Calculation of the height of radar echoes in the operating principles. Assuming the Earth is round, the radar beam in vacuum would raise according to the reverse curvature of the Earth. However, the atmosphere as an refractive index that diminish with height, due to the variation of its density. This bend the radar beam slightly toward the ground and with a standard atmosphere this is equivalent to considering that the curvature of the beam is 4/3 the actual curvature of the Earth. Depending on the elevation angle of the antenna and the other considerations, one can calculate the height above ground of the target with this formula (R. J. Doviak; D. S. Zrnic (1993). ATMS 410 – Radar Meteorology : Beam propagation (pdf).) :

${\displaystyle H=\left({\sqrt {r^{2}+(k_{e}a_{e})^{2}+2rk_{e}a_{e}sin(\theta _{e})}}\right)-k_{e}a_{e}+h_{a}}$

Where :

• r = distance radar-target
• k_e = 4/3
• a_e = Earth radius
• θ_e = elevation angle above the radar horizon
• h_a = height of the feedhorn above ground.