Physics
Extinction and refraction
The formulas behind the atmosphere.
Extinction from the weather
Section titled “Extinction from the weather”Schaefer’s (1998) empirical model, with h the site altitude, RH the relative humidity (fraction), T the temperature (°C), φ the latitude, season = 2π (month − 3) / 12 and f the aerosol load factor:
| Term | k (mag / airmass) |
|---|---|
| Molecular scattering | 0.1066 · exp(−h / 8.2 km) |
| Aerosols | 0.1 · exp(−h / 1.5 km) · (1 − 0.32 / ln RH)^1.33 · (1 + 0.33 · sign(φ) · sin(season)) · f |
| Ozone | 0.031 · (3 + 0.4 · (φ · cos(season) − cos 3φ)) / 3 |
| Water vapour | 0.031 · 0.94 · RH · exp(T / 15 °C) · exp(−h / 8.2 km) |
At first order, k depends on the altitude (pressure) and the aerosols; humidity acts mostly by swelling the aerosols, temperature very little. Typical uncertainty ±0.05.
Airmass
Section titled “Airmass”Kasten & Young (1989) formula of the apparent elevation.
Refraction
Section titled “Refraction”Sæmundsson’s formula, in arcminutes, for the true elevation h (degrees):
R = 1.02 / tan( h + 10.3 / (h + 5.11) ) × (P / 1010 hPa) × (283 K / (273 + T))with the standard pressure at the station altitude P = 1013.25 · exp(−altitude / 8400 m). The angles of a loaded measurement (true_elevation) stay geometric.