Calculates great circle distance from radar site to radar bin over spherical earth, taking the refractivity of the atmosphere into account.

$s = k_e r_e \arctan\left( \frac{r \cos\theta}{r \cos\theta + k_e r_e + h}\right)$

where $$h$$ would be the radar site altitude amsl.

Parameters
• r (numpy.ndarray) – Array of ranges [m]

• theta (scalar or numpy.ndarray) – Array broadcastable to the shape of r elevation angles in degrees with 0° at horizontal and +90° pointing vertically upwards from the radar

• sitealt (float) – site altitude [m] amsl.

• re (float) – earth’s radius [m]

• ke (float) – adjustment factor to account for the refractivity gradient that affects radar beam propagation. In principle this is wavelength- dependent. The default of 4/3 is a good approximation for most weather radar wavelengths

Returns

distance (numpy.ndarray) – Array of great circle arc distances [m]