# Statistical Analysis of Temporal Variation over a Full Year

## Spectral Variation

This section looks at the predicted variation in sound propagation resulting from all possible combinations of ground parameters (Table 8.6) and moderate downward refraction conditions obtained from the meteorological tower data over a full year.

Given that the (temporal) distribution of sound pressure levels at a single downwind location is predicted to be far from normally distributed, a distribution-independent variation descriptor is used, namely the 97.5 percentile minus the 2.5 percentile value. This range contains 95% of the values and would be equivalent to 4 times the standard deviation if there were to be a normal distribution. Additional graphs are shown later for 68% of the distribution values, equivalent to 2 times the standard deviation in a normal distribution.

Figure 8.36 shows typical patterns of the predicted 95% and 68% variations in twenty 1/3 octave bands between 50 Hz and 4 kHz for a source height of 2 m, receiver heights of 1.5 m and 4 m and ranges to 250 m. Below 100 Hz an approximately linear increase in the variation with distance is predicted.

*Figure 8.36* 95% (upper two plots) and 68% (lower two plots) variation margins in sound pressure level in twenty 1/3 octave bands at receiver heights of 1.5 m and 4 m from a 2 m high source, predicted due to changes in the (moderately) downwind refractive state of the atmospheric boundary layer throughout the year and impedance changes corresponding to 7 types of “grassland” [42]. Reproduced fromT. Van Renterghem, D. Botteldooren,Variability due to short distance favorable sound propagation and its consequences for immission assessment*,/AcousL Soc.Am.,* **143**: 3406-3417 (2018) with the permission of the Acoustical Society of America.

Above 100 Hz, the predicted variation increases rapidly until it plateaus at distances that are closer to the source as frequency increases. Near 315 Hz, the magnitude of this plateau starts to decrease, while above 1000 Hz the predicted variation is maximum within 50 m of the source. When the source height is 2 m and the receiver height is 1.5 m, the predicted 95% variation in 1/3 octave bands from 100 Hz to 200 Hz is about 30 dB. With increase in receiver height to 4 m, this variation reduces to about 25 dB. For an elevated source height of 20 m and a receiver height of 4 m the predicted 95% variation reduces to 17 dB [51].

The strong frequency dependence of the variation between 100 and 1000 Hz is consistent with the influence of refraction on the destructive interference zone associated with ground effect as discussed in Section 8.8.5 (see also Chapters 2, 5 and 6). Downward refraction of sound causes significant changes in path length and leads to multiple paths contributing to the level at a receiver. The combination of different types of grassland impedance and the wide range of refraction conditions is predicted to result in particularly strong variations between about 100 Hz and 1000 Hz which can be pronounced over several tens of metres.