Dear Alexander,

If you have a parameterization giving you the horizontal wind speed, why not using the continuity equation for getting w? This is a crude way to obtain w by integration of the horizontal wind velocity divergence. You have much more complex but efficient methods to retreive w. One is provided by the Q-vectors approach but I don't know if your data allow to access to all the terms needed to retrieve w.

See for instance the papers:

Giordani, H., L. Prieur, and G. Caniaux, 2006: Advanced insights into sources of vertical velocity in the ocean. Ocean Dynamics, 56, (5-6), doi :10.1007/s10236-005-0050-1.

Giordani, H., and G. Caniaux, 2011 : Diagnosing vertical motion in the equatorial Atlantic. Ocean Dynamics, 61, 1995-2018, doi :10.1007/s10236-011-0467-7.

 In conclusion, try to use the most simple method (continuity) and then if possible the more complex methods from the divergence equation of motion. Note that the divergence equation can be stationnarized, linearized and so on to be adapted to your own case in order to follow the methodology "go from the simplest to the most complicated".

Best,

G.C.

Thank You for the answer, Guy.

I think, it is not possible to use continuity because my parameterization gives me horizontal wind speed depending only from Z-axis, but nof from X-axis. And in this case I would have dw/dz=du/dx=0.

It is not possible to use horizontal divergence (and more complicated methods) on the same reason - I do not have data. I have only data from one sonic anemometer and solve 2-dimensional (in space) PDE for tracer on horizontal scales of 1000 m in surface layer.

I have mean vertical speed, and think, that it is somehow possible to use it...

In that case, it is a bit more difficult to answer... w being a 3D variable

G.C.

You can use the N-Vektor, whcih is the extended Q-Vektor, of P.Nevir (FU Berlin). It relates the ageostrophic wind component and the geostrophic wind components. This might be what you need. I know publications in German language only. You might contact P. Nevir directly.

Greetings, Andreas Will

This depends on the range of scales over which you are attempting to model w(t,z).

For example, at/for length scales smaller than several km, there is quite a bit of literature on flux measurement correction, such as for adjusting covariances of sonic-anemometer vertical velocity and scalar concentration; e.g. getting/removing (or w trends) in carbon-flux measurements.  

Thank you, Mark. I want to have w(t,z) on vertical scale - from 0 to 50 m, and on horizontal scale - about 1000 m. 

I have read about vertical speed correction in some papers/books. But authors give vertical velocity standard deviation as a function of z and stability (as example, [Lee et al., 2004, Handbook of Micrometeorology: p. 52]). I have't seen any functions for w(z).

If it is not so difficult, can you give some references?

The similarity theories for horizontally homogeneous surface layer normally assume w=0. Of course in real atmosphere there are different mechanisms of vertical velocity generation. I think for the lower part of atmosphere the most important mechanisms are the vertical instability and the horizontal change of friction. However except the case of very unstable conditions in surface layer shear generation of turbulence dominates. Therefore horizontal variation of drag should be the most important mechanism of the vertical velocity generation in surface layer. That mechanism is considered in paper by Ingel, 2007. Vertical Motions Associated with Inhomogeneous Friction at the Underlying Surface// Russian Meteorology and Hydrology, 2007, Vol. 32, No. 6, pp. 413–415. There w(h) is parameterized as a function of horizontal drag inhomogenity, where h is ABL height. I suppose that you can linearly interpolate towards w(0)=0 to obtain w(z)

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

In general, there are two controls of w(t,z) in surface layer:

They can influence on w(t,z) together, but sometimes only one has a real impact. 

w can be calculated on the base of regression w/u versus angle, where w - vertical speed, u - horizontal speed on the same height in the same time, angle - wind direction (in degrees or radians). Than, if you have u(t,z), you can calculate w(t,z). For my data I have this pattern (see attached figure) for real measurements of u and w on 3 meters. You can find some points about it in (Baldocchi D., Finnigan J., Wilson K., Falge E. 2000. On measuring net ecosystem carbon exchange over tall vegetation on complex terrain // Boundary-Layer Meteorology. 96(1-2), 257-291)

Also, there is data that w depends on atmospheric stability (see Aubinet, M., Heinesch, B., & Yernaux, M. (2003). Horizontal and vertical CO2 advection in a sloping forest. Boundary-Layer Meteorology, 108(3), 397-417), but for my data it doesn't work.

Dear Alexander,

Nice solution!

If I well understand you solved your problem by using a physical argument and then by using a regression between U and W. I think this is an elegant solution. The question is to know if it is not a single case and if it can be used more general cases?

Best

G.C.