General comments

Dear Authors, I have reviewed your article and would like to provide my feedback on it.

The article investigates the performance of the Proper Orthogonal Decomposition (POD) method when applied to a dataset that is obtained combining data from different flow cases. A dataset of the flow inside a wind farm is used as the case study.

I think the topic of the article can be interesting for scientists working on fluid dynamics. However, there is a lack of significant developments that are specific to wind energy research, which is the topic of this journal. The objectives, most of the methodology and a large portion of the results are about the POD method itself and not about wind energy systems. So, I think this article is not entirely appropriate for this journal and, in its current state, is more suited to a journal on fluid dynamics.

I would also say that article is not very well written: many sentences, particularly in the Methodology section, are hard to follow and it’s difficult to understand their content.

In the Discussion section, it is hard to understand what information is important. In the Conclusion there isn’t any message specific to the wind energy field.

In reason of these comments, I am against publication of this article. My suggestion is to revise the text to improve clarity of presentation. Then, if Authors would like to discuss the POD in general, I suggest considering a journal of fluid dynamics, otherwise they should make it clear which is the impact and usefulness of this research for the wind energy community.

Specific comments

• As said in the General comments, there are many sentences that are not clear and should be revised. These sentences are:
  • First sentence of the abstract. This sentence, in the position it has (the first one of the article) is obscure. I suggest adding a few lines to introduce the article content.
  • Line 35-36. These two sentences are not clear. You must explain what a single flow case is and the difference of considering multiple flow cases.
  • Line 46, “alongside … parameter space”. Not clear. This is the introduction. Try to give enough information so that any reader can understand.
  • Line 81, “which captures the wake dynamics”. Maybe you mean the wake of the upstream turbine? This is not clear, because a turbine inside the line is affected by wakes of all upstream turbines.
  • Line 101-103, “Ct of the wake-generating … in the wake”.
  • Line 104, “the operation of … of the wake”
  • Line 106-107, “where the operating … wake recovery”.
  • Line 109-110. Isn't Fig.2 showing the Ct? Explain the relation between Ct and V.
  • Line 149-150, “Consequently, … in the parameter space”.
  • Line 179-180, “these are not … POD modes”.
  • Line 201-202, “which indicates … different flows”. Not clear, must be argued better.
  • Line 211, “The basis error … of modes”.
  • Line 232-234, “It is noted … 0.4%”.
• Line 82: “one radius upstream”. The effect of induction is present also at a higher distance from the rotor. Maybe you should rephrase this sentence to explain what you mean with "reduce the influence of induction" and why you did not take the plane further upstream.
• The Data availability section is missing. Code and data should be made available to the public to reproduce the results of the article.

Technical corrections

• Line 68-69, “The grid … outlet boundaries”. If it is important, maybe it's worth adding a second panel in Fig. 1 with a sheme of the grid.
• Line 90: “and 𝑈is the velocity”, what velocity?
• Line 97: replace “atmospheric” with “undisturbed”.
• Line 274: of PS-ROM presented by Andersen and Murcia Leon (2022),
• Line 299: you should use \citep{} to make it (Andersen et al. (2015))

The present manuscript tackles a potentially interesting topic for wind energy such as the development of a general basis for model reduction using POD. The subject is interesting and relevant for wind turbine's research, but there are some points that need to be clarified or developed. 

First of all, the paper does not discuss in detail the contest of model reduction for wind turbines. In particular, the introduction lacks reference to the many previous works on POD analysis of wind turbine and wind farm flows (among others, VerHulst & Meneveau Physics of Fluids 2014, Bastine et al. Energies 2015, Hamilton et al., Wind Energy 2015 Physics of Fluids 2016, Phys. Rev. Fluids 2017, Wind Energy 2018; De Cillis et al. Wind Energy 2021, Renewable Energy 2022, Journal of Physics: Conference Series 2022). Also, DMD and ANN are mentioned but not put in the contest of wind turbine flows (see, for instance, Debnath et al. "Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes" 2017; De Cillis et al. "Dynamic-mode-decomposition of the wake of the NREL-5MW wind turbine impinged by a laminar inflow" 2022, among many others).

Moreover, I have some concerns regarding the convergence of the grid, which seems to me too coarse for the LES of 14 turbines, having only 20 points per radius in each direction. The grid convergence of the LES for the considered case needs to be shown in the manuscript, maybe in a dedicated appendix. The same can be said about the choice of the time step set for the extraction of the snapshot from the LES, as well as the total time of the simulation. This quantities are known to affect considerably the convergence of the POD algorithm over one single dataset, so the convergence with respect to this parameters need to be discussed for some of the considered dataset. Moreover, I cannot see any information about the value of the tip speed ratio, and about the whether tower and nacelle are taken into account in the simulation, which are both very relevant information for the considered flow case . In case tower and nacelle are not taken into account, I suggest to discuss the relevance of the simulations to realistic conditions, and to reformulate using the work ''rotor'' instead of "turbine".  

Also, the discussion about the choice of the global POD basis is not sufficiently developed. I understand that the global basis is constructed in an iterative manner, but I am not sure what does this means exactly. For instance, the performance of a basis is evaluated only using the velocity error? Which is the condition for adding a dataset? And why the dataset with worst performance should be added? Since the construction of the global basis is a crucial point of the paper, it needs to be discussed in much more detail. The same can be said about the case study with stochasticity, which is not sufficiently clearly explained. For instance, the authors should explain in more detail the fact that "the actual projected spectrums are used.." etc. 

Finally, I think that the performance of the POD basis cannot be measured only using an integral quantity such as the velocity error, since even if the integral error is rather low, the flow field might have some important structural differences with the simulated one. The POD-reconstructed flow fields need to be shown and compared with the LES snapshots at given times, by showing a velocity error field for each velocity component. 

Typos:

page 2, line 59: Large Eddie --> Large Eddy

page 2, line 49: the acronym LES need to be defined 

page 13, line 275: spectrums --> spectra