pvlib.atmosphere.kasten96_lt(airmass_absolute, precipitable_water, aod_bb)[source]#

Calculate Linke turbidity using Kasten pyrheliometric formula.

Note that broadband aerosol optical depth (AOD) can be approximated by AOD measured at 700 nm according to Molineaux [4] . Bird and Hulstrom offer an alternate approximation using AOD measured at 380 nm and 500 nm.

Based on original implementation by Armel Oumbe.


These calculations are only valid for airmass less than 5 and precipitable water less than 5 cm.

  • airmass_absolute (numeric) – Pressure-adjusted airmass. [unitless]

  • precipitable_water (numeric) – Precipitable water. [cm]

  • aod_bb (numeric) – broadband AOD. [unitless]


lt (numeric) – Linke turbidity. [unitless]



F. Linke, “Transmissions-Koeffizient und Trubungsfaktor”, Beitrage zur Physik der Atmosphare, Vol 10, pp. 91-103 (1922)


F. Kasten, “A simple parameterization of the pyrheliometric formula for determining the Linke turbidity factor”, Meteorologische Rundschau 33, pp. 124-127 (1980)


Kasten, “The Linke turbidity factor based on improved values of the integral Rayleigh optical thickness”, Solar Energy, Vol. 56, No. 3, pp. 239-244 (1996) DOI: 10.1016/0038-092X(95)00114-7


B. Molineaux, P. Ineichen, N. O’Neill, “Equivalence of pyrheliometric and monochromatic aerosol optical depths at a single key wavelength”, Applied Optics Vol. 37, issue 10, 7008-7018 (1998) DOI: 10.1364/AO.37.007008


P. Ineichen, “Conversion function between the Linke turbidity and the atmospheric water vapor and aerosol content”, Solar Energy 82, pp. 1095-1097 (2008) DOI: 10.1016/j.solener.2008.04.010


P. Ineichen and R. Perez, “A new airmass independent formulation for the Linke Turbidity coefficient”, Solar Energy, Vol. 73, no. 3, pp. 151-157 (2002) DOI: 10.1016/S0038-092X(02)00045-2