CNOSSOS Barrier + Ground Effect

**Strutt|Environmental Noise|CNOSSOS Barrier + Ground Attenuation** inserts attenuation (dB) into the active row of the worksheet calculated using the CNOSSOS EU noise propagation model.

Note that *either* the CNOSSOS Barrier loss or the CNOSSOS Ground Attenuation loss should be applied - not both.

The CNOSSOS barrier loss also includes the ground-reflected component on either side of the barrier.

As a test for whether the barrier effect should be applied, check whether the (signed) path difference `delta` for the diffraction edge (i.e. in the illuminated zone `delta` is negative) - if the path difference is `delta < -lambda/20` where `lambda` is the wavelength of sound at the frequency of interest, then diffraction may be neglected and the ground attenuation calculation should be used (Rayleigh's Criterion).

The CNOSSOS barrier calculation is the combination of the following terms:

- `Delta_("diff"(S,R))`, the pure diffraction loss from the true source `S` to the true receiver `R`
- `Delta_("diff"(S prime,R))`, the pure diffraction loss from the image source `S prime` to the true receiver `R`
- `Delta_("diff"(S,R prime))`, the pure diffraction loss from the true source `S` to the image receiver `R prime`
- `A_(ground(S,O))`, the ground reflection from the true source `S` to the diffraction edge `O`
- `A_(ground(O,R))`, the ground reflection from the diffraction edge `O` to the true receiver `R`

CNOSSOS is developed for propagation above varying-height ground planes, and uses the concept of *equivalent height* `z_s,z_r` - i.e. the source and receiver heights for calculating the ground effect are defined relative to the average height of the ground plane, and are not necessarily the same as the local source/receiver heights `h_s,h_r`:

In general, the source-side ground plane and the receiver-side ground plane will be at different angles of inclination relative to the barrier.

E.g. in the following example, the dashed red line is the source-barrier average ground plane, and the dashed green line is the barrier-receiver average ground plane:

To simplify the calculation, Strutt requires the user to input the following parameters:

- The source height `Delta h_S` and receiver height `Delta h_R` relative to the base of the barrier.
- The horizontal distances `x_S` and `x_R` from the source to barrier and from the barrier to receiver.
- The angles of inclination of the source plane `theta_S` and receiver plane `theta_R` in degrees.

The coordinate system and sign convention system used is with the positive `x`-direction from source to barrier, so that 'rising' terrain has positive slope (i.e. ground sloping up from source to barrier, or from barrier to receiver); conversely 'falling' terrain has negative slope (i.e. ground sloping down from source to barrier, or from barrier to receiver).

In the example above, the source-barrier ground plane (red line) has positive slope, and the barrier-receiver ground plane (green line) has negative slope. - The vertical offsets `Delta z_S` and `Delta z_R` between the source-barrier ground plane and the local ground height at the barrier, and between the barrier-receiver ground plane and the local ground height at the barrier.

E.g. in the example above, the source-barrier ground plane (red line) passes above the 'true' ground height at the base of the barrier, hence `Delta z_s` is positive, while the barrier-receiver ground plane (green line) passes below the base of the barrier and `Delta z_r` would be negative.

The CNOSSOS barrier calculation also uses the ground factors `G_(w,S)` and `G_(w,R)` over the source and receiver ground planes (i.e. proportion of porous ground). In cases where the ground plane consists of multiple ground types, the average `bar G` (weighted by the extent of each ground type) should be used.

Typical values of `G` are as follows:

- Soft, uncompacted ground (pasture, loose soil); snow etc: `G=1.0`
- Compacted soft ground (lawns, park areas): `G=0.7`
- Compacted dense ground (gravel road, compacted soil): `G=0.3`
- Hard surfaces (asphalt, concrete): `G=0.0`

The CNOSSOS model predicts the attenuation under **neutral** (or "homogenous") atmospheric conditions (constant sound speed where sound propagation paths are straight rays), as well as **adverse** (or "favourable") conditions where a sound speed gradient results in curved ray paths.

The effect of the curved ray paths is to increase the average propagation height and reduce the strength of the barrier and ground effects. The curved ray paths can also result in the receiver changing from shadow zone to illuminated zone under adverse conditions, e.g. as shown in the 2^{nd} Case below, where although the barrier intersects the straight-line from source to receiver, the curved ray paths would go over the top of the barrier:

The path difference `delta` under adverse conditions is calculated as per neutral conditions, except using the length of the curved ray paths, which are calculated as follows:

`hat (MN) = 2 Gamma sin^-1((MN)/(2 Gamma))`, where:

`hat (MN)` is the length of the curved path from point M to point N

`SR` is the straight line distance from point M to point N

`Gamma` is the curvature of the path, calculated as: `Gamma = Max(1000,8 d_(SR))`

`d_(SR)` is the source-receiver slant distance

For the special case (Case 3 above) where the line of sight from source to receiver lies above the barrier, the path difference is calculated using point `A`, the vertical projection of the barrier height to the line-of-sight from source to receiver, as follows:

`delta = 2 hat (SA) + 2 hat (AR) - hat (SO) - hat (OR) - hat (SR)`

The diffraction attenuation under neutral or adverse conditions is calculated using the same formula; only the path difference is different, as explained above:

`Delta_("diff") = {(10 C_H log_10 (3+40/lambda C_D delta) " if " 40/lambda C_D delta >= -2),(0 " otherwise") :}`

where:

`lambda` is the wavelength

`delta` is the path difference (calculated for neutral or adverse conditions as discussed above)

`C_D` is a coefficient for double diffraction:

- `C_D=1` for single diffraction
- `C_D = (1+((5 lambda)/e)^2)/(1/3 + ((5 lambda)/e)^2)` for double diffraction, where `e` is the separation of the diffraction edges

`C_H` is a coherence coefficient that reduces the strength of the barrier effect at low frequencies where the barrier size is small relative to wavelength.

`C_H="Min"((f h_("eff"))/250,1)`, where

`f` is the frequency

`h_("eff")` is the larger of the effective barrier heights `z_(O,S)`,`z_(O,R)` relative to the source/receiver ground planes.

The overall barrier + ground loss `A_("diff")` is calculated as follows:

`A_("diff")=Delta_("diff"(S,R))+Delta_(ground(S,O))+Delta_(ground(O,R))`

I.e. pure diffraction loss + ground effect (source side) + ground effect (receiver side).

The ground effect terms are calculated using the image source/receiver diffraction terms plus the ground reflection terms for the source/receiver ground planes - i.e. effectively weighting the ground reflection by the strength of the diffracted path to/from the image source/image receiver.

`Delta_(ground(S,O)) = 20 log_10(1+(10^(A_(ground(S,O))/20)-1)*10^((Delta_("diff"(S prime,R))-Delta_("diff"(S,R)))/20))`

`Delta_(ground(O,R)) = 20 log_10(1+(10^(A_(ground(O,R))/20)-1)*10^((Delta_("diff"(S,R prime))-Delta_("diff"(S,R)))/20))`

`Delta_("diff"(S,R))` is the pure diffraction loss from source to receiver

`Delta_("diff"(S prime,R)` is the pure diffraction loss from image source to receiver

`Delta_("diff"(S,R prime))` is the pure diffraction loss from source to image receiver

`A_(ground(S,O)` and `A_(ground(O,R))` are calculated using the CNOSSOS Ground Attenuation calculation.

References:

- Stylianos Kephalopoulos, Marco Paviotti, Fabienne Anfosso-Lédée (2012)
*Common Noise Assessment Methods in Europe (CNOSSOS-EU)*EUR 25379 EN. Luxembourg: Publications Office of the European Union, 2012, 180 pp.

Comments or suggestions to strutt@arup.com