Main comment

The authors present a topic of high actual relevance and which certainly represent achallenge to be addressed in the wake steering/turbine yaw angle wind farm optimization: The sensitivity of power improvements and obtained yaw angles to the different actors invoved in the optimization. They address it in a comprehensive manner, from a very simple case up to a full operational wind farm. They study the sensitivity of both variables to the analytical model used, to the optimization algorithm, and to the turbines layout or atmospeheric conditions (in terms of turbulence intesity) considered. Results show eviddence that strong sensitivities exist to most of the considered elements. However, in its current form the study requires major revisions.

Following, major, moderate and minor issues are disclosed:

Major points of concern (in order of concern):

1. I am considerably concerned with the fact that the authors claim [line 135] to be using the exponential loss of power according to the yaw angle as w=0.627 following Fleming et al., (2017), whereas w (pP therein) is therein 1.43 or 1.88 depending on the chosen turbine, and 1.41 when fitted into a cosine function. They need to justify the use of the chosen value (w=0.627) in order to being able to proceed with the paper, otherwise it would be a rejection as this parameter is applied in all the analytical models used (it is embedded in the FLORIS framework). In addition, you are applying the same w value for the different turbines considered, whereas Fleming et al. (2107) evidences a different value when considering different turbines. The validity of this parameter must be checked before proceeding with the rest of the review, because if its invalidity was verified the whole work would be needed to be re-done (thus rejected herein).
2. In sections 4.2.1 and 4.2.2 the authors show several times that, the used optimization algorithm (SLSQP) has serious problems to find global maxima for each turbine individually and therefore for the overall wind farm. Then in sect. 4.2.3 they show the results statistics or TuRBO and SLSQP, showing a clear outperforming by TuRBO, a stochastic optimization approach. Indeed, the fact that stochastic algorithms present higher skill than gradient-based algorithms is shown in contributions such as e.g, see Kuo et al., 2020: "Wind Farm Yaw Optimization via Random Search Algorithm”. For both reasons, it is worrying surprising that they do not apply TuRBO for the analysis of the long sections 4.2.1 and 4.2.2. Please re-do 4.2.1 and 4.2.2 sections (at least also) for the TuRBO algorithm, or consider dismissing such sections.
3. With their statement at Line 370: “To the best of the authors’ knowledge, the work by Dou et al. (2020) is the only published study in which wake steering optimisation is performed on the Horns Rev farm layout” the authors seem not to handle the literature in depth, as they fail to raise other contributions such as the one by Zong and Porté-Agel (2021): 'Experimental investigation and analytical modelling of active yaw control for wind farm power optimization' (Section 6). This will entail (at least) serious implications in their discussion on their obtained results.
4. As a follow-up from point 3, a flagrant lack of state of the art on wake steering optimization contributions (at least those on open-loop) is noted in the introduction.
5. Numerous descriptive elements of the introduction and methodology are misplaced (those at the introduction should be at the methodology and vice-versa), and the paper shows in general serious lack of appropriate writing style. All my comments regarding these two aspects are indicated in the attached PDF.
6. Finally, due to the fact that the analytical models used were not validated against ground truth (field campaigns) or more robust representations (e.g., wind tunnel experiments, high resolution numerical simulations as LES), it is very difficult to detect which analytical model is actually performing better. Therefore I would at least recommend to apply the optimized yaw angles obtained with a given model into the rest of models (inter-model cross-validation), and check how solutions perform.

Moderate and minor corrections:

There are around 150 moderate (highlighted in orange) or minor (highlighted in yellow) comments and corrections throughout the attached PDF. In addition there are numerous recommendations to remove small pieces of text.

Final remark: The reviewer has not authored any of the works referenced in the current review.

• The Jensen model does a poor job at wake steer modeling, I don't think it was really designed for this so the time spent describing the model or looking at results of this model I think could be given over to better use
• Then more generally, the difference of the results between models is also less interesting I think because the models were anyway designed to produce different results, so this does not need to be proved in my opinion

• It would be interesting to know more about the Turbo method, not just the general theoretical description of the method, but how specifically it is implemented in this case and why it is out-performing SLSQP
• Is this result specific to Turbo vs SLSQP, or would it be expected to generalize to similarly structured optimizers?
• A diagram of the turbo method would be welcome
• Would other optimizers compare interestingly? Genetic annealing? Serial-Refine?