  Slant path delay is computed by direct integration of differential 
equations of electromagnetic wave propagation.  Equation of 
propagation are the solution of the variational problem of wave 
propagation between the emitter and receiver. According to the 
Fermat principle, the trajectory of propagation is that that minimizes 
travel time.

  It is assumed the receiver is located at the infinity. Therefore,
the problem to find the trajectory is reduced to a solution of a system 
of non-linear differential equations of the 4th order with mixed initial 
conditions.

  After the trajectory of wave propagation is found, the path delay is 
computed by integrating the refractivity over the trajectory.

  Path delay is computed on a regular grid of azimuths elevations. 
The grid is equidistant over azimuth and non-equidistant over elevation 
angle. The minimum elevation is 3 degrees. To generate the elevation 
grid, an equidistant sequence m_i is formed on the interval 
[M(90), M(3deg)], where M is the mapping function of the ISA standard 
atmosphere. Then for each element of sequence m_i, elevation is 
computed as Mi(m_i),. where Mi is the function inverse to the mapping 
function M(e).

  In addition to path delay, surface atmospheric pressure, partial 
pressure of water vapor, air temperature, atmospheric opacity, and 
atmospheric brightness temperature are computed for each station 
for the range of frequencies. Opacity is computed by integrating 
specific opacity along the trajectory. The atmospheric brightness 
temperature temperature is found by integrating the deferral equation 
of radiative transfer under condition of local thermal equilibrium. 
The frequencies for computation of opacity and atmosphere brightness 
temperature are selected to have interpolation errors below 0.3% over 
the range of 1 to 360 GHz, with an exception of the range of oxygen 
absorption [56, 64] GHz. The atmospheric brightness temperature 
includes the contribution of the cosmic background radiation.

