the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Role of timeaveraging of eddy covariance fluxes on water use efficiency dynamics of Maize crop
Abstract. Direct measurement of carbon and water fluxes at high frequency makes eddy covariance (EC) as the most preferred technique to characterize water use efficiency (WUE). However, reliability of EC fluxes is hinged on energy balance ratio (EBR) and inclusion of lowfrequency fluxes. This study is aimed at investigating the role of averaging period to represent EC fluxes and its propagation into WUE dynamics. Carbon and water fluxes were monitored in a dripirrigated Maize field at 10 Hz frequency and are averaged over 1, 5, 10, 15, 30, 45, 60, and 120 minutes considering daytime unstable conditions. Optimal averaging period to simulate WUE fluxes for each growth stage is obtained by considering cumulative frequency (ogive) curves. A clear departure of EBR from unity was observed during dough stage of the crop due to ignorance of canopy heat storage. Error in representing water (carbon) fluxes relative to the conventional 30 min. average is within ± 3 % (± 10 %) for 10–120 min. averaging and is beyond ± 3 % (± 10 %) for other timeaverages. Ogive plots conclude that optimal averaging period to represent carbon and water fluxes is 15–30 min. for 6^{th} leaf and silking stages, and is 45–60 min. for dough and maturity stages. Dynamics of WUE considering optimal averaging periods are in the range of 1.49 ± 0.95, 1.37 ± 0.74, 1.39 ± 0.79, and 3.06 ± 0.69 μmol mmol^{1} for the 6^{th} leaf, silking, dough, and maturity stages respectively. Error in representing WUE with conventional 30 min. averaging is marginal (< 1.5 %) except during the dough stage (12.12 %). Our findings can help in developing efficient water management strategies by accurately characterizing WUE fluxes from the EC measurements.
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RC1: 'Comment on amt2023253', Anonymous Referee #2, 25 Feb 2024
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General comments
The authors present a study of the impact of eddy covariance (EC) averaging time on estimation of water use efficiency (WUE). While the impact of averaging of eddy covariance flux results has been extensively studied, the impact on WUE specifically has not. Therefore, the manuscript provides a contribution to broadening understanding of the important aspect of EC flux processing on results.
The authors perform analysis of how different averaging times (varying over a broad range of 1, 5, 10, 15, 30, 45, 60, and 120 minutes) affect the results during different stages of Maize crop development. The main finding of the study is that, whereas the commonly applied 30 min averaging is a good choice for most of the conditions, the longer averaging times yield better results during the dough development stage. The need for longer averaging period must result from different prevailing observational and/or meteorological conditions. The authors have not analyzed the underlying main drivers that determine the need for longer averaging time. They have suggested that canopy heterogeneity might be one of the reasons. I suggestion to perform additional analysis of prevailing conditions (minimum wind speed and direction, which could hind also impact of heterogeneity, and stability) during different canopy stages to be able to make link with optimal averaging times.
One important clarification is needed regarding the detrending and averaging. Section 2.2: Did you use linear detrending and then block averaging? Since linear detrending performs as additional highpass filter then this is very important to be very specific and emphasize also in Abstract and Conclusions. Without linear detrending the optimal averaging times could be different.
The main emphasis of the manuscript is to evaluate the impact of the averaging time on WUE. Please also conclude if the choice of averaging time for accurate determination of WUE is different from energy and carbon fluxes (fluxes of scalars).
Detailed comments
 9. The lowfrequency flux inclusion is not the only factor and not under all observation conditions that might affect the accuracy of the EC flux estimates. Please be more specific with statement.
 1314. Canopy heat storage should net be a significant factor over a relatively long period of time.
 1618: what were the main driving factors that the optimal averaging time differed for different stages of canopy development? See my main comment.
 32. The abstract states the error compared to 30 min averaging was marginal except for dough stage. Be more specific, e.g. 30 min averaging is not sufficient for all conditions.
 34. The sentence is missing some word, for example “Different averaging time need to be used following the crop growth stage”.
 51, the symbol colon (:) looks redundant after “water productivity”
 6162, readability would benefit from rearranging the parenthesis, e.g. “WUE is estimated as the ratio of gross primary product (GPP: proxy for photosynthesis) to evapotranspiration (ET: proxy for water consumption).
 112, the average + error after “Temperatures are high during summer” and “low during winter”: what do these errors represent?
 142143: Did you use linear detrending and then block averaging? Also, I assume this was “to derive” turbulent fluctuations and not “to correct”.
 151, what is friction velocity correction? Do you mean filtering of nighttime observations according to friction velocity threshold? Be specific here.
 159: lack of conservation should be “lack of energy balance closure”.
 168: where this specific threshold EBC >= 0.7 comes from that ensures reliability of EC fluxes? Please be more specific and/or provide references.
 180: the main challenge with realworld data is data the spectral gap is obscure or difficult to identify. Otherwise, the choice of the averaging time would be simple task.
 195, also section 2.2, did you perform coordinate rotation at the same time interval basis as the averaging?
 203204: how did you define the optimal averaging period?
 207, eq. (5), since this is RMSE error, the square root should be taken from the value in squared? Which is missing in the expression.
 221222, fig 1. Denote the subplots with relevant averaging times. Currently it is not possible to follow which plot corresponds to what averaging time.
 267, and the main comment: please analyse the potential impact of meteorological conditions (wind speed and direction, stability). The wind direction variability might provide better insight related to landscape heterogeneity; currently this remans a hypothesis.
 L. 361, Fig. 8: what does the circle size represent? Also, how did you compare e.g. 45 min and 30 min averaging (45 min period does not fully overlap with 30 min period)? Plot c) looks inconsistent (or difficult to interpret). How do you interpret that for carbon dioxide and water the correlations between different averaging times are all very good but for WUE not. One would expect that closure averaging times (for example 45 min and 30 min) correlate better than more different (e.g. 45 min and 15 min). Could the specific “pattern” of this plot be the result of periods mismatch?
Citation: https://doi.org/10.5194/amt2023253RC1 
RC2: 'Comment on amt2023253', Anonymous Referee #3, 26 Feb 2024
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The current study utilizes micrometeorological measurements to evaluate the effect of the averaging time on turbulent flux estimates obtained by the Eddy Covariance (EC) method. This topic has been extensively explored over the last few decades. However, such investigations on sites with different characteristics are always relevant. The manuscript novelty is the determination of optimal averaging time in a dripirrigated maize field site. The remarkable result is the determination of the optimal averaging time for the different plant growth stages. The turbulent fluxes, estimated using the optimal values, are compared with those obtained using the usual value of 30 min, widely used in unstable daytime periods. The authors also showed how the improvement in flux estimates affects the values of related variables such as water use efficiency (WUE).
The current version of the manuscript is well structured. All sections are also clearly presented. However, I suggest some questions and corrections that should be addressed to improve the overall manuscript.
I  Geral comments:
1) As the author mentioned in the manuscript, “Optimal averaging period (T1) should be long enough to reduce random error (Berger, 2001) and short enough to avoid nonstationarity associated with advection (Foken & Wichura, 1996)”. In summary, the core of the presented analysis is how accurate the eddy covariance method is to account for the transport associated with eddies of different sizes. Generally, the eddies sizes in an unstable boundary layer strongly depend on the wind stress and sensible heat flux at the vegetated surface, which in turn depend on the overall characteristics of the rough elements in the surface (plants). This is briefly mentioned in the text (lines 229–231) but is not linked with the obtained results.
2) Turbulent transport in an unstable (daytime) boundary layer is dominated by large convective eddies with time scales larger than 1520 minutes [1]. Is there a reason to include short averaging times (1, 5, 10, and 15 min) in the analysis?
II  Specific comments:
1) Lines 139140: IRGASON is the model of the integrated system anemoter 3D – IRGA. As mentioned in the text, it sounds like two sets of instruments are used.
2) Line 140: “to measure CO_{2} and H_{2}O fluxes …”. These instruments do not measure fluxes directly but wind speed components, air temperature, and H_{2}O and CO_{2} concentrations.
3) Line 163: “The block average method and linear detrending method”. The authors used a series of corrections and quality control tests to ensure the best flux estimates. However, the block average acts as a highpass filter depending on the block size, neglecting the fluxes associated with the lowfrequency fluctuations. This influences the results obtained in the paper. What is the block size used for this analysis?
4) Line 194: equation (2) – This equation defines the mass fluxes, as represented in eqs. (3) and (4), used to obtain WUE. To avoid being misunderstood, it is also useful to define the expressions for the turbulent energy fluxes (Le and H) used in the definition of EBR (eq. (1)).
5) Line 243: equation (7) The therm [(RnG)_{i} – (H+LE)_{i}] should be squared to ensure real values by the root squared.
6) Figure 1: To increase figure quality. The axis labels and ticks are too small. The author should indicate which subplot corresponds to each averaging time.
7) Line 281:What does “r” represent? It was not defined before.
8) Line 283: I suggest using “short” and “long” averaging periods.
9) Line 283: “Our findings show that averaging period has minimal influence in representing the energy balance terms”. This sentence is true on average for several days (and different plant stages). Individually, the averaging time effects the components of the energy balance, as represented by the large scatter in the inset plots for the short average times.
10) Line 301: “Low EBR during the crop cycle can also be attributed to the ignorance of energy transport associated with large eddies from landscape heterogeneity, which is not captured by the EC system”. Can you explain this hypothesis better? Is there such landscape heterogeneity at the studied site? In this analysis, the mentioned large addies should have characteristics time scales greater than 60–120 minutes to not be taken into account by the EC method. Is there another reason why the EC system fails to account for such eddies?
11) Line 325: “RE in estimating water vapour fluxes is found to be insignificant at all averaging periods, irrespective of growth stage.” Again, it is important to emphasize that this is true for the averaged result (several days), not for each individual flux measurement. Figure 4b) (dough and maturity) shows the large variability in the relative error determined using either shorter or longer averaging times.
12) Figures 4a) and 4b) (dough and mature stages): Following the above argument, the large variability of RE, varying between positive and negative values, suggests that larger eddies (with time scales larger than 30 min) contribute to both positive and negative transport. This fact, by itself, is an indication that averaging times greater than 45 minutes are accounting for the effects of the submesoscale (nonturbulent) motions [2][3]. Therefore, 45 minutes can be approximately the timescale of the spectral gap.
13) Figures 5a) and 5b): Just a suggestion: normalize the ogive by the maximum value of each curve (integrated up to the lowest frequency). This parameter indicates the fractional contribution of each frequency to the total cumulative energy.
14) Lines 404405 and Figure 8): “This conclude that, the need for optimal averaging period is more crucial in estimating WUE fluxes rather than individual carbon and water fluxes.” This is what can be observed in Figure 8. However, it is not clear why the large linear correlation between the fluxes with different averaging times is not observed on the WUE chart. According to May appointments 9) and 11), a large variability in RE is observed. By definition of the WUE, we have to consider the ratio of two fluxes and their respective RE. My first guess is that this loss of linear correlation is associated with the difference in RE between the fluxes of CO_{2} e H_{2}O.
III Thecnical corretions:
1) Whole text: “min” is the symbol for the time unit “minute”. Therefore, the form “min.” with a dot is unusual.
2) Line 130: Change^{ “0}C” to “^{o}C”.
3) Line 244: Change “Where” by “where”.
4) Figure 3 a) and b): If possible, write the flux units in the correct notation.
5) Figure 6: Legend – change “(red)” by “(dotted)”.
6) Figure 4 and 7: Change time units from “[Min]” to “[min]”.
7) Line 488 and 581: To correct these references, there are typing errors.
IV References:
[1] Stull, Roland B. "Boundary layer clouds." An Introduction to Boundary Layer Meteorology. Dordrecht: Springer Netherlands, 1988. 545585.
[2] Voronovich, V., and G. Kiely. "On the gap in the spectra of surfacelayer atmospheric turbulence." Boundarylayer meteorology 122 (2007): 6783.
[3] Metzger, Meredith, and Heather Holmes. "Time scales in the unstable atmospheric surface layer." Boundarylayer meteorology 126.1 (2008): 2950.
Citation: https://doi.org/10.5194/amt2023253RC2
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