m=δ(ε)δ(0°
Note 1 to entry: See also "optical thickness".
Note 2 to entry: Several equations are available to express this concept. Usually the Kasten–Young formula is used:
m= 1 [ sin γ s + 0,505 72 ( γ s + 6,079 95) −1,636 4 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aad2gacqGH9aqpdaWcaaqaaiaaigdaaeaadaWadaqaaiaabohacaqG PbGaaeOBaiaabccacqaHZoWzdaWgaaWcbaGaae4CaaqabaGccaGGGc Gaey4kaSIaaiiOaKaaajaaicdacaGGSaGaaeynaiaaicdacaqG1aGa aeiiaiaabEdacaqGYaGccaGGOaGaeq4SdC2aaSbaaSqaaiaabohaae qaaOGaaiiOaiabgUcaRiaacckajaaqcaqG2aGaaiilaiaaicdacaqG 3aGaaeyoaiaabccacaqG5aGaaeynaOGaaiykamaaCaaaleqabaGaey OeI0IaaeymaiaacYcacaqG2aGaae4maiaabAdacaaMc8Uaaeinaaaa aOGaay5waiaaw2faaaaaaaa@5F86@
where γs (= 90° − ε) is solar altitude (complementary angle of zenith angle, ε) in degree.
Note 3 to entry: When the curvature of the atmosphere and atmospheric refraction are neglected:
m= 1 cosε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aad2gacqGH9aqpdaWcaaqaaiaaigdaaeaajaaqcaqGJbGaae4Baiaa bohakiabew7aLbaaaaa@3EA5@ .
Note 4 to entry: The relative optical air mass has unit one.
Note 5 to entry: This entry was numbered 845-09-88 in IEC 60050-845:1987.
m= δ(ε) δ(0°) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aad2gacqGH9aqpdaWcaaqaaiabes7aKjaacIcacqaH1oqzcaGGPaaa baGaeqiTdqMaaiikaKaaajaaicdakiabgclaWkaacMcaaaaaaa@43BE@
m= 1 [ sin γ s + 0,505 72 ( γ s + 6,079 95) −1,636 4 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aad2gacqGH9aqpdaWcaaqaaiaaigdaaeaadaWadaqaaiaabohacaqG PbGaaeOBaiaabccacqaHZoWzdaWgaaWcbaGaae4CaaqabaGccaGGGc Gaey4kaSIaaiiOaKaaajaaicdacaGGSaGaaeynaiaaicdacaqG1aGa aeiiaiaabEdacaqGYaGccaGGOaGaeq4SdC2aaSbaaSqaaiaabohaae qaaOGaaiiOaiabgUcaRiaacckajaaqcaqG2aGaaiilaiaaicdacaqG 3aGaaeyoaiaabccacaqG5aGaaeynaOGaaiykamaaCaaaleqabaGaey OeI0IaaeymaiaacYcacaqG2aGaae4maiaabAdacaaMc8Uaaeinaaaa aOGaay5waiaaw2faaaaaaaa@5F86@