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====== Doppler Wind profiler uncertainty in a turbulent atmosphere ======

Doppler wind profilers measure the wind speed component along the direction of 'line of sight',
or direction of a beam. To derive the 3-D wind vector it is necessary to scan and measure at least 3 beams and tilt at least some of them. This results in different locations for the different Doppler speed measured at a certain height. The basic assumption is that the wind vector at this different locations is everywhere the same. But in a turbulent atmosphere this assumption is not fulfilled.

We present a method to estimate the uncertainty which arises from the violation of this principle.  It can easily applied to any arbitrary scan pattern.
On the basis of this method we can give some principle recommendations for scan patterns:
The uncertainty of the so called 'Doppler beam swinging' method with one vertical beam and two beams tilted in the principal directions has a relative large error. A scan with three tilted beams equally distributed over azimuth gives a by about 40% smaller uncertainty. For azimuth scans at constant elevation the uncertainty is the larger the larger the elevation is. Below about 40deg elevation the dependency on elevation is rather small. The uncertainty decreases with the number N of beams with 1/sqrt(N) i.e. doubling the number of beams reduces the uncertainty by about 30%.