This is not a paper, but may be helpful. It is the website from the a cloud observation site in West Germany (JOYCE): http://gop.meteo.uni-koeln.de/ag_crewell/doku.php?id=instruments:wind_lidar

- Hasager et al. Remote Sensing Observation Used in Offshore Wind Energy, IEEE Journal of Selected Topics In Applied Earth Observation and eEmote Sensing. Vol. 1, Nº 1, March 2008, Pages 67-79.  

Comparison of vertical profiles measured by cup anemometers and LIDAR

- Bañuelos-Rueda et al. Analysis and Validation of the Methodology used in the extrapolation of wind speed data at different heights. Renewable and Sustainable Energy Reviews Vol. 14, 2010, Pages 2383-2391.

Interesting Review about the topic, including cases of study

KNMI in the Netherlands has a 213 meter high tower near Cabauw for wind measurement at many levels. You may want to inform there and see their publications.

Thank you for the answer, Agustin.

But, unfortunately (if I do not make a mistake) all data in these papers are for vertical profiles of horizontal wind speed. I need vertical profiles of vertical wind speed (w, speed along Z-axis).

ok. You are right. I read your question too fast. I am sorry

We analyzed in 2010 the vertical profile of normal upper wind speed in mainland China. The work was published in Geographical Research in Chinese with English abstract, and is available on my Research Gate profile. However, we have not made any analysis of the wind speed in boundary layer.

This is not a paper, but may be helpful. It is the website from the a cloud observation site in West Germany (JOYCE): http://gop.meteo.uni-koeln.de/ag_crewell/doku.php?id=instruments:wind_lidar

Thank you, Raquel! There are vertical wind speed data approximately from 50 m on this website.

See the CASES-99 dataset (Leon (37.38N, 96.14W)). There you can get  u,v,w components of wind at 20 Hz within the surface layer, starting from 1.5 m upto 55 m height.

Probably, it will be nice, if i share info, that i found on this question by myself.

Cabauw station has w on 4 levels - 3, 60, 110 and 180 m.

And I found paper with lidar data about w vertical profiles:

Henne, S., Furger, M., Nyeki, S., Steinbacher, M., Neininger, B., De Wekker, S. F. J., ... & Prévôt, A. S. H. (2004). Quantification of topographic venting of boundary layer air to the free troposphere. Atmospheric Chemistry and Physics, 4(2), 497-509.

Alexander,

I guess you should first clarify the question what kind of vertical winds you are interested in. Over flat terrain, vertical winds should average to zero, at least near the surface. If you are just interested in turbulence, then you will find a lot of data in the literature, notably publications on measurements at the Cabauw tower. Over complex terrain, vertical winds will not average to zero, and that's what the publication of Henne et al. shows for mountain valleys. Without knowing the scope of your work, it is not possible to give you a suitable answer. Convection may also produce strong vertical winds. Vertical profiles of vertical wind may be measured with doppler radar systems. You may check out the publications by Peter May for this http://www.cawcr.gov.au/staff/ptm/#Publications

Regarding logarithmic profiles: I think that scaling considerations from which logarithmic profiles are derived for horizontal velocity in horizontally homogeneous surface layer are of no relevance for vertical velocity, which should be zero in horizontally homogeneous conditions. Vertical velocity is non-zero e.g. in developing boundary layer after change is surface conditions because of flow convergence. Horizontal length scale is of great importance in the latter case. Of course this is just one example.