the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
GradientBased Wind Farm Layout Optimization Results Compared with LargeEddy Simulations
Christopher J. Bay
Andrew P. J. Stanley
Andrew Ning
Abstract. The physics models commonly used during wind farm layout optimization include simplifying assumptions that can alter the design space compared to reality and higherfidelity simulations. Some characteristics of these simple models may negatively influence the resulting layouts. In this paper, we perform wind farm layout optimization using a simple engineering wake model and then simulate the base and optimized layouts using largeeddy simulation (LES) to confirm that the layout was actually improved and not just an artifact of the simplifying assumptions in the lowfidelity wind farm simulation. We begin by describing the physics models used, including changes specific for use with gradientbased optimization. We then compare the simple model's output to previously published model and LES results. Using the simple models described, we performed gradientbased wind farm layout optimization using exact gradients. We optimized the wind farm twice, with high and lowturbulence intensity (TI), respectively. We then recalculated annual energy production (AEP) using LES for the original and optimized layouts in each TI scenario and compared the results. For the highTI case, the simple model predicted an AEP improvement of 7.7 %, while the LES reported 9.3 %. For the lowTI case, the simple model predicted a 10.0 % AEP improvement, while the LES reported 10.7 %. We concluded that the improvements found by optimizing with the simple model are not just an artifact of the model, but are real improvements assuming appropriate wind rose fidelity. We also found that the optimization did take advantage of the number of wind directions used, often aligning wind turbines in directions that were not included in the simulation. We found that, for the case studied, at least 50 wind directions are needed to avoid having the number of wind directions in the optimization significantly impact the optimized results. Future work should investigate further LES comparisons and wind rose fidelity in wind speed.
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Jared J. Thomas et al.
Status: closed

RC1: 'Comment on wes20224', Anonymous Referee #1, 10 May 2022
The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text.
In section 2.2.3 the author detail that they used only 1 sampling point for velocity calculation during the optimization procedure, and highlight the errors in the 1 point case in Figure 3. Readers would benefit from seeing the impact of this simplification on the optimal results through some test cases where higher sampling points were taken during optimization as well.
In section 2, it may be beneficial for completeness and readability to expand a bit more upon the wake expansion continuation method and the meanings of the associated relaxation factors rather than just mentioning it as a reference.
Figure 12 show significant differences between the BP model and SOWFA, for both the base and optimized results. Earlier in the paper in section 3, the authors showed that their model is able to match reference LES results for the horns rev wind farm with a high degree of accuracy. Could the authors comment on why there are now larger errors when compared to LES for the developed wind farm layout?
Citation: https://doi.org/10.5194/wes20224RC1 
AC1: 'Reply on RC1', Jared Thomas, 10 Jun 2022
Please see excerpts of revised manuscript attached as supplements.
 "The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text."
 Thank you for your positive feedback and suggestions.
 "In section 2.2.3 the author detail that they used only 1 sampling point for velocity calculation during the optimization procedure, and highlight the errors in the 1 point case in Figure 3. Readers would benefit from seeing the impact of this simplification on the optimal results through some test cases where higher sampling points were taken during optimization as well."
 Excellent suggestion. We have added this study and it looks like one sample is sufficient for optimization, while 20 samples are enough for AEP estimation.
 See page 17, lines 362375 in attached revised manuscript excerpt
 See page 19, Fig. 12 in attached revised manuscript excerpt
 Excellent suggestion. We have added this study and it looks like one sample is sufficient for optimization, while 20 samples are enough for AEP estimation.
 "In section 2, it may be beneficial for completeness and readability to expand a bit more upon the wake expansion continuation method and the meanings of the associated relaxation factors rather than just mentioning it as a reference."
 Thank you for the suggestion. We have added a brief description of WEC. Please see page 14, lines 306314 in the revised manuscript
 "Figure 12 show significant differences between the BP model and SOWFA, for both the base and optimized results. Earlier in the paper in section 3, the authors showed that their model is able to match reference LES results for the horns rev wind farm with a high degree of accuracy. Could the authors comment on why there are now larger errors when compared to LES for the developed wind farm layout?"
 The results from the literature were normalized. We never normalized our results.
 When we used a nondimensional form, the agreement was better (see fig 14 in the revised manuscript).
 Clarification has been added in the following places:
 page 18, line 379 in the revised manuscript
 page 19, lines 393394 in the revised manuscript

AC2: 'Reply on AC1', Jared Thomas, 10 Jun 2022
FIgure 14 should have been included in the supplemental material of the previous response. Also note that all references to the revised manuscript in the previous response were intended to refer to the supplement file, which contains excerpts from the revised manuscript but not the revised manuscript in its entirety.
 "The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text."

AC1: 'Reply on RC1', Jared Thomas, 10 Jun 2022

RC2: 'Comment on wes20224', Anonymous Referee #2, 16 Jun 2022
The authors present a study on gradient based windfarm layout optimization and comparison of the optimized results with LES. An important novelty claimed by the authors is the fact that optimized layouts are compared to 'highfidelity' LES over a full wind rose. Unfortunately, there is potentially a major flaw in the presented LES results (see point 1 below). Therefore I do not believe this work can be accepted for publication in its current form
Detailed comments
 LES are performed on a domain of 5x5x1 km. This domain is much too small, and given the forced inflow conditions, will lead to domain blockage and an artificial favorable pressure gradient. This is essentially a direct result from Newtons second law when domain boundaries do not allow the momentum of the flow to freely change. When optimizing the layout, and thus changing to total windfarm thrust, this will then also lead to a larger favorable pressure gradient, hence artificially enhancing the benefits of the layout in the LES. This seems to be exactly what the authors observe when comparing their LES with the optimized wake models. Also the fact that gains that are calculated using the front row turbine's velocities as reference (as in Fig 13) are closer to the wake models than direct power (which is based on inflow reference) points to significant blockage effects. The authors should show in a revised manuscript that their selected domain size is sufficiently big to avoid blockage effects that are of the same order of magnitude as optimization gains. To this end, they should for a selected case show results on different domain sizes, showing that effects become negligible for the final selected size. It is my expectation that that size is considerably bigger than 5x5x1 km. Subsequently, all simulations should be performed on that domain size.
 Overall, the discussion on the LES setup in 2.4 and 2.5 is too brief. Based on this, the setup is simply not reproducible. The authors mention buoyancy and Coriolis effects, but it is my impression that the simulations may simply consist of a pressure driven boundary layer. If not, what is the geostrophic wind, what is the stratification profile. In addition, what is the surface roughness, friction velocity, etc. What is the precursor setup (domain size, grid size, initialization, spinup time, etc). What is the simulation cost, …
Smaller comments
 Line 84 and also later section 2.1: better justify why the nearwake region can not be simply avoided by using a minimum distance constraint in the optimization, e.g. using a constraint that is larger than x_d obtained Eq.8. In case of interest in setups where turbines are placed more closely together, the near wake model may need improvement anyway, and the heuristic adaptation proposed may not suffice.
 Throughout the paper: equations are part of the text, and phrases and punctuations should be used accordingly. Please check with other papers and publication standards to see how it is done
 Line 143: “To remove the discontinuity” > please provide a mathematical expression
 Line 152: If greater accuracy is desired > speculative. Either provide data that prove this statement or remove
 Line 212: sunflower pattern: please provide reference or formula
 Eq 19: provide units. Result is in kWh and not in J.
 Eq 21: this is not a correct definition of TI. TI is based on magnitude of fluctuating velocity that includes components in all directions
 Eq 22: to be technically precise, the “i=1…38” should be added in the subscript below “maximize”
 Line 300: forward differentiation is used. What is the advantage of this over using SNOPT without providing the gradients explicitly? I do not believe that this will be significant, since in that case SNOPT constructs gradients based on FD? This can be even less expensive than forward differentiation, and accuracy loss is often not significant (depending on implementation choices). Please discuss in more detail the gains etc. Usually, significant speedup would only follow from backward differentiation. This should be better substantiated in the manuscript, in particular since, in the abstract, you seem to claim this as an important innovation.
 Line 305: please discuss the WEC method in more detail. Also better explain why standard multistart methods do not work? If they are as good, why not use a standard from an optimization library
 Line 314: what do you mean with 400 optimizations? This is confusing. If I’m not mistaken, you solve Eq 22 only twice. Better clarify/make distinction
 Figures in general: please make as much as possible black&white friendly (some plots are not readable when printed in gray scale). For many figures this should be possible without losing attractiveness of the figure in color.
 Wind directions throughout paper: add degree symbol
Citation: https://doi.org/10.5194/wes20224RC2 
AC3: 'Reply on RC2', Jared Thomas, 11 Nov 2022
Referee 2 Comments and Author ResponseNote: The text in quotation marks is from the referee. The indented bullet points are the author response.Overview"The authors present a study on gradient based windfarm layout optimization and comparison of the optimized results with LES. An important novelty claimed by the authors is the fact that optimized layouts are compared to 'highfidelity' LES over a full wind rose. Unfortunately, there is potentially a major flaw in the presented LES results (see point 1 below). Therefore I do not believe this work can be accepted for publication in its current form"
 Thank you for your comments. Your insights helped us improve the work, including corrections and additional studies. We believe it is now ready for acceptance for publication.
Detailed comments "LES are performed on a domain of 5x5x1 km. This domain is much too small, and given the forced inflow conditions, will lead to domain blockage and an artificial favorable pressure gradient. This is essentially a direct result from Newtons second law when domain boundaries do not allow the momentum of the flow to freely change. When optimizing the layout, and thus changing to total windfarm thrust, this will then also lead to a larger favorable pressure gradient, hence artificially enhancing the benefits of the layout in the LES. This seems to be exactly what the authors observe when comparing their LES with the optimized wake models. Also the fact that gains that are calculated using the front row turbine's velocities as reference (as in Fig 13) are closer to the wake models than direct power (which is based on inflow reference) points to significant blockage effects. The authors should show in a revised manuscript that their selected domain size is sufficiently big to avoid blockage effects that are of the same order of magnitude as optimization gains. To this end, they should for a selected case show results on different domain sizes, showing that effects become negligible for the final selected size. It is my expectation that that size is considerably bigger than 5x5x1 km. Subsequently, all simulations should be performed on that domain size."
 These are excellent points. We started work on a study similar to what was outlined above. However, the theoretical domain size required to avoid blockage effects for enough cases required more computational resources than we had at our disposal for this project. We used the NREL Eagle super computer, which has 36 core nodes.The 5 kmby5 km domain had a total CPU time per simulation of approximately 756 days, or 36 hours on fourteen 36core nodes. This study required 48 simulations (one for each direction, for each TI level, for both the baseline and the optimized layouts), for a total CPU time of about 72 days on fourteen 36core nodes. We estimate that to reduce the artificial speedup effects sufficiently would require a domain size of approximately 15 kmby15 km. However, even just increasing the domain to 10 kmby10 km would require approximately 6 days on fourteen 36core nodes per simulation, or around 288 days on fourteen 36core nodes to complete all the simulations for all directions, which is more than the computational resources we had available for this project.
 We have included a figure demonstrating the estimated directional blockages and a discussion of the possible implications of having too small of a domain size. We also adjusted some of the results based on a simple estimate of the speedup due to added blockage from the base case to the optimized layout. However, because the difference in estimated blockage between the base layout and the optimized layouts is small (~1 percentage point on average), and the optimization algorithm was unable to exploit blockage effects because it was unaware of the LES, we believe that any speedup effects present due to the blockage do not change the primary conclusions of this paper, namely that the optimized layouts found using the simplified engineering model are actually good layouts.
 See lines 425465 in the revised manuscript excerpts attached
 See lines 482519 in the revised manuscript excerpts attached
 See Fig. 13 in the revised manuscript excerpts attached
 See Fig. 14 in the revised manuscript excerpts attached
 See Fig. 15 in the revised manuscript excerpts attached
 "Overall, the discussion on the LES setup in 2.4 and 2.5 is too brief. Based on this, the setup is simply not reproducible. The authors mention buoyancy and Coriolis effects, but it is my impression that the simulations may simply consist of a pressure driven boundary layer. If not, what is the geostrophic wind, what is the stratification profile. In addition, what is the surface roughness, friction velocity, etc. What is the precursor setup (domain size, grid size, initialization, spinup time, etc). What is the simulation cost, …"
 As suggested, we have included much more detail in 2.4 regarding the LES set up.
 See section 2.4 in the revised manuscript excerpts attached
Smaller comments "Line 84 and also later section 2.1: better justify why the nearwake region can not be simply avoided by using a minimum distance constraint in the optimization, e.g. using a constraint that is larger than x_d obtained Eq.8. In case of interest in setups where turbines are placed more closely together, the near wake model may need improvement anyway, and the heuristic adaptation proposed may not suffice."
 A constraint on the minimum turbine distance is included, but the size of the near wake region is variable and the turbine separation constraints are nonlinear. SNOPT minimizes infeasibility for nonlinear constraints, so infeasible solutions may be attempted during the optimization and the near wake model may be used at some point during the optimizaiton.
 We have added clarification around
 Lines 8590 in the attached revised manuscript excerpts
 Lines 151171 in the attached revised manuscript excerpts
 "Throughout the paper: equations are part of the text, and phrases and punctuations should be used accordingly. Please check with other papers and publication standards to see how it is done"
 We have made this change throughout the manuscript. Thank you for the suggestion.
 "Line 143: “To remove the discontinuity” > please provide a mathematical expression"
 Good suggestion. We have added clarification
 See lines 154161 in the attached revised manuscript excerpts
 See Eqs. 9 and 10 in the attached revised manuscript excerpts
 "Line 152: If greater accuracy is desired > speculative. Either provide data that prove this statement or remove"
 We have adjusted this statement slightly to clarify that we are not making a claim, but rather providing a suggestion and reference for readers interested in a more accurate nearwake model.
 See lines 162171 in the attached revised manuscript excerpts
 "Line 212: sunflower pattern: please provide reference or formula"
 Thank you for the suggestion. The formulas, along with citations and explanation, have been added.
 See section 2.2.3 in the attached revised manuscript excerpts
 "Eq 19: provide units. Result is in kWh and not in J."
 Thank you for the suggestion, we have clarified the units.
 See Eq. 23 and related discussion in the attached revised manuscript excerpts
 "Eq 21: this is not a correct definition of TI. TI is based on magnitude of fluctuating velocity that includes components in all directions"
 We used this definition as an estimate of the turbulence intensity. Our simulations did not include significant lateral or vertical flow components and so we included only the variations in the primary flow direction. We have added some clarification.
 See lines 310319 in the attached revised manuscript excerpts
 "Eq 22: to be technically precise, the 'i=1…38' should be added in the subscript below 'maximize'"
 Thank you for pointing this out. To make things cleaner we have just removed the underset (x_i,y_i) because they are redundant with the shown objective inputs.
 See Eq. 26 in the attached revised manuscript excerpts
 "Line 300: forward differentiation is used. What is the advantage of this over using SNOPT without providing the gradients explicitly? I do not believe that this will be significant, since in that case SNOPT constructs gradients based on FD? This can be even less expensive than forward differentiation, and accuracy loss is often not significant (depending on implementation choices). Please discuss in more detail the gains etc. Usually, significant speedup would only follow from backward differentiation. This should be better substantiated in the manuscript, in particular since, in the abstract, you seem to claim this as an important innovation."
 Thank you for bringing this up. Our explanation was not clear enough. ForwardDiff.jl does not use the forward finite difference method, but rather forward mode algorithmic differentiation (AD). We have added more detail in section 2.7 to clarify this point. AD has been shown to be much less computationally costly and more accurate than finite difference methods, such as the one provided in SNOPT.
 See lines 340347 in the attached revised manuscript excerpts

 "Line 305: please discuss the WEC method in more detail."
 Good suggestion, we have added more detail about the WEC method in section 2.7.
 See lines 348359 in the attached revised manuscript excerpts
 "Also better explain why standard multistart methods do not work? If they are as good, why not use a standard from an optimization library"
 WEC is a continuation optimization method, not a multistart method. However, using it with a multistart method is recommended. We have provided an explanation of, and motivation for, our multistart approach in section 2.7
 See lines 365368 in the attached revised manuscript excerpts
 "Line 305: please discuss the WEC method in more detail."
 "Line 314: what do you mean with 400 optimizations? This is confusing. If I’m not mistaken, you solve Eq 22 only twice. Better clarify/make distinction"
 This should be more clear with our additions made to section 2.7. We ran 400 optimizations for each case (high TI and low TI). The final optimized result shown is the best of the 400. Each optimization used a different starting layout, but all were compared to the single base case provided in the paper. Multistart is a common approach for wind farm layout optimization.
 See line 365 (and all of 2.7) in the attached revised manuscript excerpts
 "Figures in general: please make as much as possible black&white friendly (some plots are not readable when printed in gray scale). For many figures this should be possible without losing attractiveness of the figure in color."
 While we recognize that the color scheme may not be ideal for printing, we would like to leave it as is. The colors were selected for colorblind readers, as requested in the WES submission guidelines. Since most readers will be seeing the article online, we believe that having a colorblindfriendly palet is more important than having a printer friendly one. That said, we did adjust some figures to be more clear in black and white using marker styles instead of color.
 See Figs. 14 and 15 in the attached revised manuscript excerpts
 "Wind directions throughout paper: add degree symbol"
 Thank you for noting the inconsistency. We have added the degree symbol in the appropriate locations throughout the paper.
Status: closed

RC1: 'Comment on wes20224', Anonymous Referee #1, 10 May 2022
The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text.
In section 2.2.3 the author detail that they used only 1 sampling point for velocity calculation during the optimization procedure, and highlight the errors in the 1 point case in Figure 3. Readers would benefit from seeing the impact of this simplification on the optimal results through some test cases where higher sampling points were taken during optimization as well.
In section 2, it may be beneficial for completeness and readability to expand a bit more upon the wake expansion continuation method and the meanings of the associated relaxation factors rather than just mentioning it as a reference.
Figure 12 show significant differences between the BP model and SOWFA, for both the base and optimized results. Earlier in the paper in section 3, the authors showed that their model is able to match reference LES results for the horns rev wind farm with a high degree of accuracy. Could the authors comment on why there are now larger errors when compared to LES for the developed wind farm layout?
Citation: https://doi.org/10.5194/wes20224RC1 
AC1: 'Reply on RC1', Jared Thomas, 10 Jun 2022
Please see excerpts of revised manuscript attached as supplements.
 "The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text."
 Thank you for your positive feedback and suggestions.
 "In section 2.2.3 the author detail that they used only 1 sampling point for velocity calculation during the optimization procedure, and highlight the errors in the 1 point case in Figure 3. Readers would benefit from seeing the impact of this simplification on the optimal results through some test cases where higher sampling points were taken during optimization as well."
 Excellent suggestion. We have added this study and it looks like one sample is sufficient for optimization, while 20 samples are enough for AEP estimation.
 See page 17, lines 362375 in attached revised manuscript excerpt
 See page 19, Fig. 12 in attached revised manuscript excerpt
 Excellent suggestion. We have added this study and it looks like one sample is sufficient for optimization, while 20 samples are enough for AEP estimation.
 "In section 2, it may be beneficial for completeness and readability to expand a bit more upon the wake expansion continuation method and the meanings of the associated relaxation factors rather than just mentioning it as a reference."
 Thank you for the suggestion. We have added a brief description of WEC. Please see page 14, lines 306314 in the revised manuscript
 "Figure 12 show significant differences between the BP model and SOWFA, for both the base and optimized results. Earlier in the paper in section 3, the authors showed that their model is able to match reference LES results for the horns rev wind farm with a high degree of accuracy. Could the authors comment on why there are now larger errors when compared to LES for the developed wind farm layout?"
 The results from the literature were normalized. We never normalized our results.
 When we used a nondimensional form, the agreement was better (see fig 14 in the revised manuscript).
 Clarification has been added in the following places:
 page 18, line 379 in the revised manuscript
 page 19, lines 393394 in the revised manuscript

AC2: 'Reply on AC1', Jared Thomas, 10 Jun 2022
FIgure 14 should have been included in the supplemental material of the previous response. Also note that all references to the revised manuscript in the previous response were intended to refer to the supplement file, which contains excerpts from the revised manuscript but not the revised manuscript in its entirety.
 "The manuscript presents a rigorous methodology for wind farm layout optimization using simplified engineering models. The main strength of the study is in comparing their model’s output against large eddy simulation results. The text is very well written, with the methodology and results presented in a clear and concise manner to aid in reproducibility. The following points could improve the readability of the text."

AC1: 'Reply on RC1', Jared Thomas, 10 Jun 2022

RC2: 'Comment on wes20224', Anonymous Referee #2, 16 Jun 2022
The authors present a study on gradient based windfarm layout optimization and comparison of the optimized results with LES. An important novelty claimed by the authors is the fact that optimized layouts are compared to 'highfidelity' LES over a full wind rose. Unfortunately, there is potentially a major flaw in the presented LES results (see point 1 below). Therefore I do not believe this work can be accepted for publication in its current form
Detailed comments
 LES are performed on a domain of 5x5x1 km. This domain is much too small, and given the forced inflow conditions, will lead to domain blockage and an artificial favorable pressure gradient. This is essentially a direct result from Newtons second law when domain boundaries do not allow the momentum of the flow to freely change. When optimizing the layout, and thus changing to total windfarm thrust, this will then also lead to a larger favorable pressure gradient, hence artificially enhancing the benefits of the layout in the LES. This seems to be exactly what the authors observe when comparing their LES with the optimized wake models. Also the fact that gains that are calculated using the front row turbine's velocities as reference (as in Fig 13) are closer to the wake models than direct power (which is based on inflow reference) points to significant blockage effects. The authors should show in a revised manuscript that their selected domain size is sufficiently big to avoid blockage effects that are of the same order of magnitude as optimization gains. To this end, they should for a selected case show results on different domain sizes, showing that effects become negligible for the final selected size. It is my expectation that that size is considerably bigger than 5x5x1 km. Subsequently, all simulations should be performed on that domain size.
 Overall, the discussion on the LES setup in 2.4 and 2.5 is too brief. Based on this, the setup is simply not reproducible. The authors mention buoyancy and Coriolis effects, but it is my impression that the simulations may simply consist of a pressure driven boundary layer. If not, what is the geostrophic wind, what is the stratification profile. In addition, what is the surface roughness, friction velocity, etc. What is the precursor setup (domain size, grid size, initialization, spinup time, etc). What is the simulation cost, …
Smaller comments
 Line 84 and also later section 2.1: better justify why the nearwake region can not be simply avoided by using a minimum distance constraint in the optimization, e.g. using a constraint that is larger than x_d obtained Eq.8. In case of interest in setups where turbines are placed more closely together, the near wake model may need improvement anyway, and the heuristic adaptation proposed may not suffice.
 Throughout the paper: equations are part of the text, and phrases and punctuations should be used accordingly. Please check with other papers and publication standards to see how it is done
 Line 143: “To remove the discontinuity” > please provide a mathematical expression
 Line 152: If greater accuracy is desired > speculative. Either provide data that prove this statement or remove
 Line 212: sunflower pattern: please provide reference or formula
 Eq 19: provide units. Result is in kWh and not in J.
 Eq 21: this is not a correct definition of TI. TI is based on magnitude of fluctuating velocity that includes components in all directions
 Eq 22: to be technically precise, the “i=1…38” should be added in the subscript below “maximize”
 Line 300: forward differentiation is used. What is the advantage of this over using SNOPT without providing the gradients explicitly? I do not believe that this will be significant, since in that case SNOPT constructs gradients based on FD? This can be even less expensive than forward differentiation, and accuracy loss is often not significant (depending on implementation choices). Please discuss in more detail the gains etc. Usually, significant speedup would only follow from backward differentiation. This should be better substantiated in the manuscript, in particular since, in the abstract, you seem to claim this as an important innovation.
 Line 305: please discuss the WEC method in more detail. Also better explain why standard multistart methods do not work? If they are as good, why not use a standard from an optimization library
 Line 314: what do you mean with 400 optimizations? This is confusing. If I’m not mistaken, you solve Eq 22 only twice. Better clarify/make distinction
 Figures in general: please make as much as possible black&white friendly (some plots are not readable when printed in gray scale). For many figures this should be possible without losing attractiveness of the figure in color.
 Wind directions throughout paper: add degree symbol
Citation: https://doi.org/10.5194/wes20224RC2 
AC3: 'Reply on RC2', Jared Thomas, 11 Nov 2022
Referee 2 Comments and Author ResponseNote: The text in quotation marks is from the referee. The indented bullet points are the author response.Overview"The authors present a study on gradient based windfarm layout optimization and comparison of the optimized results with LES. An important novelty claimed by the authors is the fact that optimized layouts are compared to 'highfidelity' LES over a full wind rose. Unfortunately, there is potentially a major flaw in the presented LES results (see point 1 below). Therefore I do not believe this work can be accepted for publication in its current form"
 Thank you for your comments. Your insights helped us improve the work, including corrections and additional studies. We believe it is now ready for acceptance for publication.
Detailed comments "LES are performed on a domain of 5x5x1 km. This domain is much too small, and given the forced inflow conditions, will lead to domain blockage and an artificial favorable pressure gradient. This is essentially a direct result from Newtons second law when domain boundaries do not allow the momentum of the flow to freely change. When optimizing the layout, and thus changing to total windfarm thrust, this will then also lead to a larger favorable pressure gradient, hence artificially enhancing the benefits of the layout in the LES. This seems to be exactly what the authors observe when comparing their LES with the optimized wake models. Also the fact that gains that are calculated using the front row turbine's velocities as reference (as in Fig 13) are closer to the wake models than direct power (which is based on inflow reference) points to significant blockage effects. The authors should show in a revised manuscript that their selected domain size is sufficiently big to avoid blockage effects that are of the same order of magnitude as optimization gains. To this end, they should for a selected case show results on different domain sizes, showing that effects become negligible for the final selected size. It is my expectation that that size is considerably bigger than 5x5x1 km. Subsequently, all simulations should be performed on that domain size."
 These are excellent points. We started work on a study similar to what was outlined above. However, the theoretical domain size required to avoid blockage effects for enough cases required more computational resources than we had at our disposal for this project. We used the NREL Eagle super computer, which has 36 core nodes.The 5 kmby5 km domain had a total CPU time per simulation of approximately 756 days, or 36 hours on fourteen 36core nodes. This study required 48 simulations (one for each direction, for each TI level, for both the baseline and the optimized layouts), for a total CPU time of about 72 days on fourteen 36core nodes. We estimate that to reduce the artificial speedup effects sufficiently would require a domain size of approximately 15 kmby15 km. However, even just increasing the domain to 10 kmby10 km would require approximately 6 days on fourteen 36core nodes per simulation, or around 288 days on fourteen 36core nodes to complete all the simulations for all directions, which is more than the computational resources we had available for this project.
 We have included a figure demonstrating the estimated directional blockages and a discussion of the possible implications of having too small of a domain size. We also adjusted some of the results based on a simple estimate of the speedup due to added blockage from the base case to the optimized layout. However, because the difference in estimated blockage between the base layout and the optimized layouts is small (~1 percentage point on average), and the optimization algorithm was unable to exploit blockage effects because it was unaware of the LES, we believe that any speedup effects present due to the blockage do not change the primary conclusions of this paper, namely that the optimized layouts found using the simplified engineering model are actually good layouts.
 See lines 425465 in the revised manuscript excerpts attached
 See lines 482519 in the revised manuscript excerpts attached
 See Fig. 13 in the revised manuscript excerpts attached
 See Fig. 14 in the revised manuscript excerpts attached
 See Fig. 15 in the revised manuscript excerpts attached
 "Overall, the discussion on the LES setup in 2.4 and 2.5 is too brief. Based on this, the setup is simply not reproducible. The authors mention buoyancy and Coriolis effects, but it is my impression that the simulations may simply consist of a pressure driven boundary layer. If not, what is the geostrophic wind, what is the stratification profile. In addition, what is the surface roughness, friction velocity, etc. What is the precursor setup (domain size, grid size, initialization, spinup time, etc). What is the simulation cost, …"
 As suggested, we have included much more detail in 2.4 regarding the LES set up.
 See section 2.4 in the revised manuscript excerpts attached
Smaller comments "Line 84 and also later section 2.1: better justify why the nearwake region can not be simply avoided by using a minimum distance constraint in the optimization, e.g. using a constraint that is larger than x_d obtained Eq.8. In case of interest in setups where turbines are placed more closely together, the near wake model may need improvement anyway, and the heuristic adaptation proposed may not suffice."
 A constraint on the minimum turbine distance is included, but the size of the near wake region is variable and the turbine separation constraints are nonlinear. SNOPT minimizes infeasibility for nonlinear constraints, so infeasible solutions may be attempted during the optimization and the near wake model may be used at some point during the optimizaiton.
 We have added clarification around
 Lines 8590 in the attached revised manuscript excerpts
 Lines 151171 in the attached revised manuscript excerpts
 "Throughout the paper: equations are part of the text, and phrases and punctuations should be used accordingly. Please check with other papers and publication standards to see how it is done"
 We have made this change throughout the manuscript. Thank you for the suggestion.
 "Line 143: “To remove the discontinuity” > please provide a mathematical expression"
 Good suggestion. We have added clarification
 See lines 154161 in the attached revised manuscript excerpts
 See Eqs. 9 and 10 in the attached revised manuscript excerpts
 "Line 152: If greater accuracy is desired > speculative. Either provide data that prove this statement or remove"
 We have adjusted this statement slightly to clarify that we are not making a claim, but rather providing a suggestion and reference for readers interested in a more accurate nearwake model.
 See lines 162171 in the attached revised manuscript excerpts
 "Line 212: sunflower pattern: please provide reference or formula"
 Thank you for the suggestion. The formulas, along with citations and explanation, have been added.
 See section 2.2.3 in the attached revised manuscript excerpts
 "Eq 19: provide units. Result is in kWh and not in J."
 Thank you for the suggestion, we have clarified the units.
 See Eq. 23 and related discussion in the attached revised manuscript excerpts
 "Eq 21: this is not a correct definition of TI. TI is based on magnitude of fluctuating velocity that includes components in all directions"
 We used this definition as an estimate of the turbulence intensity. Our simulations did not include significant lateral or vertical flow components and so we included only the variations in the primary flow direction. We have added some clarification.
 See lines 310319 in the attached revised manuscript excerpts
 "Eq 22: to be technically precise, the 'i=1…38' should be added in the subscript below 'maximize'"
 Thank you for pointing this out. To make things cleaner we have just removed the underset (x_i,y_i) because they are redundant with the shown objective inputs.
 See Eq. 26 in the attached revised manuscript excerpts
 "Line 300: forward differentiation is used. What is the advantage of this over using SNOPT without providing the gradients explicitly? I do not believe that this will be significant, since in that case SNOPT constructs gradients based on FD? This can be even less expensive than forward differentiation, and accuracy loss is often not significant (depending on implementation choices). Please discuss in more detail the gains etc. Usually, significant speedup would only follow from backward differentiation. This should be better substantiated in the manuscript, in particular since, in the abstract, you seem to claim this as an important innovation."
 Thank you for bringing this up. Our explanation was not clear enough. ForwardDiff.jl does not use the forward finite difference method, but rather forward mode algorithmic differentiation (AD). We have added more detail in section 2.7 to clarify this point. AD has been shown to be much less computationally costly and more accurate than finite difference methods, such as the one provided in SNOPT.
 See lines 340347 in the attached revised manuscript excerpts

 "Line 305: please discuss the WEC method in more detail."
 Good suggestion, we have added more detail about the WEC method in section 2.7.
 See lines 348359 in the attached revised manuscript excerpts
 "Also better explain why standard multistart methods do not work? If they are as good, why not use a standard from an optimization library"
 WEC is a continuation optimization method, not a multistart method. However, using it with a multistart method is recommended. We have provided an explanation of, and motivation for, our multistart approach in section 2.7
 See lines 365368 in the attached revised manuscript excerpts
 "Line 305: please discuss the WEC method in more detail."
 "Line 314: what do you mean with 400 optimizations? This is confusing. If I’m not mistaken, you solve Eq 22 only twice. Better clarify/make distinction"
 This should be more clear with our additions made to section 2.7. We ran 400 optimizations for each case (high TI and low TI). The final optimized result shown is the best of the 400. Each optimization used a different starting layout, but all were compared to the single base case provided in the paper. Multistart is a common approach for wind farm layout optimization.
 See line 365 (and all of 2.7) in the attached revised manuscript excerpts
 "Figures in general: please make as much as possible black&white friendly (some plots are not readable when printed in gray scale). For many figures this should be possible without losing attractiveness of the figure in color."
 While we recognize that the color scheme may not be ideal for printing, we would like to leave it as is. The colors were selected for colorblind readers, as requested in the WES submission guidelines. Since most readers will be seeing the article online, we believe that having a colorblindfriendly palet is more important than having a printer friendly one. That said, we did adjust some figures to be more clear in black and white using marker styles instead of color.
 See Figs. 14 and 15 in the attached revised manuscript excerpts
 "Wind directions throughout paper: add degree symbol"
 Thank you for noting the inconsistency. We have added the degree symbol in the appropriate locations throughout the paper.
Jared J. Thomas et al.
Jared J. Thomas et al.
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