Effects of spatial filtering, prefiltering, and aliasing in measurements from applied technologies` Sonic K-Probe

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Courtesy of Applied Technologies, Inc. (ATI)

The Applied Technologies' Inc. (ATI) K-probe measures wind components along three mutually orthogonal axes separated spatially from each other to minimize flow distortion errors. The sonic anemometer samples the wind at a 100-Hz rate but constructs 0.1-s (10-point) non-overlapping block averages to provide. a 10-Hz data train for internal processing. This digital prefiltering is designed to minimize the effects of aliasing high-frequency spectral energy back into the region below the Nyquist frequency (5 Hz). The internal processing consists mainly of corrections for transducer shadowing error in the two horizontal wind measurements and correcting the sonic temperature, measured along the vertical velocity path, for cross-wind contamination. No shadow corrections are applied to the vertical velocity (w) component because of the low wind inclination angles typically encountered near the surface.

In this note all factors affecting the sonic anemometer spectral response are examined to arrive at a final form for the measured w spectrum (the only one spared the transducer Shadow correction). The processes are easy to demonstrate graphically on log-log paper where the multiplication process translates to simple addition of distances on the graph.
We start in Figure 1 with an idealized -5/3 spectrum (I) extending from 1 to 100 Hz. The original 100-Hz sampling aliases the energy above 50 Hz primarily into the region from 10 to 50 Hz. The energy near the Nyquist frequency is raised by a factor slightly above 2, if one includes the second and third folds. But this spectral distortion is too far removed from the 5-Hz Nyquist frequency in the 10-point block-averaged output to affect the final spectrum.

Spatial averaging for the 15-cm path has only a very small effect at frequency ƒ < 5 Hz. The transfer function in Figure 2 corresponds to the curve for w for a wind speed of 5 ms-1. The half-power point falls approximately at a wavelength of 15 cm (the path length), or a frequency of 33.3 Hz. The spatially averaged spectrum (II) in Figure 1 represents the form for the 100-Hz data train.

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