Ag, The excess attenuation due to ground reflection is obtained by combining the direct wave and the reflected wave incoherently, that is the energy from the ground wave is added to the direct wave.
R = Z sin(β) - ρc
Z sin(β) + ρc
where
β is the angle the reflected wave makes with the ground
Z is the complex ground impedance (a function of the flow resistivity);
ρ is the density of air; and
c the speed of sound.
The reflection loss AR is given by -20*log10(R)
Ag = -10log10(1 + 10-AR/10)
Geometry of Reflected Path
Reflection loss in dB
Flow Resistivity values for ground objects in PEN3D
The ground reflection attenuation (or ground effects) will be between 0 and -3dB ( a negative value is an increase in noise levels) for all cases.
This contrasts with the coherent reflection approach. The coherent approach is considered to be an “exact” method. For those situations where the source and receiver are located close to the same very hard reflecting plane and the path difference between the direct path and the reflected path is small, then the addition of the reflected wave and the direct wave will result in 6 dB increase rather than a 3 dB increase. However, at large distances the sound pressure level reduces at 12 dB per doubling with the coherent model (not 6 dB as per the incoherent model). This approach, while “exact”, it is dubious as DTM models are rarely of sufficient accuracy nor can noise models truly account for the effects of atmospheric turbulence.
Other methods such as the Nordic method or ISO 9613 divide the region between the source and receiver into three zones, and those zones closest to the source and to the receiver can potentially have higher absorption values.
It follows then that if a noise source was measured at a distance of 30 m and the sound power level is calculated by the commonly adopted formula PWL = SPL + 10log10(2 π r2) then the calculations using the PEN3D methodology will remain conservatively high for all distances.
PEN Implementation
The ground reflection (or ground effects) is a complex calculation using the flow resistivity for the surface likely to provide the ground reflection and the likely angle of incidence of the reflected wave to the ground. In those instances where the ground is highly absorptive the excess correction will approach zero. For those surfaces which are highly reflective the correction will be - 3dB, ie will lead to an increase in noise levels of 3 dB(A) (simulates hemispherical propagation).
While there are numerous methods to calculate ground effect (and some of which provide significant attenuation (reduction of noise levels)). This is one of the more conservative estimate of ground effect in the far field and in the opinion of Bies & Hansen “as the distance from the source or frequency increases, the incoherent model will become more appropriate”.