the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 May 2025
Squeezing Turbulence Statistics out of a Pulsed Lidar
Abstract. Accurate estimation of second-order turbulence statistics using pulsed Doppler lidar has been a challenge for a long time, mainly due to the negative influence of probe volume averaging. The present study aims to investigate a novel approach to extracting first- and second-order turbulence statistics directly from the average Doppler spectra in the frequency domain. The main hypothesis is that averaging Doppler spectra over 10-minute intervals can mitigate the influence of probe volume averaging and random noise in velocity retrievals, thereby improving estimates of velocity variance. To achieve this, we develop a new analytical model for the time-averaged Doppler spectrum, beginning with a theoretical formulation based on the beat signal within the interrogation window. The model is applied to 10-minute averaged Doppler spectra collected by a pulsed lidar system pointing toward a sonic anemometer mounted on a meteorological mast in front of a Vestas V52 wind turbine at the DTU Risø campus in Denmark. Validation results demonstrate that the Doppler spectra model, when fitted to 400 ns nominal pulse durations, closely matches sonic anemometer measurements in both mean radial velocities and standard deviations. This agreement is quantified by the least orthogonal square fit slopes of 0.978 for the mean velocities and 0.967 for the standard deviations. In comparison to the conventional time-domain approach, which accounts for only 70.6 % of the standard deviation, the proposed spectral method captures 96.7 %, corresponding to an 88.7 % reduction in estimation loss. However, this model does not accurately estimate variances using the short pulse (200 ns) of the instrument. Despite this limitation for the short pulse, the proposed method is an important step towards better turbulence estimation from pulsed Doppler lidars.
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RC1: 'Comment on egusphere-2025-2226', Anonymous Referee #1, 23 Jun 2025
This is a well-written article describing a new method to estimate the mean and standard deviation of radial velocities from pulsed Doppler lidars. The authors derive a model to estimate these parameters directly from the frequency power spectra, which helps reduce the influence of probe volume averaging and random noise in velocity retrievals. Among other results, the authors find remarkable agreement when comparing the mean and variance for the 400 ns nominal 10-pulse durations with those from a co-located sonic anemometer.
Before recommending publication, I have one major suggestion and a few minor questions and comments.
Major comment:
The article mentions in the Introduction and Conclusion sections that this method could help better characterize turbulence, but little to no detail is given about this point. I understand that this is not the main focus of the paper, but I think it could significantly benefit from more details in this respect. This would allow the reader to get an idea of the particular physical phenomena that the measurements of this method would be targeting.
Some questions associated with this point are: What is the type of turbulence that this method would allow to study? Is it isotropic turbulence? What spatial and temporal scales would benefit from these measurements? Would these scales correspond to the inertial subrange? Viscous subrange?
Answering these questions would add value to the paper, as they add context, not only encapsulating it to be “useful for wind energy applications”.
Minor comments:
Line 50: What attribute of the pulses has a Gaussian temporal profile? Please clarify.
Line 55: Please expand on or provide a citation for the term “interrogation window.” As far as I’m aware, this is not widely used terminology.
Line 140: “However, when the standard deviation is low, the model occasionally estimates zero.” Is this an expected behavior? What causes it? This seems to be the main source of error in your comparison.
Line 150: Why does the model show reduced effectiveness under conditions of lower frequency resolution?
Citation: https://doi.org/10.5194/egusphere-2025-2226-RC1 -
RC2: 'Comment on egusphere-2025-2226', Anonymous Referee #2, 12 Aug 2025
The paper is a useful advance in a field of current relevance. The results are generally clearly presented, but the description of the methodology confused me in places. I have some specific suggestions below of areas for possible improvement. Also, some of the experiments details should be clarified. The paper would be enhanced with a small amount of additional information and analysis.
Specific comments and suggestions below:
On P4, the parameter “s” needs to be more clearly defined. Eqns 1 and 3 imply it has dimensions of time, but line 65 states it is a position and furthermore, line 67 states it “has a concise velocity”, which confused me further. Possibly s is the range (distance) to the scatterer and the corresponding time in the eqns should be 2s/c? However, Figure 3 introduces another parameter x defined by t=x/c, but x does not appear elsewhere in the document.
What is the height of the lidar relative to the sonic? If not the same, then would horizontal beam path possibly give better results?
What is the likely sensitivity to wind direction: we could expect better agreement if the wind aligns along the beam? P6 line 119 implies the measurements were taken with “westerly inflow”: were the data filtered for a range of wind directions around West. If not, what was the distribution of wind directions during the measurement period, and could the analysis be performed with different levels of direction filtering to examine the impact?
Assumption of Gaussian turbulence spectrum (Eqn 5, p9 line 163): can we see some example spectra? Or possibly some analysis of higher order statistics to indicate the validity of the assumption?
P8: what causes the zero values of stdvn? The authors should attempt at least a tentative explanation, e.g. negative (unphysical) values brought about by noise, rounded up to zero?
P8: I have a small objection to the phrase “captures 96.7% of stdvn” since there may be other contributions present, for example, instrumental and other noise sources that are nothing to do with the wind.
P14, fig 11, clearly explain “scale” axis – presumably the level of added noise?
Citation: https://doi.org/10.5194/egusphere-2025-2226-RC2
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