This is an excellent paper about an important and relevant topic. I have just a few remarks, mainly to improve clarity:

- Eq. (22), mention that, refer to Eq. (5), n1=-cos phi, n2=cos theta * sin phi and n3=sin theta *sin phi

- line 181: explain in a few sentences why "we need at least six radial velocity variances from different beam directions"

- line 268: "below 0.2 m/s"; shouldn't it be "above"?

- line 269: why 100? (perhaps a reference can be added)

- caption Fig. 5: introduce "beam index"

- line 292: explain "bore point"

- section 4.3.2: perhaps a 3rd option can be applied, according to the IEC: sigma_v=0.7 sigma_u, sigma_w=0.5 sigma_u

- Fig. 15: add titles on top of the 3 rows: "maximum", "median", "centroid"

- Fig. 16: add titles on top of the 3 rows: "LSP sigma_u^2", "LSP isotropy", "U variance"

The manuscript presents the potential benefits of the SpinnerLidar in estimating the Reynold stress terms. This is a useful study, and the results are promising. However, before I recommend the manuscript for publication, several comments need to be addressed/clarified.

General comments:

The writing of the article can be improved. 

Specific comments:

L11-13: Should the authors clearly explain in conclusion why “the variances of the radial velocities estimated from the maximum of the Doppler spectrum are less affected by the lidar probe volume compared to those estimated from the median or the centroid of the Doppler spectrum.”?

L99: What is λ in Equation 8.

L157-158: Is this a good approach?

L177-182: I am not sure I understood it correctly. Which six beams have been used to retrieve the six Reynolds stress terms? It looks like the authors have considered all the combinations of six beams. Is it correct? Is this retrieval at a particular distance? Have you considered the curvature of the scan?