What is the Priestley-Taylor Wet-Surface Evaporation Parameter? Testing Four Hypotheses

Crago, Richard; Szilagyi, Joszef; Qualls, Russell

doi:https://doi.org/10.5194/egusphere-2022-712

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https://doi.org/10.5194/egusphere-2022-712

Preprints

24 Oct 2022

| 24 Oct 2022

What is the Priestley-Taylor Wet-Surface Evaporation Parameter? Testing Four Hypotheses

Richard Crago, Joszef Szilagyi, and Russell Qualls

Abstract. This study compares four different hypotheses regarding the nature of the Priestley-Taylor parameter α. They are: 1) α is a universal constant; 2) the Bowen ratio (H/LE, where H is the sensible and LE is the latent heat flux) for equilibrium (i.e. saturated air column near the surface) evaporation is a constant times the Bowen ratio at minimal advection (Andreas et al., 2013); 3) minimal advection over a wet surface corresponds to a particular relative humidity value, and 4) α is a constant fraction of the difference from the minimum value of one to the maximum value of α proposed by Priestley and Taylor (1972). Formulas for α are developed for the last three hypotheses. Weather, radiation and surface energy flux data from 171 FLUXNET eddy covariance stations were used. The condition LE_ref/LE_p>0.90, was taken as the criterion for nearly-saturated conditions (where LE_ref is the reference and LE_p is the apparent potential evaporation rate from the Penman (1948) equation). Daily and monthly average data from the sites were obtained. All formulations for α include one model parameter which is optimized such that the root mean square error of the target variable was minimized. For each model, separate optimizations were done for predictions of the target variables α, wet surface evaporation (α multiplied by equilibrium evaporation rate) and actual evaporation (the latter using a highly-successful version of the complementary relationship of evaporation). Overall, the second and fourth hypotheses received the best support from the data.

Received: 28 Jul 2022 – Discussion started: 24 Oct 2022

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Journal article(s) based on this preprint

08 Sep 2023

What is the Priestley–Taylor wet-surface evaporation parameter? Testing four hypotheses

Richard D. Crago, Jozsef Szilagyi, and Russell J. Qualls

Hydrol. Earth Syst. Sci., 27, 3205–3220, https://doi.org/10.5194/hess-27-3205-2023,https://doi.org/10.5194/hess-27-3205-2023, 2023

Short summary

Richard Crago, Joszef Szilagyi, and Russell Qualls

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-712', Anonymous Referee #1, 25 Nov 2022

Please see the attached file.

Citation: https://doi.org/10.5194/egusphere-2022-712-RC1
- AC1: 'Reply on RC1', Richard Crago, 24 Jan 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-712/egusphere-2022-712-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-712-AC1
RC2:
'Comment on egusphere-2022-712', Anonymous Referee #2, 09 Dec 2022

This manuscript comparatively tests four hypotheses of the Priestley-Tyalor wet-surface evaporation and calculated the corresponding parameters. It is an interesting work for the research on evaporation, from both the theoretical and application perspetives. I think it is worth for publishing after addressing several comments below.

Major comments:

1. The criterion of LEref>0.9LEp for wet surface conditions requires acurate wind function f(u) for LEp. The actual wind function may vary with the aerodynamic conditions, the boundary layer characteristics, or even the magnitude of wind speed. The wind function (3) with the fixed canopy height used in this study may derivate from the actual one (Han et al., 2021), especially with the growth of the vegetation. Let’s write Ep with fixed wind function (3) as Ep’. E=alpha*Ee is equivalent to E/Ep’= alpha*Ee/Ep’. Then, E/Ep’ may be substantially less than 0.9 by using wind function (3) with fixed canopy height, and substantial data which should be taken as under wet surface conditions may be excluded. Under this conditions, the RH may be limited to large values artificially to make sure that Ee/Ep’>0.9. So, an evaluation on the result of the chosen for near wet surface conditions is needed, against other methods, or on the real wet surfaces, such as wetlands. What is the proportion of data left for a permanent wetlands by this criterion with the fixed wind function?

2. The result of the third hypothesis with large values of RH near the unity (Table 2 and 3) may be affected by above data chosen method, as Ee/Ep’>0.9 requires large RH.

3. For the hypothesis 4. Are the days of months with negative Href were excluded? Then, the data outside the range of Eq. (6) were excluded. The results may be influenced by this.

4. Table 2 and 3 only supply the optimized parameter of the other three hypotheses. How the calculated alpha varies? Are the mean or median values related with ac?

5. Line 397: The Priestley-Taylor coefficient was not regarded a constant in Han and Tian (2018), but with seasonal variations, to the best of my knowledge. Please refer to Han et al., (2021).

6. Lines 400-410. The performance with constant ac is good by considering all the data. But bias exist under the conditions with small values or large values of LEref, as shown in Figure 3. Is it possible to give some discussion?

Other comments:

1. Page 16 and 17, Typo for Table 2 and 3.

2. Table 2. The intercept of RH with optimized LE is 15.54, but 15.52 in Figure 4.

3. Line 342: four hypotheses?

Reference:

Han, S., Tian, F., Wang, W., & Wang, L. (2021). Sigmoid generalized complementary equation for evaporation over wet surfaces: A nonlinear modification of the Priestley–Taylor equation. Water Resources Research, 57(9), e2020WR028737. doi:10.1029/2020wr028737

Citation: https://doi.org/10.5194/egusphere-2022-712-RC2
- AC2: 'Reply on RC2', Richard Crago, 24 Jan 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-712/egusphere-2022-712-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-712-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-712', Anonymous Referee #1, 25 Nov 2022

Please see the attached file.

Citation: https://doi.org/10.5194/egusphere-2022-712-RC1
- AC1: 'Reply on RC1', Richard Crago, 24 Jan 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-712/egusphere-2022-712-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-712-AC1
RC2:
'Comment on egusphere-2022-712', Anonymous Referee #2, 09 Dec 2022

This manuscript comparatively tests four hypotheses of the Priestley-Tyalor wet-surface evaporation and calculated the corresponding parameters. It is an interesting work for the research on evaporation, from both the theoretical and application perspetives. I think it is worth for publishing after addressing several comments below.

Major comments:

1. The criterion of LEref>0.9LEp for wet surface conditions requires acurate wind function f(u) for LEp. The actual wind function may vary with the aerodynamic conditions, the boundary layer characteristics, or even the magnitude of wind speed. The wind function (3) with the fixed canopy height used in this study may derivate from the actual one (Han et al., 2021), especially with the growth of the vegetation. Let’s write Ep with fixed wind function (3) as Ep’. E=alpha*Ee is equivalent to E/Ep’= alpha*Ee/Ep’. Then, E/Ep’ may be substantially less than 0.9 by using wind function (3) with fixed canopy height, and substantial data which should be taken as under wet surface conditions may be excluded. Under this conditions, the RH may be limited to large values artificially to make sure that Ee/Ep’>0.9. So, an evaluation on the result of the chosen for near wet surface conditions is needed, against other methods, or on the real wet surfaces, such as wetlands. What is the proportion of data left for a permanent wetlands by this criterion with the fixed wind function?

2. The result of the third hypothesis with large values of RH near the unity (Table 2 and 3) may be affected by above data chosen method, as Ee/Ep’>0.9 requires large RH.

3. For the hypothesis 4. Are the days of months with negative Href were excluded? Then, the data outside the range of Eq. (6) were excluded. The results may be influenced by this.

4. Table 2 and 3 only supply the optimized parameter of the other three hypotheses. How the calculated alpha varies? Are the mean or median values related with ac?

5. Line 397: The Priestley-Taylor coefficient was not regarded a constant in Han and Tian (2018), but with seasonal variations, to the best of my knowledge. Please refer to Han et al., (2021).

6. Lines 400-410. The performance with constant ac is good by considering all the data. But bias exist under the conditions with small values or large values of LEref, as shown in Figure 3. Is it possible to give some discussion?

Other comments:

1. Page 16 and 17, Typo for Table 2 and 3.

2. Table 2. The intercept of RH with optimized LE is 15.54, but 15.52 in Figure 4.

3. Line 342: four hypotheses?

Reference:

Han, S., Tian, F., Wang, W., & Wang, L. (2021). Sigmoid generalized complementary equation for evaporation over wet surfaces: A nonlinear modification of the Priestley–Taylor equation. Water Resources Research, 57(9), e2020WR028737. doi:10.1029/2020wr028737

Citation: https://doi.org/10.5194/egusphere-2022-712-RC2
- AC2: 'Reply on RC2', Richard Crago, 24 Jan 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-712/egusphere-2022-712-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-712-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (25 Feb 2023) by Stan Schymanski

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.

Hide

AR by Richard Crago on behalf of the Authors (06 Apr 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (30 May 2023) by Stan Schymanski

RR by Anonymous Referee #1 (04 Jun 2023)

RR by Anonymous Referee #2 (30 Jun 2023)

ED: Publish subject to minor revisions (review by editor) (20 Jul 2023) by Stan Schymanski

AR by Richard Crago on behalf of the Authors (25 Jul 2023) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (27 Jul 2023) by Stan Schymanski

AR by Richard Crago on behalf of the Authors (27 Jul 2023) Author's response Manuscript

Journal article(s) based on this preprint

08 Sep 2023

What is the Priestley–Taylor wet-surface evaporation parameter? Testing four hypotheses

Richard D. Crago, Jozsef Szilagyi, and Russell J. Qualls

Hydrol. Earth Syst. Sci., 27, 3205–3220, https://doi.org/10.5194/hess-27-3205-2023,https://doi.org/10.5194/hess-27-3205-2023, 2023

Short summary

Richard Crago, Joszef Szilagyi, and Russell Qualls

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https://doi.org/10.5194/egusphere-2022-712-supplement

Richard Crago, Joszef Szilagyi, and Russell Qualls

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Short summary

The Priestley-Taylor equation is widely used in hydrologic, climate and meteorological models to estimate evaporation. Alpha represents the impact of dry air that is carried into the region; this occurs even in extensive saturated regions. Four hypotheses regarding the nature of alpha are evaluated. Data from 171 FLUXNET stations were used to test the hypotheses. The best-supported hypothesis sees alpha as a constant fraction of the distance between theoretical minimum and maximum values.

What is the Priestley-Taylor Wet-Surface Evaporation Parameter? Testing Four Hypotheses

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