Atmospheric Refraction - Calculating Refraction

Calculating Refraction

Rigorous calculation of refraction requires numerical integration, using a method such as that of Auer and Standish (2000). Bennett (1982) developed a simple empirical formula for calculating refraction from the apparent altitude, using the algorithm of Garfinkel (1967) as the reference; if h_a is the apparent altitude in degrees, refraction R in arcminutes is given by

the formula is accurate to within 0.07′ for the altitude range 0°–90° (Meeus 1991, 102). Sæmundsson (1986) developed a formula for determining refraction from true altitude; if h is the true altitude in degrees, refraction R in arcminutes is given by

the formula is consistent with Bennett’s to within 0.1′. Both formulas assume an atmospheric pressure of 101.0 kPa and a temperature of 10 °C; for different pressure P and temperature T, refraction calculated from these formulas is multiplied by

(Meeus 1991, 103). Refraction increases approximately 1% for every 0.9 kPa increase in pressure, and decreases approximately 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases approximately 1% for every 3 °C decrease in temperature, and decreases approximately 1% for every 3 °C increase in temperature.