Remarks on the Definition and Estimation of Friction Velocity

One of the mainscaling parameters in similarity theory of the atmospheric boundary layer is friction velocity. Unfortunately, several definitions of friction velocity exist in the literature. Some authors use the component of the horizontal Reynolds stress vector in the direction of the mean wind vector to define friction velocity. Others define the friction velocity by means of the absolute value of the horizontal Reynolds stress vector. The two definitions coincide only if the direction of the mean wind vector is parallel to the horizontal Reynolds stress vector. In general, the second definition gives larger values for the friction velocity. Over complex terrain the situation is further complicated by the fact that the terrain following flow is not necessarily horizontal. Thus, several authors have proposed to use terrain following coordinate systems for the definition of friction velocity. By means of a large dataset of fast-response wind measurements with an ultrasonic anemometer the friction velocities resulting from the different definitions are compared. Furthermore, it is shown that friction velocity can be well estimated from horizontal wind speed, and even better from simple horizontal or vertical turbulence parameters.