## 3 Surface-Based In-Situ Measurement Techniques
### Sonic anemometers  
Sonic anemometers have become standard instruments in micrometeorological research and monitoring today (e.g., [60]). They use ultrasonic frequencies and pulse repetition rates of the order 50-100 Hz, which are then block averaged to provide output frequencies of 1-20 Hz. Moreover, different types of sonic anemometers have been introduced, with one (provides only one wind component), two (for horizontal wind) or three measurement axes (provides the full 3D wind vector), which can be either orthogonal or non-orthogonal, the latter being more common in 3D sonic anemometers nowadays (Figure 3). Wind velocity component(s) are derived from the composition of travel times of sound pulses along the sonic axes. The wind velocity component along one sonic path is:  
\[v_{s}=\frac{d}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right), \tag{17}\]  
where \(d\) is the length of the sonic path and \(t_{1}\) and \(t_{2}\) are the travel times of the sound pulse in the two directions along the sonic path. The speed of sound can be approximated as:\[c_{0}\approx\frac{d}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right). \tag{18}\]  
However, when there is a wind component perpendicular to the sonic path, a correction for the cross-wind component (\(v_{cw}\)) must be introduced. The true speed of sound is then:  
\[c=\sqrt{c_{0}^{2}-v_{cw}^{2}}. \tag{19}\]  
Some of the sonic anemometers perform the cross-wind correction internally (e.g., CSAT3 by Gampbell Scientific, Inc., Logan, UT, USA), but in some configurations, it must be applied afterwards [61]. The sonic temperature can then be derived from the speed of sound as:  
\[T_{S}=\frac{c^{2}}{\gamma_{d}R_{d}}, \tag{20}\]  
where \(\gamma_{d}=1.4\) and \(R_{d}\) is the gas constant for dry air (\(R_{d}=287.04\) JK\({}^{-1}\)kg\({}^{-1}\)), giving \(\gamma_{d}R_{d}\approx 403\) m\({}^{2}\)s\({}^{-2}\)K\({}^{-1}\)[61; 62]. Sonic temperature is given by \(T_{S}=T(1+0.51q)\)[62], where \(T\) is the true air temperature and \(q\) the specific humidity. It is noteworthy that \(T_{s}\) is very close to the virtual air temperature \(T_{v}=T(1+0.61q)\)[63]. If a sonic anemometer is combined for example with a fast-response hygrometer or an infrared gas analyzer, the turbulent fluxes of heat and moisture, greenhouse gases and/or other contaminants can be measured (e.g., [64; 60; 61; 62]). Sonic anemometers are in many ways superior to other instrumentations used in turbulence measurements. The wind velocities are measured directly, so there is no anemometer inertia involved in the measurement. The high measurement frequencies allow good coverage of the turbulent fluctuations of all scales. The response characteristics are only limited by the length of the sonic paths, which are typically about 10-20 cm only, an order of magnitude smaller than the response length of cup anemometers (Section 3.1 and [18]). Therefore, sonic anemometers are suitable for reference measurements for wind gusts, as well. However, there are several sources of error for sonic anemometers, as well. Transducers may affect the measurement accuracy by causing a wake along the sonic path, and therefore, the absolute values of the measured wind may be biased low [65; 66]. Flow distortion can also be caused by the support struts of the transducer array [66]. A proper design of the anemometer, by optimizing the ratio of the diameter of the transducer head to the sonic path length and by alignment of the sonic paths with a large angle with the horizontal, can reduce the wake effects on the measured wind. Different designs of support struts have also been introduced, as seen in Figure 3. The flow distortion effects are usually corrected by built-in calibration tables [66].