the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Aug 2025
Wake-resolving acoustic tomography: advances through numerical covariance methods
Abstract. Acoustic tomography offers path-integrated measurements of atmospheric velocity and temperature fluctuations with high spatial resolution. Classical implementations of time-dependent stochastic inversion rely on homogeneous, isotropic covariance models that are poorly suited to the anisotropic structure of wind turbine wakes. By directly estimating heterogeneous covariances from large-eddy simulations (LES) into the time-dependent stochastic inversion operator, we relax implicit assumptions in the analytical models used historically. Retrievals using these LES-informed models improve agreement with true fields in variance, turbulent kinetic energy, and spectral content compared to analytical and precursor-based covariance models. The results indicate that LES-informed covariance models can enhance the accuracy of acoustic tomography retrievals in complex, anisotropic flows such as wind turbine wakes in some cases and highlight instances where analytical models still offer competitive performance, despite their simplifying assumptions.
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Status: final response (author comments only)
- RC1: 'Comment on wes-2025-137', Anonymous Referee #1, 07 Jan 2026
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RC2: 'Comment on wes-2025-137', Anonymous Referee #2, 01 Feb 2026
This paper investigates acoustic tomography applied to a wind turbine wake. Atmospheric acoustic tomography deduces a field of wind speeds and temperatures typically in a plane from travel times from a multitude of travel times between pairs of acoustical transducers (loudspeakers/microphones). The study is purely numerical. Detailed large-eddy simulations (LES) of a turbine wake are performed and the acoustic travel times of an array of transducers is calculated. Then those travel times are inverted to reconstruct the turbulent fields. Atmospheric acoustic tomography has a long history and was pioneers by people like D. W. Thomson, D. K Wilson, Ostashev and Vecherin, mainly in the 90’ies and early 2000’s. The expressions relating the velocities and temperature along the beams connecting the pairs need to be inverted, and the authors of this paper uses time-dependent stochastic inversion, which required information about the correlation structure of the turbulent fields. Common for the historical efforts with atmospheric acoustic tomography is that, although interesting, the technique has not provided very valuable measurements of atmospheric statistics. Acoustic tomography does not provide anything for wind energy research that other techniques do provide. For example, Doppler lidar provides measurement much easier, more precise, with fewer assumptions and with less effort. One fundamental problem with acoustic tomography is the requirement of prior knowledge of the correlation structure of the fields. The authors show clearly that the results are very dependent on these correlations whether they come from the actual LES of the wake flow, LES of the flow without the turbine, or a model correlation function tuned to the problem. So, in order to measure the flow one needs detailed information about the flow in advance. This is not a good situation for any measurement technique.Â
While the simulations, the inversion, the figures and the discussion are all well performed and prepared, I have a hard time seeing the relevance of this work for wind energy. The technique has for decades not obtained a break-through in actual atmospheric applications. The fundamental problems with the dependence on the assumed correlation structure of the flow will be dwarfed by the economic and technical problems arising an actual experimental situation. For a modern size turbine with a hub height exceeding 150 m one would have to erect (at least) seven mast of the same height, which would be a multimillion dollar expense in itself. Some of the acoustic beams would pass the rotor of the turbines, which is a strong source is acoustic noise, and thus corrupting the travel time estimations.Â
While I do not dispute the quality of the research, I cannot see the relevance and perspectives for wind energy. I therefore have to recommend rejection of this manuscript.
Citation: https://doi.org/10.5194/wes-2025-137-RC2 - AC1: 'Comment on wes-2025-137', Nicholas Hamilton, 26 Feb 2026
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Summary
This article describes a virtual experiment comparing new implementations of the Time-Dependent Stochastic Inversion (TDSI) underlying acoustic travel-time tomography (ATT), an immature sensing technique. Â The article uses a Large Eddy Simulation (LES) of a wind turbine wake in convective and neutral conditions as a measurement domain, and computes retrievals of a virtual ATT array using different assumptions about the spatial correlation of different points in and around the virtual turbine. The new methods include one that uses the LES itself as the source for the correlation matrix. While seemingly circular, this approach represents a useful upper bound on expected performance for ATT arrays in challenging, heterogeneous conditions such as wind turbine wakes. In fact, the results of this benchmark case do not perfectly recreate the u', v', and T' fields, showing that even with nearly perfect spatial correlation information, the sensor returns imperfect (but very compelling) results. Â The results clearly demonstrate the need for more sophisticated covariance models if ATT arrays are to be used to research wind turbine wakes and other complex-structured flows. The baseline correlation techniques are not adequate, but do demonstrate some skill in capturing the irregular flows in the turbine wake. Even this is quite compelling. While reading the article, many new ideas occurred to me about potential next steps, which is one of the intended outcomes of research such as this, exploring new implementations of a promising sensing technique. For immature sensing techniques, and new applications, this type of intermediate, building-block research is highly useful.Â
Comment #1
The article is lacking a clear description of the virtual ATT array deployed in the experiment. Section 2 describes the theory underlying ATT and mentions the ATom toolbox on line 47. Details about the virtual array footprint are briefly mention on line 225. In line 256 it is noted that all reconstructions use N_f = 4. Line 320 and Figure 7 illustrate the paths of the ATT array in space. In lines 513-515, the Discussion section, it is noted that there is no treatment for instrumental noise, spatial resolution limits, or other uncertainties in physical measurements. In order for follow-up studies to duplicate the results herein, these details need to be included clearly in Chapter 2 to describe:Â
- pulse shape of outbound signals (if it's an impulse, state this). This limits the accuracy of the TOF retrieval
- polar pattern for each outbound signal (if circular, state this)
- polar pattern for the microphone (if circular, state this)
- signal processing detail, if any, of receiver, zero padding, acquisition time, window function, sample acquisition rate
- timing of outbound pulses, e.g. "each transmitter simultaneously issues a perfect impulse with with a 1 Hz sampling frequency"
- Exact coordinates of the ATT nodes
- Multipath echoes (i.e. Tx1 reflects off of Tx2 structure and arrives at Tx3 at t=x seconds) if any are modeled
- Interference of multiple signals arriving at the same receiver (if no treatment, state this)
Many of these configuration settings appear in the ATom toolbox example notebooks. Include the exact implementation to allow for follow-up articles to reference the configuration contained in this article. Particularly in this case, where the base theory is being expanded, it's critical to guide readers through the subtleties.Â
Comment #2
All of the normalized results for temperature fluctuation retrievals in neutral conditions are essentially meaningless. Fig 5 (b), bottom graphs, Fig 6 leftmost graph, Fig 13 bottom right... all useless. It is stated that the T' fluctuations are small for the neutral case in lines 291-295 and 419-421 -- this is understood -- I believe that the NRMSE is so large; nonetheless, it would be better to show simply RMSE for T' instead of NRMSE, for both the convective and neutral cases. There is no value in showing the enormous NRMSE. Retain your explanations why T' is shown this way, and the weaknesses in the neutral case, but show the actual errors so the reader gains an understanding of the absolute error (which may show that the values are quite close, if small) and retain the commentary about the T' ~ 0.1 practical limit for high frequency temperature retrievals. Â
Minor Technical Comment
In Figure 5, the N_r legend interferes with the data in the two leftmost graphs. This should be formatted more clearly.Â
The three approaches for the covariance model choices should be listed in a table along with the additional detail about the virtual ATT array. These three methods are clear in the results, but it would help the reader to have this crystal clear in the description of the experimental setup.Â