This model calculates the attenuation of signals
that propagate through atmospheric gases.

Electromagnetic signals attenuate when they propagate through the atmosphere. This effect is
due primarily to the absorption resonance lines of oxygen and water vapor, with smaller
contributions coming from nitrogen gas. The model also includes a continuous absorption
spectrum below 10 GHz. The ITU model *Recommendation ITU-R P.676-10: Attenuation by
atmospheric gases* is used. The model computes the specific attenuation
(attenuation per kilometer) as a function of temperature, pressure, water vapor density, and
signal frequency. The atmospheric gas model is valid for frequencies from 1–1000 GHz and
applies to polarized and nonpolarized fields.

The formula for specific attenuation at each frequency is

The quantity *N"()* is the imaginary part of the complex
atmospheric refractivity and consists of a spectral line component and a continuous component:

The spectral component consists of a sum of discrete spectrum terms
composed of a localized frequency bandwidth function,
*F(f)*_{i}, multiplied by a spectral line strength,
*S*_{i}. For atmospheric oxygen, each spectral line
strength is

For atmospheric water vapor, each spectral line strength is

*P* is the dry air pressure, *W* is the
water vapor partial pressure, and *T* is the ambient temperature. Pressure
units are in hectoPascals (hPa) and temperature is in degrees Kelvin. The water vapor
partial pressure, *W*, is related to the water vapor density, ρ, by

The total atmospheric pressure is *P* +
*W*.

For each oxygen line, *S*_{i} depends on two parameters,
*a*_{1} and
*a*_{2}. Similarly, each water vapor line depends
on two parameters, *b*_{1} and
*b*_{2}. The ITU documentation cited at the end
of this section contains tabulations of these parameters as functions of frequency.

The localized frequency bandwidth functions *F*_{i}(f) are
complicated functions of frequency described in the ITU references
cited below. The functions depend on empirical model parameters that
are also tabulated in the reference.

To compute the total attenuation for narrowband signals along
a path, the function multiplies the specific attenuation by the path
length, *R*. Then, the total attenuation is *L*_{g}=
R(γ_{o} + γ_{w}).

You can apply the attenuation model to wideband signals. First,
divide the wideband signal into frequency subbands, and apply attenuation
to each subband. Then, sum all attenuated subband signals into the
total attenuated signal.