed in more detail, in particular, the Kohonen self-organising map method.  I can see that proper citations are given, and that this method has been applied to evaporation modelling before. However, I think that the paper would benefit greatly from an introduction to the Kohonen method. Then all 3 methods could be explained to the reader alongside the relevance to the physical process being studied.  Why were these methods chosen in the first place?  What are the pros and cons to these methods?

2. Figure 5 should be explained. I can see that this is related to figure 3 but the links are not made clear. The x and y axes are not labelled in either figure. How do the hexagons map to the inputs or outputs? I can't figure this out from reading the manuscript. Also, I found no definition for "importance" in the caption. This is part of the lack of time spent discussing and explaining the relevance of the methods used in the study.

3. Tables 1 and 2 are very large and comprehensive. While I think that the information is critical to explaining the conclusions of the paper, I do not think that the information in them is easy to make sense of. Is there any way that the tables could be re-organised or even some of the information could be turned into figures to display the information in a clearer way? One suggestion for table 2 is to keep  information for the correlation values only in the tables, but to put all the statistics (max, min, mean, std. dev.) in a figure with sub panels.  Are all the statistics relevant?  Perhaps the authors could be a bit more selective?  I agree that information on the full, training and testing data should be presented. 

4. Figure 1 was not displayed with very high resolution. Could the authors provide a higher quality figure?

5. Figure 4 box plot whiskers and circles are not clearly defined.  Software packages which compute these types of diagrams are not all the same.  Please could the range (and meaning) of the box lenghth, whiskers and circles  be stated explicitly.

6. Table 1 has three lines at the bottom saying "Based on observed means" but I don't know what these lines are referring to. Is it the full, training and testing data sets?

Minor corrections

In figures with multiple panels, the sub-panels should be labeled with letters (a, b, c,...) in order to make the discussion of the results clearer in the body of the paper and make it easier to clarify the definitions in the captions. 

L167 "displays a regular pattern" does not make sense to me. Can the authors make clearer what the Relative humidity and global radiation statistics are exhibiting and why it is important to notice this?

 

L178 Where is F defined?  I could not find it.

L241 Please change "few" to "little"

L247 Please change "researches" to studies"

L273 Please change neural network to "a neural network approach". 

L290 the range or tuple presented is unclear. Is "(-0.42-0.44)" really (-0.42 to -0.44) or (-0.42, -0.44)?  Also, it seems strange to put the larger number -0.42 in front of -0.44 if indeed they both are negative.

L296 Please change "has high priority" to "is superior to".  I'm not sure about the phrase "prediction precision"  precision sounds like a computational error here. Are you talking about skill? High correlation or low RMSE?  Is there a better way to phrase this? 

TITLE: Estimation Standard And Seeded Pan Evaporation Using Modelling Approach

Reviewers' comments:

In this paper, K-SOM and other methods are used to improve the estimation of lake evaporation, which is conducive to accurately estimate the total lake evaporation and improve the climate effect of the lake under the background of climate change. I recommend publication of the paper in HESS after revision.

Major comments

Has this article been studied by simulation at Keszthely, Hungary. However, how do you consider the effect of the evaporation of non-uniform underlying surfaces, such as mountains, and grass?

This paper improves the calculation method of lake evaporation, and further analysis of lake evaporation and its climate effects are needed on the Lake Balaton in the future.

Minor comments

Figure 1 should be topography.

L.47 The unsupervised NNs, including Kohonen Self Organizing Maps (K-SOM), has several advantages (Kohonen, 1982). Full name should be given for the first occurrence‘NN’.

L.16-20 Performances of the different models were compared using statistical indices, which included the root mean square error (RMSE), mean absolute error (MAE), scatter index (SI) and Nash-Sutcliffe efficiency (NSE). The results showed that the MLR method provided close compliance with the observed pan evaporation values, but the K-SOM method gave better estimates than the other methods. Overall, K-SOM has high accuracy and huge potential for Ep estimation for water bodies 20 where freshwater submerged macrophytes are present. This section need to be rewrite.

L.84 (latitude: 46°44′N, longitude: 17°14ʹE, elevation: 124 m above sea level) ‘above sea level’ Can be abbreviated as a.s.l.

L.231 From the figure, it can be observed that most of the estimated daily Ep values are close to the observed daily Ep values for all three pan treatments.

Which figure?

Many researchers have conducted research with neural networks aimed at the estimation of Ep as a function of meteorological variables (Keskin and Terzi, 2006). Several of these researchers found better results in Ep estimation with neural network than those obtained from the Priestley-Taylor and the Penman methods (Rahimikhoob, 2009; Malik et al., 2020). Consistent with other studies, this study demonstrated that modelling of Ep is possible through the use of K-SOM technique in addition to the 275 FAO56-PM and MLR methods. The comparison results indicated that, in general, the K-SOM model was superior to the FAO56-PM and MLR methods. Chang et al. (2010) used different methods to estimate pan evaporation, including also the KSOM and the FAO56-PM. According to the results of Chang et al. (2010), K-SOM was the best of the studied methods, and it was found that the Penman-Monteith method is also likely to underestimate evaporation. Malik et al. (2017) used four heuristic approaches and two climate-based models to approximate monthly pan evaporation, where the K-SOM model performed better than the climate-based models. The regression line in scatter plots has R2 as 0.937 for K-SOM model at Pantnagar and Ranichauri (India), respectively. In the study of Malik et al. (2017), RMSE values were 0.685 and 1.126 for K-SOM, when 50% of the total available data was used in the testing of models in two stations. This section should be put in the introduction.

Line 280 The regression line in scatter plots has R2 as 0.937 for K-SOM model at Pantnagar and Ranichauri (India), respectively. ‘Respectively’ can be deleted.

Can the confidence of the correlation coefficient pass the significance test?

In this manuscript, the authors use three methods to calculate daily evaporation during summer months (Jun to Sep) at a experimental site in Hungary. The three methods are the FAO Penman Monteith (PM) method, multiple stepwise regression and Kohonen self-organizing (SOM) maps. All methods are provided with observed meteorological time series for the years 2015 to 2020 as input. Simulated values are then compared to the observed evaporation estimates of three evaporation pans. The difference between the three pans is that one is a standard open water pan, one pan is partly filled with sedimentes and one with water living plants. Overall, the Kohonen self-organizing maps yield by far the closest match to observed evaporation estimates for all three pans.

The topic of evaporation estimates is fundamental to land-surface hydrology. For example, the PM method is frequently used to estimated potential evaporatin in hydrologic models. Errors in the PM methods will bias any subsequent hydrologic modeling. Despite the fact, that the topic of the manuscript is of general importance, the structure of the manuscript is poor and needs to increase substantially. One important issue is that I could not find that all findings listed in the abstract and the conclusions mentioned in the abstract are supported by the main text. Additionally, the methods part does not provide all details to follow what the authors did exactly. This does concern the PM method and the SOM method. I am convinced that the comparison of evaporation estimation methods for the three pans (in particular Figure 6) are valuable findings that should be reported, but the manuscript needs to be substantially improved.

Most importantly, the authors should decide what their main focus of the study is. Is it the effect of macrophytes on evaporation or is it the different estimation methods? At the moment, this is not clear. I would suggest the former to be the more interesting subject.

Abstract:

L. 14ff: I don't think that the statement regarding the correlation of RH is supported by the findings of this study. See my comment below regarding L. 218ff.

The conclusion mentioned in the abstract on line 19f is not given anywhere else in the manuscript. It is unclear how the authors come to this conclusion or what they mean with "potential".

Introduction:

Section starting at line 52 is a collection of statements that do not follow a apparent logical structure. It is not clear to me what the authors wish to express here.

Methods:

L. 110f: The data described in Section 2.1 is not sufficient to apply the Penman-Monteith equation. Section 2.1 states that global radiation R_s is measured but Penman-Monteith equation requires net radiation and ground heat flux. How are the latter two derived?

Results:

L. 187f: There are only four lines describing the results of table 2. This is not well balanced. Either the text needs to be expanded or the table shortened.

L. 206f: I am not an expert in self organizing maps. I don't know how to interprete characteristics shown in table 3 and the authors only describe the last two lines in this table.

L. 218ff: "Thus, the correlation..." This sentence is confusing to me. First, it should state observed values and not modeled values. Second, it is shown in table 2 that RH is negatively correlated with E_p which is expected. Here, the authors state that red colors in Figure 5 show high correlation. For RH, the values are substantially higher than for any other variable suggesting a higher impact. This suggests to me that the SOM algorithm is not able to reproduce the relationships reported in table 2.

L. 231: I disagree with this statement. How can the authors state that all three methods are close to observed values, when coefficient of determination varies from 0.11 for Penman-Monteith method to 0.97 for self-organizing maps. I think it is fair to state that the Penman-Monteith method is not able to reproduce the observed values. It is not clear to me whether the authors did apply the Penman-Monteith equation correctly because not all details are provided in the manuscript (see comment above).

Discussion:

L. 256f: There are results reported in the discussion section. This should be moved to the results section and is not a clear manuscript structure.

L. 271ff: This section lists findings of other studies but does not provide a discussion of these results against the findings of the present study. 

Minor comments:

L. 9: There is a misleading typo here: the A should not be capital.

L. 110f: Which equation was used to derive e_s and e_a from RH?

L. 118ff: Section 2.4 is not understandable to readers who are not familiar to SOM. It needs to be rewritten using an easier language. Figure 3 is also very confusing. Also, E_p is mentioned in Figure 3 as input variable, but this cannot be correct. I guess that observed E_p is used during training to compute an error measure.

L. 139: The sentence regarding the splitting of the data is incomplete.

L. 184: Table 1 can be moved to the appendix because it is not central to the goal of the manuscript.