Formula for sun's atmospheric refraction below the horizon I have searched in Google and found interesting articles for atmospheric refraction influence on sun's elevation above the horizon (from 0° till 90°).
eg. Bennett G.G. etc.
I would like to know if there is a formula that approximates the refraction when the sun's center is below the horizon (from 0° to ca. -3°) and taking in account for temperature and air pressure.
Without taking temperature and pressure into account, from my old code I found this approximate formula: (angles in degrees)

$\Delta \alpha_{reflect} = tan[(90°-\alpha_{technical}) \times 0.9679] \times 0.023626$

If this calculated reflection angle exceeds $\frac{34.9}{60}$ degrees, use that.

Observed elevation would be $\alpha_{observed}=\alpha_{technical}+\Delta\alpha_{reflect}$

Example


a point technically (without atmosphere) 34.9' (minutes of arc) below horizon, appears on the horizon.
a point technically on the horizon, appears 28.1' above the horizon.