the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Behavior and Mechanisms of Doppler Wind Lidar Error in Varying Stability Regimes
- 1Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado, USA
- 2Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, Colorado, USA
- 3National Renewable Energy Laboratory, Golden, Colorado, USA
- 1Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado, USA
- 2Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, Colorado, USA
- 3National Renewable Energy Laboratory, Golden, Colorado, USA
Abstract. Wind lidar are widespread and important tools in atmospheric observations. An intrinsic part of lidar measurement error is due to atmospheric variability in the remote sensing scan volume. This study describes and quantifies the distribution of measurement error due to turbulence in varying atmospheric stability. While the lidar error model is general, we demonstrate the approach using large ensembles of virtual WindcubeV2 lidar performing profiling doppler-beam-swinging (DBS) scans in quasi-stationary large-eddy simulations (LES) of convective and stable boundary layers. Error trends vary with the stability regime, time-averaging of results, and observation height. A systematic analysis of the observation error explains dominant mechanisms and supports the findings of the empirical results. Treating the error under a random variable framework allows for informed predictions about the effect of different configurations or conditions on lidar performance. Convective conditions are most prone to large errors, driven by the large vertical velocities in convective plumes and exacerbated by the high elevation angle of the scanning beams. The violations of the assumption of horizontal homogeneity due to filtered turbulent velocity variances dominate the error variance, with the vertical velocity variations of particular importance. Range gate weighting contributes little to the variability of the error, but induces an underestimating bias into the horizontal velocity near the surface shear layer. Error in the horizontal wind speed and direction computed from wind components is sensitive to the background wind speed but has negligible dependence on the relative orientation of the instrument. Especially during low winds and in the presence of large errors in the u and v velocity estimates, the reported wind speed is subject to a systematic positive bias. Vector time-averaged measurements can improve the behavior of the error distribution with a predictable effectiveness related to the number of decorrelated samples in the time window. The approach in decomposing the error mechanisms with the help of the LES flow field extends to more complex measurement scenarios and scans.
Rachel Robey and Julie K. Lundquist
Status: final response (author comments only)
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CC1: 'Comment on amt-2022-73', Andrew Black, 22 Mar 2022
What interesting research, and seemingly powerful tools to use for years to come!
Figures 12 and 14 really bring the simulation data and lidar error to life. Could these be presented earlier in the paper? Perhaps swapping sections 2.1 and 2.2, and showing the 2D cross section of LES data with lidar beam overaly in the beginning to allow the reader to visualize the dataset.
The ridgeline plots are very compelling. Could you add one that includes the all of the 10-minute averaged data? This would illustrate the reduction in errors through time averaging you describe.
In figures showing statistical moments by height, the x-axes are scaled to the data. In some cases, this highlights interesting trends, and they should remain, but I wonder if auto-scalaing obscures a conclusion: the errors are small. Deciding when errors are significant, and when they are insignificant is a key part of this paper.
p15, L351 "inflection point"
p176, L374 "will converge"
In Section 4, did you consider illustrating some of the error trends as functions of atmospheric parameters like instantaneous (or 10-minute) wind shear, turbulence, etc? Perhaps you could pick only one measurement height to do this instead of the full profile, and then illustrate various errors as functions of upstream errors.
In Fig 14, add color-coded trendlines for each stability class (instead of only the dashed white line). The positive bias in the low speed Strong CBL seems to be a key finding. Highlight it as best you can. Could you show the same graph but perhaps for the most and least biased heights?
Section 4.5 illustrate the rapid decay of error with time averaging, it's very steep and interesting for wind energy folks who only ever think of 10-minute averages.
How can your illustrations complement your conclusions most strongly? In some cases you might want to clearly focus on one height instead of showing the whole profile.
Forgive me if any of my comments are addressed elsewhere in the paper. There is a lot to digest. This paper is so thorough and really excellent.
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RC1: 'Comment on amt-2022-73', Anonymous Referee #1, 27 Mar 2022
General comments:
This is an interesting study that tackles a fundamental problem for the Doppler wind lidar observations which is the better understanding of the measurements’ error. The authors used large-eddy simulations for different atmospheric stability conditions and analyzed which mechanisms drive the errors under each condition. This study can be very useful for researchers studying turbulence as observed by a Doppler wind lidar. It could help them understand possible error biases or the cause of large errors. It also shows the importance of multiple scans so that the observations can be averaged over time to decrease the error. I believe this study is worth publishing. Nevertheless, the authors should make several changes in the manuscript in order to improve it’s structure. In the current state, it is difficult to read through. Introduction, methodology, results and conclusions are mixed, the authors should set apart these chapters to improve the flow of the manuscript. In the current version, parts of the introduction are presented in the methodology, whereas parts of the methodology are introduced in the results and some results are presented but discussed in a later section. In the conclusions, a summary of the work with the main points of the results should be presented, however the authors make a comparison of their results with previous studies and furthermore they introduce new references. Regarding the abstract, the results should be supported by numbers so it will be evident that these are the results of the current study. Some terms should be explained better throughout the study, so it is clear to the reader what is the magnitude of terms such as the “strong winds” or the “large structures”. The figures and their captions need corrections as well. All the important information should be included in the plot with the description written in the caption, rather than important information, such as the colour of the lines, only explained in the caption. The language in the manuscript is fluent. Please find my comments below.
Scientific comments:
Page 2 Line 27-29: The authors mention that lidar data offer an indirect representation of the flow field. Although it is true that the wind lidar observations most likely need extra steps to extract the wind components compared to sonic anemometers, it is possible to directly observe the wind components if the beams are aligned with the wind direction e.g. horizontal beams with no elevation angle alongside the wind direction or vertical beams for the vertical wind.
P2 L45-47: Similarly to my previous comment. In the phrase “Questions about measurements of vertical velocities”; do the authors mean vertical velocities variances? Because vertical velocity can be directly measured by the Doppler wind lidar and in fact even the vertical velocity variance is the “easiest” turbulence parameter that can be estimated using wind lidar observations, see Bonin et al. 2016: “Improvement of vertical velocity statistics measured by a Doppler lidar through comparison with sonic anemometer observations”.
P2-3 L59-62: The sentence “Compared to field studies of instrument accuracy, studies with virtual instruments in LES ….” should be supported by some relevant references for such studies.
P3 L67: The PALM model was developed by Raasch and Schroter, 2001: “A large-eddy simulation model performing on massively parallel computers”. The reference should be added in this sentence.
P4 L78-79: The Skamarock, 2008: “A description of the Advanced Research WRF version” reference should be included in this sentence.
P4 L82: The Chow et al., 2005 is not relevant here as they do not mention the WRF model in their study.
P10-11 L248-270: The authors state that they selected cases with “strong” and “weak” convective boundary layers. In line 262, these cases are characterized well-mixed layers. However, in Figure Table 1 we can see that the for the weak cbl the abl height is 525 m. This value seems to correspond to a developing boundary layer and not a well mixed. The authors should comment on that and whether these values can occur only in an ideal case of the simulation with a flat, homogeneous terrain etc. Moreover, the vertical range of the Windcube is portrayed in Figure 3 but it is not mentioned in the text and even in Table 2 it is not directly shown. This information should be included along with an explanation of this selection. The value is higher than the ABL height under stable conditions (170 m). Wouldn’t this affect the comparison? See also my comment regarding Figure 4.
P11 L266-267: The authors mention the limitation of the lidar range to include the entrainment zone. For the instrument, it is practically difficult to measure at this height due to the scarcity of aerosol in the zone. Do the authors refer to the instrument or the simulations? What are the limitations for a simulation?
P14: In Figure 4 panel (c), for the lower altitudes the median of the curve is not at zero as it also stated by the authors in P15 L356. The authors should explain at this point of the manuscript why this occur only at these particular levels of the SBL. It is also apparent from panel (c) that for the levels above the ABL height (170 m) the distribution becomes similar to the one near the surface. Any comments regarding this? Was this something the authors expected?
P15 L355: What could be the cause for overestimation during convective conditions?
P24 L506-507: The terms strong winds and strong shear are vague. Can you quantify these parameters? Is the underestimation expected above a specific threshold? Additionally, the argument that surface shear is one of the cause of the underestimation should be supported by some results in the form of Figures. Maybe the authors could add a secondary y axis with the wind speed and wind shear values at the different given heights in Figures 9, 10, 11. The estimation of the wind shear can be tricky but this claim should be supported by results.
P26 L540 & 548-550: Similarly to my previous comment, the term “large coherent structures” is vague. It is evident from Figure 12a that there are structures, upward motions followed by downward motions, of approximately 1 km size. On the contrary, for the stable boundary layer (Figure 12b) the size of the structures seems to be equal to few hundred meters. The lifecycle of such structures should be different. Do the authors categorize both structures’ sizes as large? The authors also mention larger scale structures above the boundary layer in the SBL. Do they mean from 170 m up to 350 m that is shown in Figure 12b or in higher altitudes? Either way it should be clear to the reader what are the sizes of the structures and these should correspond to the figures presented in the manuscript.
Technical comments:
P1 L1: Lidars instead of lidar.
P3: The full name for the abbreviation DBS should not be included in the caption of Figure 1, but rather in P4 L76.
In the first three instances Figure 1 is written with a capital F in the text, whereas in all the other instances figures in the text are written in parenthesis with a minor f. The citation of the figures should be consistent throughout the text.
P3 L72: The full name for the abbreviation SOWFA should be given here.
P3 L73: The full name for the abbreviation WRF-LES should be given here.
P7 L156: The parameter “c” is defined after the equation 7, although it is also part of the equations 5 and 6. In order to avoid confusion, I suggest to move the definition before or after the equation 5.
P7 L161: The sentence “Using parameters …. can be made concrete” needs rephrasing. It is confusing in its’ current state.
P7 L167-170: The paragraph “The form of the pulsed lidar …. further distances by a pulsed lidar” is more suitable for the introductory section. The comparison of the RWF between pulsed and continuous lidar seems out of place in the methodology as only the pulsed lidar was used for this study.
P7 L172: Remove the word “found”.
P7 L173: The “Spe” in the parenthesis is a missing reference?
P8 L185-188: The paragraph “Interpolation dominates … subsequent developments” comments on the interpolation method and possible improvements in the data and methodology section. This paragraph is more suitable for a section like Conclusions/Discussion.
P8 L190-199: In the first paragraph of Section 2.1.2 the authors provide some general information regarding the lidar and the different scanning methods such as RHI and PPI. As these methods are not used in the particular study, they should not be mentioned in the data and method section. In my opinion, this paragraph should be removed entirely from the manuscript as it does not provide any valuable information for the study.
P10: In Figure 3 the explanation for the different lines (solid, dashed etc) representing the parameters is only included in the captions and not in the figures, hence it is not practical for the reader to study these figures, similarly for Figures 5, 6 etc.
P13 L303: The claim that the components of equation 10 are commonly used should be supported by some examples-references.
P13 L305-308: A figure showcasing the sign convention could be useful for the reader.
P14: The authors have introduced several parameters for the wind speed such as ulidar or horizontal wind speed, therefore it should be clear in Figure 4 which one is shown including its’ name as defined by the authors.
P14 L324: Remove “the”.
P15-P16: The caption of the Figures 5 and 6 mention dashed and dotted lines but only dashed and solid lines are depicted. The figures should be corrected and additionally there should be a legend in the figure with this information.
P15: Figures should be easily readable even when separated from the rest of the text. In Figure 8, the caption is linked to the parameters of Figure 5 which should be corrected. The parameters should be included in the caption and the legend of Figure 8 independently from Figure 5.
P17 L374: Converge instead of converges.
P18 L401: The phrase “their respective height trends are similar to the previous section” should be accompanied by the respective values as a reminder for the reader.
P19-P33: In Chapter 4 the authors introduce several new equations. In my opinion, a manuscript flows better when all the equations and tools are presented in the data and methods chapter and subsequently the results are presented and discussed. So instead of presenting the figures in Chapter 3 and then using the equations to describe the results in Chapter 4, I believe it would be better if all the equations are already presented in Chapter 2 and the discussion of the results is moved to the corresponding figures. For example the explanation of the underestimation of the wind error although mentioned in Chapter 3 is explained much later in Chapter 4. By moving the equations to Chapter 2, the authors will also avoid repeating themselves.
P20: The caption of Figure 9 seems more like a part of the manuscript than a caption. It should be rephrased in a way to resemble a caption.
P21-22: It would be easier to interpret the results from Figures 9, 10, 11 if these figure were merged in multiple panels and thus it would be possible to use the same caption for all instead of linking to the caption of Figure 9 which makes the Figures unreadable independently.
P29 L616: The word “term” is used two times.
P30: The height of the wind speed is not mentioned in Figure 14. It should be included as part of the xaxis title.
P32: The legend showcasing the parameters that correspond to the colour lines is missing in Figure 16.
P32: The panels in Figure 16 are not numbered with (a), (b), (c) etc and the authors refer to the different plots as left and right panels. I believe it will be easier to use the numbering. Similarly the Figures 5, 6, 8, 9, 10, 11, 13, 17, 18 and the ones presented in Appendices A, D, E also miss the numbering.
P36-39: The comparison of the authors’ results with previous studies should be included in the sections of the results and not in the conclusions. The authors should summarize the key points of their study and not include new information in this chapter. Although it is possible to include some previously mentioned references in the conclusions, it is not recommended to introduce new references such as Klaas and Emeis, 2021 and Teschke and Lehmann 2017. These references should be introduced earlier in the manuscript.
P38 L840: Add the word of - “The form of our error….”
P52 L1117: Remove typo “ ”.
P52 L1119: Remove typo “&ndash”.
- RC2: 'Comment on amt-2022-73', Anonymous Referee #2, 11 Apr 2022
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EC1: 'Additional comments by Andrew H. Black on amt-2022-73', Ulla Wandinger, 28 Apr 2022
Dear authors,
We have received some additional comments on your manuscript after the open discussion had been closed. These comments are certainly valuable, and you may wish to consider them when preparing the revised version of your manuscript. Please find these comments attached in the supplement.Ulla Wandinger
Handling Editor of amt-2022-73
Rachel Robey and Julie K. Lundquist
Data sets
Supporting virtual lidar and LES files for "Behavior and Mechanisms of Lidar Error in Varying Stability Regimes" Rachel Robey, Julie K. Lundquist https://doi.org/10.5281/zenodo.6112629
Model code and software
Virtual Lidar Python Rachel Robey https://gitlab.com/raro0632/virtual-lidar
Rachel Robey and Julie K. Lundquist
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