First the reference spectrum is corrected to remove the SAE AIR-1845 atmospheric attenuation α_n,ref:

where L_n(d_ref) is the unattenuated spectrum at d_ref = 305 m and α_n,ref is the coefficient of atmospheric absorption for the frequency band n taken from Table D-1 (but expressed in dB/m).

Next the corrected spectrum is adjusted to each of the 10 standard NPD distances d_i using attenuation rates for both (i) the SAE AIR-1845 atmosphere and (ii) the user-specified atmosphere (based on SAE ARP-866A).

1. (i)

   For the SAE AIR-1845 atmosphere:

   Ln,ref(di) = Ln(dref) – 20,lg(di/dref) – αn,ref · di

   (D-2)

2. (ii)

   For the user atmosphere:

   Ln,866A(T,RH,di) = Ln(dref) – 20,lg(di/dref) – αn,866A(T,RH) · di

   (D-3)

where α_n,866A is the coefficient of atmospheric absorption for the frequency band n (expressed in dB/m) calculated using SAE ARP-866A with temperature T, and relative humidity RH.

At each NPD distance d_i the two spectra are A-weighted and decibel-summed to determine the resulting A-weighted levels L_A,866A and L_A,ref — which are then subtracted arithmetically:

$\mathrm{\Delta L}\left({\mathrm{T,RH,d}}_i\right)=L_{\mathrm{A,866A}}-L_{\mathrm{A,ref}}=10\times \lg \sum _{n=1}^{24}{10}^{\left(L_{\mathrm{n,866A}}\left({\mathrm{T,RH,d}}_i\right)-A_n\right)∕10}-10\times \lg \sum _{n=1}^{24}{10}^{\left(L_{\mathrm{n,ref}}\left(d_i\right)-A_n\right)∕10}$

(D-4)