the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Jul 2023
Gaussian wake model fitting in a transient event over Alpha Ventus wind farm
Abstract. Engineering wake models are defined by mathematical expressions and a set of coefficients. Because of their simplicity, the models may be rigid in transient events such as open cellular convection (OCC), characterized by a strong wind speed and direction change within tens of minutes. We use the results of a multiscale wind-wake modeling during an OCC event at the Alpha Ventus wind farm in the Southern North Sea to study how Gaussian models capture wake deficit variabilities. We find that the Jensen-Gaussian model would benefit from a constant coefficient tuning. On the contrary, the Bastankhah and Porté-Agel model and the super-Gaussian model are consistent without tuning but perform best with different deficit distribution shapes.
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RC1: 'Comment on wes-2023-79', Anonymous Referee #1, 18 Aug 2023
This work discusses and presents how engineering wake models capture wake deficit variabilities in case of a transient events (like open cellular convection). Mnuscript is nicely framed and written and this study makes a nice addition to a body of literature in the field.
Still, I have a few minor comments/sugesstions:
I think that more work is done in the field (like work done by Tuhfe Göçmen et al 2020 J. Phys.: Conf. Ser. 1618 062014 ) that might be relevant for this study and would be worth of mentioning.
Bakhoday-Paskyabi et al., 2022b study used high-frequency observations and it would be nice to include a sentence or two on LES performance and reliability. Also, why none of available observations used in that study are not suitable for this study.
What about other wake models? I think it would be nice to include a sentence or two about other available wake modes and justify choice of three used in this study. Also, based on the study results and the fact that all analyzed wake models have some shortcomings, it would be nice to have some idea/suggestion if some other wake model could be more appropriate for this type of events.
Line 45 and 47: double dots for x/D = 2..10 and r/D = −2..2 need to be fixed.Citation: https://doi.org/10.5194/wes-2023-79-RC1 -
RC2: 'Comment on wes-2023-79', Anonymous Referee #2, 05 Sep 2023
Overall
The paper presents a method for tuning analytic wake models during rapid transient events. The method, a baseline, and an idealized approach are applied to three Gaussian wake models for one test case and the efficacy is evaluated by comparing to higher-fidelity simulations (LES). The method improved the performance for one of the three wake models, but that model still performed so poorly it was not recommended for use during rapid transient events. The method did not improve performance for the other two wake models. One of those two wake models was nonetheless found to perform well. While the method presented in this work didn’t end up proving useful, that in and of itself is a helpful finding. The additional finding that the super Gaussian wake model performs well for rapid transient events is also informative. The topic and results of the paper are worth publishing. However, significant revision needs to be made throughout the paper to make it clear and easier to follow. I’ve suggested specific changes below.
Abstract
“We use the results of a multiscale wind-wake modeling during an OCC event at the Alpha Ventus wind farm in the Southern North Sea to study how Gaussian models capture wake deficit variabilities.”Could you also add more clarity in the abstract to where these results come from? Are these results you generated or that have already been published but that you’re re-analyzing?
“On the contrary, the Bastankhah and Porté-Agel model and the super-Gaussian model…perform best with different deficit distribution shapes.” Could you please finish this comparison by saying what the shapes should be different from. As written it’s unclear if the shapes should be different from those used in the previously mentioned Jensen-Gaussian model, different from those used in previous works, or something else.
Introduction
It would be helpful to cite and describe what work has already been done related to this paper and then to clarify how this paper differs from previous work. Right now only one paper is cited in the introduction and it’s written by the authors of this paper. In particular, it would be good to discuss any existing literature for (1) tuning wake models, (2) using wake models during rapid transient events esp. OCC, and (3) tuning wake models during rapid transient events esp. OCC. E.g. (2), it would be useful to know whether previous studies have identified which wake models perform well/poorly during rapid transient events. Make sure to specify whether BPA, Jensen-Gaussian, and/or super Gaussian models been tested on rapid transient events? If so, how did they perform? If not, say that to your knowledge none of these models have been tested on rapid transient events. For (3) it would be useful to know whether any previous work has tuned wake models during rapid transient events and, if so, what they found. Furthermore, it would be helpful to know if any wake models have been applied to/tuned for OCC events.
This work also frequently references the authors’ previous works (Bakhoday-Paskyabi et al., 2022a, b). Could you please explain in the introduction what research those previous works presented and how this paper differs from those works?
Data
Are the high-fidelity numerical simulations results used the result of your previous work (Bakhoday-Paskyabi et al., 2022b) or did you run new simulations not presented in that previous work? Please clarify.
If you ran new simulations, please add sufficient information for a reader to reproduce your work. E.g. you say the LES consists of two nested domains but only specify the dimensions and grid sizes for the inner domain not the outer domain.
If you didn’t run new simulations, please double-check that the information you do provide in this section matches that in your previous work. E.g. you say the grid size is 10x10x5m but in that previous work you say the grid size is 11x11x5m.
Methodology: 3.1
“corrected fit”: did you try fitting the coefficients to the OCC phase? If so, can you specify how you did that? Based on the results it seems like you tried fitting the coefficients for this phase and it didn’t work well; it would be useful to know what you tried.
“The fit uses already known simulation data for the passing period”: what do you mean by the passing period? I don’t think “passing” is the right word.
“We also tune coefficients of each model to find the best fit to WRF-LES results” and “The best fit is optimized for all cross-sections in a 10-minute period to avoid tuning models to a specific part of the wake.” Do these two sentences use “best fit” to refer only to the “best fit” method or are they referring in general to the idea of fitting model coefficients? If it’s the former, please make this more clear. If it’s the later, please say something other than “best fit” in those sentences.
“Overall, this similarity allows using AV1 inflow characteristics and thrust coefficient to estimate wakes for both turbines. An ensemble wake is calculated by summing up the normalized wake deficit from the AV1 wake at the regarded cross-section and the deficit at the respective cross-section of the AV4 wake.” These two sentences seem to contradict each other. Do you tune the coefficients using the wake estimated from the AV1 as described in the first sentence or using the ensemble wake described in the second sentence?
Please add the actual equations you use to tune coefficients through the “corrected fit” and “best fit” methods and then describe them. As is, it’s unclear how exactly you tuned the model coefficients.
Figure 2: Could you please describe the figure more in the caption? What does each panel refer to? What about the axis? What about the legend? What about the peak transition line?
Figure 2: could you please describe and analyze this figure more fully in the main body of the text? It’s only referenced in passing in a single sentence: “The inflow probes for AV4 generally return similar values, except for the time stamp 1:40 (Fig. 2)…” This sentence would be more clear if you took the time to introduce and describe the figure e.g. “Figure 2 shows the 10-minute averaged inflow characteristics upstream of both AV1 and AV4 as well as the thrust coefficient of AV1 and AV4. The figure shows the inflow probes for AV1 and AV4 generally return similar values except for at the time stamp 1:40…”
Results
Could you provide the results of the model fitting that you described in section 3.1? Aka what values did you get for each coefficient in Table 1 when using the corrected fit and best fit methods? Could extend Table 1 or add additional tables.
In general, this section would be easier to follow if you take the time to introduce each figure rather than just stating your results and referencing the figure in passing. E.g. rather than “The general behavior of all models follows similar trends (Fig. 3).” say something along the lines of “We calculate the RMSE of….and plot these results in Figure 3. The figure shows that the general behavior of all models follows similar trends.”
“During the peak transition phase at 1:50, … Model fitting for the period ending on 1:50 returns unrealistic coefficients, e.g., a negative wake decay coefficient k for the Jensen-Gaussian model.”
- Please specify in the text here that for this reason you don’t show results in figures 3 and 4 for time 1:50 using the corrected fit and best fit coefficients.
- I would suggest you include the results for time 1:50 using the default coefficients in figures 3 and 4. It would still be interesting to see what the RMSE and what the wake deficit is during the transition and how that varies by wake model.
Figure 3: please describe how the figure is laid out in the caption to make it easier for the reader to orient themselves. Please specify:
- The top three panels use the BPA method; the middle three Jensen-Gaussian, and the bottom super-Gaussian.
- The left three panels show results for pre-OCC and the right three panels results for post-OCC.
- Each column refers to a downstream location.
- Rows are grouped into sets of three corresponding to the RMSE for a time period, e.g. 1:10.
- Within each group, the rows are labeled “default”, “corr. fit”, and “best fit”, which correspond to results using the coefficients found using the default, corrected fit, and best fit methods.
Figure 3: why do you use different color scales for pre-OCC and post-OCC? It makes it hard to compare the RMSE between the two panels. Could you either provide a compelling reason to use different colors or change them to use the same color?
You say “The agreement to WRF-LES is good for the stabilized flow in the pre-OCC phase but declines as the convective cell approaches the wind farm.” That isn’t clear to me based on Figure 3. For the pre-OCC panels, the RMSE goes up to 2.0. In contrast, for the post-OCC panels, the RMSE only goes up to .15. Doesn’t this mean that the error is actually higher for the post-OCC panels than the pre-OCC panels?
Figure 4: similar to for figure 3, could you please describe the figure more in the caption to help orient the reader. Please talk about what each column and row of figures is and then within each figure please define what the horizontal and vertical axes are. Please also describe the legend aka what does each line refer to.
Figure 4: can you please discuss the results from all the columns? 4b and 4d are never discussed.
Conclusions
Could you please discuss how you envisioned the corrected fit extending to simulations with more turbines and for longer time periods? Do you imagine tuning the coefficients for each turbine once before and once after each OCC event? How will you identify when an OCC event is about to occur? How will you identify when an OCC event has just finished?
Spelling and grammar:
Abstract: “We use the results of a multiscale wind-wake modeling during an OCC event at the Alpha Ventus wind farm in the Southern North Sea to study how Gaussian models capture wake deficit variabilities.” This sentence should be “the results of multiscale wind-wake modeling” (no a) or “the results of a multiscale wind-wake model”.
First paragraph of the introduction: either refer to engineering wake models as plural or singular throughout for consistency aka either say “engineering wake models…models’…the models…models’ ” or say “an engineering wake model…model’s…the model…model’s ”.
Introduction paragraph 3: it should be “the models’ coefficients are corrected” since you’re referring to multiple models.
Figures 1 and 2: Typically units are reported in parenthesis or brackets; could you switch to this convention? E.g. rather than Y, m say “Y [m]”.
Figure 1: Could you please use complete sentences in your caption? E.g. “the OCC event is about to begin, the wind farm is not yet affected” is not a complete sentence; it’s a comma splice.
Figure 2: Could you change the label to time stamp rather than time for consistency with the rest of your discussion?
Methodology 3.2: “is defined similarly to the Jensen model“ should be “is defined similarly to in the Jensen model”
Methodology 3.2: “less parameterized coefficients.” should be “fewer parameterized coefficients.”
Methodology 3.2: “The label ’T’ ”. Fix the first apostrophe so it curls the correct direction.
Methodology 3.2: “proposes two method” should be “proposes two methods” (methods b/c it’s plural.)
You’re often missing articles before nouns. E.g. “at 1:50 time stamp” should be “at the 1:50 time stamp”. Could you please check throughout your article for any nouns missing articles and add the appropriate article, e.g. “a”, “an”, or “the”?
Commas are only used before “but” when they separate two independent clauses not when connecting an independent clause and a sentence fragment. E.g. “low thrust, but high wind speed” should not have a comma. Please check all uses of “, but” and correct where there shouldn’t be a comma.
Please check for typos. E.g. “The turbulence intensity fluctuates withing”, “withing” should be “within”. “x/D = 2..10”and “r/D = −2..2” -> not sure what this should be but something is off. “We did not account the deflection” should be “We did not account for the deflection” (you need to say “for”). “maximums positions” should be “maximum positions”.
Citation: https://doi.org/10.5194/wes-2023-79-RC2 - RC3: 'Comment on wes-2023-79', Anonymous Referee #3, 12 Sep 2023
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AC1: 'Final response', Maria Krutova, 22 Dec 2023
Sorry for the delay. Unfortunately, the original response deadline collided with the delivery of my PhD thesis and other urgent work. I am grateful to the editors for extending the deadline so I would have time to cycle through ideas and see how I can provide better insight into the wake models' behavior in the transient event.
I would also like to thank the reviewers for their valuable comments, which not only helped me improve the article directly but also inspired a few ideas I could use when revising.
Please, find the detailed response in the attachment.
Status: closed
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RC1: 'Comment on wes-2023-79', Anonymous Referee #1, 18 Aug 2023
This work discusses and presents how engineering wake models capture wake deficit variabilities in case of a transient events (like open cellular convection). Mnuscript is nicely framed and written and this study makes a nice addition to a body of literature in the field.
Still, I have a few minor comments/sugesstions:
I think that more work is done in the field (like work done by Tuhfe Göçmen et al 2020 J. Phys.: Conf. Ser. 1618 062014 ) that might be relevant for this study and would be worth of mentioning.
Bakhoday-Paskyabi et al., 2022b study used high-frequency observations and it would be nice to include a sentence or two on LES performance and reliability. Also, why none of available observations used in that study are not suitable for this study.
What about other wake models? I think it would be nice to include a sentence or two about other available wake modes and justify choice of three used in this study. Also, based on the study results and the fact that all analyzed wake models have some shortcomings, it would be nice to have some idea/suggestion if some other wake model could be more appropriate for this type of events.
Line 45 and 47: double dots for x/D = 2..10 and r/D = −2..2 need to be fixed.Citation: https://doi.org/10.5194/wes-2023-79-RC1 -
RC2: 'Comment on wes-2023-79', Anonymous Referee #2, 05 Sep 2023
Overall
The paper presents a method for tuning analytic wake models during rapid transient events. The method, a baseline, and an idealized approach are applied to three Gaussian wake models for one test case and the efficacy is evaluated by comparing to higher-fidelity simulations (LES). The method improved the performance for one of the three wake models, but that model still performed so poorly it was not recommended for use during rapid transient events. The method did not improve performance for the other two wake models. One of those two wake models was nonetheless found to perform well. While the method presented in this work didn’t end up proving useful, that in and of itself is a helpful finding. The additional finding that the super Gaussian wake model performs well for rapid transient events is also informative. The topic and results of the paper are worth publishing. However, significant revision needs to be made throughout the paper to make it clear and easier to follow. I’ve suggested specific changes below.
Abstract
“We use the results of a multiscale wind-wake modeling during an OCC event at the Alpha Ventus wind farm in the Southern North Sea to study how Gaussian models capture wake deficit variabilities.”Could you also add more clarity in the abstract to where these results come from? Are these results you generated or that have already been published but that you’re re-analyzing?
“On the contrary, the Bastankhah and Porté-Agel model and the super-Gaussian model…perform best with different deficit distribution shapes.” Could you please finish this comparison by saying what the shapes should be different from. As written it’s unclear if the shapes should be different from those used in the previously mentioned Jensen-Gaussian model, different from those used in previous works, or something else.
Introduction
It would be helpful to cite and describe what work has already been done related to this paper and then to clarify how this paper differs from previous work. Right now only one paper is cited in the introduction and it’s written by the authors of this paper. In particular, it would be good to discuss any existing literature for (1) tuning wake models, (2) using wake models during rapid transient events esp. OCC, and (3) tuning wake models during rapid transient events esp. OCC. E.g. (2), it would be useful to know whether previous studies have identified which wake models perform well/poorly during rapid transient events. Make sure to specify whether BPA, Jensen-Gaussian, and/or super Gaussian models been tested on rapid transient events? If so, how did they perform? If not, say that to your knowledge none of these models have been tested on rapid transient events. For (3) it would be useful to know whether any previous work has tuned wake models during rapid transient events and, if so, what they found. Furthermore, it would be helpful to know if any wake models have been applied to/tuned for OCC events.
This work also frequently references the authors’ previous works (Bakhoday-Paskyabi et al., 2022a, b). Could you please explain in the introduction what research those previous works presented and how this paper differs from those works?
Data
Are the high-fidelity numerical simulations results used the result of your previous work (Bakhoday-Paskyabi et al., 2022b) or did you run new simulations not presented in that previous work? Please clarify.
If you ran new simulations, please add sufficient information for a reader to reproduce your work. E.g. you say the LES consists of two nested domains but only specify the dimensions and grid sizes for the inner domain not the outer domain.
If you didn’t run new simulations, please double-check that the information you do provide in this section matches that in your previous work. E.g. you say the grid size is 10x10x5m but in that previous work you say the grid size is 11x11x5m.
Methodology: 3.1
“corrected fit”: did you try fitting the coefficients to the OCC phase? If so, can you specify how you did that? Based on the results it seems like you tried fitting the coefficients for this phase and it didn’t work well; it would be useful to know what you tried.
“The fit uses already known simulation data for the passing period”: what do you mean by the passing period? I don’t think “passing” is the right word.
“We also tune coefficients of each model to find the best fit to WRF-LES results” and “The best fit is optimized for all cross-sections in a 10-minute period to avoid tuning models to a specific part of the wake.” Do these two sentences use “best fit” to refer only to the “best fit” method or are they referring in general to the idea of fitting model coefficients? If it’s the former, please make this more clear. If it’s the later, please say something other than “best fit” in those sentences.
“Overall, this similarity allows using AV1 inflow characteristics and thrust coefficient to estimate wakes for both turbines. An ensemble wake is calculated by summing up the normalized wake deficit from the AV1 wake at the regarded cross-section and the deficit at the respective cross-section of the AV4 wake.” These two sentences seem to contradict each other. Do you tune the coefficients using the wake estimated from the AV1 as described in the first sentence or using the ensemble wake described in the second sentence?
Please add the actual equations you use to tune coefficients through the “corrected fit” and “best fit” methods and then describe them. As is, it’s unclear how exactly you tuned the model coefficients.
Figure 2: Could you please describe the figure more in the caption? What does each panel refer to? What about the axis? What about the legend? What about the peak transition line?
Figure 2: could you please describe and analyze this figure more fully in the main body of the text? It’s only referenced in passing in a single sentence: “The inflow probes for AV4 generally return similar values, except for the time stamp 1:40 (Fig. 2)…” This sentence would be more clear if you took the time to introduce and describe the figure e.g. “Figure 2 shows the 10-minute averaged inflow characteristics upstream of both AV1 and AV4 as well as the thrust coefficient of AV1 and AV4. The figure shows the inflow probes for AV1 and AV4 generally return similar values except for at the time stamp 1:40…”
Results
Could you provide the results of the model fitting that you described in section 3.1? Aka what values did you get for each coefficient in Table 1 when using the corrected fit and best fit methods? Could extend Table 1 or add additional tables.
In general, this section would be easier to follow if you take the time to introduce each figure rather than just stating your results and referencing the figure in passing. E.g. rather than “The general behavior of all models follows similar trends (Fig. 3).” say something along the lines of “We calculate the RMSE of….and plot these results in Figure 3. The figure shows that the general behavior of all models follows similar trends.”
“During the peak transition phase at 1:50, … Model fitting for the period ending on 1:50 returns unrealistic coefficients, e.g., a negative wake decay coefficient k for the Jensen-Gaussian model.”
- Please specify in the text here that for this reason you don’t show results in figures 3 and 4 for time 1:50 using the corrected fit and best fit coefficients.
- I would suggest you include the results for time 1:50 using the default coefficients in figures 3 and 4. It would still be interesting to see what the RMSE and what the wake deficit is during the transition and how that varies by wake model.
Figure 3: please describe how the figure is laid out in the caption to make it easier for the reader to orient themselves. Please specify:
- The top three panels use the BPA method; the middle three Jensen-Gaussian, and the bottom super-Gaussian.
- The left three panels show results for pre-OCC and the right three panels results for post-OCC.
- Each column refers to a downstream location.
- Rows are grouped into sets of three corresponding to the RMSE for a time period, e.g. 1:10.
- Within each group, the rows are labeled “default”, “corr. fit”, and “best fit”, which correspond to results using the coefficients found using the default, corrected fit, and best fit methods.
Figure 3: why do you use different color scales for pre-OCC and post-OCC? It makes it hard to compare the RMSE between the two panels. Could you either provide a compelling reason to use different colors or change them to use the same color?
You say “The agreement to WRF-LES is good for the stabilized flow in the pre-OCC phase but declines as the convective cell approaches the wind farm.” That isn’t clear to me based on Figure 3. For the pre-OCC panels, the RMSE goes up to 2.0. In contrast, for the post-OCC panels, the RMSE only goes up to .15. Doesn’t this mean that the error is actually higher for the post-OCC panels than the pre-OCC panels?
Figure 4: similar to for figure 3, could you please describe the figure more in the caption to help orient the reader. Please talk about what each column and row of figures is and then within each figure please define what the horizontal and vertical axes are. Please also describe the legend aka what does each line refer to.
Figure 4: can you please discuss the results from all the columns? 4b and 4d are never discussed.
Conclusions
Could you please discuss how you envisioned the corrected fit extending to simulations with more turbines and for longer time periods? Do you imagine tuning the coefficients for each turbine once before and once after each OCC event? How will you identify when an OCC event is about to occur? How will you identify when an OCC event has just finished?
Spelling and grammar:
Abstract: “We use the results of a multiscale wind-wake modeling during an OCC event at the Alpha Ventus wind farm in the Southern North Sea to study how Gaussian models capture wake deficit variabilities.” This sentence should be “the results of multiscale wind-wake modeling” (no a) or “the results of a multiscale wind-wake model”.
First paragraph of the introduction: either refer to engineering wake models as plural or singular throughout for consistency aka either say “engineering wake models…models’…the models…models’ ” or say “an engineering wake model…model’s…the model…model’s ”.
Introduction paragraph 3: it should be “the models’ coefficients are corrected” since you’re referring to multiple models.
Figures 1 and 2: Typically units are reported in parenthesis or brackets; could you switch to this convention? E.g. rather than Y, m say “Y [m]”.
Figure 1: Could you please use complete sentences in your caption? E.g. “the OCC event is about to begin, the wind farm is not yet affected” is not a complete sentence; it’s a comma splice.
Figure 2: Could you change the label to time stamp rather than time for consistency with the rest of your discussion?
Methodology 3.2: “is defined similarly to the Jensen model“ should be “is defined similarly to in the Jensen model”
Methodology 3.2: “less parameterized coefficients.” should be “fewer parameterized coefficients.”
Methodology 3.2: “The label ’T’ ”. Fix the first apostrophe so it curls the correct direction.
Methodology 3.2: “proposes two method” should be “proposes two methods” (methods b/c it’s plural.)
You’re often missing articles before nouns. E.g. “at 1:50 time stamp” should be “at the 1:50 time stamp”. Could you please check throughout your article for any nouns missing articles and add the appropriate article, e.g. “a”, “an”, or “the”?
Commas are only used before “but” when they separate two independent clauses not when connecting an independent clause and a sentence fragment. E.g. “low thrust, but high wind speed” should not have a comma. Please check all uses of “, but” and correct where there shouldn’t be a comma.
Please check for typos. E.g. “The turbulence intensity fluctuates withing”, “withing” should be “within”. “x/D = 2..10”and “r/D = −2..2” -> not sure what this should be but something is off. “We did not account the deflection” should be “We did not account for the deflection” (you need to say “for”). “maximums positions” should be “maximum positions”.
Citation: https://doi.org/10.5194/wes-2023-79-RC2 - RC3: 'Comment on wes-2023-79', Anonymous Referee #3, 12 Sep 2023
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AC1: 'Final response', Maria Krutova, 22 Dec 2023
Sorry for the delay. Unfortunately, the original response deadline collided with the delivery of my PhD thesis and other urgent work. I am grateful to the editors for extending the deadline so I would have time to cycle through ideas and see how I can provide better insight into the wake models' behavior in the transient event.
I would also like to thank the reviewers for their valuable comments, which not only helped me improve the article directly but also inspired a few ideas I could use when revising.
Please, find the detailed response in the attachment.
Data sets
Gaussian wake model fitting to a transient event simulated with WRF-LES Maria Krutova https://doi.org/10.5281/zenodo.8135542
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