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

Based on the site distance may be calculated as

$s = k_e r_e \arcsin\left( \frac{r \cos\theta}{k_e r_e + h_n(r, \theta, r_e, k_e)}\right)$

where $$h_n$$ would be provided by bin_altitude.

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

• binalt (numpy.ndarray) – site altitude [m] amsl. same shape as r.

• 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]